The Bunkum Mystification of Quantum Mechanics by Non-Physicists

[LilWabbit]

The problem with the italicized portion is that we don't know to what extent a notion of "actual behavior" may be meaningful, if at all.

That's correct, we don't. But even then the problem of conflation, described in my 3rd point in the previous post, applies. But with a positivist slant, where "actual behaviour" translates better into "actually observed behaviour" or something in the same vein.

An enormous amount of ink has been spilled on the question of "elements of reality" (terminology commonly attributed to Einstein), which today might be called "hidden variables", with the eventual result of the vast majority of physicists regarding the problem as hopeless and working on something else. The mystery is not in interpreting the quantum state as a recipe for calculating probabilities of experimental outcomes; that's straightforward. The mystery, for those who see a mystery, is that nobody's been able to come up with a classical statistical ensemble that's described by the quantum rules, and not for lack of trying.

Indeed, a consideration which I also tried to weave into my 2nd point in the previous post.

I'm not sure what you mean here. Take the example of the classical Brownian particle: it has a well-defined position at all times.

Right, I'm not disagreeing with the overall point that it's important to avoid mistaking the model for the physical system, and that many routinely do, and that doing so is a big source of confusion. But at the same time it's not "just" classical stochastic behavior and the fact that measuring small things is hard.

This is correct (that it's not "just" classical stochastic behaviour) in terms of the specifics, but not in terms of the general idea of propensity probability (a sort of 'guided' stochasticism) which exists also in other fields and which was discussed under the 1st point of my previous post.

That's the case with the amplituhedron. It seems computationally advantageous to calculate scattering amplitudes by just computing the volume of some polytope instead of adding up Feynman diagrams and keeping careful track of the many cancellations that come with N=4 super Yang-Mills' highly supersymmetric structure, but that's assuming you want to calculate scattering amplitudes in the first place. There are other questions to be asked of a particle theory, and for other questions the perturbative diagrammatic approach may be more convenient.

The amplituhedron is not just about computational benefits to calculate scattering amplitudes. Besides, by so stating you aptly captioned the main disconnect in the way the entire project of science is understood between many (not all) quantum physicists and 'classical' physicists; Namely, 'computational advantage' in predicting observations, as opposed to 'understanding physical reality' underlying observations (i.e. Bohr's positivism vs. Einstein's realism).

Be as it may, it's my understanding that for Nima Arkhani-Hamed, his collaborators and those most impressed by his discovery it's more the potential which similar geometric models could have in describing gravity, and to account for the existence of particles, and the spacetime, in the first place. His project is therefore far more ambitious than particle interactions. It's about discovering a more fundamental math underlying and unifying all physics. Which may or may not succeed.

Unless and until quantum physicists, on the whole, gain a deeper understanding of n-dimensional geometric function spaces (which they usually know zilch about), they do not yet have much say in the potential quantum mechanical applicabilities of models like the amplituhedron. Which brings us back to the matter of inadequacy of currently used language raised in the OP. Indeed, it would be a formidable task for a non-Arabic-speaking evolutionary biologist to comment on, let alone to correct, an Arabic-speaker's lecture on the topic.

 

[Rory]

I was reading something not related to quantum physics and came across the following passages, and wondered if you guys could comment on whether you think the author's interpretation is right please?

As it happens, Lucretius and Newton were mistaken. The fundamental laws of physical reality are nothing like [how they described them in the preceding paragraphs]. They are collections of force fields. In the early twentieth century, physicists showed that these force fields, the 'quantum' level of our universe, do not necessarily obey the "laws of nature" with which we are familiar.

So what is the fundamental quantum level of our universe like? Electrons (the negative charges of atoms), for example, do not definitely exist in space and time. They are a cloud of probabilities; their existence at any given point is only a potential. When they jump from one state of energy to another they do not "pass through" the space in between, they simply reappear in a higher or lower state. One way to understand this is to picture a three-way bulb, a light bulb that emits 50, 100, or 150 watts as the switch is turned, but nothing in between. There is nothing in between.

Even more strangely, if we measure these electrons we make their existence at a given point real, at least for our purposes. So, in a sense, we are creating the thing we want to measure. There is a principle for this called the Heisenberg uncertainty (indeterminacy) principle. It says that subatomic particles do not occupy definite positions in space or time; we can find out where they are only as a series of probabilities about where they might be (we must decide what we want to know).

[Furthermore], physicists have found that if they observe an unstable elementary particle continuously, it never decays - even though it would almost certainly decay if it were not observed. In quantum physics it is not possible to separate the observer entirely from the thing observed. They are part of the same system. The physicists are, essentially, holding the unstable particle in a given state by the act of continuing to measure it. [This is known as the quantum Zeno effect].

 

[LilWabbit]

I was reading something not related to quantum physics and came across the following passages, and wondered if you guys could comment on whether you think the author's interpretation is right please?

As it happens, Lucretius and Newton were mistaken. The fundamental laws of physical reality are nothing like [how they described them in the preceding paragraphs]. They are collections of force fields. In the early twentieth century, physicists showed that these force fields, the 'quantum' level of our universe, do not necessarily obey the "laws of nature" with which we are familiar.

So what is the fundamental quantum level of our universe like? Electrons (the negative charges of atoms), for example, do not definitely exist in space and time. They are a cloud of probabilities; their existence at any given point is only a potential. When they jump from one state of energy to another they do not "pass through" the space in between, they simply reappear in a higher or lower state. One way to understand this is to picture a three-way bulb, a light bulb that emits 50, 100, or 150 watts as the switch is turned, but nothing in between. There is nothing in between.

Even more strangely, if we measure these electrons we make their existence at a given point real, at least for our purposes. So, in a sense, we are creating the thing we want to measure. There is a principle for this called the Heisenberg uncertainty (indeterminacy) principle. It says that subatomic particles do not occupy definite positions in space or time; we can find out where they are only as a series of probabilities about where they might be (we must decide what we want to know).

[Furthermore], physicists have found that if they observe an unstable elementary particle continuously, it never decays - even though it would almost certainly decay if it were not observed. In quantum physics it is not possible to separate the observer entirely from the thing observed. They are part of the same system. The physicists are, essentially, holding the unstable particle in a given state by the act of continuing to measure it. [This is known as the quantum Zeno effect].

Thanks @Rory for sharing. This snippet is a prime example of what was discussed earlier. Namely, what happens when people attempt to interpret realistically (i.e. as descriptions of reality) the instrumentalistic (i.e. statistically useful) mathematical models of quantum mechanics, which were not even seriously entertained as direct descriptions of physical reality. This obviously results in confusions, and is vulnerable to unnecessary mystification of quantum mechanics whereby various authors refer to QM as proof of the inherent spirituality or non-physicality of the universe.

You of all know I'm not a materialist, and yet I am convinced the type of QM mystification that I read in your citation represents precisely the very bunkum this whole thread was meant to address. And hence, the citation was very useful and illustrative!

 

[markus]

That's correct, we don't. But even then the problem of conflation, described in my 3rd point in the previous post, applies. But with a positivist slant, where "actual behaviour" translates better into "actually observed behaviour" or something in the same vein.

If you stick to observations only, everyone agrees. I must be misunderstanding you, do you have an example?

Indeed, a consideration which I also tried to weave into my 2nd point in the previous post.

That's fair. But IMO, positivism here is not part of the disease, but the cure: you stick to what you can say for a fact, and you'll never run into the problem of conflation. s you say, the problem appears when you forget to be careful in that way. That said, I don't think your points (1) and (2) are really distinct: the 'positivism' (which here I'm talking to mean exclusively the narrow sense of using quantum mechanics to predict experimental results and not provide a classical model of the observation-independent universe) is really mandated by the formalism; quantum mechanics really has nothing in it that lets you talk about what the electron is "really" doing.

I agree with your point (3).

This is correct (that it's not "just" classical stochastic behaviour) in terms of the specifics, but not in terms of the general idea of propensity probability (a sort of 'guided' stochasticism) which exists also in other fields and which was discussed under the 1st point of my previous post.

Right, of course in the end the calculation turns into a probability that is then tested against experiment, but I'm not sure how much useful the comparison is beyond that. I mean, I'm sure there are those who are confused about classical probability as well, but I doubt that, collectively, it even approaches the volume of paper and ink spilled trying to "interpret" quantum mechanics (or, to say it plainly, to invent another theory to supersede it while making the exact same predictions). This, I'm convinced, is due to the lack of a "model" for quantum mechanics analogous to that which ensembles provide for classical probability theory (which works always, even for one-off events or probability-as-ignorance situations). This might be the key point where we disagree: I think this lack of a model is a pretty crucial difference that sets quantum mechanics apart from every other situation where stochasticity is involved, you seem to believe the difference is not too important.

The amplituhedron is not just about computational benefits to calculate scattering amplitudes.

Well, I think it's too soon to say whether it's "just" about anything. The result itself, while interesting and very, very clever, is rather limited in scope. All it does for now is make it easier to compute scattering amplitudes for =4 super Yang-Mills in the large N limit. It's certainly not nothing, but it's not a theory that describes the world (or is even intended for that purpose); nor is it particularly representative of what we actually see (supersymmetry, if it exists in the real world, is broken at low energies; does the trick still work with theories rich enough for that to happen?). Rather, it's a theory with lots of structure, and lots of cancellations. It's quite plausible that the amplituhedron (or even something like it) works only here and nowhere else.

What it does give, and that's the one thing that is clear, is a computationally advantageous way to compute scattering amplitudes for =4 SYM in the large N limit. Computational advantage is not to be dismissed; the Feynman path integral is also a "computationally advantageous" way of representing quantum field theory which drastically increases the number of problems we can actually solve. Having a significant computational advantage is the difference between understanding a theory and not having a clue.

But, more relevant to the topic here, =4 SYM is still a quantum mechanical model, still mysterious/uncomfortable to the same model-independent extent as it was before the trick was introduced. Insofar as potential implications to foundational questions, the amplituhedron sits as a particular implementation of the S-matrix program, which is not particularly new. If anything, the S-matrix point of view is even more abstract, more uncomfortable than the comparatively friendly diagrammatic perturbation theory-based approaches: here, as always in quantum mechanics, there is no story that can be told about what the theory is doing in the transition between in and out states. All you get is the amplitude. With the diagrammatic approach you get mini-stories which interfere to produce the final answer, which can be misleadingly interpreted as having "actually occurred", so perhaps having an approach where there's no story at all represents progress*. But the puzzles we grapple with in quantum mechanics have nothing to do with the language used to describe them.

* We already have such an approach for the strong interaction, called Lattice Gauge Theory. Diagrammatic perturbation theory didn't go away, though. The various different (but equivalent) approaches are each good for different things.

 

[markus]

I was reading something not related to quantum physics and came across the following passages, and wondered if you guys could comment on whether you think the author's interpretation is right please?

That passage seems pretty confused/muddled. I actually can't make sense of what the author is trying to convey, so I'll do the next best thing and look at a few individual sentences.

As it happens, Lucretius and Newton were mistaken. The fundamental laws of physical reality are nothing like [how they described them in the preceding paragraphs]. They are collections of force fields.

"Force fields" out of context like this makes this sound like classical physics. In quantum field theory the closes thing you could call "force fields" are the force-carrying particles, which really are bona-fine degrees of freedom and can have "independent" existence, that is, they're not merely relegated to the menial job of fetching forces from here to there. The photon carries the electromagnetic force, but it can also travel the breadth of the universe.

This is pretty minor so far though.

In the early twentieth century, physicists showed that these force fields, the 'quantum' level of our universe, do not necessarily obey the "laws of nature" with which we are familiar.

A puzzling sentence out of context, but I'm sure it's fine in the book.

So what is the fundamental quantum level of our universe like? Electrons (the negative charges of atoms), for example, do not definitely exist in space and time. They are a cloud of probabilities; their existence at any given point is only a potential. When they jump from one state of energy to another they do not "pass through" the space in between, they simply reappear in a higher or lower state. One way to understand this is to picture a three-way bulb, a light bulb that emits 50, 100, or 150 watts as the switch is turned, but nothing in between. There is nothing in between.

Here's where he loses me, for several reasons.

1. Electrons are not really "clouds of probabilities"; it's we who describe them using clouds of probabilities. He's confusing the map with the territory.

2. What he's describing sounds like nonrelativistic quantum mechanics, which is fine, but please don't call it the "fundamental quantum level of the universe". The "fundamental quantum level of the universe" is described by quantum field theory, where individual particles lose their identities altogether. Whether you have one electron or 10 or a billion (or even an infinite number), they are all excitations of the same underlying electron field. While the rules of quantum mechanics are the same for the relativistic and nonrelativistic case, the idea of the "wavefunction" and the "probability clouds" is tied to the approximation where the number of particles remains constant throughout an experiment, which happens to be exactly the same as the nonrelativistic limit. If your experiment happens at energies so high that detecting a particle involves creating a bunch of new ones, thinking about where the particle "is" kinda loses a little bit of sense.

3. An energy state and a location in space are very much not the same thing, so saying something like "When they jump from one state of energy to another they do not "pass through" the space in between, " sounds rather absurdist. Indeed, energy and position don't commute (they are incompatible observables) so when you know the energy perfectly precisely, you don't know the position at all. The statement given here makes no sense, and I suspect the author still has a Bohr model-like conception in his mind. In the Bohr model of the hydrogen atom the various energy levels are associated with discrete circular orbits, so a jump in energy is indeed linked to a jump in position. Not so in quantum mechanics. In quantum mechanics, you either talk about energy, or location, but not both.

Even more strangely, if we measure these electrons we make their existence at a given point real, at least for our purposes. So, in a sense, we are creating the thing we want to measure.

There is a sense in which when you measure something you create the quantity you're measuring, yes. But we can do without the quasi-mystical baggage of "making their existence real" etc. that has no operational definition (it doesn't mean anything).

There is a principle for this called the Heisenberg uncertainty (indeterminacy) principle. It says that subatomic particles do not occupy definite positions in space or time; we can find out where they are only as a series of probabilities about where they might be (we must decide what we want to know).

The uncertainty principle is about incompatible observables as I just briefly mentioned. It's about pairs of quantities where knowledge of one necessitates ignorance of the other. It doesn't have anything (directly) to do with the fact that measurement results are "created" at the moment of measurement (that's a consequence of all rules taken together, and established by the Kochen-Specker theorem). It doesn't say that subatomic particles do not occupy definite positions in space (the closest correct statement to this, that position measurements in a given state are distributed according to a probability distribution, is established by the measurement postulate). It certainly doesn't say that subatomic particles do not occupy definite positions in time, which in nonrelativistic quantum mechanics they most certainly do: time is a parameter of the theory, not a statistically distributed observable like position. Things are a little more complicated relativistically but saying particles "do not occupy definite positions in time" is still confusing and not very helpful. It also, like the previous point, confuses the map with the territory.

[Furthermore], physicists have found that if they observe an unstable elementary particle continuously, it never decays - even though it would almost certainly decay if it were not observed. In quantum physics it is not possible to separate the observer entirely from the thing observed. They are part of the same system. The physicists are, essentially, holding the unstable particle in a given state by the act of continuing to measure it. [This is known as the quantum Zeno effect].

This paragraph is fine.

All in all, I agree with LilWabbit that this text is an example of the conflation between theory and reality that he rightly attacks in this thread.

 

[Rory]

Thanks guys, much appreciated. It's all Greek to me - but I get the sense you know what you're talking about and that the passage I quoted has some serious flaws.

Boxes ticked.

 

[LilWabbit]

If you stick to observations only, everyone agrees. I must be misunderstanding you, do you have an example?

It seems we are getting into semantics on this particular point since you already agreed with my third point on 'measurement/observation causes the wavefunction to collapse' being a terminologically misleading expression, vulnerable to mystification. I was later merely pointing out an additional nuance whereby even a positivist interpretation of the statement would not eliminate the logically unwarranted conflation that it does between 'possible' and 'actual' measurements. Philosophically, 'possible' and 'actual' are nowhere near the same thing, and never describing the exact same 'entity' as opposed to what the 'wavefunction collapse' seems to (sloppily) imply.

It is irrelevant to this conclusion whether the matrix of 'possibilities' (and by extension 'probabilities') is described using Hilbert spaces or standard statistical probability distributions. That part of the statement still concerns 'possible' measurements, whereas the part after 'collapse' concerns 'actual' measurements. Conflating them is both epistemologically and ontologically problematic and essentially no different than saying: On Tuesday Mike could have had his lunch at McDonald's, Burger King and Taco Bell. These options collapsed by him actually having his lunch at Burger King.

Options don't 'collapse' by the choice of one of them. This is sloppy language.

That's fair. But IMO, positivism here is not part of the disease, but the cure: you stick to what you can say for a fact, and you'll never run into the problem of conflation.

Discussed above.

s you say, the problem appears when you forget to be careful in that way. That said, I don't think your points (1) and (2) are really distinct: the 'positivism' (which here I'm talking to mean exclusively the narrow sense of using quantum mechanics to predict experimental results and not provide a classical model of the observation-independent universe) is really mandated by the formalism; quantum mechanics really has nothing in it that lets you talk about what the electron is "really" doing.

If QM is, by default, regarded an essentially positivistic exercise, it would indeed have 'nothing' to do with the actual behaviour of the electron. I happen to agree with 'classical' physicists that it's a kind of a scientific copout to accept such a dogmatically anti-realist view about what quantum mechanics is and what it shouldn't be. And this doesn't mean I'm instead a promoter of Bohmian mechanics, GRW theory, much less Everettian interpretations.

The reason positivism is so popular within QM is, in my view, more a function of general discomfort amongst physicists with indeterminism. This discomfort is reflected, in different ways, in all the interpretations (including Bohr's, not just Einstein's, de Broglie's, Bohm's, Ghirardi's, Everett's, et al). Indeterminism, reinforced by an entire catalogue of weird stochastic behaviours at a much more fundamental level (quantum-scale), kind of threw everyone off guard. Since classical determinist avenues for explaining these indeterminisms proved quickly unsuccessful (assuming some fundamental but sophisticated determinism underlying the 'apparent' indeterminism), Bohr's nihilism -- i.e. 'let's not even be bothered about what actually happens' -- became mainstream. This nihilism was coupled with the great predictive success of the Schrödinger equation which was instrumentalist (non-realist) by design. This initial pessimism towards realist quantum mechanical research and representational theories by the great founding daddies of QM has been historically inherited as the standard attitude. In my view such a mindset is less a function of the impossibility of doing realist science in QM. It's more a function of difficulty.

Right, of course in the end the calculation turns into a probability that is then tested against experiment, but I'm not sure how much useful the comparison is beyond that. I mean, I'm sure there are those who are confused about classical probability as well, but I doubt that, collectively, it even approaches the volume of paper and ink spilled trying to "interpret" quantum mechanics (or, to say it plainly, to invent another theory to supersede it while making the exact same predictions). This, I'm convinced, is due to the lack of a "model" for quantum mechanics analogous to that which ensembles provide for classical probability theory (which works always, even for one-off events or probability-as-ignorance situations). This might be the key point where we disagree: I think this lack of a model is a pretty crucial difference that sets quantum mechanics apart from every other situation where stochasticity is involved, you seem to believe the difference is not too important.

Whilst not a particular fan of the determinism, and the problematic additional assumptions, inherent in the 'pilot wave' interpretation, Bohmian mechanics has, in the least, demonstrated the 'possibility' ('possibility' seems to be the buzzword of the day ) of a more classical probability distribution for QM (while obviously borrowing from the Schrödinger equation) where definite behaviours of the electron precede measurement.

I am not one to deny Schrödinger's equation and the Hilbert space as mathematical models uniquely applicable to QM. But this uniqueness is, in my view, more a function of our current technical challenges to measure the behaviour of the same electron repeatedly throughout its evolution. In my view it's also a function of genuinely stochastic behaviour at the quantum-scale, rather than the electron not actually having definite behaviours at all times. Schrödinger offered a temporary solution to help with our predictions which cleverly avoids the necessity to assign the electron definite behaviours before measurement.

As to what's actually happening, it's obviously unresolved. But I don't think unresolvable. I'm personally drawn to the notion that the electron is always definite, but always stochastic, while globally 'guided' into interference patterns by some fundamental physical geometry, call it wave-like or not. Hence my curiosities towards amplituhedrons and similar geometric models.

Rather, it's a theory with lots of structure, and lots of cancellations. It's quite plausible that the amplituhedron (or even something like it) works only here and nowhere else.

Possible yes. But we're not yet in a position to say 'plausible' until quantum physicists, on the whole, gain a deeper understanding of n-dimensional geometric function spaces (which they usually know zilch about), number theory, and both of their potentials in broader physical theories including in QM. Hence Nima's intimate collaboration with mathematicians who themselves are fascinated by the novelty of the amplituhedron as a unique type of a polytope defining the positive Grassmanian.

It ain't over till the fat lady sings.

 

[markus]

I was later merely pointing out an additional nuance whereby even a positivist interpretation of the statement would not eliminate the logically unwarranted conflation that it does between 'possible' and 'actual' measurements. Philosophically, 'possible' and 'actual' are nowhere near the same thing, and never describing the exact same 'entity' as opposed to what the 'wavefunction collapse' seems to (sloppily) imply.

Right, that's what I'm confused about. What do you mean by "possible" vs "actual" measurements here?

If QM is, by default, regarded an essentially positivistic exercise, it would indeed have 'nothing' to do with the actual behaviour of the electron.

Not necessarily, just like a classical probability distribution for a classical particle does have something to do with the actual behavior of the particle: the distribution you pick gets evaluated against experiment, and may pass or fail in an objective sense. It may be a stronger tie as the Bohmians and Everettians hope, but they've never been able to actually explain how that would work.

I happen to agree with 'classical' physicists that it's a kind of a scientific copout to accept such a dogmatically anti-realist view about what quantum mechanics is and what it shouldn't be. And this doesn't mean I'm instead a promoter of Bohmian mechanics, GRW theory, much less Everettian interpretations.

What "quantum mechanics is" is something we can establish comparatively easily, and it is indeed this kind of positivist exercise. It's mandated by the formalism. Objecting to that is a form of the conflation you criticize: just because quantum mechanics is this doesn't mean that it's the ultimate truth, or that one should be satisfied with it, etc. It's about one specific framework and its limits, not nature herself.

The reason positivism is so popular within QM is, in my view, more a function of general discomfort amongst physicists with indeterminism. This discomfort is reflected, in different ways, in all the interpretations (including Bohr's, not just Einstein's, de Broglie's, Bohm's, Ghirardi's, Everett's, et al).

Ghirardi's? But Ghirardi's interpretation contains an indeterministic component, and it's not what anyone criticizes about the approach. Despite all the "God does not play dice" talk, it's not indeterminism these days that causes most of the discomfort. We've have 100 years to get used to that. It's the lack of a observer-independent model of reality. Like I've been saying, the theory itself is positivist. Nobody's ever found a way to make it not so.

Whilst not a particular fan of the determinism, and the problematic additional assumptions, inherent in the 'pilot wave' interpretation, Bohmian mechanics has, in the least, demonstrated the 'possibility' ('possibility' seems to be the buzzword of the day ) of a more classical probability distribution for QM (while obviously borrowing from the Schrödinger equation) where definite behaviours of the electron precede measurement.

Proponents of Bohmian mechanics (like proponents of Everettian interpretations) like to leave some pretty important things out. The fact is Bohmian mechanics doesn't work. It demands a world that's nonrelativistic, whereas our world is obviously relativistic; and it does so in an extremely rigid, uncorrectable sense. This is for several reasons. First, without some infinite amount of fine tuning the theory allows for faster than light communication (by which I mean actually sending messages, not just the modest correlations of entanglement), which is quite sick. Secondly, the theory structurally requires only the consideration of a fixed number of particles, where in the real world one must consider processes where particles are created and destroyed. This halts the Bohmian program in its tracks since its subquantum particles aren't real degrees of freedom, nor do they carry any dynamical consequence. For many years since its inception proponents have tried to get it to work with relativity, without success.

You can, without too much trouble, come up with a hidden variables (or a classically stochastic but ultimately indeterministic, take your pick) model that describes the observations of any single observer (trivial proof: make a list of all observations that observer makes. That's the model). It's the description of an observer-independent classical reality that is problematic, and that is something that Bohmian mechanics ultimately fails to provide (as does Many Worlds, for that matter).

As to what's actually happening, it's obviously unresolved. But I don't think unresolvable. I'm personally drawn to the notion that the electron is always definite, but always stochastic, while globally 'guided' into interference patterns by some fundamental physical geometry, call it wave-like or not. Hence my curiosities towards amplituhedrons and similar geometric models.

Maybe. But the track record for such approaches is not good, and there are many hurdles in its way. It could also be a number of other things. Maybe the entire way of thinking about dynamics, about one thing causally following another, needs revision. What's more important in my estimation is to not artificially limit the possibilities, which is why I favor sticking to the positivism that the framework demands.

Possible yes. But we're not yet in a position to say 'plausible' until quantum physicists, on the whole, gain a deeper understanding of n-dimensional geometric function spaces (which they usually know zilch about), number theory, and both of their potentials in broader physical theories including in QM. Hence Nima's intimate collaboration with mathematicians who themselves are fascinated by the novelty of the amplituhedron as a unique type of a polytope defining the positive Grassmanian.

You can find elegant geometrical structure in all sorts of places. You take an inverse square force, and the trajectories come out as conic sections. You take a linear force, like a spring, and they also come out as conic sections! That's utterly beautiful, but also utterly specific to those forces. It doesn't hold generically even for central forces. This is the generic situation: when you write down a physics problem and the solution has some elegant structure, the natural expectation is that the structure is tied to the specific symmetries and the specific character of the problem. N=4 SYM is not your average field theory. I'm not dismissing the result, I think it's important, and I don't think it's too unlikely that it
could be applicable more broadly. But "plausible" is the right word here.

At any rate, say for the sake of argument that the program succeeds beyond even Nima's wildest dreams and amplituhedra can be shown to exist for every important quantum field theory. The result is even more "positivist" than quantum field theory, and it's hard to see how it could be otherwise: after all, quantum field theory is just one specific implementation of the same rules of quantum mechanics that forced us to view it in a positivist light to begin with.

 

[LilWabbit]

Right, that's what I'm confused about. What do you mean by "possible" vs "actual" measurements here?

For instance 'superpositions' vs. 'measured definite positions'. The first concerns statistical probabilities (i.e. types of 'possibilities' as to where the electron could be located) while the latter concerns an act of measurement (i.e. types of 'actual' events providing description of where the electron is located), irrespective of whether the measurement result in and of itself tells us anything about the quantum-scale physical reality or not (realism vs. positivism). Even within the positivist interpretation of QM, a measurement result is still an actual measurement result (despite not necessarily being a description of actual subatomic events). A real act of measurement was carried out and it produced an actual result of some kind, providing what we've chosen to call 'a location' of what we've chosen to call 'an electron'. Therefore, as an actual measurement result it is still fundamentally different from a description of many possible measurement results.

Nothing collapsed.

To repeat, conflating 'possible' with 'actual' is, at best, linguistically sloppy. At worst, a logical contradiction.

Not necessarily, just like a classical probability distribution for a classical particle does have something to do with the actual behavior of the particle:

I was merely recycling your own previous statement "quantum mechanics really has nothing in it that lets you talk about what the electron is "really" doing" and agreeing that, indeed, that is essentially what 'positivism' implies. Now you seem to be fine-tuning that statement in a manner which I have no issues with. Besides, 'possibility' "having something to do with" 'actuality' does not mean they are the same thing. This is, in fact, the standard stumbling block with all conflation errors -- mistaking connection, correlation or even causality between two variables for identity.

What "quantum mechanics is" is something we can establish comparatively easily, and it is indeed this kind of positivist exercise. It's mandated by the formalism.

Now you are describing 'a positivist interpretive tradition' of quantum mechanics and conflating it with 'quantum mechanics'. Furthermore you are (to my ear 'dogmatically', pardon the expression as I mean no disrespect by it) claiming that the received formalism in QM, which is a product (mind you, in many ways a brilliant and useful product) of such a positivist interpretive tradition, defines all that quantum mechanics is.

In other words, we're back to the definist fallacy where we can claim any two different statements as referring to the same thing if no further justification is provided. No further questions are allowed. Not to blame you at all since Bohr was infamous for this type of dogmatism. You merely seem to echo the tradition. Maybe I misunderstood. But if not, more power to you if that's your thing.

The Encyclopedia Britannica definition of quantum mechanics, whether or not we regard it as an authority of any kind, is, in my view, more generous and scientific:

Article:

quantum mechanics, science dealing with the behaviour of matter and light on the atomic and subatomic scale. It attempts to describe and account for the properties of molecules and atoms and their constituents—electrons, protons, neutrons, and other more esoteric particles such as quarks and gluons. These properties include the interactions of the particles with one another and with electromagnetic radiation (i.e., light, X-rays, and gamma rays).

Source: https://www.britannica.com/science/quantum-mechanics-physics

I tend to agree with this definition under which positivist interpretive traditions would represent, despite their popularity, only one way to "account for the properties of molecules and atoms and their constituents—electrons, protons, neutrons, and other more esoteric particles such as quarks and gluons."

We've have 100 years to get used to that.

Misses my point which concerned the initial surprise and sense of inexplicable indeterministic weirdness out of which a particular (positivist) interpretive tradition arose and later gained major currency. The later Copenhagenists have simply mainstreamed this interpretive tradition to apply to all the other weirdnesses of QM as well, including to the interpretation of the observer effect and the measurement problem.

It's the lack of a observer-independent model of reality. Like I've been saying, the theory itself is positivist. Nobody's ever found a way to make it not so.

Indeed, the current formalism is positivist by default. No qualms there. Philosophically, by the way, even "the lack of an observer-independent model of reality" concerns a kind of epistemological indeterminacy. But you would be right to say it doesn't necessarily reflect the indeterminacy of a stochastic process.

Proponents of Bohmian mechanics (like proponents of Everettian interpretations) like to leave some pretty important things out. The fact is Bohmian mechanics doesn't work. It demands a world that's nonrelativistic, whereas our world is obviously relativistic; and it does so in an extremely rigid, uncorrectable sense.

Here we agree on the main shortcomings of Bohmian mechanics which I already alluded to in the previous post. Is it doomed? I don't know. Possibly, but I'm less certain than you are. I'm not particularly hopeful either. David Albert seems to think there are new promising trends even on the Bohmian front. In any event, these are related but separate topics to which entire threads could be devoted. Perhaps on another platform too.

It's the description of an observer-independent classical reality that is problematic, and that is something that Bohmian mechanics ultimately fails to provide (as does Many Worlds, for that matter).

We are on the same page. Where we seem to disagree is whether or not realist quantum mechanics is doomed to failure, or even likely to fail. We do not disagree on previous attempts of realist QM having been largely unsuccessful. I do think, though, that the cultural monopoly of the positivist interpretive tradition within QM (and only within QM from amongst all of physics), and the attendant cultural bias towards alternatives, is not conducive to empowering brilliant novel efforts towards realist QM. And hence any argument for "implausibility" propounded by a firm Copenhagenist strikes me both as (1) biased as well as (2) dismissive of the creativity-dampening effect of the cultural hegemony of the positivist tradition within the QM community as far as innovating novel realist theories are concerned.

Obviously the Copenhagenist would see it the opposite way, namely the long-standing dominance of the positivist tradition within QM being a function of its superiority over all possible alternatives.

The result is even more "positivist" than quantum field theory, and it's hard to see how it could be otherwise: after all, quantum field theory is just one specific implementation of the same rules of quantum mechanics that forced us to view it in a positivist light to begin with.

Then you mean by positivism something entirely different than I do. Nima's project is certainly not positivist but realist in the (ahem, correct ) philosophical sense of attempting a description of an actual observer-independent physical geometry that causes certain observable behaviours and properties in the actual physical universe.

P.S. You rightly pointed out GRW theory is very comfortable with indeterminism. Thanks for correcting me. I mispoke.

 

[markus]

For instance 'superpositions' vs. 'measured definite positions'. The first concerns statistical probabilities (i.e. types of 'possibilities' as to where the electron could be located) while the latter concerns an act of measurement (i.e. types of 'actual' events providing description of where the electron is located), irrespective of whether the measurement result in and of itself tells us anything about the quantum-scale physical reality or not (realism vs. positivism). Even within the positivist interpretation of QM, a measurement result is still an actual measurement result (despite not necessarily being a description of actual subatomic events). A real act of measurement was carried out and it produced an actual result of some kind, providing what we've chosen to call 'a location' of what we've chosen to call 'an electron'. Therefore, as an actual measurement result it is still fundamentally different from a description of many possible measurement results.

Nothing collapsed.

To repeat, conflating 'possible' with 'actual' is, at best, linguistically sloppy. At worst, a logical contradiction.

I agree with that. The point I was making before is that it's a framework of classical physics that lets you make statements about objects that remain valid when you're not looking, and it's the lack of a comparable framework in the quantum world that makes people scratch their heads. So it's being careful to avoid conflation of what you're describing as "possible" and "actual" that leads one to say statements such as "it's meaningless to discuss the position of an electron if no position measurement has been performed."

I was merely recycling your own previous statement "quantum mechanics really has nothing in it that lets you talk about what the electron is "really" doing" and agreeing that, indeed, that is essentially what 'positivism' implies. Now you seem to be fine-tuning that statement in a manner which I have no issues with. Besides, 'possibility' "having something to do with" 'actuality' does not mean they are the same thing. This is, in fact, the standard stumbling block with all conflation errors -- mistaking connection, correlation or even causality between two variables for identity.

Fair point.

Now you are describing 'a positivist interpretive tradition' of quantum mechanics and conflating it with 'quantum mechanics'. Furthermore you are (to my ear 'dogmatically', pardon the expression as I mean no disrespect by it) claiming that the received formalism in QM, which is a product (mind you, in many ways a brilliant and useful product) of such a positivist interpretive tradition, defines all that quantum mechanics is.

In other words, we're back to the definist fallacy where we can claim any two different statements as referring to the same thing if no further justification is provided. No further questions are allowed. Not to blame you at all since Bohr was infamous for this type of dogmatism. You merely seem to echo the tradition. Maybe I misunderstood. But if not, more power to you if that's your thing.

In order to conflate two things, there must be in fact two identifiable things to conflate. All we have here is quantum mechanics, in its essentially unique definition (see e.g. Ballentine, chapter 2):

1. To each dynamical variable (physical concept) there corresponds a linear operator (mathematical object), and the possible values of the dynamical variable are the eigenvalues of the operator.
1a. To each dynamical variable there is a Hermitian operator whose eigenvalues are the possible values of the dynamical variable.
2. To each state there corresponds a unique state operator. The average value of the dynamical variable R, represented by the operator R, in the virtual ensemble of events that may result from a preparation procedure for the state, represented by the operator rho, is
<R> = Tr(rho * R) / Tr (rho)
2a. To each state there corresponds a unique state operator, which must be Hermitian, nonnegative, and of unit trace.

There exist other formulations of quantum mechanics written in terms of different axioms, but they all describe exactly the same structure. It is clear that this is a positivist definition, in the sense that all it tells you about are measurement results. Indeed, that's the only thing the formalism can provide. No "realist" theory explaining the same observations has ever been found.

The Encyclopedia Britannica definition of quantum mechanics, whether or not we regard it as an authority of any kind, is, in my view, more generous and scientific:

Article:

quantum mechanics, science dealing with the behaviour of matter and light on the atomic and subatomic scale. It attempts to describe and account for the properties of molecules and atoms and their constituents—electrons, protons, neutrons, and other more esoteric particles such as quarks and gluons. These properties include the interactions of the particles with one another and with electromagnetic radiation (i.e., light, X-rays, and gamma rays).

Source: https://www.britannica.com/science/quantum-mechanics-physics

I tend to agree with this definition under which positivist interpretive traditions would represent, despite their popularity, only one way to "account for the properties of molecules and atoms and their constituents—electrons, protons, neutrons, and other more esoteric particles such as quarks and gluons."

That's not a definition, it's a description of the theory's scope. I can't use this description to come up with predictions of the theory. Quantum mechanics is a theory (or a framework for building theories) with a specific definition (the one quoted above); if it turns out that subatomic particles don't quite behave according to its rules, quantum mechanics will lose its fundamental status and be replaced with something else. "Quantum mechanics" is to "the behaviour of matter and light on the atomic and subatomic scale" as "general relativity" is to "gravity".

Misses my point which concerned the initial surprise and sense of inexplicable indeterministic weirdness out of which a particular (positivist) interpretive tradition arose and later gained major currency.

As I explain in the previous point, it's not so much an interpretive tradition, but a mathematical demand.

Indeed, the current formalism is positivist by default. No qualms there. Philosophically, by the way, even "the lack of an observer-independent model of reality" concerns a kind of epistemological indeterminacy. But you would be right to say it doesn't necessarily reflect the indeterminacy of a stochastic process.

I think the word "indeterminacy" here is being used in two slightly different ways.

Here we agree on the main shortcomings of Bohmian mechanics which I already alluded to in the previous post. Is it doomed? I don't know. Possibly, but I'm less certain than you are. I'm not particularly hopeful either. David Albert seems to think there are new promising trends even on the Bohmian front. In any event, these are related but separate topics to which entire threads could be devoted. Perhaps on another platform too.

Agreed. I could complain at length about the shortcomings of Bohmian mechanics but it would certainly be off-topic here.

We are on the same page. Where we seem to disagree is whether or not realist quantum mechanics is doomed to failure, or even likely to fail.

I wouldn't say realistic quantum mechanics is doomed to failure; I would say it's a contradiction: it makes about as much sense as relativistic Newtonian mechanics. The mathematical structure generated by the above axioms is extremely well-understood, and we know they describe something akin to probability theory except it's the squared absolute values of the relevant quantities that must add up to 1. There's no way to make that "realist" in a classical physics sense. This may sound like a pedantic point, but I promise it's not: there's essentially two unique possibilities for what a "probability-like" theory might look like, which one might call "classical probability" and "quantum mechanics". All other generalizations (say it's the cubes that sum to one, or the exponentials, or whatever) generate theories in which nothing non-trivial can ever happen, since anything other than a relabeling of the initial states would violate probability conservation. This is to say that the mathematics of quantum mechanics has a privileged place and will remain so even if it's ultimately superseded by something "realist".

Now, what I do think, and I think this is what I meant, is that the history of failed attempts to derive a realist theory to underlie quantum mechanics (which often gets misleadingly called "interpretation" by proponents) leads me to think the entire approach is fundamentally flawed. This realist theory hasn't been completely ruled out, but it must live in a very small corner that seems restricted in an almost maliciously inelegant way, so my instinct is that we should look elsewhere.

Then you mean by positivism something entirely different than I do.

What I mean by "positivism" for the purposes of this discussion is the idea of restricting oneself to making predictions of experimental outcomes, without attempting a realist description (classical physics). I'm not talking about any other aspects of the work of Auguste Comte et al.

Nima's project is certainly not positivist but realist in the (ahem, correct ) philosophical sense of attempting a description of an actual observer-independent physical geometry that causes certain observable behaviours and properties in the actual physical universe.

No, it's not. Let's take a look at their paper:

https://arxiv.org/abs/1312.2007

Specifically equation (1.1) and the discussion surrounding it. The object being computed is the scattering amplitude M, which is a basic building block for calculating experimentally relevant quantities such as cross-sections and decay rates. It represents a transition from "in states", which are the incoming waves in the infinitely far past, to "out waves", which are the resulting scattered products in the infinitely far future. With the usual perturbative methods it's given by the sum of Feynman diagrams at the given order, with the right external legs to represent the process under consideration. In eq (1.1) these are encoded in the state vector |lambda_a, lambda~_a, eta~_a> (these are variables in the so-called spinor-helicity formalism -- don't worry about it). This is a state vector in the usual quantum mechanical sense; in Ballentine's language above we can write a state operator as

rho_0 = |lambda_a, lambda~_a, eta~_a><lambda_a, lambda~_a, eta~_a|

which is associated with the preparation procedure that set up those incoming waves. The amplituhedron simply tells you what the state vector/operator will look like in the infinitely far future after all the waves have had a chance to interact with and scatter off one another. In order to connect this to experimentally relevant quantities, first you must decide what to measure (such as a particle momentum or polarization state), write down the Hermitian operator corresponding to that quantity, and compute

<R> = Tr(rho * R) / Tr (rho)

to find out the expected value. Because the state vector enters twice in this expression (once in the bra |...>, once in the ket <...|), so will the amplituhedron-computed amplitude M, which will enter this expression as an absolute value squared |M|^2.

In other words, the amplituhedron is a recipe for computing the quantum state in the infinite far future from the quantum state in the infinite far past. It allows no description of what's happening in between, and the final result of the calculation is just a state, something that is given physical meaning only once someone comes along and actually makes a measurement -- the choice of what measurement being up to them. So all the issues that caused discomfort such as the apparent subjectivity of observation remain in this picture, completely unaltered. It's still quantum mechanics, fundamentally positivist.

 

[LilWabbit]

It seems we've moved forward on a number of points. Therefore, in the following, I won't focus on those.

In order to conflate two things, there must be in fact two identifiable things to conflate. All we have here is quantum mechanics, in its essentially unique definition (see e.g. Ballentine, chapter 2):

1. To each dynamical variable (physical concept) there corresponds a linear operator (mathematical object), and the possible values of the dynamical variable are the eigenvalues of the operator.
1a. To each dynamical variable there is a Hermitian operator whose eigenvalues are the possible values of the dynamical variable.
2. To each state there corresponds a unique state operator. The average value of the dynamical variable R, represented by the operator R, in the virtual ensemble of events that may result from a preparation procedure for the state, represented by the operator rho, is
<R> = Tr(rho * R) / Tr (rho)
2a. To each state there corresponds a unique state operator, which must be Hermitian, nonnegative, and of unit trace.

Here I would kindly remind that this is the archetype of conflation. You are conflating the received formalism of QM with quantum mechanics. However, you merely repeating a claim of identity between two different statements ('quantum mechanics' and 'the formalism summarized by Ballentine') does not demonstrate their identity. Formalism does not even provide a theory in the known scientific sense (a description of reality). It merely offers a nifty tool for calculations. Where there is no consensus amongst physicists (and which is apparent also in our discussion) is whether the project of quantum mechanics should be merely a 'shut up and calculate' exercise as you and other Copenhagenists suggest, or something that goes beyond the received formalism and attempts to describe actual physical reality like the rest of physics attempts. But just repeating this dogma doesn't make it any truer. Only louder.

For me, science dies the moment scientists themselves preach with conviction that we should stop asking the question 'what is it really?' Science dies that much more painfully when we justify such a prohibition of further questioning by stating religiously that some questions are impossible to answer, especially because our brilliant founding daddies couldn't answer them and therefore asked the rest of us religiously obedient lesser children to also not ask. 'Shut up and calculate'. That's when science transforms into mysticism and blind obedience.

That's not a definition, it's a description of the theory's scope. I can't use this description to come up with predictions of the theory. Quantum mechanics is a theory (or a framework for building theories) with a specific definition (the one quoted above); if it turns out that subatomic particles don't quite behave according to its rules, quantum mechanics will lose its fundamental status and be replaced with something else. "Quantum mechanics" is to "the behaviour of matter and light on the atomic and subatomic scale" as "general relativity" is to "gravity".

As I explain in the previous point, it's not so much an interpretive tradition, but a mathematical demand.

The received formalism of quantum mechanics is a clever mathematical toolkit, based on observations, to predict observations. We both agree this formalism doesn't even attempt to describe reality. If the purpose of science is to merely provide predictions of observations and to account for them in a technologically useful way (i.e. positivism and instrumentalism), then you would be right to say that the received formalism of QM is "but a mathematical demand" of science. However, in so stating you are, in fact, interpreting the whole project of science within QM in a positivist way. In other words, stating 'quantum mechanics is its formalism' is essentially a dogmatic statement based on a particular way (positivism) to interpret the purpose of science, or at least the science of QM.

Now, what I do think, and I think this is what I meant, is that the history of failed attempts to derive a realist theory to underlie quantum mechanics (which often gets misleadingly called "interpretation" by proponents) leads me to think the entire approach is fundamentally flawed.

But is it flawed because realist QM is impossible in principle, or flawed because the known attempts each have faced certain serious theoretical stumbling-blocks (such as non-locality) that could be potentially addressed. I'm more with Tim Maudlin and consider all these various interpretive attempts warmly welcome, each highlighting different nuggets of a possible broader theory worthy of further development as well as major errors worthy of dismissal. However, in the received positivist culture QM realism is culturally prepared for failure. Not because it's intellectually or theoretically doomed.

Spacetime is clearly an inadequate picture and may contain further observer-independent structures in the universe -- preferred foliations or the like -- that account for quantum entanglement amongst other things. That's why all fresh projects in QFT or relativity in pursuit of a more fundamental math are very welcome, despite all the various stumbling blocks they will inevitably encounter. That's just science. Attempts at describing reality, with one failed attempt after another, persistently, consistently, painstakingly, until a comparatively more fundamental picture emerges as compared to earlier pictures.

No, it's not. Let's take a look at their paper:

https://arxiv.org/abs/1312.2007

Specifically equation (1.1) . . .

My statement "Nima's project is certainly not positivist but realist" (to which you replied "no, it's not", and offered an unnecessary summary of the amplituhedron) was not a reference to the mathematical object of the amplituhedron. I thought we had already moved on. We have already established what Nima encapsulates in the paper you cited. That the amplituhedron, technically, is "a mathematical object whose "volume" directly computes the scattering amplitude". In that sense you are right, that the amplituhedron is a neat mathematical model, a clever computational tool, not attempting a direct description of physical reality. However, that's not all it is in Nima's mind, when it comes to its possible implications for physics.

I was referring to his broader ongoing project of discovering a fundamental structure in the universe, describable by sophisticated geometry -- involving n-dimensional geometrical functional spaces, the number theory and other mathematical axiomatic systems that haven't been properly explored in quantum physics or physics in toto, some of them such as the mathematical implications of the amplituhedron haven't been properly explored even within mathematics -- out of which both spacetime and quantum mechanics emerge.

The 'amplituhedron' to Nima is just a concrete example of a theory that seems capable of such a description but within a very narrow region (on which we seem to agree). Nima is far from certain the project will succeed, and aware of its various challenges. Unlike the received formalism of quantum mechanics (which you conflated with the entire project of quantum mechanics by appeal to Ballentine's definition), Nima's broader project isn't interested in merely providing a mathematical recipe but an actual description of an underlying physical reality. When asked about the implications of the amplituhedron, Nima replies (bold italics added highlighting his realist ambitions):

Article:

"The entire drama of twentieth-century physics has been learning how to combine the rules of quantum mechanics and the rules of relativity at the same time. While we have found various ways of making these principles work together, we realize we don't understand very deeply what it is we are dealing with yet. This is tied to one of our deepest challenges in the twenty-first century: what are the building blocks out of which spacetime emerges? It's not obvious where this is going. Maybe it will be something spectacular. Maybe it will just be a curiosity. We don't know. But it's something. And it's a beautiful something."—Nima Arkani-Hamed"

Source: https://www.ias.edu/ideas/nima-arkani-hamed-amplituhedron

His realist project is here summarized in his own words (bold italics added):

Article:

"The ascension to the tenth level of intellectual heaven would be if we find the question to which the universe is the answer, and the nature of that question in and of itself explains why it was possible to describe it in so many different ways."

Source: https://www.newyorker.com/science/elements/a-different-kind-of-theory-of-everything

If too lazy to watch the entire lecture, from 1:09:50 till 1:12:00 Nima outlines his speculation of the potential for physics that the discovery of the "baby example", that is the amplituhedron, unfolds, and which both the mathematicians and physicists involved in the project are treating with equal novelty and fascination:


Source: https://www.youtube.com/watch?v=z1-QDXReDTU


I think Nima's is a valuable and fascinating project the implications of which are obviously not clear. Let's not tell him, or similar clever and enthusiastic physicists with an ambition to understand the universe, to just 'shut up and calculate'.

 

[Edward Current]

For me, science dies the moment scientists themselves preach with conviction that we should stop asking the question 'what is it really?' Science dies that much more painfully when we justify such a prohibition of further questioning by stating religiously that some questions are impossible to answer, especially because our brilliant founding daddies couldn't answer them and therefore asked the rest of us religiously obedient lesser children to also not ask.

For me, the criticism of science dies the moment people suggest that science actually does that, and that science is a religion.

 

[LilWabbit]

For me, the criticism of science dies the moment people suggest that science actually does that, and that science is a religion.

A science that preaches "don't ask why because Bohr said so" is not a science and essentially no different from the argument of the Catholic Church in the Middle Ages. That's what positivism does. Most scientists aren't positivists despite its relative popularity in QM.

 

[markus]

Here I would kindly remind that this is the archetype of conflation. You are conflating the received formalism of QM with quantum mechanics. However, you merely repeating a claim of identity between two different statements ('quantum mechanics' and 'the formalism summarized by Ballentine') does not demonstrate their identity.

Well, I would suggest that the burden of proof is on you to demonstrate that quantum mechanics is anything other than the theory with its mathematically rigorously established foundation, as axiomatized via the postulates I cited or some other equivalent formulation. The content of these axioms and the mathematical structure generated by them are agreed upon by virtually all practicing physicists. Not even the "interpreters" of quantum mechanics disagree that quantum mechanics (as actually used) is given by the axioms above.

Formalism does not even provide a theory in the known scientific sense (a description of reality).

That's because quantum mechanics is not a theory like, say, general relativity. It's a framework for building theories. Quantum field theory is also a framework, albeit a more specialized one. What we would call a "theory" in the narrow prescriptivist sense favored by some science communicators (that doesn't actually find much hold at all in physics, but I digress) is the standard model of particle physics. It's not an accident that models in particle physics, even 'fake' toy models like N=4 SYM, all get called "theories".

Like I said in the previous one, quantum mechanics is an analogue of probability theory. Corollary, building quantum theories is a lot like building probabilistic models. But just because you need to do more work before your probabilistic model gets off the ground doesn't mean that the axiomatic formulation of probability is in dispute.

It merely offers a nifty tool for calculations. Where there is no consensus amongst physicists (and which is apparent also in our discussion) is whether the project of quantum mechanics should be merely a 'shut up and calculate' exercise as you and other Copenhagenists suggest,

Does it make sense to ask if Newtonian mechanics "should" be relativistic?

For me, science dies the moment scientists themselves preach with conviction that we should stop asking the question 'what is it really?' Science dies that much more painfully when we justify such a prohibition of further questioning by stating religiously that some questions are impossible to answer, especially because our brilliant founding daddies couldn't answer them and therefore asked the rest of us religiously obedient lesser children to also not ask. 'Shut up and calculate'. That's when science transforms into mysticism and blind obedience.

That's conflating 'quantum mechanics' with 'reality'. Quantum mechanics, like Newtonian mechanics, is a theory/framework with a specific scope. There's nothing in principle saying that we can't find something more fundamental -- that thing just won't be called "quantum mechanics", that name is taken.

The received formalism of quantum mechanics is a clever mathematical toolkit, based on observations, to predict observations. We both agree this formalism doesn't even attempt to describe reality. If the purpose of science is to merely provide predictions of observations and to account for them in a technologically useful way (i.e. positivism and instrumentalism), then you would be right to say that the received formalism of QM is "but a mathematical demand" of science.

That's not what I said. I said positivism is a mathematical demand of the mathematical structure of quantum mechanics (in any formulation, whether "received" or otherwise).

But is it flawed because realist QM is impossible in principle, or flawed because the known attempts each have faced certain serious theoretical stumbling-blocks (such as non-locality) that could be potentially addressed.

It's flawed in the same sense that the idea of a square circle is flawed in plane geometry.

Spacetime is clearly an inadequate picture and may contain further observer-independent structures in the universe -- preferred foliations or the like -- that account for quantum entanglement amongst other things.

That's the kind of structure I meant by "almost maliciously inelegant". It's logically possible that really deep down there's a preferred reference frame and the laws of physics all conspire to hide it, so that relativity is an illusion and the low energy theory looks very different from the high energy theory but some it's just like the ultra-high energy theory, but is there any evidence that suggests we should pursue that sort of theory? I think there's very little.

My statement "Nima's project is certainly not positivist but realist" (to which you reply "no, it's not", and offered an unnecessary summary of the amplituhedron) was not a reference to the mathematical object of the amplituhedron. I thought we had already moved on. We have already established what Nima encapsulates in the paper you cited. That the amplituhedron, technically, is "a mathematical object whose "volume" directly computes the scattering amplitude". In that sense you are right, that the amplituhedron is a neat mathematical model, a clever computational tool, not attempting a direct description of physical reality. However, that's not all it is in Nima's mind, when it comes to its possible implications for physics.

I think the summary was necessary because in the previous post you had written "Nima's project is certainly not positivist but realist (...) attempting a description of an actual observer-independent physical geometry (...)", which sounds like you meant the amplituhedron. Now, at the cost of perhaps boring you a little, what was meant has been sharpened, so I make no apologies

I was referring to his broader ongoing project of discovering a fundamental structure in the universe, describable by sophisticated geometry -- involving n-dimensional geometrical functional spaces, the number theory and other mathematical axiomatic systems that haven't been properly explored in quantum physics or physics in toto, some of them such as the mathematical implications of the amplituhedron haven't been properly explored even within mathematics -- out of which both spacetime and quantum mechanics emerge.

The 'amplituhedron' to Nima is just a concrete example of a theory that seems capable of such a description but within a very narrow region (on which we seem to agree).

I agree that (assuming that the general conjecture is valid -- the amplituhedron was proved only at tree-level) the amplitudes can be calculated in a simplified manner that doesn't require other foundational concepts, but given your earlier characterization as "observer-independent" I'm hesitant to express further agreement: I think in the context of this discussion it's more important to emphasize that the mathematical structures that have been proposed here, even if they do ultimately come from something fundamentally different (e.g. lacking any notion of spacetime), will still be part of some quantum mechanical theory, because that's the arena we're playing in. That's why I made sure to connect what he was doing to the axioms of quantum mechanics, and to point out that this is a development of the old and venerable S-matrix program.

Nima is far from certain the project will succeed, and aware of its various challenges. Unlike the received formalism of quantum mechanics (which you conflated with the entire project of quantum mechanics by appeal to Ballentine's definition),

Pick any other definition you like, they're all provably equivalent.

Nima's broader project isn't interested in merely providing a mathematical recipe but an actual description of an underlying physical reality. When asked about the implications of the amplituhedron, Nima replies (bold italics added highlighting his realist ambitions):

Article:

"The entire drama of twentieth-century physics has been learning how to combine the rules of quantum mechanics and the rules of relativity at the same time. While we have found various ways of making these principles work together, we realize we don't understand very deeply what it is we are dealing with yet. This is tied to one of our deepest challenges in the twenty-first century: what are the building blocks out of which spacetime emerges? It's not obvious where this is going. Maybe it will be something spectacular. Maybe it will just be a curiosity. We don't know. But it's something. And it's a beautiful something."—Nima Arkani-Hamed"

Source: https://www.ias.edu/ideas/nima-arkani-hamed-amplituhedron

His realist project is here summarized in his own words (bold italics added):

Article:

"The ascension to the tenth level of intellectual heaven would be if we find the question to which the universe is the answer, and the nature of that question in and of itself explains why it was possible to describe it in so many different ways."

Source: https://www.newyorker.com/science/elements/a-different-kind-of-theory-of-everything

I think Nima's is a valuable and fascinating project the implications of which are obviously not clear. Let's not tell him, or similar clever and enthusiastic physicists with an ambition to understand the universe, to just 'shut up and calculate'.

That's not a "realist project". Asking "what are the building blocks out of which spacetime emerges" could, for example, have the answer "[something stringy]". Nima is a believer in string theory, as the QFT savvy might suspect from his interest in N=4 SYM, and he even believes he can prove it. Is string theory a quantum mechanical model? You bet: it's what you get from the axioms of quantum mechanics if you build a theory whose elementary degrees of freedom are extended objects, not just points (to mean they have infinite internal degrees of freedom). So asking this sort of question doesn't indicate any interest in "realism". On the contrary, chances are he would strongly push back against a characterization of his project as "realist".

Similarly, when he says he'd like to find the question "to which the universe is the answer", he's not talking about finding some realist model underlying quantum mechanics. He's talking about finding the fundamental, almost certainly quantum mechanical principles that lead to physics like that of our universe (and his talk about proving string theory falls neatly here too).

If you doubt my interpretation, listen to this, straight from the horse's mouth:


Source: https://youtu.be/t-C5RubqtRA?t=5070


1h24m30s in (already cued up), an audience member asks:

Your presentation is based on the fact or assumption that the quantum reality or quantum foundations are concrete and you develop your logic from that basis but going back to the quantum foundation itself where consciousness related questions, related to objective reduction and the quantum measurement itself, what role consciousness plays...

Nima interrupts:

Okay let me answer this question so I'm gonna give an answer that your thirty years ago was the answer 99.9% of theoretical physicists would give but it's somehow politically incorrect to say these days so I will say it. There is nothing interesting going on in the foundations of quantum mechanics. Zero. Okay? There's nothing in this subject that's not understood, unless the words 'gravity' or 'cosmology' make an appearance. Then not only are they relevant but that's the first twenty minutes of this talk: it was actually exactly about those those issues, you see. What forced us to talk about these observables that live at infinity? It's because quantum mechanics needed you to do to these experiments with infinitely large apparatuses, alright? That's where this business about the foundations has teeth. It has teeth, it has beef, it has consequences, and you follow up those consequences and you actually do learn sort of radical things about the way you're supposed to talk about the world, but you don't go anywhere with them unless unless you know that and you pursue them where they matter.

There is nothing interesting or deep or strange going on when a random graduate student does a random quantum measurement in a random basement laboratory somewhere. And everything there is fully, completely understood, within the ordinary logic of quantum mechanics (something by the way which the founders of quantum mechanics understood perfectly).

I realize this is not engaging your question but I'm making such a strong statement because I want to tell you the right answer.

(excerpts lightly edited for clarity).

The first 20 minutes was essentially giving the description I gave above of scattering processes that come from infinity and go to infinity and why he believes emphasizing that is the fundamentally right approach. The key thing to understand here is that he's not trying to come up with anything "realist". If anything, he's going further in an even more positivist direction: he makes explicit his belief that our "brilliant founding daddies" had the right idea all along, and that the questions one must grapple with in order to make fundamental progress are questions of a necessarily different character. I wholeheartedly endorse those statements.

Nima is an incredibly outspoken, extravagantly passionate individual. If he was in the business of bringing back realism, trust me, we'd know.

If you're still unconvinced, here's another one, even more explicit:


Source: https://youtu.be/pup3s86oJXU?t=2862

I mean they're meaningless statements as statements about the universe. So let's say we take the statement I said that what is the position and velocity of that electron (...) It's conceivable [that the statement could be made meaningful again], now, I think it's incredibly unlikely, and there's lots of reasons to believe that we're never going to return to these deterministic pictures of the world, and that there is no more primitive theory underlying quantum mechanics in at least in that sort of simple-minded way. But if there are some miraculous loophole then then that sentence will only make sense if every word in it means something completely different than what it means now.

Once again I agree with everything he's saying here.

Now, really this is kind of off-topic: Nima is just one guy and it doesn't really matter what his opinion is. But if his work is to be taken as an example of possible developments towards a "realist" theory to explain the same observations that currently fall in the scope of quantum mechanics, it's important to clarify the context of what he's doing and what his own motivations are.

 

[LilWabbit]

I will address your science and positivism related arguments in a separate post. It's a broader and more relevant discussion anyway, although perhaps deserving a thread of its own. But since you attempted to provide counter-examples demonstrating Nima's alleged 'positivism' that were, to me, evident misunderstandings of his statements on your part, let me respond to them first:

If you doubt my interpretation, listen to this, straight from the horse's mouth:


Source: https://youtu.be/t-C5RubqtRA?t=5070


1h24m30s in (already cued up), an audience member asks:

Your presentation is based on the fact or assumption that the quantum reality or quantum foundations are concrete and you develop your logic from that basis but going back to the quantum foundation itself where consciousness related questions, related to objective reduction and the quantum measurement itself, what role consciousness plays...

Nima interrupts:

Okay let me answer this question so I'm gonna give an answer that your thirty years ago was the answer 99.9% of theoretical physicists would give but it's somehow politically incorrect to say these days so I will say it. There is nothing interesting going on in the foundations of quantum mechanics. Zero. Okay? There's nothing in this subject that's not understood, unless the words 'gravity' or 'cosmology' make an appearance. Then not only are they relevant but that's the first twenty minutes of this talk: it was actually exactly about those those issues, you see. What forced us to talk about these observables that live at infinity? It's because quantum mechanics needed you to do to these experiments with infinitely large apparatuses, alright? That's where this business about the foundations has teeth. It has teeth, it has beef, it has consequences, and you follow up those consequences and you actually do learn sort of radical things about the way you're supposed to talk about the world, but you don't go anywhere with them unless unless you know that and you pursue them where they matter.

There is nothing interesting or deep or strange going on when a random graduate student does a random quantum measurement in a random basement laboratory somewhere. And everything there is fully, completely understood, within the ordinary logic of quantum mechanics (something by the way which the founders of quantum mechanics understood perfectly).

I realize this is not engaging your question but I'm making such a strong statement because I want to tell you the right answer.

(excerpts lightly edited for clarity).

Nima is discussing the foundations of quantum mechanics (i.e. the very formalism we've been discussing and its various usages) as something where "nothing interesting" has been going on for a long time. I wholeheartedly agree. He is not discussing the foundations of quantum-scale phenomena as being in any sense uninteresting or "fully, completely understood".

If you're still unconvinced, here's another one, even more explicit:


Source: https://youtu.be/pup3s86oJXU?t=2862

I mean they're meaningless statements as statements about the universe. So let's say we take the statement I said that what is the position and velocity of that electron (...) It's conceivable [that the statement could be made meaningful again], now, I think it's incredibly unlikely, and there's lots of reasons to believe that we're never going to return to these deterministic pictures of the world, and that there is no more primitive theory underlying quantum mechanics in at least in that sort of simple-minded way. But if there are some miraculous loophole then then that sentence will only make sense if every word in it means something completely different than what it means now.

I've watched this discussion before. Your editing (omission) at a critical point somewhat dilutes the gist of what he was saying. Nima is merely pointing out that any discussion on the position and velocity of an electron is meaningless unless and until we have a more sophisticated understanding of what any of these phenomena (electron, position and velocity) really are (pun intended). He then speculates that this could be the case maybe far in the future when we've understood both quantum phenomena and spacetime better. (His own project is about understanding both spacetime and quantum phenomena as 'emergent' from something more fundamental, so to interpret him here as referring to the current quantum-mechanical formalistic understanding as the most fundamental in his mind is simply erroneous and taken out of context.) He also seems to say that the old classical ways to describe the position and velocity of the electron in a deterministic manner is a simple-minded way of discussing these phenomena which we are not going back to. That's pretty much a platitude. A truism.

Nothing in here or in his previous example implies positivism. Quite to the contrary, as he cleverly summarizes in the self-same clip you shared:

"Often the concepts that we need to understand things more deeply are so foreign to the ideas that we have now that we can't even articulate the correct question before we happen to be in the neighbourhood of the right answer."

By the way, "understanding things more deeply" is classic realist language.

 

[LilWabbit]

Well, I would suggest that the burden of proof is on you to demonstrate that quantum mechanics is anything other than the theory with its mathematically rigorously established foundation, as axiomatized via the postulates I cited or some other equivalent formulation.

While not claiming there is no burden on my side, your 'suggestion' that the burden rests exclusively on my side is logically unfounded. This seems to me due to your sincere but persistent unawareness of two factors that underpin your position:

(1) Unawareness that your claim 'QM is defined by its formalism' is a function of Bohrean positivism rather than the other way around, while the said underlying positivism is taken as a given for QM without a burden of proof (see factor #2 below). Bohrean positivism attempted, from the very historical beginnings of QM, to dogmatically restrict what quantum physics can and cannot be as a scientific pursuit. Instead, you seem to make the opposite and circular claim (also without proof): That Bohrean positivism (i.e. a philosophical theory of science) -- which historically prescribed the scientific mission of QM to merely provide a mathematical formalism for measurements -- somehow logically/mathematically follows said formalism.

No philosophical theory of science can be mathematically inferred from the formalism of QM (or from any other mathematical formalism for that matter). If you think it can, please demonstrate by using known deductive rules within known mathematical or logical axiomatic systems. However, what you can say logically is that the formalism of QM is, by design, positivistic in that it does not attempt a description of reality as is. Neither can you infer from the formalism itself, no matter how positivist by design, that all physicists who make use of it, and engage in its further development, are logically necessitated to espouse positivism as a philosophical theory. The formalism doesn't logically preclude even a direct realist interpretation for the wavefunction (despite the evident silliness of such projects in my view and it seems also in yours).

(2) Unawareness that the Bohrean positivism underlying your claim 'QM is defined by its formalism' (see factor #1 above) inheres a positive philosophical claim (a kind of 'belief' in fact) that assigns an onus of proof on the claimant. That is, the belief that 'only individual events observable under well-defined experimental conditions are reliably knowable, while nothing beyond these observables is'. (I'm here using Bohr's language of "individual events observable under well-defined experimental conditions" verbatim.)

As to my burden, it can be addressed variously. For reasons of verbal economy, let me concisely tackle it by highlighting the inherent paradox in your positivist claim. Demonstrating the paradox of the positivist philosophical claim adds credence, by the logical inference rule of contraposition, to its logical alternatives, including the realist claim. The paradox reads quite simply as follows:

I reliably know only individual events observable under well-defined experimental conditions. Any aspect of reality beyond these individual events, including their real causes, is not reliably knowable. Yet the foregoing claim is not an individual event observable under well-defined experimental conditions.

(A pertinent footnote: Bohr was not as radical as a solipsist or a phenomenalist denying reality beyond observations. He just denied reliable knowledge of that reality.)

(Another pertinent footnote: This paradox applies to all variants of the positivist claim, irrespective of whether that which is reliably knowable is defined as 'observations', 'measurements', 'statements on observations', 'descriptions of measurements', 'the scientist's consciousness of the linguistic meanings of measurement reports', 'statements verifiable by observation', et cetera.)

Another version of the paradox, formulated in 'belief' language: I have a scientifically unobservable belief that scientific observation is the only reliable means to acquire knowledge.

Logically, to make a positive claim on reliable knowledge being restricted to the domain of experimentally measured events, is to pronounce a blind metaphysical belief in a universe where any other possible domain is forever bound to be inaccessible to reliable knowledge. Experimentally, however, there is no possible way to know such a sweeping truth about all reality. It's purely speculative. Such a notion therefore resides firmly in the realm of philosophy, unapproachable by science.

Positivism is just another scientifically unfalsifiable and unverifiable philosophical theory. To think one is engaging in any thought process or rational behaviour -- whether scientific, professional or mundane -- without a single philosophical assumption (belief) is an exercise in self-deception. 'Positivists' as well as 'realists' amongst physicists often perpetrate this blissful ignorance.

The scientific pursuit is replete with philosophical assumptions as regards its purpose, scope, method, domain and discipline-specific postulations. The realism vs. positivism debate offers two mutually contradictory positions on the purpose of science.

Any statement on the fundamental nature and value of science as a knowledge-pursuit is by logical necessity a higher-order statement above purely scientific statements, and hence non-scientific by default (or meta-scientific, to be precise). All such statements fall under an academic discipline better known as Philosophy of Science, regardless of whether or not the one making such a statement is aware he's engaging in a philosophical discourse, and whether the statement was casual or formal.

Historically, the positivist tradition in quantum mechanics did not arise out of a thorough exploration and comparison of viable philosophical theories for the science of quantum physics, but rather from the intellectual influence exerted by certain positivist philosophers on the likes of Bohr and Heisenberg.

Logical positivism was a philosophical project undertaken by the Vienna Circle, a group of analytical philosophers in the early part of the 20th century, some of which are still regarded as philosophical 'heavy weights' that did pioneering work on the foundations of logic and mathematics. Amongst others, Rudolf Carnap and Kurt Gödel were members of the Circle while the likes of Quine, Hempel and Tarski were closely associated with it. The Circle had a significant impact on Danish intellectual climate before WWII. In the 1930s members of the Vienna Circle had established close relations with Danish scientists and philosophers. Especially Otto Neurath (a philosopher, a logical positivist, a Comtean and a main author of the Vienna Circle manifesto) influenced Niels Bohr somewhat as further detailed in this article.

Having met twice in Copenhagen in 1934, Bohr and Neurath corresponded over the next couple of years during which Neurath's criticized Bohr for his initially realist language. When Bohr faced Einstein's last challenge the following year, Bohr's language had changed somewhat, adopting a much more positivist tone.

Article:

Up to 1935 Bohr believed that physicists, through their measurement of an atomic object, disturbed the object in such a manner that they could not exactly determine its position and momentum at the same time. This way of talking made it sound as if the atomic object could be considered as a Kantian thing-in-itself. The atomic object had some values or properties, when nobody interacted with it, but it took on different values or properties during its observation when it was disturbed by the experimental equipment.

Neurath, however, contrary to Einstein, would find any talk of the disturbance of such things-in-themselves very problematic if not complete nonsensical.

Source: http://philsci-archive.pitt.edu/3737/

While this may not be the case amongst a significant proportion of quantum physicists, in the scientific community there exists a general consensus (excluding a handful of anti-realist naysayers) that scientific truth is observer-independent but relative. Far from being perfect or absolutely accurate, the history of science demonstrates an ever-improving approximation of observer-independent truth. The claim that real-world referents of our approximate but ever-refining descriptions of 'black holes', 'entities with a mass', 'locations in space', 'locations in time','objects in motion', 'light', and 'gravity' exist with some correspondence to these descriptions even when they are not observed or described is far less radical than its positivist alternative. The more extraordinary positivist claim therefore calls for more extraordinary proof. Ptolemaic, Aristotelian, Copernican, Newtonian and Einsteinian science, each and all, improved the terms, the scope, and the resolution of our understanding and description of observer-independent physical reality even though some of the terms of the succeeding paradigms were incompatible with earlier terms, and even though some of the earlier assumptions and axioms have had to be entirely decommissioned.

Sometimes the paradigm shift is so radical that even fundamental axioms are redefined (e.g. Newtonian mass is conserved, Einsteinian is convertible with energy). And yet, the concept of mass has never been discarded as referring to a real thing, nor does the Einsteinian paradigm render Newtonian predictions invalid at lower velocities.

The philosophical assumption of (i) a mind-independent reality (realism, as opposed to solipsism or phenomenalism), and that (ii) for every observed phenomenon there must be a cause or causes that explain it (the Principle of Sufficient Reason, a.k.a. PoSR), are meaningful, sensible and productive assumptions at the core of scientific pursuit, enabling predictive explanation rather than mere prediction, and requiring little further 'defense' than these four properties against any alternative claim. Does this mean positivist science cannot be productive? Obviously not, and demonstrably not as per the formalism of QM. Especially as far as applied science is concerned. Do they need to be mutually exclusive scientific pursuits? I hope not, and 'live and let live', in the event their practitioners cannot find intellectual reconciliation.

The content of these axioms and the mathematical structure generated by them are agreed upon by virtually all practicing physicists. Not even the "interpreters" of quantum mechanics disagree that quantum mechanics (as actually used) is given by the axioms above.

They don't disagree that the current foundations of quantum mechanics are provided by such axioms. They would disagree on whether that's all that quantum mechanics is, and always must be. Let me offer here an olive branch: If quantum mechanics is defined by its current formalism and by no scientific pursuit or theorization above and beyond that formalism (even if it builds on said formalism), then under that definition we agree quantum mechanics is complete and its practitioners should just 'shut up and calculate'.

Does it make sense to ask if Newtonian mechanics "should" be relativistic?

Responded in the above.

That's conflating 'quantum mechanics' with 'reality'. Quantum mechanics, like Newtonian mechanics, is a theory/framework with a specific scope. There's nothing in principle saying that we can't find something more fundamental -- that thing just won't be called "quantum mechanics", that name is taken.

Responded in the above.

That's not what I said. I said positivism is a mathematical demand of the mathematical structure of quantum mechanics (in any formulation, whether "received" or otherwise).

Responded in the above.

That's the kind of structure I meant by "almost maliciously inelegant".

Depends on what such a structure may turn out to be if it exists. If it's even remotely like the amplituhedra I'd say it's beautifully elegant and simple. And it wouldn't eliminate spacetime nor render it a mere illusion. It would merely offer a more fundamental, but also a more abstract, description out of which spacetime emerges.

I think in the context of this discussion it's more important to emphasize that the mathematical structures that have been proposed here, even if they do ultimately come from something fundamentally different (e.g. lacking any notion of spacetime), will still be part of some quantum mechanical theory, because that's the arena we're playing in. That's why I made sure to connect what he was doing to the axioms of quantum mechanics, and to point out that this is a development of the old and venerable S-matrix program.

While significant as a historical backdrop for Nima's project, the latter is not logically reducible to the S-matrix program. S-matrices employ linear algebra. The amplituhedra and binary surfacehedra employ algebraic geometry and number theory, providing a far richer and more profound mathematical language that remains as yet largely unexplored in physics, and not fully understood even in mathematics.

We would all be in a far better position to spell plausible doom to Nima's project if we'd have a far more profound understanding of the potential of algebraic geometry and number theory, some of the most advanced areas of modern mathematics, to provide at least a one notch more fundamental mathematical language for physics. Until then, the rest of us should really just 'shut up and calculate'.

In Nima's own words (37:30 onwards):

Algebraic geometry and number theory have never been part of physics before. The reason they haven't been discovered before is because we're insisting on describing physics in a way that made quantum mechanics and spacetime manifest in our face.

Source: https://youtu.be/OzSDZ_EPiXk


The persistent challenge to extend QM theory to multi-electron atoms suggests major limitations in its basic mathematical axioms. In QM, the commitment to calculus (especially linear differential calculus) seems a possible cause for these challenges. As it happens, it's precisely the search for a more fundamental and sophisticated math for physics that seems relevant and which Nima's project is concerned with.

However, for an educated discussion on the prospects of Nima's project, we'd have to gain a far deeper understanding of certain structures in quiver categories underlying the seemingly "magical" (in Nima's words) manner in which binary geometric surfacehedra satisfy certain string-theoretical equations, handing us parametrizations of these equations as certain polynomials associated with n-dimensional space and n-variables. I on my part will readily admit not being sufficiently well-versed in quiver categories and algebraic geometry to engage in such an educated discussion.

That's not a "realist project".

As is apparent from the above interview, not only is Nima a realist but in fact a romantic realist.

When asked about his greatest current passion in physics, Nima replies:

(34:40): "You want to know what spacetime really is."

(35:50): "The problem is incremental in the sense that there's truth sitting there. The wonderful thing about truth is that it's a great attractor. All you have to do is to get somewhere in its vicinity. . . . Having nature as your guide is a tremendous thing even if you're a slow worker."

(37:30): "I've felt this that the few things I've done in my career that I think are worth even something small have very much had this feeling to them that you were not inventing things. That there are things that are out there, and that we are sort of wandering around and that we have to be sensitive to their presence."

Asking "what are the building blocks out of which spacetime emerges" could, for example, have the answer "[something stringy]". Nima is a believer in string theory, as the QFT savvy might suspect from his interest in N=4 SYM, and he even believes he can prove it. Is string theory a quantum mechanical model? You bet: it's what you get from the axioms of quantum mechanics if you build a theory whose elementary degrees of freedom are extended objects, not just points (to mean they have infinite internal degrees of freedom).

Since we're on the subject, I've put a link below for a fascinating very recent lecture (summer 2021) by Nima on the broader application of what he calls 'surfacehedra'. He outlines his current explorations into the applicability of surfacehedra to string theory.

Surfacehedra (dual geometry for particles, binary geometry for strings) is no longer just about scattering amplitudes, but also "stringy amplitudes", a way of thinking about string theory without conformal field theory, worldsheets and elliptical functions.

Binary surfacehedra are different from dual surfacehedra in that the latter polytopes capture all the compatibility information associated with the curves on the surface, whereas the binary sufracehedra are completely locked (the constants are not floppy like with dual polytopes).

In Nima's characteristically enthusiastic words:

"These are highly nonlinear equations and its crazy they are consistent."

He mentions in his lecture he's currently also exploring the potential to extract "gravity" amplitudes from this binary geometry.


Source: https://www.youtube.com/watch?v=0JFoS0DfNK0

If Nima's baby steps to the beach are even seemingly taking him forward, let him take them and let's support him. Even if he ultimately only manages to fall in the ditch and die. For even that is a scientific result.

 

[markus]

Nima is discussing the foundations of quantum mechanics (i.e. the very formalism we've been discussing and its various usages) as something where "nothing interesting" has been going on for a long time. I wholeheartedly agree. He is not discussing the foundations of quantum-scale phenomena as being in any sense uninteresting or "fully, completely understood".

No, Nima is very clear when he says:

There is nothing interesting or deep or strange going on when a random graduate student does a random quantum measurement in a random basement laboratory somewhere. And everything there is fully, completely understood, within the ordinary logic of quantum mechanics (something by the way which the founders of quantum mechanics understood perfectly).

He's talking about the typical experiments involving polarizers, interferometers, single photon sources, etc. He's saying that in those experiments, in the act of actually running those experiments in the real world, nothing interesting happens. He's not talking about the formalism alone.

As for whether his position is "positivist", notice that when he says that nothing interesting is happening in the research on quantum foundations and that the brilliant founding daddies had it right all along, he's essentially characterizing all the research on different "interpretations" as a complete waste of time and declaring himself an avowed Copenhagist. Notice he's doing it with much stronger commitment than myself: my Copenhagism is out of agnosticism, his is out of conviction that there's nothing interesting there at all in reality, as he just declared in the strongest possible terms without any conceivable ambiguity.

I've watched this discussion before. Your editing (omission) at a critical point somewhat dilutes the gist of what he was saying.

Here's the quote in full:

I mean they're meaningless statements as statements about the universe. So let's say we take the statement I said that what is the position and velocity of that electron, right. I think perhaps it's perhaps it's possible in some far-off future theory that that might be a meaningful question but it will only be a meaningful question if what we mean by position and velocity and electron change okay. If what we mean by those things are what we mean by them now, it is a meaningless question and I think we can know that it is a meaningless question, it's a meaningless statement about the universe. So this is something important: again, that often, the concepts that end up being relevant that we end up needing to understand things more deeply our so foreign to to the ideas we have now that we can't even articulate the correct question before we happen to be in the neighborhood of the right answer, okay.

That's a fascinating thing about the way this part of science works that's that's completely not like the sort of cookie cutter description that "someone makes a hypothesis and then an experimentalist goes and it checks whether the hypothesis is true yes you're right no you're not right they go back to make another hypothesis", oh it's this ridiculous picture of how science works, it is not remotely close to the truth, and in fact, especially in this business especially involving involving deep conceptual questions. As I said we don't even know for asking the right question until we happen to be in the vicinity of the right answer and the cart comes before the horse a lot, and very often we have the correct equations for a number of years before we know what they mean and so nothing works in this straightforward way. But that means that we always have to be wary about about what precisely the words are supposed to mean, and now today we have a precise thing that we mean by electron even what we mean today by the electron is not quite what was meant 200 years ago by the electron because they didn't know about quantum mechanics then and we know something about quantum mechanics now.

So it won't be very useful to you, but but what I really mean when I say the electron right now is an irreducible representation of the Poincaré group with spin 1/2, okay, that's not something that, I mean doesn't mean anything to you, maybe it does, but that's not the way JJ Thompson who discovered the electron would describe it. So even the same word which for good reasons -- of course there are very good reasons to keep calling up the electron because it's the quantum version of that thing that he discovered which is associated with the language I just used to describe it -- but we have to continually update what our words mean as we learn more about nature. So I'll come back and say what I said: therefore, it's conceivable, now, I think it's incredibly unlikely, and there's lots of reasons to believe that we're never going to return to these deterministic pictures of the world, and that there is no more primitive theory underlying quantum mechanics in at least in that sort of simple-minded way. But if there are some miraculous loophole then then that sentence will only make sense if every word in it means something completely different than what it means now.

The section I cut out is merely expounding on how the language of science has to evolve to match improvement in fundamental understanding, (which is really kind of an obvious point if you think about it, not at all critical), and how that relates to the caveat in his answer to the question. I cut it out because we both understand this and because it's a really long tangent that would dilute the actual gist here, which is the part where he actually answers the question and says it's extremely unlikely quantum mechanics will be replaced by something so naive that questions of the sort "what is the position and velocity of that electron" have meaning. I concentrated the gist with my elision.

Nima is merely pointing out that any discussion on the position and velocity of an electron is meaningless unless and until we have a more sophisticated understanding of what any of these phenomena (electron, position and velocity) really are (pun intended). He then speculates that this could be the case maybe far in the future when we've understood both quantum phenomena and spacetime better.

And then clarifies that he finds this extremely unlikely.

(His own project is about understanding both spacetime and quantum phenomena as 'emergent' from something more fundamental, so to interpret him here as referring to the current quantum-mechanical formalistic understanding as the most fundamental in his mind is simply erroneous and taken out of context.)

It's neither. He says it explicitly that he thinks it's extremely unlikely something more fundamental than quantum mechanics will be found. He caveats saying that if it is, it'll be very different than what people expect, but that doesn't change the fact that he said it, explicitly, without any chance for ambiguity or taking out of context, which when combined with his "money quote" above concerning random graduate students, should leave zero doubt what his position is.

As for his project "understanding both spacetime and quantum phenomena as 'emergent' from something more fundamental", I believe you are missing some crucial context. Quantum mechanics, as I defined it in this thread, is a (the) possible modification of probability theory, a means to ask and answer questions and reason about propositions. This bare-bones formalism doesn't include any physical laws, as you yourself noted; these have to be supplied by the model-builder. Up to now those laws included some form of equations of motion that lay out how observable operators / states evolve over time. That's the stuff he believes is not fundamental but emergent -- those quantum laws--, not the bare formalism itself: the final answer he gets with his program is, and must be, a probability amplitude. He'll never move beyond quantum mechanics in this sense, and he's not looking to. If he were, his remarks about the "random graduate student" would be quite different.

He also seems to say that the old classical ways to describe the position and velocity of the electron in a deterministic manner is a simple-minded way of discussing these phenomena which we are not going back to. That's pretty much a platitude. A truism.

Nothing in here or in his previous example implies positivism. Quite to the contrary, as he cleverly summarizes in the self-same clip you shared:

"Often the concepts that we need to understand things more deeply are so foreign to the ideas that we have now that we can't even articulate the correct question before we happen to be in the neighbourhood of the right answer."

Nothing in that quote implies realism, not even in a glancing way. Really it's not even specific to this field but rather often applicable to any time one tries to understand hard problems, regardless of area of study. Contrast this with his explicit endorsement of the BFD's understanding (aka the Copenhagen interpretation).

By the way, "understanding things more deeply" is classic realist language.

Not at all. "Deep" is standard vocabulary in physics (and one the highest compliments). We want to understand things, not just punch numbers into a black box neural net-type thing and have predictions come out. In a quantum paradigm it's flat out impossible to have a realist description, but that doesn't mean that understanding, deep understanding in particular, is impossible. We were led to quantum mechanics because it led us to deeper understanding of the universe, not the opposite! There's abundant work that's been described as "deep" by generations of physicists of all interpretational denominations.

Lastly, it's important to note that in the first 20 minutes of his SLAC talk above, he explains that his interest in S-matrix-like techniques is not borne of technical necessity (as it often the case in quantum field theory) but rather an ideological commitment to avoid discussing any sort of internal dynamics, which he believes are not fundamental. As I said before, he's going even further into positivism than quantum mechanics as usually practiced does (where things are described in terms of equations of motion and you can at least talk about a state/observable in intermediate times of an experiment, etc). He's burning all that away, and keeping only "inputs" and "outputs", nothing but pure causality in its elemental form.

In his picture, you can't talk about that intermediate stuff just like we can't talk about the position and momentum of an electron. Only the experiment preparation and final measurement have meaning. So, not only is the language he uses "positivist" in the sense I described above, the actual beef of his research is "positivist" as well. If he has any dreams of this stuff eventually leading to a realist theory, he's surely kept them secret.

Again, this sort of hagiography really is off-topic, but it's important to put this research in its proper context. Unless you can find somewhere where he makes an explicit claim of realism (not just using some word like "deep" that would be at best a cryptic reference to it), the idea that his overall project is one akin to Bohmian mechanics in a search for a hidden variables model looks like the polar opposite of the truth.

 

[LilWabbit]

We should launch an online lecture series by the name of 'Nima Exegesis', with an introductory lecture: "What the hell does Nima mean whenever he opens his trap?" You and I can then represent bitterly opposing interpretations.

The point being: We're literally reading the same sentences by Mr. Nima in entirely opposite ways.

To me it seems clear (maybe I'm wrong) you haven't really watched/listened to his talks and interviews, especially as regards his more generic views on fundamental physics, and hence you're mining for snippets and reading into them by inserting a lot of Copenhagenist assumptions into his words which he himself explicitly hasn't. His approach to quantum mechanics is far less committed, and far more open.

No, Nima is very clear when he says:

There is nothing interesting or deep or strange going on when a random graduate student does a random quantum measurement in a random basement laboratory somewhere. And everything there is fully, completely understood, within the ordinary logic of quantum mechanics (something by the way which the founders of quantum mechanics understood perfectly).

As for whether his position is "positivist", notice that when he says that nothing interesting is happening in the research on quantum foundations and that the brilliant founding daddies had it right all along, he's essentially characterizing all the research on different "interpretations" as a complete waste of time and declaring himself an avowed Copenhagist. Notice he's doing it with much stronger commitment than myself:

I think you are reading heavily into his words "completely understood" and interpreting them as some kind of a formal pronouncement of firm commitment to positivism. Maybe a formalist is more inclined to read others in a formalistic way. However, I would caution against over-reading, rigid reading, selective reading and confirmatory bias. Meanwhile, you ignore all the other realist statements, including the ones I quoted in my previous post.

Here's a diametrically opposite reading: Even a graduate student performing "random quantum measurements" in a "random basement laboratory" already has a complete understanding of how to predict and measure experimental outcomes within the ordinary logic of quantum mechanics. Nima says there's nothing "interesting", "deep" or "strange" going on and hence the current foundations of quantum mechanics are effectively boring and uninteresting. Maybe this is a function of my bias (which I'm consciously trying to avoid but obviously could subconsciously perpetrate) that I detect in Nima's words even a hint of contempt at the graduate-level simplicity of the foundational formalism to which quantum mechanics is stuck due to "insistence" on using received mathematical language.

It's neither. He says it explicitly that he thinks it's extremely unlikely something more fundamental than quantum mechanics will be found.

No he doesn't. He only says it's extremely unlikely there's a "simple-minded" and "deterministic" way to describe any theory that would be more primitive than the current foundations of quantum mechanics. You're reading into his words.

Not at all. "Deep" is standard vocabulary in physics (and one the highest compliments). We want to understand things, not just punch numbers into a black box neural net-type thing and have predictions come out.

And I would argue that's the honest scientist, the unwitting realist, that devilishly lurks deep within even the physicists who outwardly/publicly declare "Copenhagen" while actually also really just 'want to understand things'. A true positivist is not interested in understanding things. He's only interested in predicting and collating measurable outcomes by the virtue of whatever mathematical model that does the job best. Those models need not have any conceptual meaning that needs to be "deeply understood". And, as it happens, they do not, as far as the current formalism of QM is concerned.

Let me illustrate. If we apply the most basic law of propositional logic -- the law of identity (for all a: a = a) -- to the notion of 'understanding things', we can present the following simple reformulation: For all propositions x (including mathematical configurations) produced by my understanding, I already have a full understanding of x. Hence, the claim that one needs to understand more deeply something that one's understanding has generated is logically contradictory. A true positivist is therefore satisfied with the current formalism of quantum mechanics and there's nothing more to understand. 'Shut up and calculate'. His understanding is complete. However, if he chooses to use any terminology of wanting to 'understand things' more 'deeply' (whether within or without quantum mechanics), then the person isn't a true positivist. He either has some realist intuitions or solipsist/phenomenalist intuitions of deeper things that he needs to delve further into. And I'm absolutely sure Nima isn't a solipsist/phenomenalist.

Moreover, to think that a mathematical model is, by the very fact of being mathematical or purely abstract, automatically instrumentalist/positivist (not real) is a misunderstanding of both mathematics as well as its philosophical foundations and interpretations. The divide between realists and formalists is a well-known one also amongst mathematicians.

A basic concern of foundational study in mathematics is to determine the nature of mathematical entities and the extent to which it is legitimate to consider them 'real' entities. There are three classic schools of foundational study providing three possible answers to this question. Realism, intuitionism/constructivism and formalism/nominalism.

Everyone in each school, however, agrees that mathematical activity involves all three processes: the contemplation of abstractions, the generation of mental constructions, and the explicit formulation of rules for symbolic manipulation. The philosophical differences arise when we consider the question of the relative status of these activities and the extent to which they comprise all or part of mathematics.

For example the quantum wavefunction, as described by the current formalism of quantum mechanics, is almost purely formalistic, except for expressing a real statistical truth on aggregate measurement outcomes (while measurement outcomes for individual particles remain unpredictable). It's a contrived mathematical construct using calculus and linear algebra, statistically summarizing historically amassed experimental outcomes.

Whereas the amplituhedron is a discovered mathematical construct after expressing linear algebra (Feynman diagrams, also resulting from historically amassed experimental outcomes) in differential geometry (twistor theory) and algebraic geometry (positive Grassmanian), revealing an elegant new type of mathematical structure which may or may not be representational of actual physical reality (an open question that interests Nima very much). Both Nima and his mathematician associates were genuinely surprised by this discovery. If some types of amplituhedra indeed underlie physical reality (although now being just a toy model), they would exhibit global determinism and local indeterminism (much like fractals). Hence, by definition, they would be very different, far more elegant, and far more advanced as physical structures than the simplistic determinism of Bohmian mechanics.

This research team has demonstrated that, in the right regions (selected by the structure of the Amplituhedron), the amplitudes they've calculated so far are positive. They state this as the first basic requirement for the amplitude "to actually literally be a volume", and not just as a toy model, while acknowledging they're still far from establishing the case. As one of the authors humbly states about the result:

Article:

Of course, this doesn't prove anything. There's still a lot of work to do to actually find the thing the amplitude is the volume of, and this isn't even proof that such a thing exists. It's another, small piece of evidence. But it's a reassuring one, and it's nice to begin to link our approach with the Amplituhedron folks.

Source: https://4gravitons.com/2016/11/25/hexagon-functions-meet-the-amplituhedron-thinking-positive/

However, the wavefunction, as handed down to us, needs no further understanding. The amplituhedron does. Math is weird and yet fascinating in that way. It's precisely due to these reasons that you have both realists as well as formalists amongst mathematicians.

He says it explicitly that he thinks it's extremely unlikely something more fundamental than quantum mechanics will be found.

No he doesn't. He only says it's extremely unlikely there's a "simple-minded" and "deterministic" way to describe any theory that would be more primitive than the current foundations of quantum mechanics. You're reading into his words.

So even the same word which for good reasons -- of course there are very good reasons to keep calling up the electron because it's the quantum version of that thing that he discovered which is associated with the language I just used to describe it -- but we have to continually update what our words mean as we learn more about nature. So I'll come back and say what I said: therefore, it's conceivable, now, I think it's incredibly unlikely, and there's lots of reasons to believe that we're never going to return to these deterministic pictures of the world, and that there is no more primitive theory underlying quantum mechanics in at least in that sort of simple-minded way.

He's less interested in replacing the current foundations of quantum mechanics than he is in finding a more fundamental theory from which the same probability amplitudes arise as well as spacetime. However, you'd be right in saying that in some interviews he says he's more confident the mathematical models being explored in algebraic geometry will produce a more primitive theory underlying spacetime than he is in the same succeeding with quantum mechanics.

And yet there's no ambiguity when he says (47:10 onwards) that also in quantum mechanics (in addition to relativity) there's an insistence to describe physics with the same mathematical language that was handed down to us. He is unambiguous that there's a more fundamental way to formulate physics from which both spacetime and quantum mechanics emerge:

"There is a way to talk about physics that doesn't put in spacetime and doesn't put in quantum mechanics, and gets the answers out in a very direct way. And that way involves a whole host of new really interesting structures in mathematics that are even new to the mathematicians."

"Algebraic geometry and number theory have never been part of physics before. The reason they haven't been discovered before is because we're insisting on describing physics in a way that made quantum mechanics and spacetime manifest in our face. And we're not there yet, and we're not completely done. But there's completely clearly now these fantastic new stuctures which are not speculative, just talking about standard physics, but in a very different way. I'm hopeful that it will go somewhere sort of more generally beyond the very special and simple theories that we're starting to understand this way, to reveal something deeper about the way the nature actually works."

"I would be thrilled if we would find some way of talking about all of standard physics, not just the toy models that we're looking at, but all the standard physics in a way that doesn't but spacetime in and doesn't but quantum mechanics in, and gets the answers out. And ultimately then, if we really understand it, then we'll have the beginning of an understanding, a starting point, from which we can see the emergence of spacetime and quantum mechanics."

If what Nima here describes is not a project embracing both physical realism and a search for a fundamental theory underlying both spacetime and quantum mechanics, then no description is.

 

[markus]

We should launch an online lecture series by the name of 'Nima Exegesis', with an introductory lecture: "What the hell does Nima mean whenever he opens his trap?" You and I can then represent bitterly opposing interpretations.

Sure -- but I'm reading them in the usual meaning that his words literally have, whereas you have been engage in some serious interpretive work by assuming that e.g. "understand things more deeply" means something realist when he told you with an abundance of clarity that the Copenhagen school was right and everything that followed as a waste of time.

To me it seems clear (maybe I'm wrong) you haven't really watched/listened to his talks and interviews, especially as regards his more generic views on fundamental physics, and hence you're mining for snippets

This quote

There is nothing interesting or deep or strange going on when a random graduate student does a random quantum measurement in a random basement laboratory somewhere. And everything there is fully, completely understood, within the ordinary logic of quantum mechanics (something by the way which the founders of quantum mechanics understood perfectly).

isn't some cherry-picked snippet. It's him being as clear as he can be about this question. And this, together with the fact that his research approaches fundamental questions with an even stronger form of positivism than that demanded by ordinary quantum mechanics makes the point clearer still.

and reading into them by inserting a lot of Copenhagenist assumptions into his words which he himself explicitly hasn't. His approach to quantum mechanics is far less committed, and far more open.

Explicitly? Where?

I think you are reading heavily into his words "completely understood" and interpreting them as some kind of a formal pronouncement of firm commitment to positivism. Maybe a formalist is more inclined to read others in a formalistic way. However, I would caution against over-reading, rigid reading, selective reading and confirmatory bias. Meanwhile, you ignore all the other realist statements, including the ones I quoted in my previous post.

You didn't quote even a single realist statement. Not one! Contrast with his explicit and unambiguous declaration that the foundations of quantum mechanics were already completely understood by the Copenhagen school.

Here's a diametrically opposite reading: Even a graduate student performing "random quantum measurements" in a "random basement laboratory" already has a complete understanding of how to predict and measure experimental outcomes within the ordinary logic of quantum mechanics. Nima says there's nothing "interesting", "deep" or "strange" going on and hence the current foundations of quantum mechanics are effectively boring and uninteresting. Maybe this is a function of my bias (which I'm consciously trying to avoid but obviously could subconsciously perpetrate) that I detect in Nima's words even a hint of contempt at the graduate-level simplicity of the foundational formalism to which quantum mechanics is stuck due to "insistence" on using received mathematical language.

Your continued use of the word "received" is very strange. The truth is, quantum mechanics has been reformulated in many, many different ways, using many different sets of axioms as starting points. These varied and different formulations are all equivalent, and if you trapped brilliant but ignorant physicists in a desert island with access to only the relevant experimental data, eventually they'd come up with something equivalent too. Why? Because this is actually an important insight, not something that's been handed down from above as some unquestioned truth that today's unwashed physicists are afraid to question. Quantum mechanics is powerful because it survived the crucible of experiment and the barrage of continuous skepticism, not because physicists are fanboys.

As for Nima's contempt, you're right: he's showing contempt for the "interpreters" of quantum mechanics, when he's convinced the founding fathers had it right all along, as he said explicitly and without any ambiguity.

No he doesn't. He only says it's extremely unlikely there's a "simple-minded" and "deterministic" way to describe any theory that would be more primitive than the current foundations of quantum mechanics. You're reading into his words.

In context, he's saying it's unlikely a theory in which questions such as "what's the position and velocity of this electron" have meaning. What he's referring to here are pairs of non-commuting observables, which in the logic of quantum mechanics correspond to operators that cannot be simultaneously diagonalized and therefore have no meaning as simultaneous descriptors of a state. He's saying it's extremely unlikely questions of that sort will have answers, unless things change so much that all the words in the sentence take on completely new meanings. This is saying that either quantum mechanics is the final thing or whatever's below has to have an utterly different form, which is also something I've been saying. Together with the money quote above it's pretty clear where he stands.

And I would argue that's the honest scientist, the unwitting realist, that devilishly lurks beneath even those physicists who outwardly/publicly declare "Copenhagen" while actually also really just 'want to understand things'. A true positivist is not interested in understanding things. He's only interested in predicting and collating measurable outcomes by the virtue of whatever mathematical model that does the job best. Those models need not have any conceptual meaning that needs to be "deeply understood". And, as it happens, they do not, as far as the current formalism of QM is concerned.

Your "true positivist" is not anywhere among real physicists. I cautioned that what I meant by 'positivist' in this context is merely the humbleness in accepting that we don't have a "classical physics" observer independent model, and that the best that can be done is predicting experimental outcomes, precisely for this reason. But even disregarding that, "whatever mathematical model that does the job best" is an astoundingly vague sentence. Perhaps you realize this. There's a reason why statisticians define performance metrics such as the adjusted R2 that aim to characterize model performance using parsimoniousness criteria in addition to accuracy. This is dealing with bare data, you see, showing that even in the most utter "positivist" sense one wants models that do better than predicting data. A map that's exactly as big as the territory it describes is rigorously useless.

In physics, beyond parsimoniousness one may also wish to fulfill criteria of mathematical elegance and an ill-defined but extremely useful "ring of truth" where one seeks what principles seem plausible as having fundamental status. Obviously what this "ring of truth" is will change as we gain deeper understanding, but regardless, the point is, physicists are always looking to "understand things more deeply" and this has nothing, truly nothing whatsoever, to do with a desire for a realist theory.

Let me illustrate. If we apply the most basic law of propositional logic -- the law of identity (for all a: a = a) -- to the notion of 'understanding things', we can present the following simple reformulation: For all propositions x (including mathematical configurations) produced by my understanding, I already have a full understanding of x. Hence, the claim that one needs to understand more deeply something that one's understanding has generated is logically contradictory. A true positivist is therefore satisfied with the current formalism of quantum mechanics and there's nothing more to understand. 'Shut up and calculate'. His understanding is complete.

Physicists know they don't know everything. Otherwise, they'd stop. That doesn't mean someone like Nima is looking for a realist theory, when he'll explicitly tell you he is not.

However, if he chooses to use any terminology of wanting to 'understand things' more 'deeply' (whether within or without quantum mechanics), then the person isn't a true positivist. He either has some realist intuitions or solipsist/phenomenalist intuitions of deeper things that he needs to delve further into. And I'm absolutely sure Nima isn't a solipsist/phenomenalist.

False dichotomy. That's not how physicists think.

Moreover, to think that a mathematical model is, by the very fact of being mathematical or purely abstract, automatically instrumentalist/positivist (not real)

Who claimed that?

It's a contrived mathematical construct

That's just, like, your opinion man.

Whereas the amplituhedron is a discovered mathematical construct

That's just, like, your opinion man.

This research team has demonstrated that, in the right regions (selected by the structure of the Amplituhedron), the amplitudes they've calculated so far are positive.

That's a random result that has nothing to do with this discussion.

However, the wavefunction, as handed down to us, needs no further understanding. The amplituhedron does.

It's not "wavefunction" (really the quantum state, the terms are not equivalent) or the amplituhedron. It's the quantum state and the amplituhedron. What you get at the end of the amplituhedron calculation is a quantum state. He hopes to formulate things in a way that obviates the need for local dynamical evolution so that this may be shown to be emergent, but he's not questioning the framework for reasoning about propositions about experiment. I addressed this in my last one.

No he doesn't. He only says it's extremely unlikely there's a "simple-minded" and "deterministic" way to describe any theory that would be more primitive than the current foundations of quantum mechanics. You're reading into his words.

Addressed above. "You're reading into his words." is a strange charge when you use him saying "understanding things more deeply" as a dog whistle for hidden realist desires that he'll never discuss openly while at the same time saying explicitly that the Copenhagen school was right and the interpreters were wrong.

He's less interested in replacing the current foundations of quantum mechanics than he is in finding a more fundamental theory from which the same probability amplitudes arise as well as spacetime. However, you'd be right in saying that in some interviews he says he's more confident the mathematical models being explored in algebraic geometry will produce a more primitive theory underlying spacetime than he is in the same succeeding with quantum mechanics.

And yet there's no ambiguity when he says (47:10 onwards) that alsoin quantum mechanics (in addition to relativity) there's an insistence to describe physics with the same mathematical language that was handed down to us:

Algebraic geometry and number theory have never been part of physics before. The reason they haven't been discovered before is because we're insisting on describing physics in a way that made quantum mechanics and spacetime manifest in our face.

He's not talking language here. He's talking principles.

Incidentally, the assertion that "Algebraic geometry and number theory have never been part of physics before" is incorrect, but that's not important right now.

 

[LilWabbit]

.He's not talking language here. He's talking principles.

Kindly reread the end of the previous post and Nima's unmistakable words. There is much more that he said. He's talking about reality. His realism and his search for foundational principles and language is unmistakable (from which both QM and spacetime emerges), and these are not mutually exclusive. Once more:

"There is a way to talk about physics that doesn't put in spacetime and doesn't put in quantum mechanics, and gets the answers out in a very direct way. And that way involves a whole host of new really interesting structures in mathematics that are even new to the mathematicians."

"But there's completely clearly now these fantastic new stuctures which are not speculative, just talking about standard physics, but in a very different way. I'm hopeful that it will go somewhere sort of more generally beyond the very special and simple theories that we're starting to understand this way, to reveal something deeper about the way the nature actually works."

"I would be thrilled if we would find some way of talking about all of standard physics, not just the toy models that we're looking at, but all the standard physics in a way that doesn't but spacetime in and doesn't but quantum mechanics in, and gets the answers out. And ultimately then, if we really understand it, then we'll have the beginning of an understanding, a starting point, from which we can see the emergence of spacetime and quantum mechanics."

If what Nima here describes is not a project pursuing a fundamental theory of physics which is realist and from which both spacetime and quantum mechanics emerge, then no description is.

As to the rest of your post, I read a lot of misreadings and sloppy readings of what I wrote although you did much better earlier when you studied your counterpart's written expression with patience. The digging-heels persistence in a rigid Nima exegesis through a Copenhagen filter seems apparent. But since we've already been digressing for sometime, let it be.

I've enjoyed this discussion for the most part.

 

[Mendel]

Let me illustrate. If we apply the most basic law of propositional logic -- the law of identity (for all a: a = a) -- to the notion of 'understanding things', we can present the following simple reformulation: For all propositions x (including mathematical configurations) produced by my understanding, I already have a full understanding of x. Hence, the claim that one needs to understand more deeply something that one's understanding has generated is logically contradictory.

Your written description uses terms like "produced by my understanding" and "understandiung has generated" which are not properly reflected in your small tautology.

If we designate "understanding" as an efficient formal system (employing a mathematical/logical axiomatic description) that enables us to formulate statements and to decide them, then it follows from Goedel's Incompleteness Theorems that some of these statements that can be proposed must be undecidable, i.e. it is unknowable within that "understanding" whether these statements are true or not.

Or we could say it with Aristotle — 'The more you know, the more you know you don't know.'

 

[LilWabbit]

Your written description uses terms like "produced by my understanding" and "understandiung has generated" which are not properly reflected in your small tautology.

If we designate "understanding" as an efficient formal system (employing a mathematical/logical axiomatic description) that enables us to formulate statements and to decide them, then it follows from Goedel's Incompleteness Theorems that some of these statements that can be proposed must be undecidable, i.e. it is unknowable within that "understanding" whether these statements are true or not.

I am not claiming the 'formal system' is fully knowable from within the system and never would. Let's represent Gödel in more precise terms.

The second fundamental result of K. Gödel (which you are attempting to employ here) establishes that if a foundational mathematical system S is consistent, then its consistency can be proved only in a stronger system. Gödel's second result shows explicitly how to deduce a formal contradiction "p and not-p" within any foundational system S, once given a proof within S of the consistency of S.

I'm not giving proof of the consistency of S within S. Nor never would even attempt to. Nor would it be relevant to the point I was making.

For example, since infinitary mathematics contains finitary mathematics as a subsystem, one cannot therefore use the latter to prove the consistency of the former, if the former is consistent (anything is provable in a contradictory system).

 

[LilWabbit]

For those who haven't had the time or the interest to study in-depth the long-winded exchange between @markus and myself, it may be worthwhile to encapsulate our main point of agreement as relates to the title of this read. This point of agreement is also the most relevant point in terms of the motive idea of MetaBunk.

Namely, that an unfounded mystification of quantum mechanics in the form of pseudo-scientific bunk happens when people attempt to interpret realistically (i.e. as descriptions of reality) the instrumentalistic (i.e. experimentally useful) mathematical formalism of quantum mechanics, which was never seriously entertained by its designers as a direct description of physical reality. This obviously results in confusions, and is vulnerable to a misreading of quantum mechanics whereby various authors refer to QM as proof of the inherent spirituality of the universe (mystifications by people with religious or spiritualist leanings) or as proof for the existence of multiple or parallel universes (mystifications by people enamoured by science fiction some of whom may be decidedly anti-religious and anti-spiritual).

Often this mystification is calculated and contrived for the purpose of seeking validation for one's personal beliefs rather than being based on a sincere interest in, and investigation into, the actual history and formulation of the foundations of quantum mechanics. We also seem to agree that the alternative interpretations of quantum mechanics that are not describable as 'Copenhagenist' (i.e. 'Copenhagenist' as in largely stemming from Bohr's and Heisenberg's later understanding of quantum mechanics), and yet which are explored and upheld by many theoretical physicists, tend to stumble upon the very same error of attributing realism to something instrumental by design which many non-physicists perpetrate.

 

[jplaza]

wich was never seriously entertained by its designers as a direct description of physical reality.

To me you sound like they deliberately chose to make QM that way. However, QM is the result of a combined effort of many people.

None of them ever seriously tried to make it a direct description of reality? I would say this is the best they could come up with, whether you like it or not - and there were (and still) are people not comfortable with it. Either case, no one has been able to propose a 'realistic' QM, (which doesn't mean it cannot be done)

All that labeling (realist, positivist, materialist, whateverist), sounds like any scientist wil get a different (even if equivalent) theory. But we dont have a realistic classical mechanics nor a positivist classical mechanics (and the same for quantum). In the end, we have a single theory, which you may label as you like, but I doubt that label was in the mind of the scientist(s) who designed it.

 

[LilWabbit]

In the end, we have a single theory, which you may label as you like, but I doubt that label was in the mind of the scientist(s) who designed it.

I agree with your point about scientists in general not having labels in mind in terms of the philosophical assumptions they may espouse and apply in their work. Labelled or not, however, instrumentalism as an idea was something that Niels Bohr clearly had in mind back in 1948 when he described the formalism of QM:

Article:

"The entire formalism is to be considered as a tool for deriving predictions of definite or statistical character, as regards information obtainable under experimental conditions described in classical terms and specified by means of parameters entering into the algebraic or differential equations of which the matrices or the wave-functions, respectively, are solutions. These symbols themselves, as is indicated already by the use of imaginary numbers, are not susceptible to pictorial interpretation; and even derived real functions like densities and currents are only to be regarded as expressing the probabilities for the occurrence of individual events observable under well-defined experimental conditions."

Source: http://philsci-archive.pitt.edu/3737/

This idea was largely due to the intellectual influence of the Vienna Circle, especially through Otto Neurath, with whom Bohr had encounters and correspondence in 1934-5. This historical background was briefly outlined in this post.

 

[markus]

While not claiming there is no burden on my side, your 'suggestion' that the burden rests exclusively on my side is logically unfounded. This seems to me due to your sincere but persistent unawareness of two factors that underpin your position:

(1) Unawareness that your claim 'QM is defined by its formalism' is a function of Bohrean positivism rather than the other way around,

Not all theories in physics have a concise and well-understood axiomatic formulation, but quantum mechanics does, and this axiomatic foundation enjoys broad agreement among all practicing physicists. Some might choose a different set of axioms to start from but the mathematical structure spanned by those axioms is provably equivalent. Characterizing this as "QM is defined by its formalism" undercuts the fact that we have a formalism-independent mathematical structure that we understand extremely well, and that structure is what forces the positivist interpretation, not whatever specific axiomatic formulation one may choose.

If by this you meant that quantum mechanics should be understood as the "science dealing with the behaviour of matter and light on the atomic and subatomic scale," as you previously quoted from the Britannica, I've explained before the inadequacy of this as a definition. Quantum mechanics is defined how it's defined. You may pick one axiomatic formulation or another, it makes no difference. It's nature and experiment telling us how to do this, not Bohr.

while the said underlying positivism is taken as a given for QM without a burden of proof (see factor #2 below).

Yes, I think that's a statement that doesn't merit any explanation, which is why I spent so many words explaining some key theorems and experimental results that show just how difficult it is to come up with an observer-independent classical ensemble that is statistically described by the rules of quantum mechanics. Please.

No philosophical theory of science can be mathematically inferred from the formalism of QM (or from any other mathematical formalism for that matter).

Good thing nobody claimed that it can, then. I've cautioned multiple times against interpreting "positivism" in this context beyond the restricted sense of using quantum mechanics to predict statistical distributions of experimental outcomes rather than attempting a classical physics description of the world. This is what the theory is and how it works -- take it or leave it -- but I never said anything about whether you should be satisfied with this.

In other words; there's no request for the user of quantum mechanics to accept any "philosophical theory" whatsoever. The formalism of quantum mechanics is inherently positivist in the sense discussed previously, but that doesn't mean anyone must accept positivism in their hearts as the one true approach to fundamental physics. As I said many times, this is conflating the theory with reality.

(2) Unawareness that the Bohrean positivism underlying your claim 'QM is defined by its formalism' (see factor #1 above) inheres a positive philosophical claim (a kind of 'belief' in fact) that assigns an onus of proof on the claimant. That is, the belief that 'only individual events observable under well-defined experimental conditions are reliably knowable, while nothing beyond these observables is'. (I'm here using Bohr's language of "individual events observable under well-defined experimental conditions" verbatim.)

As to my burden, it can be addressed variously. For reasons of verbal economy, let me concisely tackle it by highlighting the inherent paradox in your positivist claim. Demonstrating the paradox of the positivist philosophical claim adds credence, by the logical inference rule of contraposition, to its logical alternatives, including the realist claim. The paradox reads quite simply as follows:

I reliably know only individual events observable under well-defined experimental conditions. Any aspect of reality beyond these individual events, including their real causes, is not reliably knowable. Yet the foregoing claim is not an individual event observable under well-defined experimental conditions.

As I explained, that's not my claim, and that "paradox" defeats only a straw man. Even someone who's ideologically and radically "positivist" in some stronger sense would necessarily also assume some measure of reliability of their own ability to judge logical propositions and the consistency of logical systems. They'd also be free to assert axioms and definitions as necessary, with the usual proviso that such axioms represent assumptions to be verified a posteriori and revised if necessary, like Euclid's fifth postulate was with the discovery of general relativity. There's nothing wrong with any of this.

Furthermore, Bohr and everyone else are acutely aware that our own ordinary day to day experience constitutes 'measurement' of some quantum mechanical system in some sense, except the vast majority of it doesn't occur in the context of "well-defined experimental conditions". Yet I'm pretty sure Bohr was able to reliably find his way up a flight of stairs. In other words, that paradox you identified doesn't show inconsistencies in anyone's actual position.

Historically, the positivist tradition in quantum mechanics did not arise out of a thorough exploration and comparison of viable philosophical theories for the science of quantum physics, but rather from the intellectual influence exerted by certain positivist philosophers on the likes of Bohr and Heisenberg.

That may be of interest to historians, but it doesn't change anything about the mathematical structure of the theory that forces that interpretation on us anyway.

While this may not be the case amongst a significant proportion of quantum physicists, in the scientific community there exists a general consensus (excluding a handful of anti-realist naysayers) that scientific truth is observer-independent but relative. Far from being perfect or absolutely accurate, the history of science demonstrates an ever-improving approximation of observer-independent truth. The claim that real-world referents of our approximate but ever-refining descriptions of 'black holes', 'entities with a mass', 'locations in space', 'locations in time','objects in motion', 'light', and 'gravity' exist with some correspondence to these descriptions even when they are not observed or described is far less radical than its positivist alternative.

Here you are once more conflating the theory with the actual reality it describes, or at least conflating the perception of the theory with the perception of said reality in the minds of your opponents.

The philosophical assumption of (i) a mind-independent reality (realism, as opposed to solipsism or phenomenalism), and that (ii) for every observed phenomenon there must be a cause or causes that explain it (the Principle of Sufficient Reason, a.k.a. PoSR), are meaningful, sensible and productive assumptions at the core of scientific pursuit, enabling predictive explanation rather than mere prediction, and requiring little further 'defense' than these four properties against any alternative claim. Does this mean positivist science cannot be productive? Obviously not, and demonstrably not as per the formalism of QM. Especially as far as applied science is concerned. Do they need to be mutually exclusive scientific pursuits? I hope not, and 'live and let live', in the event their practitioners cannot find intellectual reconciliation.

Well, why not? The positivism or lack thereof of an idea is not really the most important aspect by which a theory of nature should be judged. We can hopefully still talk about how promising each idea is as a potential development of fundamental science, however, and there one's strategy may well depend on their broader philosophical outlook. One can try to develop something realist, or (and I admit I'm being somewhat provocative here ) one can go in an even more positivist direction like Nima does.

They don't disagree that the current foundations of quantum mechanics are provided by such axioms. They would disagree on whether that's all that quantum mechanics is, and always must be.

No, they disagree on whether a classical underlying theory exists and what that classical underlying theory would look like. Quantum mechanics as currently formulated is what it is, and in particular its privileged status as the unique nontrivial generalization of probability theory means it'll always be useful in that exact precise formulation even if a deeper explanation for its empirical adequacy is found.

Let me offer here an olive branch: If quantum mechanics is defined by its current formalism and by no scientific pursuit or theorization above and beyond that formalism (even if it builds on said formalism), then under that definition we agree quantum mechanics is complete and its practitioners should just 'shut up and calculate'.

As I explained, there are no "shoulds" in anything I said. I'm not a moral philosopher. Like I said in the previous paragraph however, quantum mechanics in this positivist sense is not something you can get rid of, any more than you can get rid of classical probability theory.

Depends on what such a structure may turn out to be if it exists. If it's even remotely like the amplituhedra I'd say it's beautifully elegant and simple.

I don't know what you could have in mind since the amplituhedron project by its nature ignores any sort of spacelike foliation and hopes all the features normally associated with spacetime are found a posteriori in the structure of amplitudes that come out.

While significant as a historical backdrop for Nima's project, the latter is not logically reducible to the S-matrix program.

I have no idea what "logically reducible" is supposed to mean here. The S-matrix program is the attempt to describe particle interactions without reference to any intervening interactions in spacetime, merely providing relations between in states in the far past and out states in the far future. Does that describe Nima's project? The answer is yes, it clearly does, and so his project is clearly and unambiguously part of the S-matrix program. The term "S-matrix" itself is a technical term and means precisely the matrix of amplitudes for scattering between the far past and far future, i.e. exactly the thing he's trying to calculate.

S-matrices employ linear algebra. The amplituhedra and binary surfacehedra employ algebraic geometry and number theory, providing a far richer and more profound mathematical language that remains as yet largely unexplored in physics, and not fully understood even in mathematics.

Saying the S-Matrix program "employs linear algebra" is a bit like saying the space shuttle "employs rivets". If your intent with saying this was to contrast his approach with earlier efforts in the S-matrix program, such a contrast falls immediately flat since one of the most notable exponents of the program, string theory, makes copious use of algebraic geometry and number theory. Nima's assertion that nobody ever used algebraic geometry and number theory in physics before is nonsense.

Furthermore, Nima's research "employs linear algebra" precisely to the same extent as everything else in the S-matrix program, since the output of his calculations are the coefficients of a linear transformation between in states and out states!

I don't mean to be indelicate, but when a key component of the case you're building is that the vast majority of physicists are celebrity-worshiping trend-chasing dimwits, it helps to have some understanding of what has actually been done.

We would all be in a far better position to spell plausible doom to Nima's project if we'd have a far more profound understanding of the potential of algebraic geometry and number theory, some of the most advanced areas of modern mathematics, to provide at least a one notch more fundamental mathematical language for physics. Until then, the rest of us should really just 'shut up and calculate'.

1. The fanciness of the tools doesn't change the fact that N=4 SYM is a highly symmetric theory filled with pretty cancellations and lots of structure, very much unlike the standard model, in which this sort of project is much more promising to start with, and he's doing all this work in the planar large-N limit where even more stuff drops out! (For a point of comparison, in QCD, the closest real world analogue, N=3).
2. A method is not automatically better just because it uses fancier tools.

Algebraic geometry and number theory have never been part of physics before.

Like I said, this is nonsense. In particular (but by no means solely), string theory, which dates back to the 70s.

The persistent challenge to extend QM theory to multi-electron atoms suggests major limitations in its basic mathematical axioms.

There's no trouble whatsoever with QM theory and multi-electron atoms, let alone anything to do with the fundamental axioms.

In QM, the commitment to calculus (especially linear differential calculus) seems a possible cause for these challenges.

What challenges?

As it happens, it's precisely the search for a more fundamental and sophisticated math for physics that seems relevant and which Nima's project is concerned with.

The likelihood of anyone ever using amplituhedra et al to describe multi-electron atoms is comparable to the likelihood of anybody using general relativity to build a house.

As is apparent from the above interview, not only is Nima a realist but in fact a romantic realist.

His own words say otherwise, as does the very focus of the project under discussion. Nima says, clearly and without ambiguity: the founding fathers of quantum mechanics knew _exactly_ how to interpret every experiment under the purview of quantum theory. He tells you, clearly and without ambiguity, that the difficulty in making sense of spacetime in a fundamental sense means one must focus on scattering amplitudes.

When asked about his greatest current passion in physics, Nima replies:

I must once more insist that you refrain from mind-reading. If you want to argue that Nima is a realist, please find an actual quote where he explicitly says as much, just like I found an actual quote where he proclaims explicit and passionate agreement with the Copenhagen school.

Since we're on the subject, I've put a link below for a fascinating very recent lecture (summer 2021) by Nima on the broader application of what he calls 'surfacehedra'. He outlines his current explorations into the applicability of surfacehedra to string theory.

Surfacehedra (dual geometry for particles, binary geometry for strings) is no longer just about scattering amplitudes, but also "stringy amplitudes",

Those are still scattering amplitudes. My previous admonition that it's important to know the context to actually discuss this meaningfully applies here. Remember: Nima has an ideological belief that scattering amplitudes are the only objects from the current formulation of physics that would survive in the final theory! Why would he abandon that belief when moving from particles to strings?

If Nima's baby steps to the beach are even seemingly taking him forward, let him take them and let's support him. Even if he ultimately only manages to fall in the ditch and die. For even that is a scientific result.

I don't have anything against his project. I'm just telling you it's not what you want it to be.

 

[markus]

Kindly reread the end of the previous post and Nima's unmistakable words.

These words are unmistakable:

There is nothing interesting or deep or strange going on when a random graduate student does a random quantum measurement in a random basement laboratory somewhere. And everything there is fully, completely understood, within the ordinary logic of quantum mechanics (something by the way which the founders of quantum mechanics understood perfectly).

Nothing he said in your quotes indicates any sort of realist project whatsoever. Again, no mind reading. Explicit quotes, like the one I just pasted once more, if you please.

As to the rest of your post, I read a lot of misreadings and sloppy readings of what I wrote

I disagree.

 

[LilWabbit]

Nothing he said in your quotes indicates any sort of realist project whatsoever. Again, no mind reading. Explicit quotes, like the one I just pasted once more, if you please.

The parts in red read together with the rest of Nima's words are unmistakably explicit. Your quote does nothing to counter such an explicitly realist and ambitious project pursuing a more fundamental language from which both QM and spacetime emerge.

"But there's completely clearly now these fantastic new stuctures which are not speculative, just talking about standard physics, but in a very different way. I'm hopeful that it will go somewhere sort of more generally beyond the very special and simple theories that we're starting to understand this way, to reveal something deeper about the way the nature actually works."

What part of "to reveal something deeper about the way the nature actually works" isn't explicitly realist in orientation and purpose? You mean the part where "actually" should rather read "really" for you to accept the exact same 'realist' meaning as explicit? If anything, 'actually' is an even more poignant semantic equivalent of 'really' in this context.

And if that indeed is the (unreasonable) burden you assign to me, in that case you should in kind quote something where Nima explicitly says he's "a positivist" in the way he interprets his broader project of exploring these "fantastic new structures".

"I would be thrilled if we would find some way of talking about all of standard physics, not just the toy models that we're looking at, but all the standard physics in a way that doesn't but spacetime in and doesn't but quantum mechanics in, and gets the answers out. And ultimately then, if we really understand it, then we'll have the beginning of an understanding, a starting point, from which we can see the emergence of spacetime and quantum mechanics."

What part of "talking about all of standard physics" in a way "from which we can see the emergence of spacetime and quantum mechanics" suggests anything other than Nima searching for a more fundamental language underlying quantum mechanics from which it emerges?

How is it even possible to read the above two statements without seeing that Nima's project pursues a fundamental theory of physics underlying both QM and spacetime that accounts for something deeper about the way the nature actually works (realism)?

P.S. I think it's safe to say Nima, like you and me, interprets the mathematical foundations of QM in the positivist sense they were designed. Let's clarify that first in case there was a miscommunication. But now we're talking about whether he's a positivist with respect to his broader scientific project, and with regard to the explanatory potential of structures akin to, but more sophisticated than, surfacehedra as a fundamental physical theory.

 

[LilWabbit]

Not all theories in physics have a concise and well-understood axiomatic formulation, but quantum mechanics does, and this axiomatic foundation enjoys broad agreement among all practicing physicists. Some might choose a different set of axioms to start from but the mathematical structure spanned by those axioms is provably equivalent. Characterizing this as "QM is defined by its formalism" undercuts the fact that we have a formalism-independent mathematical structure that we understand extremely well, and that structure is what forces the positivist interpretation, not whatever specific axiomatic formulation one may choose.

I think we fully agree in the sense that the "formalism-independent" mathematical structure at the foundation of QM was specifically designed to predict measurements rather than to describe the reality from which these measurement results arise, as conventional scientific theories do. However, the math would still remain a function of a deliberately positivist exercise rather than the other way around. Therefore you're not really refuting my statement to which you are ostensibly responding. Perhaps you didn't even mean to in which case ignore this response.

In the same sense of 'providing the motive and impetus to the said mathematical structure' one could maybe say that the structure "forces the positivist interpretation". And I feel I'm being too generous with this acknowledgement. But to say it's somehow mathematically required makes no sense unless one can provide a mathematical proof that moves soundly from QM axioms and ends with positivism as a mathematical theorem. One can say positivism is the only way to interpret the received mathematical structure of QM as it was intended. But there's nothing within the mathematical structures of probability distributions within a Hilbert space themselves that logically necessitates interpreting these structures in one philosophical way or the other (positivist, realist, phenomenalist, whatnotist). However, to interpret realistically something that was never intended as a realist description seems silly and abortive from the very outset. On that point we seem to consistently agree.

If by this you meant that quantum mechanics should be understood as the "science dealing with the behaviour of matter and light on the atomic and subatomic scale," as you previously quoted from the Britannica, I've explained before the inadequacy of this as a definition. Quantum mechanics is defined how it's defined.

It seems to me the term "quantum mechanics" is bandied about by physicists in roughly the following two senses, depending on the context: (1) In reference to the received mathematical structure providing the basic subatomic probability distributions of measurement outcomes for the rest of quantum physics (i.e. your strict usage which you claim as the only correct usage); (2) In reference to the science that purports to understand the physical reality underlying and causing these measurement outcomes without being inextricably tethered to any particular mathematical structure or theory (while making full use of whatever helpful mathematical models and theories that already exist). There's also a third sense for 'quantum mechanics' which is found in encyclopaedias and proliferated especially by non-physicists: (3) A synonym for quantum physics.

I agree the third sense is far too sloppy while I wouldn't go as far as saying that it's seriously misleading and should be done away with. I disagree that the 1st sense is the only appropriate way to employ the term "quantum mechanics", or the only way a proper self-respecting physicist in the field uses the term. The latter strikes me as unfairly and religiously rigid and dogmatic. Whether it is your position or not.

In other words; there's no request for the user of quantum mechanics to accept any "philosophical theory" whatsoever. The formalism of quantum mechanics is inherently positivist in the sense discussed previously, but that doesn't mean anyone must accept positivism in their hearts as the one true approach to fundamental physics.

Fair enough.

Furthermore, Bohr and everyone else are acutely aware that our own ordinary day to day experience constitutes 'measurement' of some quantum mechanical system in some sense, except the vast majority of it doesn't occur in the context of "well-defined experimental conditions". Yet I'm pretty sure Bohr was able to reliably find his way up a flight of stairs. In other words, that paradox you identified doesn't show inconsistencies in anyone's actual position.

It shows that the claim 'reliable knowledge is experimentally measurable' does not fall within the domain of reliable knowledge under its own definition, and hence the claim itself is unreliable under its own definition. Hence, a classical logical paradox. It applies to Bohr as well as the rest of us since we all unwittingly behave in a manner that treats a whole bunch of everyday observations and philosophical assumptions as reliably true which, nonetheless, may logically contradict philosophical assumptions that we consciously espouse (such as positivism, phenomenalism, physicalism or idealism). This is especially the case with the vast number of unconscious realist assumptions displayed by the formally anti-realist in his everyday behaviour.

Here you are once more conflating the theory with the actual reality it describes, or at least conflating the perception of the theory with the perception of said reality in the minds of your opponents.

Feel free to demonstrate how am I doing either of those things.

Well, why not? The positivism or lack thereof of an idea is not really the most important aspect by which a theory of nature should be judged. We can hopefully still talk about how promising each idea is as a potential development of fundamental science

Not if we disagree sharply on what's the meaning of 'fundamental science'. If science is not about understanding reality with ever-increasing resolution, then the scientists that so believe are bound to feel demoralized and discouraged amongst those who regard realism a waste of time, and at the expense of actual scientific progress they could have contributed to. A self-fulfilling prophecy really.

No, they disagree on whether a classical underlying theory exists and what that classical underlying theory would look like.

While many of them seem to use the term 'quantum mechanics' in the #2 sense of the term as articulated in the above. Not only in the #1 sense. And hence confirming my initial statement to which you are responding in the above.

Quantum mechanics as currently formulated is what it is, and in particular its privileged status as the unique nontrivial generalization of probability theory means it'll always be useful in that exact precise formulation even if a deeper explanation for its empirical adequacy is found.

Makes sense. No qualms with that.

As I explained, there are no "shoulds" in anything I said. I'm not a moral philosopher. Like I said in the previous paragraph however, quantum mechanics in this positivist sense is not something you can get rid of, any more than you can get rid of classical probability theory.

Well put. Again, we're in agreement as far as the received formalism is concerned.

I have no idea what "logically reducible" is supposed to mean here.

Logically reducible means explaining a particular mathematical or logical system entirely in terms of another. The surfacehedra are not mathematically reducible to the preceding models in S-matrix program and hence to state dismissively that they're merely a continuation of the latter is both inaccurate and misleading. The fact that all these models are independent of spacetime has nothing to do with my statement on logical irreducibility. You shouldn't waste your breath on that front.

Saying the S-Matrix program "employs linear algebra" is a bit like saying the space shuttle "employs rivets". If your intent with saying this was to contrast his approach with earlier efforts in the S-matrix program, such a contrast falls immediately flat since one of the most notable exponents of the program, string theory, makes copious use of algebraic geometry and number theory. Nima's assertion that nobody ever used algebraic geometry and number theory in physics before is nonsense.

Not at all in the deeper sense of special structures in quiver categories underlying the way in which binary geometric surfacehedra satisfy string-theoretical equations. Not at all in the more novel sense of parametrizing these equations as polynomials associated with n-dimensional space and n-variables. If this is nonsense, please demonstrate how received S-matrices and received string theory has made "copious use" of the above structures "since the 70s", or alternatively how the received structures are equal in their mathematical sophistication?

Furthermore, Nima's research "employs linear algebra" precisely to the same extent as everything else in the S-matrix program, since the output of his calculations are the coefficients of a linear transformation between in states and out states!

This has absolutely nothing to do with what I stated in the above, nor does it contradict with it in the least.

I don't mean to be indelicate, but when a key component of the case you're building is that the vast majority of physicists are celebrity-worshiping trend-chasing dimwits, it helps to have some understanding of what has actually been done.

Feel free to be indelicate! But you'd still be pounding a strawman. What you describe above is not my 'case' in the least. If you want clarifications as to my 'case', I am glad to provide them in response to specific questions where further clarity is sought.

1. The fanciness of the tools doesn't change the fact that N=4 SYM is a highly symmetric theory filled with pretty cancellations and lots of structure, very much unlike the standard model, in which this sort of project is much more promising to start with

You're entitled to your belief. My apologies if your 'word' against Nima's as to what's promising or unpromising isn't unquestioningly swallowed by your counterpart.

2. A method is not automatically better just because it uses fancier tools.

Strawman. Nothing of the sort has been claimed.

What challenges?

The inadequacy of received QM formalism to account for the interactions studied in QFT. Providing one pillar of the foundations of QFT calculations does not equate to QM fully accounting for the latter. Far more must be postulated beyond QM formalism to succeed in providing any viable QFT. And that 'more' is turning out to be far more mathematically sophisticated too.

I don't have anything against his project. I'm just telling you it's not what you want it to be.

Or what Nima wants it to be. If impassioned claims by appeal to the authority of an anonymous internet warrior, no matter how versed in physics, were enough, you would have convinced me already.

 

[jplaza]

I think we fully agree in the sense that the "formalism-independent" mathematical structure at the foundation of QM was specifically designed to predict measurements rather than to describe the reality from which these measurement results arise, as conventional scientific theories do. .

Being myself an 'end user' rather than a 'developer' of QM (experimental vs fundamental physicist), I understand QM analog in classical mechanics is Hamiltonian Mechanics, which is not a theory in itself. So I feel that all of your criticism to QM can also be applied to Classical Mechanics.

Hamiltonian just puts together the kinetic and potential energy of the system. The 'physics'(or interactions, or reality, or whatever you want to call it) are expressed (modeled) in the potential energy term. That means you can plug a real thing or even a made up, totally unreal physics, and then develop a theory.

Plug in the gravitational potential, and that's the classical theory of gravitation from which you can predict planet orbits.

In the same way, a quantum hamiltonian(Schrödinger eq.) also contains both kinetic and potential terms, and you model your reality in the potential term. Plug in an electrostatical potential, and you have a theory for the atom, how the electrons occupy orbitals, and the energy the absorb or emit when changing from one to another. Plug in a periodic electrostatic potential, and you get a theory that describes how the most external electrons of atoms form bands in a solid, and why some behave like conductors, isolators, or semiconductors.

From my point of view difficulty in understanding QM comes from the fact that in Classical Mechs, you start with reality and model it mathematically. But QM became the other way around, where you start with maths, and then try to find a way to understand what kind of reality is describing, since it is a reality out of our everyday (classical) experience.

 

[LilWabbit]

From my point of view difficulty in understanding QM comes from the fact that in Classical Mechs, you start with reality and model it mathematically. But QM became the other way around, where you start with maths, and then try to find a way to understand what kind of reality is describing, since it is a reality out of our everyday (classical) experience.

In many ways QM also models reality mathematically insofar as 'reality' is understood as 'measurement outcomes'. It's just that the microscopic physical 'reality' accessible to us through these experiments is by default far more limited in the variety and richness of the observations produced as compared to macroscopic reality. The stochastic character as well as the strange 'action-at-a-distance' property of some of these measurements adds to the dilemma. Consequently, such a 'reality' does not easily lend itself to 'conventional' scientific theorizing -- i.e. the formulation of hypotheses purporting to explain the underlying causes of these measurement outcomes, from which new predictions can be easily inferred and put to the test. These challenges, together with the strongly instrumentalist philosophy of science of the likes of Bohr and Heisenberg (in opposition to Einstein's realist -- a more classical -- philosophy of science), contributed to QM evolving into an essentially 'calculational device'. Ever since, attempts to really understand what's going on have sometimes even been frowned upon in many physics departments the world over at least as far as quantum mechanicians are concerned. Or at least declared hopeless or moot at the very outset.

A rare classical physicist accepts this instrumentalist view as it risks returning physics to its pre-Newtonian role where the Ptolemaic calculational rules (circles on circles) could generate remarkably accurate predictions of planetary activity when observed from Earth, while these convolutions in no wise represented the actual motions of the planets in space. The Copernican Revolution occurred because it offered a richer model of actual reality although for a long time its predictions were not as accurate as the Ptolemaic outcomes. Nonetheless, influential intellectuals in the 17th century (both academicians and theologians) strongly resisted these threats to the status quo. One could say history has repeated itself on a smaller sociological scale within quantum mechanics throughout the past few decades.

 

[markus]

Namely, that an unfounded mystification of quantum mechanics in the form of pseudo-scientific bunk happens when people attempt to interpret realistically (i.e. as descriptions of reality) the instrumentalistic (i.e. experimentally useful) mathematical formalism of quantum mechanics, which was never seriously entertained by its designers as a direct description of physical reality. This obviously results in confusions, and is vulnerable to a misreading of quantum mechanics whereby various authors refer to QM as proof of the inherent spirituality of the universe (mystifications by people with religious or spiritualist leanings) or as proof for the existence of multiple or parallel universes (mystifications by people enamoured by science fiction some of whom may be decidedly anti-religious and anti-spiritual).

I think your description of our points of agreement is mostly fair but I must add a point of clarification concerning e.g. many worlds. I don't think many worlds is a silly or mystical idea. I think it's a fair, reasonable project to find a classical ensemble described by quantum rules, albeit one that has pretty much failed. It's surface implausibility is not (to me) an argument any more serious than, say, the surface implausibility of special relativity. I am unconvinced by many worlds not because it's an extravagant ontology, but because proponents haven't made any meaningful progress in sharpening answers to the key questions that would take their idea from the realm of bar table speculation to that of precise quantitative science. Namely, what is a "world", when do they split, how many worlds do exist, why and how do we get randomly chosen outcomes to experiments when the theory's completely deterministic, etc. These are all excellent questions to which they give pithy handwavy explanations, despite decades of combined attack by objectively brilliant people the handwave is the best we got. That stagnation is what hints (to me) that we should look elsewhere, not any superficial silliness. We know the constraints that "the next theory" has to satisfy, and those all but guarantee that if we ever get anything else, it'll sound comparably silly.

I do agree that the error they made in initially deriving many worlds is that the quantum state is treated as a classical, objectively existing quantity, and I do believe that's wrong for the reasons already discussed, but I don't think that sort of error (at least when committed by the competent physicists in the project) is a result of a mystification or unwitting conflation, but an active and willful relaxation of the rules of quantum mechanics to see where that leads us. I think the net result is that we found out we don't get anywhere by modifying the quantum axioms in that particular way, but I don't begrudge them for trying.

The parts in red read together with the rest of Nima's words are unmistakably explicit. Your quote does nothing to counter such an explicitly realist and ambitious project pursuing a more fundamental language from which both QM and spacetime emerge.

I'm sorry, but they simply aren't. You're mistaking his desire for understanding for the desire to find a classical, observer-independent reality. As far as I can tell, he never even gave the smallest hint that he's looking for the latter. That's why I'm asking you to find explicit quotes in support of that.

What part of "to reveal something deeper about the way the nature actually works" isn't explicitly realist in orientation and purpose?

All of it. There's nothing in there that indicates a realist desire to find a classical, observer-independent reality. You think "actually works" means it has to be classical physics. He doesn't think that, and he explicitly said he doesn't think that (see the above quotes which I don't see much point in pasting again).

You mean the part where "actually" should rather read "really" for you to accept the exact same 'realist' meaning as explicit?

That wouldn't change anything.

If anything, 'actually' is an even more poignant semantic equivalent of 'really' in this context.

And neither indicates a desire to find a classical physics model of an observer-independent reality.

And if that indeed is the (unreasonable) burden you assign to me, in that case you should in kind quote something where Nima explicitly says he's "a positivist" in the way he interprets his broader project of exploring these "fantastic new structures".

I already did. He said, clearly and without ambiguity, that the Copenhagen school had it right to begin with and understood this perfectly. He expressed explicit and enthusiastic support for what you derisively called the "received formalism of quantum mechanics". That's why I quoted that bit multiple times.

What part of "talking about all of standard physics" in a way "from which we can see the emergence of spacetime and quantum mechanics" suggests anything other than Nima searching for a more fundamental language underlying quantum mechanics from which it emerges?

"A more fundamental language" doesn't mean a classical physics model of an observer-independent reality.

How is it even possible to read the above two statements without seeing that Nima's project pursues a fundamental theory of physics underlying both QM and spacetime that accounts for something deeper about the way the nature actually works (realism)?

That's not what realism means. Realism means a classical physics model of an observer-independent reality.

P.S. I think it's safe to say Nima, like you and me, interprets the mathematical foundations of QM in the positivist sense they were designed. Let's clarify that first in case there was a miscommunication.

Ok, it looks like I do have to quote the bit again:

There is nothing interesting or deep or strange going on when a random graduate student does a random quantum measurement in a random basement laboratory somewhere. And everything there is fully, completely understood, within the ordinary logic of quantum mechanics (something by the way which the founders of quantum mechanics understood perfectly).

He's talking about experiment, not formalism.

But now we're talking about whether he's a positivist with respect to his broader scientific project, and with regard to the explanatory potential of structures akin to, but more sophisticated than, surfacehedra as a fundamental physical theory.

And I explained that's even more 'positivist' than quantum mechanics as usually practiced. In ordinary quantum mechanics I at least get to see the results of my experiment before waiting an infinite amount of time, and then set up a different experiment depending on the results of the first, etc. The theory produces meaningful predictions in that sort of situation. His idea is that this is the sort of thing that must be abandoned, i.e., not only must you be a positivist, but all you can really talk about are scattering experiments between infinite past and infinite future, with nothing whatsoever in between.

 

[Mendel]

The philosophical assumption of (i) a mind-independent reality (realism, as opposed to solipsism or phenomenalism), and that (ii) for every observed phenomenon there must be a cause or causes that explain it (the Principle of Sufficient Reason, a.k.a. PoSR), are meaningful, sensible and productive assumptions at the core of scientific pursuit, enabling predictive explanation rather than mere prediction, and requiring little further 'defense' than these four properties against any alternative claim.

What are the four properties?

Where can I read more about the PoSR?
It feels like it posits determinism, is that correct?
If I roll a doice and it comes up with the number 6, what is the reason for that?

How do I falsify the PoSR, i.e. how do I distinguish something that happens with no reason from something that has a reason that has not been found yet?

 

[markus]

I think we fully agree in the sense that the "formalism-independent" mathematical structure at the foundation of QM was specifically designed to predict measurements rather than to describe the reality from which these measurement results arise,

No, it's not "designed". It's the unique nontrivial generalization of probability theory. If instead of asking probabilities to add up to 1, you ask for their absolute squares to add up to 1, you get quantum mechanics, and any other rule results in a whole bunch of nothing (trivial theories in which all that can ever happen are trivial permutations and relabeling of objects). Quantum mechanics is not "contrived". It's a natural, beautifully simple, and elegant generalized way to think about propositions.

as conventional scientific theories do. However, the math would still remain a function of a deliberately positivist exercise rather than the other way around.

That's why I made the point of saying, so many times, that any efforts to do more have crashed and burned. Don't you think physicists had precisely these sorts of questions when quantum mechanics first arose? Do you think abandoning a classical description of an observer-independent reality was something that was done lightly? So there's zero doubt, let's be clear that no, it wasn't.

But to say it's somehow mathematically required makes no sense unless one can provide a mathematical proof that moves soundly from QM axioms and ends with positivism as a mathematical theorem.

There are several ways to think about that sort of question. One way is to point you to the nearest set of axioms and show how the only connection with experiment is the measurement postulate (and possibly the isomorph state preparation postulate, depending on the specific formulation). You might say that's facile, but like I explained above quantum mechanics is the unique nontrivial generalization of probability theory, so it's "positivist" in the exact same sense probability theory itself is. Any realist model would have to be in a level underneath. Another way to think about it is to wonder if quantum mechanics is indeed distinct from classical probability theory, i.e., can it be derived? I don't think it's been proved that it cannot, but we do have an enormous amount of results and no-go theorems (Bell inequalities, Kochen-Specker, Leggett inequalities, GHZ states etc) that show that any such derivation would be just as unsatisfying to those that use "positivist" as an insult as quantum mechanics itself. It's what I've been talking about this entire thread!

One can say positivism is the only way to interpret the received mathematical structure of QM as it was intended.

You can say that, but that's not the only thing that can be said. See above.

But there's nothing within the mathematical structures of probability distributions within a Hilbert space themselves that logically necessitates interpreting these structures in one philosophical way or the other (positivist, realist, phenomenalist, whatnotist).

Yes, there is! You may investigate for example the claim that you have a "probability distribution" hidden in Hilbert space (I suspect you simply misspoke here, but I'm running with the example anyway). Is there? The answer is clearly no, as it would violate the Kochen-Specker theorem! We can actually make precise statements about these things that actually are constraining of what sorts of philosophical interpretations are consistent with the formalism. Philosophy is naturally slippery due to the reliance on natural language but as long as the terms are defined carefully we can surely talk about what can and can't be said. This isn't an "ought-from-is" type situation.

However, to interpret realistically something that was never intended as a realist description seems silly and abortive from the very outset. On that point we seem to consistently agree.

Sure, but it's important to emphasize that the intent has nothing to do with it. I'll bet my life's savings that if we ever meet aliens and get to discuss this sort of thing with them, we'll find out they have their own version of quantum physics that will be completely isomorphic to ours. Why? Because it's nature leading us to think this way, not Bohr or Heisenberg or whoever else.

It seems to me the term "quantum mechanics" is bandied about by physicists in roughly the following two senses, depending on the context: (1) In reference to the received mathematical structure providing the basic subatomic probability distributions of measurement outcomes for the rest of quantum physics (i.e. your strict usage which you claim as the only correct usage); (2) In reference to the science that purports to understand the physical reality underlying and causing these measurement outcomes without being inextricably tethered to any particular mathematical structure or theory (while making full use of whatever helpful mathematical models and theories that already exist).

Who ever used quantum mechanics in that second sense? If you read a quantum mechanics textbook, how will they be using the term? If you read a paper on quantum foundations, how will they be using the term?

There's also a third sense for 'quantum mechanics' which is found in encyclopaedias and proliferated especially by non-physicists: (3) A synonym for quantum physics.

Quantum physics is indeed synonymous with quantum mechanics, but you'll typically find physicists using the former rather than the latter, almost to the point of being a shibboleth. I don't know why but I suspect it is because it feels more precise to contrast the rules of classical mechanics with the rules of quantum mechanics rather than all of physics, but it doesn't matter too much. The important point is that there's no distinction between the two.

It shows that the claim 'reliable knowledge is experimentally measurable' does not fall within the domain of reliable knowledge under its own definition,

Which is a claim without any teeth whatsoever. Even Comtean positivists accept axiomatic knowledge.

Feel free to demonstrate how am I doing either of those things.

You previously said "fair enough" to a statement with very similar content as that one, so what gives?

Not if we disagree sharply on what's the meaning of 'fundamental science'.

Science is, in a very broad and safe sense, about improvement in understanding of the natural world. If you reject an idea that could lead to improvement because it's "positivist" or vice versa, are you really interested in doing science?

While many of them seem to use the term 'quantum mechanics' in the #2 sense of the term as articulated in the above. Not only in the #1 sense. And hence confirming my initial statement to which you are responding in the above.

Can you name one?

Logically reducible means explaining a particular mathematical or logical system entirely in terms of another.

Then that previous statement is category error since the S-matrix program is a broad label for a wide class of ideas that have in common the focus on in-out amplitudes rather than dynamical evolution. That is, "the S-matrix program" is a set, and amplituhedra et al. are elements of that set. You can ask if one element of the set is "logically reducible" to another but you can't really meaningfully ask whether the element is "logically reducible" to the set itself.

The surfacehedra are not mathematically reducible to the preceding models in S-matrix program and hence to state dismissively that they're merely a continuation of the latter is both inaccurate and misleading.

It is a continuation of the program. There's nothing inaccurate or misleading about that. It's merely a factual statement. Again, what is Nima calculating?

The fact that all these models are independent of spacetime has nothing to do with my statement on logical irreducibility. You shouldn't waste your breath on that front.

It has everything to do with adequately characterizing these models and placing them in their historical and theoretical context, though.

Not at all in the deeper sense of special structures in quiver categories underlying the way in which binary geometric surfacehedra satisfy

Yes, the novel structure Nima and his collaborators identified is indeed novel. That's not the claim, though. The claim is that algebraic geometry and number theory have never been used in physics, a claim that's crassly false.

received S-matrices and received string theory

Have you ever noticed how to you everything Nima does is "discovered" while everything anyone else did is "received"?

This has absolutely nothing to do with what I stated in the above, nor does it contradict with it in the least.

It has something to do with the preceding statements and contradicts them to precisely the same extent as "the S-matrix program employs linear algebra" is a useful characterization of it. You're free to choose how you intended that, and my response should therefore scale automatically.

Feel free to be indelicate! But you'd still be pounding a strawman. What you describe above is not my 'case' in the least. If you want clarifications as to my 'case', I am glad to provide them in response to specific questions where further clarity is sought.

Oh? Can you please clarify what you meant here, then?

For me, science dies the moment scientists themselves preach with conviction that we should stop asking the question 'what is it really?' Science dies that much more painfully when we justify such a prohibition of further questioning by stating religiously that some questions are impossible to answer, especially because our brilliant founding daddies couldn't answer them and therefore asked the rest of us religiously obedient lesser children to also not ask. 'Shut up and calculate'. That's when science transforms into mysticism and blind obedience.

Because I don't think this paragraph is really meaningfully different from characterizing the vast majority of physicists as celebrity-worshiping idiots, even if the specific words you chose seem superficially less harsh.

You're entitled to your belief. My apologies if your 'word' against Nima's as to what's promising or unpromising isn't unquestioningly swallowed by your counterpart.

Who said it's not promising? I just said it's plausible that the same structure doesn't generalize. That's a vastly different statement.

Strawman. Nothing of the sort has been claimed.

Not explicitly, but I'm not convinced it wasn't thought, which is why I felt the clarification was necessary.

The inadequacy of received QM formalism to account for the interactions studied in QFT.

What inadequacy? It works perfectly. If you mean Feynman diagrams, that has nothing to do with the axiomatic foundations of the formalism. It's a specific formulation of perturbation theory, a mathematical trick that has proved useful. Not fundamental.

Providing one pillar of the foundations of QFT calculations does not equate to QM fully accounting for the latter. Far more must be postulated beyond QM formalism to succeed in providing any viable QFT.

Yes, and?

And that 'more' is turning out to be far more mathematically sophisticated too.

Always has been. So what?

Or what Nima wants it to be.

What Nima wants it to be is not what you want it to be, either.

If impassioned claims by appeal to the authority of an anonymous internet warrior, no matter how versed in physics, were enough, you would have convinced me already.

Who appealed to whose authority?

 

[qed]

While on the topic of demystifying those aspects of QM that can be demystified (non-locality being one that cannot be), I recall that the interference patterns of the double slit experiment for electromagnetic radiation is entirely derivable from classical wave mechanics.

• Is this correct, and if so, what is a more precise way of saying this? (I purposely avoided using the term photon.)

I cannot recall where I read this, but grabbed this from Physics Stack Exchange.

 

[markus]

While on the topic of demystifying those aspects of QM that can be demystified (non-locality being one that cannot be), I recall that the interference patterns of the double slit experiment for electromagnetic radiation is entirely derivable from classical wave mechanics.

• Is this correct, and if so, what is a more precise way of saying this? (I purposely avoided using the term photon.)

I cannot recall where I read this, but grabbed this from Physics Stack Exchange.

Right, interference phenomena on their own are not that strange. You don't even need to talk about electromagnetic radiation, surface waves on water behave the exact same way, as does sound in air, etc. As long as the relevant dynamical laws admit solutions that oscillate in space and time (such as the wave equation or the Schrödinger equation), there'll be some sort of interference effect. What's different in the quantum context is that of course radiation is quantized, and that's where you can start talking about questions that have no analogue in classical electromagnetism.

For example, in classical electromagnetism you can have radiation that's as faint as you like, whereas in quantum mechanics radiation must come in discrete packets with energy proportional to the frequency. Once you come close to that limit the only way to make radiation fainter is to have those discrete pulses come out more and more infrequently. When it's infrequent enough that you can tell apart individual pulses you're in the "single photon" regime. You see for example that the interference pattern builds up stochastically (in classical wave mechanics it builds continuously); you can ask "which slit" the pulse went through, and you can design experiments that give you some information about that and see what happens to the interference pattern (namely, if you know which slit the photon went through, you also don't see any interference), and so on.

 

[Mendel]

Can you name one?

That sounds awfully familiar because I asked the same question at the start of this conversation, to no avail.

 

[LilWabbit]

I think your description of our points of agreement is mostly fair but I must add a point of clarification concerning e.g. many worlds. I don't think many worlds is a silly or mystical idea. I think it's a fair, reasonable project to find a classical ensemble described by quantum rules, albeit one that has pretty much failed. It's surface implausibility is not (to me) an argument any more serious than, say, the surface implausibility of special relativity. I am unconvinced by many worlds not because it's an extravagant ontology, but because proponents haven't made any meaningful progress in sharpening answers to the key questions that would take their idea from the realm of bar table speculation to that of precise quantitative science.

The above statement in its entirety is a testament to your integrity as a scientist (which I gather you are?). It was a pleasure to read.

There are several ways to think about that sort of question.

Mathematically there's not. Pardon my lack of tactfulness in return, but you've repeatedly made the mathematically nonsensical and imprecise statement that it is "the mathematical structure of the theory that forces that interpretation on us anyway". I asked you to demonstrate such a mathematical necessity which can only be shown by the virtue of the axiomatic method (which is a very precise – read: mathematical – form of proof and has nothing to do with interpretations), whereby a philosophical theory (in this case 'positivism') mathematically follows the mathematical axioms underlying QM. You first responded that I'm poking a strawman since this is not your claim anyway, only to repeat the statement of a particular philosophical interpretation being mathematically forced on us. You may wish to adjust your statement insofar as mathematics are concerned. If not, you've failed to produce the requested mathematical proof while responding with vague references to no-go theorems. That's not a proof. You seem to mistake 'the only sensible interpretation' of the mathematical axioms of QM for a 'mathematically necessary' interpretation. I'm open to correction if I'm reading you wrong.

It is principally to mathematics that physics owes the axiomatic method, which consists in organizing a large body of knowledge by explicitly deducing every single proposition from a few explicitly designated assumptions. The assumed propositions are, of course, called axioms and the deduced (or derived) propositions theorems. I presume the foregoing is basics for you too. Lest you're tempted to fire back at philosophy for imprecision, it's principally to philosophers of logic and mathematics (Frege, Russell, Gödel, et al) that we owe the foundations of both classical and modern mathematics. Also logical positivism.

If anything is 'slippery', it's the imprecise manner in which some physicists conflate specific philosophical theories such as positivism or realism with mathematical formalisms and empirical statements, and mistake the former for necessary fixtures of the latter.

Pure instrumentalists amongst scientists (especially in applied science), just as pure formalists in mathematics, would hold that abstract mathematics are truly useful only when they yield algorithms (i.e. finite sets of instructions that can be carried out mechanically in a finite number of discrete steps). The received formalism of QM is essentially an algorithm. Nima finds such a basic algorithmic treatment of quantum mechanics utterly boring and uninteresting because it has -- when further parameters such as gravity aren't brought into the fray (QFT) -- yielded "nothing interesting or deep" to science for decades. You mistake his tacit intellectual condescension for its ability to fully predict measurement outcomes mainly at the level of basement quantum measurements by graduate school students for a tribute to the foundations. Does this mean he's thankless and disrespectful to the foundations? Certainly not. He's relied on them for all his career. But it does bring us back to your curious manner of reading Nima's statements:

There is nothing interesting or deep or strange going on when a random graduate student does a random quantum measurement in a random basement laboratory somewhere. And everything there is fully, completely understood, within the ordinary logic of quantum mechanics (something by the way which the founders of quantum mechanics understood perfectly).

You said:

Contrast with his explicit and unambiguous declaration that the foundations of quantum mechanics were already completely understood by the Copenhagen school.

And contrast this with his statement that he:

... would be thrilled if we would find some way of talking about all of standard physics, not just the toy models that we're looking at, but all the standard physics in a way that doesn't put spacetime in and doesn't put quantum mechanics in, and gets the answers out. And ultimately then, if we really understand it, then we'll have the beginning of an understanding, a starting point, from which we can see the emergence of spacetime and quantum mechanics.

He's explicit about searching for a more fundamental understanding from which we can see "the emergence of … quantum mechanics". Hence, to interpret your citation as Nima regarding the Copenhagen foundations of quantum mechanics as the most fundamental understanding of quantum mechanics is patently false, or else Nima would be flagrantly contradicting himself. He is not, since he provides in your citation the explicit qualifiers whereby "graduate student" "quantum measurements" in a "basement laboratory" can be "completely understood within the ordinary logic of quantum mechanics". In other words, if our purpose is to predict measurement outcomes at the graduate student level, then Copenhagen has already produced the perfect algorithm for that. Any other, or any further, interpretation of your citation conflicts with his other statements in addition to heavily reading into the citation with a bias of a Copenhagen apologist.

Furthermore, to replicate your logic (pardon for creatively paraphrasing your earlier statement that you made against my realist interpretation of Nima), 'there's nothing in your citations of Nima that indicates that his broader project, discussed in my citations, seeks to find an observer-dependent fundamental structure underlying spacetime and quantum mechanics.' Observer-dependency is just your own insertion into Nima's explicit words.

Nima is merely talking like a classical scientist would talk, seeking to understand reality deeper:

But there's completely clearly now these fantastic new stuctures which are not speculative, just talking about standard physics, but in a very different way. I'm hopeful that it will go somewhere sort of more generally beyond the very special and simple theories that we're starting to understand this way, to reveal something deeper about the way the nature actually works.

The burden of proof is on the claimant advancing "Nima assumes observer-dependency in his statement of seeking a theory that reveals something deeper about the way the nature actually works" -- a statement that is evidently realist to the unbiased reader of the statement/watcher of the video. The claimant should especially account for the inference rule according to which the statement a theory revealing something deeper about the way the nature actually works is actually (pun intended) a statement about a theory revealing something deeper about the way the observer predicts measurement outcomes, or a theory revealing something deeper about our subjective theoretical constructs about nature, or any other equivalent positivist misrepresentation of what he's actually saying (I shall also scale the response accordingly ).

The above statement by Nima as well as many of his other statements in various lectures and interviews are in full accord with scientific realism understood as:

Article:

Scientific theories are in a historical process of progress towards a true account of the physical world.

Source: https://en.wikipedia.org/wiki/Scientific_realism

It may be worthwhile to remind about the further nuance with respect to sophisticated scientific realism. While it doesn't regard scientific truth to be observer-dependent, sophisticated scientific realism still regards it as relative to the language and experimental setups available to us at any given point in time, while both are subject to modification and evolution overtime. Therefore, far from being a perfectly accurate representation of observer-independent reality, the history of science demonstrates an ever-improving approximation of observer-independent reality. There is no reason to believe, unless proven otherwise, that Nima disputes this standard understanding of scientific truth. His statements rather suggest the very contrary.

Quantum physics is indeed synonymous with quantum mechanics, but you'll typically find physicists using the former rather than the latter, almost to the point of being a shibboleth.

Quantum physics, semantically, is more a description of a science, less a description of a theory or a mathematical model (a subset of that science). To conflate the two without explanation begs the question. But I did list 'quantum physics' as the 3rd sense in which the term 'quantum mechanics' has been interchangeably used as a sociological fact.

Can you name one?

For me it appears David Bohm (pilot wave), Hugh Everett (superposition as ontic rather than epistemic), Giancarlo Ghirardi (particles undergo spontaneous wave-function collapses that occur randomly in time and in space) use the 2nd sense. Their theories purport to describe the physical reality underlying and causing QM measurement outcomes (some deterministically, some indeterministically) without being strictly tethered to the idea that QM foundations cannot be modified or that they should be treated as positivist. For them quantum mechanics is 'a science' of exploring how best to explain these outcomes, rather than being satisfied with no explanation, and mere calculation. All three surely make full use of QM foundations, but with modifications, and by interpreting key constructs in either the foundations or in their modifications as having real physical referents.

They do not represent the 1st sense of the term 'quantum mechanics' since they do not treat QM foundations as a mere calculational device (positivism), nor as complete. Neither do they represent the 3rd sense since they're not engaged in QFT, quantum chemistry or other such exercises that could be broadly regarded as subsets of quantum physics.

No, it's not "designed". It's the unique nontrivial generalization of probability theory. If instead of asking probabilities to add up to 1, you ask for their absolute squares to add up to 1, you get quantum mechanics, and any other rule results in a whole bunch of nothing (trivial theories in which all that can ever happen are trivial permutations and relabeling of objects). Quantum mechanics is not "contrived". It's a natural, beautifully simple, and elegant generalized way to think about propositions.

"The unique nontrivial generalization of probability theory" is precisely what I mean by 'contrived' or 'designed'.

It is a product of a known mathematical theory (probability theory) applied to a (then) new context of quantum states with absolute squares to avoid negative and imaginary amplitudes. It was consciously developed to predict measurement outcomes. It's a brilliant work of applied mathematics, but it's not a discovery of a new higher-order mathematical construct (such as the amplituhedron). Yes, the latter also predicts measurement outcomes, but it also presents a novel and richer mathematical language that may have much broader ramifications when explored further. Like Nima says, there's nothing further to understand in the foundations of QM. There's still a lot more to understand with the surfacehedra. Both mathematically and physics-wise.

Disclaimer: By stating the foregoing about 'contrived' and 'discovered', I'm not trying to insert into Nima's work some wishful thinking, subjective opinion or ideological preference on my part (if I do, then it's unintentional). It's just the way these constructs seem to me to have historically evolved and which Nima has also described in his account on how he stumbled upon these new polytopes.

Maybe the following reiteration will bore you, but you did not really refute the scheme I presented as regards the fundamental meaninglessness of 'understanding' applied (i.e. 'contrived') mathematical constructs more deeply. If we apply the most basic law of propositional logic -- the law of identity (for all a: a = a) -- to the notion of 'understanding propositions', we can present the following simple reformulation: For all propositions x (including mathematical configurations) produced by my current understanding, I already have a full understanding of x. Hence, the claim that one needs to understand more deeply something that one's understanding has generated is logically contradictory.

A true positivist is therefore satisfied with the current algorithmic math at the foundations of quantum mechanics, and thereby regards the foundations of quantum physics as being completely understood. There's nothing more to understand. 'Shut up and calculate'. However, if he chooses to use any terminology of wanting to 'understand nature' more 'deeply' (whether within or without quantum mechanics), then the person isn't a true positivist. He may be a positivist in the restricted sense you described, treating received QM primarily as the helpful calculational device it was intended as. But he's still a scientist with realist intuitions (not excluding Bohr himself), naturally curious about the actual causes and underlying dynamics of observed phenomena, existing irrespective of whether we observe them or not. These intuitions are human, healthy and ever-present despite the fact that the specific scientific field of a quantum mechanician may have thus far historically lent itself poorly to realist theories.

The rationale for depicting the 'toothlessness' (e.g. the inherent paradox) of the philosophical theory of positivism was to demonstrate the risk of justifying any scientific programme by appeal to such problematic theories. It was not to describe Bohr or anyone else as being able, or particularly interested, to practice their positivism beyond their scientific work, which is by default ridiculous. This very fact (that nobody is actually a true positivist) further highlights the toothlessness of the philosophical theory that is positivism. In conclusion, positivism is at best a helpful generator of algorithms, ordinarily a mere philosophical curiosity, while at worst (which applies to all manner of 'ideological zealots') an ideological obstacle to scientific exploration of observer-independent reality.

It may produce, and indeed has produced, tremendously helpful calculations for science and technology. I've already stated that. Bohr has probably earned all his awards. I've never claimed all physicists are positivists, but rather highlighted the historical fact that a positivist view of the scientific project (i.e. beyond being merely restricted to promoting the algorithmic usage of QM foundations) seems more common amongst quantum mechanicians than other physicists.

Why? I've offered some reasons on this thread, summarized once more in my previous post in response to @jplaza. Bohr's 'conversion' into positivism through Otto Neurath and the Vienna Circle has been one key element that cannot be trivialized when we look at his philosophical influence and legacy on later quantum mechanicians, the hegemony of the Copenhagenist culture of science-making amongst later quantum mechanicians, as well as the instrumentalist mathematical formalism he was part of designing.

You can ask if one element of the set is "logically reducible" to another but you can't really meaningfully ask whether the element is "logically reducible" to the set itself.

I didn't. I was specifically referring to 'S-matrices' rather than the 'S-matrix program' when I mentioned the logical irreducibility of the surfacehedra to S-matrices. It's a crucial distinction when discussing whether or not Nima has brought new math to the table or whether he's merely continuing received math as provided in the program.

Yes, the novel structure Nima and his collaborators identified is indeed novel. That's not the claim, though. The claim is that algebraic geometry and number theory have never been used in physics, a claim that's crassly false.

Not when understood in the context of the more advanced structures of algebraic geometry and number theory which Nima has specified as being novel to physics. In terms of other contexts, I'd be interested in you backing up your claim "crassly false" by providing examples on the wide previous usage of algebraic geometry and number theory in physics? The Calabi-Yau manifold would indeed qualify as algebraic geometry whereas most complex manifolds are differential geometry.

 

[LilWabbit]

What are the four properties?

The parts in italics.

Where can I read more about the PoSR?

https://plato.stanford.edu/entries/sufficient-reason/#WhatSuffReas

It feels like it posits determinism, is that correct?

No. PoSR is philosophically deliberately non-specific as to the type of reasons or causes implied. In other words, any entity, property or behaviour can theoretically have both deterministic or indeterministic causes ('law-likeness' vs. 'chanciness'). Furthermore, the entity, or its property or behaviour, may have causes both/either within the entity (self-caused) or outside the entity (other-caused). And yet furthermore, causes may be total causes (causes for the very existence of an entity) or partial causes (causes for a particular property or behaviour of an entity). And yet furthermore, and closely related, causes may be composite (many causes) or simple (single cause). Even the foregoing list is not exhaustive in terms of all logically possible types of causes.

However, all of the above types of causes are worth exploring in any exercise purporting to describe itself as 'scientific'. What PoSR squarely disagrees with is the philosophical alternative that an entity, property or a behaviour can be/occur without any cause whatsoever. This fundamental rule posited by the PoSR is often justified by appeal to the philosophical dictum ex nihilo nihil fit ("nothing comes out of nothing").

According to the dictum, while it's logically possible that there be an entity or a property that has no cause whatsoever, it's an absurd and unhelpful possibility. Hence, for instance, the known universe may be, under the PoSR, rationally explored either as having a sufficient reason within itself for its own existence (self-caused) or without itself (other-caused). But the third option that there is no sufficient reason for the universe to exist is regarded as absurd, for the question can always be reasonably asked: If the universe does not have a sufficient reason to exist at all, how come it exists nonetheless? The proponents of the third option forbid the question 'why' or 'how' and insist on acceptance of its existence as a brute fact.

Footnote: Philosophically the question 'what causes time?' (irrespective of whether time has an infinite past or not) is perfectly reasonable and hence the simplistic and popular physicalist understanding that causality logically necessitates a cause-and-effect relation in time is both incorrect and superficial. Hence, a self-caused universe that has always existed is a perfectly logical statement when understood in terms of 'the universe containing within itself a sufficient reason for its own existence'. Similarly 'a universe that has always existed may have a sufficient reason for its existence outside of itself' is also perfectly logical. The dilemma is a metaphysical (philosophical) one and hence unresolvable scientifically. Any effort to do the latter stumbles upon a category mistake.

If I roll a doice and it comes up with the number 6, what is the reason for that?

If the question is understood as a scientific question, the answer is, a complex of possible deterministic and indeterministic physical as well as psychological causes that we do not yet fully understand in toto.

If the question is intended as an allegorical device depicting a case of pure randomness (which scientifically is not the case in die-rolling, but could however be the case at a more fundamental level such as radioactive decay or quantum fluctuations), then the answer is equipossibility of outcomes inherent in the perfect symmetry of the dice combined with the absence of other causes favouring one particular outcome above another.

How do I falsify the PoSR, i.e. how do I distinguish something that happens with no reason from something that has a reason that has not been found yet?

We cannot empirically falsify, or verify, either the PoSR or its logical negation ('there are no causes') since both are fundamental philosophical assumptions that are logically possible in all logically possible worlds and all possible empirical outcomes. However, the absurdity and non-utility (including in scientific pursuit) of 'something coming out of nothing' is the very reason the PoSR was formulated in the first place.

Even positivists like Niels Bohr do not claim that the outcomes of quantum mechanical measurements arise from nowhere. He merely highlights the futility of trying to understand that 'something' and therefore instructs focusing on calculating measurement outcomes rather than wasting time on classical theorizing.

One last point worthy of clarification. 'Classical', in the usage of physicists, often (but not always) seems to assume some manner of determinism. However, 'classical theorizing' in science need not imply anything purely deterministic. It need not mean anything further than the pursuit of theories attempting to explain phenomena in terms of the real reasons/causes for their occurrence, and testing those theories through experiments. Such explanations may be determinist or indeterminist or a combination of both. But they're still classical in the sense of providing explanations rather than pure predictions.

 

[Mendel]

need not mean anything further than the pursuit of theories attempting to explain phenomena in terms of the real reasons/causes for their occurrence, and testing those theories through experiments

Hmm, looks like gravity was a well-chosen example after all:

Article:

Newton's law of gravitation, the linchpin of his new cosmology, broke with explanatory conventions of natural philosophy, first for apparently proposing action at a distance, but more generally for not providing "true", physical causes. The argument for his System of the World (Principia, Book III) was based on phenomena, not reasoned first principles. This was viewed (mainly on the continent) as insufficient for proper natural philosophy.

Source: https://plato.stanford.edu/entries/scientific-method/

You're fighting a 17th-century fight here, explicitly taking Leibniz's side against Newton with the PSR. From Leibniz's Philosophy of Physics :

Article:

A second, more philosophical, line of attack pivots on Leibniz's commitment to the Principle of Sufficient Reason (PSR). [...] Leibniz argues that if the PSR is granted, the apparent possibility of absolute space and time can be undermined.

Source: https://plato.stanford.edu/entries/leibniz-physics/

Newton features heavily in that article, whereas Leibniz and Cartesian thinking feature heavily as counterpoint to Newton's Philosophy:

Article:

Leibniz's criticisms of the Newtonians were not restricted to questions about the nature of space and time; he also revived his old complaint—one shared by Huygens, as we have seen above—that Newton's physical theory commits him to the possibility, if not to the reality, of action at a distance among the planetary bodies. In one passage in his fourth letter, for instance, Leibniz writes (Clarke and Leibniz 1717: L 4: 45):

It is also a supernatural thing that bodies should attract one another at a distance without any intermediate means and that a body should move around without receding in the tangent, though nothing hinders it from so receding. For these effects cannot be explained by the nature of things.

[...]

Indeed, a late-seventeenth-century debate between Cartesian and Newtonian ideas was supplanted by an early eighteenth century debate between Leibnizian and Newtonian views; the latter debate would continue in one form or another for the rest of the century.

Source: https://plato.stanford.edu/entries/newton-philosophy/

Scientists in Newton's tradition are simply not looking for nature of things. This "shortcoming" has enabled over 3 centuries of progress.