The Bunkum Mystification of Quantum Mechanics by Non-Physicists

LilWabbit

Active Member
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.
 
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Rory

Senior Member.
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?

 

LilWabbit

Active Member
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?


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

Active Member
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

Active Member
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.

"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.

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

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.

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).

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.

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

Senior Member.
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

Active Member
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

Active Member
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

Active Member
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).


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.
 
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markus

Active Member
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).


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

Active Member
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


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.”


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'.
 
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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

Active Member
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

Active Member
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


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.”


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:

Nima interrupts:

(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


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

Active Member
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:

Nima interrupts:

(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'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

Active Member
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.


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.
 
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