Are you serious? "How the world behaves" depends a lot on what beings with any intelligence can do with new discoveries:
SR gave us nuclear energy
GR gave us accurate gps (and possibly a warp drive in the future, if combined with dark energy)
Maxwell gave us wireless communication
QED gave us quantum computers

And this list of about 100 years of new scientific discoveries is far from complete, of course.

So yes, these new theories have a HUGE impact on how our world behaves. But they need to be combined with some creative intelligence to make a difference. And I do hope we are not the most intelligent beings in the universe. What a waste of space that would be...

no, these new theories have a huge impact on how we behave

by telling us more about how the world behaves, every single one of these theories restricted what we could potentially do and added to what we could actually do

(space can't be "wasted". if you store the universe most space-efficiently, a big bang results)

Is there a way within the framework of current physics models such that one could cross any given cosmic distance in an arbitrarily short period of time, while never breaking the speed of light? This is the question that motivated Miguel Alcubierre to develop and publish a possible mathematical solution to the question back in 1994 [5]. Since the expansion and contraction of space does not have a speed limit, Alcubierre developed a model (metric) within the domain of general relativity that uses this physics loop hole and has almost all of the desired characteristics of a true interstellar space drive, much like what is routinely depicted in science fiction as a “warp drive”.

See my quote from that same paper in my previous post. General relativity nor any other of our current theories of physics predicts this inflation, so there are observations which require an update of our laws of physics. An update which must include the inflation observed and currently labeled as "dark energy".

Let's slow down just a tad and keep two things clear to ensure that we are indeed talking about the same thing while at least attempting to be as scientific as possible in the process.

Firstly: Cosmic inflation is an unproventheory (disputed especially by Roger Penrose), not an observation. Metric expansion of the universe is an observation which the theory of cosmic inflation attempts to explain and in doing so suggests an exponential expansion of the universe. This exponential expansion (again, a theory) is further explained by the theory of dark matter. So we have a theory that explains a theory about a fact. That's how far-out in speculation we are already whilst still remaining within the confines of theoretical physics to be distinguished from pure science fiction.

The potential energy curve of the inflation in the theory of cosmic inflation is criticised to be contrived ad hoc to fit almost any possible observation and hence the whole theory of cosmic inflation can be criticized for playing clever mathematical gimmickry to fit any and all observations. So can the theory of negative mass, in the hands of alien civilization enthusiasts, be criticized for motivated reasoning and mathematical gimmickry to be fit-for-purpose. Whereas science, at its purest, is only interested in what's true and what's not without any strings attached.

Secondly: It's true that GR does not predict exponential expansion (which, as discussed above, is an unproven theory that still requires stronger empirical support). If, however, exponential expansion were a fact, then GR would indeed require an update on that particular point. And yet, not an update which flippantly assumes, as a contrived ad hoc mathematical solution to conveniently fit any and all observations, a violation of a fundamental assumption that all energy should be positive (i.e. the energy condition). This fundamental violation would be the case with the assumption of negative mass/energy entailed by various notions of warp drive.

The energy condition (i.e. the ontological rejection of negative energy as a real possibility in the real word) is a generic criterion that describes observed properties common to all states of matter and all non-gravitational fields that are well-established in physics. As such, the energy condition keeps any and all future theories empirically grounded in reality and puts a limit to wild speculations and motivated mathematical gimmickry to satisfy observations.

So once more, to be very clear, in serious science you don't get to put too much stock on assumptions (negative mass) that destroy other stronger and empirically more grounded assumptions (positive energy) unless the contradicting assumption is empirically more grounded. We're far from that point as yet.

All talk of negative mass and energy unavoidably concerns a much more profound philosophical question on the nature of the very property of existence no less. This deeper philosophical question isn't usually addressed in any of the mathematical formulations of specific energy conditions contrived for various physical theories nor in the mathematical counterexamples (negative mass calculations) violating these conditions in theoretical physics.

The fundamental philosophical question on the existence of energy can be logically addressed as follows:

(1) If all that exists is energy in an infinite variety of forms (in keeping with the Law of Conservation of Energy), then the only universally generalizable property of energy is its existence.

(2) Existence is by logical necessity a positive property since negative existence is logically equivalent to non-existence.

(3) Negative energy, as advanced by negative energy speculations amongst physicists, means energy that exists but in a negative form which contradicts 2, unless it means the non-existence of energy which is not what's advanced by negative energy speculations.

(4) If 1 is true, negative energy is logically impossible.

If the above logical schema is sound, negative energy is theoretically possible only under hypothetical superior alien logic which observes hypothetical superior logical rules above and beyond human formal logic. If so, we should cease forthwith discussing the topic using human logic and simply resign to uncritically accepting as brute fact that aliens are supernatural beings operating beyond all known rules of reason and observable reality. How anthropomorphic of us to rely on human logic and observation!

I'm not quite ready to make such a leap of faith and summary rejection of my cognitive powers just yet.

Are you serious? "How the world behaves" depends a lot on what beings with any intelligence can do with new discoveries:
SR gave us nuclear energy
GR gave us accurate gps (and possibly a warp drive in the future, if combined with dark energy)
Maxwell gave us wireless communication
QED gave us quantum computers

And this list of about 100 years of new scientific discoveries is far from complete, of course.

So yes, these new theories have a HUGE impact on how our world behaves. But they need to be combined with some creative intelligence to make a difference. And I do hope we are not the most intelligent beings in the universe. What a waste of space that would be...

My question was "Which realm do you think we've not probed?" Listing realms that we've probed supports my argument that we're running out of realms to probe.

Huge impact, eh? Not even "Huge". but "HUGE"? Do you really think that GPS is any neater than bats' echo location? I have access to GPS, and have done for over a decade, and I don't use it, ever. If I had echo location, I could walk home with my eyes closed, and I'd do that every night. That's way cooler. Where's the echo location that I demand - I don't give a monkey's about this GPS thing.

And Maxwell's equations did not give us wireless communication. We could have taken advantage of the propagation of electromagnetic waves without knowing the solutions to equations that model them. Do you really think that birds know the solution to the Navier-Stokes equations? If they do, we should be trasining them to speak as a high priority, to get them to explain them to us, because we humans still don't have that, yet we do have aeroplanes, and rockets. And we ought to be giving more respect to the dogs for solving differential equations, as there's no other way they could predict the path of the ball or stick that's thrown towards them.

All talk of negative mass and energy unavoidably concerns a much more profound philosophical question on the nature of the very property of existence no less. This deeper philosophical question isn't usually addressed in any of the mathematical formulations of specific energy conditions contrived for various physical theories nor in the mathematical counterexamples (negative mass calculations) violating these conditions in theoretical physics.

(1) If all that exists is energy in an infinite variety of forms (in keeping with the Law of Conservation of Energy), then the only universally generalizable property of energy is its existence.

If the above logical schema is sound, negative energy is theoretically possible only under hypothetical superior alien logic which observes hypothetical superior logical rules above and beyond human formal logic. If so, we should cease forthwith discussing the topic using human logic and simply resign to uncritically accepting as brute fact that aliens are supernatural beings operating beyond all known rules of reason and observable reality. How anthropomorphic of us to rely on human logic and observation!

if you doubt the existence of negative quantities, have a look at your thermometer on a frosty day. surely you won't argue that it took alien visitation to set up a flourishing thermometer business on Earth?

Did you have a constructive and substantive point to make? Or was the intent of the foregoing sudden and out-of-the-blue hostile remark only to obfuscate the uncomfortable fact that you didn't understand a word of what was written?

Now you're yourself deep in the 'sophistry' of philosophical ontology and no longer discussing mere physics. Even if there were a simple way of stating that energy has a finite variety of 'kinds' (qualia) of expression (which there isn't and hence your declarative unfounded statement is moot), if even one of those expressions scales along R, then the potential amount of forms of energy scales to infinity. We know a great many of those qualia scale in R. In fact, I don't know any that don't. By the way, did you forget that mass is also a form of energy? Do you think mass has only a finite N set of potential forms in the universe in term of physical dimensions, resistance to acceleration, strength of its gravitational attraction, amount of matter, etc.? Not to even mention black holes some of the properties of which can be claimed to scale to infinity along N.

What? Joule is not a property of energy. It's an artificial man-made unit of measuring transferred energy on a practical human scale, and in fact pretty useless at smaller or greater scales or in describing other forms of energy. Mass is also energy.

Yet energy is not 'just a number' and negative energy as a real thing makes no empirical nor logical sense as demonstrated earlier. Negative energy is a mathematical construct and calculational device, not reality. As is pi or the quadratic equation. Hence the earlier point on mathematical gimmickry and contrivance as a persistent challenge amongst many theoretical physicists not even trying to anchor their formulae in reality.

if you doubt the existence of negative quantities, have a look at your thermometer on a frosty day. surely you won't argue that it took alien visitation to set up a flourishing thermometer business on Earth?

That's a totally bogus argument. C.f.
1) The value on a normal die is an integer, therefore it can be -10
2) The amplitudes in quantum mechanics are complex, therefore they can be 1+2i
3) The probabilities in quantum mechanics are numbers, therefore they can be -sqrt(5).

You just did (3), but all three arguments are the same error. That a scale can measure certain quantities doesn't mean that the property being measured can attain those quantities.

For electromagnetic quanta, E = h.nu
h is positive. nu is positive.
There's no admissible negative energy for photons. The anti-photon created in an electron-positron collison, being still just a photon, also has positive energy.

if you doubt the existence of negative quantities, have a look at your thermometer on a frosty day.

Frosty day - check. Thermometer - phone has an sensor - so check. /sys/devices/platform/omap34xx_temp/temp1_input_raw says 27. Looks positive to me. If you can use an arbitrary scale for measuring temperatures, so can I - mine's a TI ADC that will always give an unsigned 7 bit value, so never negative. There are no non-arbitrary temperature scales, but the ones that have the least number of contrivances in them all have absolute zero as their zero. Also, even when the thermometer reads -7 C (which is what my ADC value 27 represents: https://www.mail-archive.com/linux-omap@vger.kernel.org/msg01425.html ), it's still telling you that there's plenty of thermal energy out there, and "plenty" is a positive quantity.

My question was "Which realm do you think we've not probed?" Listing realms that we've probed supports my argument that we're running out of realms to probe.

New insights into existing realms can already extend our abilities and hence the nature of 'our' world, i.e., the world we live in and partly create or at least influence ourselves. (It's obvious of course that the part of nature that we do not influence in any way will not change one iota if we discover new laws that govern its behavior.)

But to give my view on your question: We can explain a lot with our current scientific worldview of particles and forces acting in spacetime, but not everything. Things we still cannot explain with this worldview include:

The quantummechanical measurement problem and related phenomena like quantum entanglement and the famous double slit experiment.

(the hard problem of) Consciousness and related phenomena like the placebo effect, hypnosis, dreams, and (dare I say on a sceptic forum) psi phenomena that have been shown to yield statistically significant results.

Dark matter and dark energy (which form 95% of the energy content of our universe).

All attempts to explain these phenomena with our scientific worldview of particles and forces acting in spacetime have failed thusfar. I know many scientists expect we will ultimately succeed but I do not share their optimism.

I think we have to somehow expand our scientific worldview and often ponder whether we have the intellectual ability to do so. A gorilla will never understand differential equations, and a human will also have limitations to what their mind can grasp. Maybe some features of reality are simply forever beyond our reach but within the reach of more intelligent beings, who knows? I guess only time will tell.

You just did (3), but all three arguments are the same error. That a scale can measure certain quantities doesn't mean that the property being measured can attain those quantities.

The idea of negative probabilities later received increased attention in physics and particularly in quantum mechanics. Richard Feynman argued[2] that no one objects to using negative numbers in calculations: although "minus three apples" is not a valid concept in real life, negative money is valid. Similarly he argued how negative probabilities as well as probabilities above unity possibly could be useful in probability calculations.

I believe your argument goes "I know dice without negative numbers, therefore dice have no negative numbers. I know physical scales without negative numbers, therefore physical scales have no negative numbers". If it doesn't, I don't really see how it applies to my argument, "since that amount is a number, it can theoretically be negative". Since dice have numbers on their faces, these numbers can theoretically be negative—proven true by dice where the numbers are practically negative.

I looked up "negative energy" on wikipedia and thought it was well-defined and plausible enough for me to accept the concept.

Energy density includes energy densities associated with pressure:

In cosmological and other general relativistic contexts, however, the energy densities considered are those that correspond to the elements of the stress–energy tensor and therefore do include mass energy as well as energy densities associated with pressure.

According to general relativity, the pressure within a substance contributes to its gravitational attraction for other objects just as its mass density does. This happens because the physical quantity that causes matter to generate gravitational effects is the stress–energy tensor, which contains both the energy (or matter) density of a substance and its pressure.

Independently of its actual nature, dark energy would need to have a strong negative pressure to explain the observed acceleration of the expansion of the universe.

I believe your argument goes "I know dice without negative numbers, therefore dice have no negative numbers. I know physical scales without negative numbers, therefore physical scales have no negative numbers". If it doesn't, I don't really see how it applies to my argument, "since that amount is a number, it can theoretically be negative". Since dice have numbers on their faces, these numbers can theoretically be negative—proven true by dice where the numbers are practically negative.

I looked up "negative energy" on wikipedia and thought it was well-defined and plausible enough for me to accept the concept.

Does that answer the proximal question asked? Top tip - if I'm repeating the word "normal", then perhaps that's an important word in the question.

And, no, your first sentence is pure straw man, I've never said anything like what you've put in quotes, and have no idea where you got that from. It seems a bit like projection, simply taking your own argument and flipping its parity somehow, as it much more closely resembles what you've previously said than anything from me.

All talk of negative mass and energy unavoidably concerns a much more profound philosophical question on the nature of the very property of existence no less. This deeper philosophical question isn't usually addressed in any of the mathematical formulations of specific energy conditions contrived for various physical theories nor in the mathematical counterexamples (negative mass calculations) violating these conditions in theoretical physics.

I must agree with @Mendel, as the comparison with Jordan Peterson and his rambling struck me forcibly when I first read it. It's like two people conversing on a bus, where one says "This is my stop" and gets off, while the other contemplates the meaning of the words and the philosophy of existence until the bus gets to the end of the line and he finds himself miles from his destination.

Our destination was the physical possibilities of space travel, if I recall, and the "philosophical questions" strike me as NOT being "much more profound", but more of a diversion down a blind alley. And, unless you think aliens could magically define themselves as negative numbers, mathematical manipulations are insufficient to show physical possibilities.

It's my understanding that those "statistically significant" results are themselves occurring randomly in a manner entirely predictable by statistics, much like the blind squirrel that occasionally finds an acorn. If you have solid evidence that well-controlled "psi" experiments on the whole have shown positive results more often than chance, I'd really like a citation.

I must agree with @Mendel, as the comparison with Jordan Peterson and his rambling struck me forcibly. It's like two people conversing on a bus, where one says "This is my stop" and gets off, while the other contemplates the meaning of the words and the philosophy of existence until the bus gets to the end of the line and he finds himself miles from his destination.

Our destination was the physical possibilities of space travel, if I recall, and the "philosophical questions" strike me as NOT being "much more profound", but more of a diversion down a blind alley. And, unless you think aliens could magically define themselves as negative numbers, mathematical manipulations are insufficient to show physical possibilities.

So let me be clearer then. The profound philosophical question is "why is it absurd to talk about negative temperature?" while it's not absurd to talk about "negative numbers on a temperature scale where the zero is set at a particular physically significant point such as the freezing point of water which is not the same as negative temperature". As we've been trying to explain with @FatPhil, in the real universe there's no such thing as negative temperature. There's only temperature approaching absolute zero with the coldest place in the known universe being the Boomerang Nebula at crisp 1 degree Kelvin.

The absurdity of talking about negative energy as a real physical phenomenon outside mathematics is a closely related problem which I attempted to outline with the earlier logical schema. That it wasn't understood is clear. That I could be clearer may also be a valid point. That it's mere sophistry is but an impolite and inaccurate derailment aimed personally out of bratty spite. That it's irrelevant to this discussion hasn't been demonstrated. It provides one rational justifcation for the energy condition (all energy should be positive) -- a real theoretical condition employed variously in physics -- which warp drive ideas violate.

Some issues are by their very nature highly abstract, ambiguous and subtle. What energy ultimately constitutes at the subatomic level is one of those questions since all classical notions of energy and mass go out the window. Since the ultimate nature of energy is so hard to pin down, it only adds to the ridiculousness of discussing negative energy/mass as a meaningful concept explaining warp drives. Rather, it strengthens the argument that negative mass is merely a mathematical contrivance.

It's my understanding that those "statistically significant" results are themselves occurring randomly in a manner entirely predictable by statistics, much like the blind squirrel occasionally finds an acorn. If you have solid evidence that well-controlled "psi" experiments on the whole have shown positive results more often than chance, I'd really like a citation.

Why bother? People keep rambling on about negative energy even after my post #136 so they don't seem to read anything besides the stuff they post themselves...
But included is an interesting piece of research if you're interested. I suggest we leave it at this to not derail your thread any further. The topic is pretty much irrelevant to this thread and I shouldn't have mentioned it in the first place

But included is an interesting piece of research if you're interested. I suggest we leave it at this to not derail your thread any further. The topic is pretty much irrelevant to this thread and I shouldn't have mentioned it in the first place

That's an impolite assumption itself, when it seems to me that @Mendel's use of the word (and my endorsement of his analysis) was out of sheer frustration at trying to plow through all your chaff in search of the wheat. And it's that wordy obfuscation you employ that is so reminiscent of Peterson. You make some good points, but you really could use a good editor.

It's my understanding that those "statistically significant" results are themselves occurring randomly in a manner entirely predictable by statistics, much like the blind squirrel that occasionally finds an acorn. If you have solid evidence that well-controlled "psi" experiments on the whole have shown positive results more often than chance, I'd really like a citation.

Various investigators have claimed to have observed highly significant 'paranormal' results (in the statistical sense of significance). The best known is probably J. B. Rhine, whose work on the subject was mainly in the 1930s. But other investigators have not been able to replicate his results, and possible sources of error in Rhine's experiments have been suggested. The Wikipedia article on Rhine summarises the evidence:

That's an impolite assumption itself, when it seems to me that @Mendel's use of the word (and my endorsement of his analysis) was out of sheer frustration at trying to plow through all your chaff in search of the wheat.

I beg to differ @Ann K. The proper polite response to not fully understanding someone else's post is to kindly ask for a clarification. Not to disdainfully dismiss it as 'sophistry' to play down one's own poor reading comprehension, even if some editing on my part could have produced clearer and shorter verbiage. In the case of Mendel, it's not just frustration. It's also personal. You are clearly not privy to all the facts. Besides you're not exactly a neutral broker here.

And while we're at it, 'hitting back' at your attacker by calling out the attack and its petty motive may seem impolite. But to a fair-minded observer it seems far fairer and less impolite than the initial unprovoked attack out of the blue.

I find Peterson to be somewhat articulate so I take it as an unintended compliment. Indeed, as Peterson would probably agree, there are issues that are more abstract and nuanced and cannot be easily simplified/edited to the uninitiate without doing great violence to the actual argument. You can go ahead and "edit" string theory to be more understandable to non-string theorists. But you'd end up talking about something entirely other than string theory.

(1) If all that exists is energy in an infinite variety of forms (in keeping with the Law of Conservation of Energy), then the only universally generalizable property of energy is its existence.

That is not a meaningful statement -- contrast for instance "all that exists is velocity is an infinite variety of forms". Energy is just one conserved quantity among many, associated with the symmetry of physical systems under time translations. Other symmetries are associated with other conservation laws, e.g. the U(1) gauge symmetry of electromagnetism is associated with conservation of electric charge. In fact, since, in general relativity, spacetime is dynamic, the required time translational symmetry required to define an "energy" is not satisfied: energy, generically speaking, is not conserved. Example: a photon across the expanding universe will redshift and thus become less energetic. Where does its energy go? It doesn't go anywhere, it's just not conserved in that particular situation.

That is equivocating two unrelated meanings for the words "positive" and "negative".

I would advise that hyperfocusing on positive vs negative energy is not a very useful way of discussing the feasibility (or lack thereof) of exotic solutions in general relativity. It certainly seems likely that negative energy cannot be procured in the amounts and densities required to make such contraptions work, but negative energy densities cannot be ruled out in general. In fact, they are unavoidable; see the 1965 paper by Epstein, Glaser, and Jaffe.

It is shown that a positive definite local energy density is incompatible with the usual postulates of local field theory.

So any argument that tries to establish that negative energies cannot exist fails at the outset because it proves too much.

For physics it matters not whether energies are nonnegative in an absolute sense but rather whether energies are bounded from below. Not because of some dogma or rationalistic justification where one declares to nature how it must or must not be, but because if energy is not bounded from below you get a system that's utterly unstable, which probably doesn't look much like our universe.

(By the way, negative absolute temperatures may not be the best example about something that cannot exist, because they absolutely do and are technologically very useful. All you need is a system with a bounded upper energy and a population inversion. A laser is a good example of a situation where this happens.

A system with a truly negative temperature on the Kelvin scale is hotter than any system with a positive temperature. If a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system.[2][3] A standard example of such a system is population inversion in laser physics.

)

On the subject of inflation, we don't think of theories as being proved or unproven, but rather supported or unsupported by evidence. Is inflation supported by evidence? You bet. Trying to say that warp drive is on shaky ground because inflation is supposedly on shaky ground also "proves too much".

It is more fruitful, IMO, to discuss the problems of warp drive on their own merits:

1. Warp bubbles seem to require matter to move locally superluminally in order to maintain the bubble geometry. This objection has been phrased in the past as "it takes one to build one" but the matter is rather more serious because it reveals that Alcubierre's original solution is mathematically inconsistent.

2. It takes a lot of negative energy to build one, much more than the usual order-of-hbar effects we know from quantum field theory, so actually establishing the required energy density would almost certainly require distinctly new physics. Note that, contrary to statements in some recent reports, the need for negative energy is unavoidable for any solution of general relativity allowing superluminal travel.

I propose a definition of superluminal travel which requires that the path to be traveled reach a destination surface at an earlier time than any neighboring path. With this definition (and assuming the generic condition) I prove that superluminal travel requires weak-energy-condition violation.

3. The front of a warp bubble is separated from the interior by an event horizon, which means it cannot be steered, but also that its stability is in question. How would you prevent the two "halves" from separating if they cannot interact due to a causal horizon?

4. Quantum field theory calculations of warp drive geometries in 2d spacetimes show that the stress-energy tensor diverges near the causal horizons, which is evidence of unphysicality.

The expectation value of the stress-energy tensor of a free conformally invariant scalar field is computed in a two-dimensional reduction of the Alcubierre ``warp drive'' spacetime. The stress-energy is found to diverge if the apparent velocity of the spaceship exceeds the speed of light.

5. And, of course, as discussed before, superluminal travel straightforwardly creates grandfather paradoxes.

Why bother? People keep rambling on about negative energy even after my post #136 so they don't seem to read anything besides the stuff they post themselves...

Your post #136 merely reiterates speculations that violate the energy condition without being better empirically grounded than the overall justification for preserving the energy condition.

In parapsychology, noetics is a fringe branch of pseudoscience concerned with the study of mind as well as intellect.
... Quackwatch lists the Institute of Noetic Science on its Questionable Organizations list.

I've followed the subject in the past, from Rhine onward, but the entire field seems to suffer from the problem of "counting the hits and ignoring the misses". There is also the problem of declaring particular methods to be used, without explaining why or how, if indeed there is such an ability, it would be expected to work in one particular testing method and not another. Influences ranging from inadvertent body language to outright cheating have also been found.

If mass and matter are fundamentally forms of energy as Einstein suggests then velocity is far less meaningfully applicable to them as a fundamental property. But I could be wrong about my 'if'.

Energy is just one conserved quantity among many, associated with the symmetry of physical systems under time translations. Other symmetries are associated with other conservation laws, e.g. the U(1) gauge symmetry of electromagnetism is associated with conservation of electric charge.

If electric charge is a form of energy, then you're contradicting yourself by differentiating it from energy. But maybe I'm misunderstanding the gist of your point and you did not differentiate between the two. If you did, then you're employing a narrower and more classical definition of energy than Einstein.

In fact, since, in general relativity, spacetime is dynamic, the required time translational symmetry required to define an "energy" is not satisfied: energy, generically speaking, is not conserved. Example: a photon across the expanding universe will redshift and thus become less energetic. Where does its energy go? It doesn't go anywhere, it's just not conserved in that particular situation.

Are you sure it doesn't go anywhere? I came across this article:

Article:

So yes, it's actually true: as the Universe expands, photons lose energy. But that doesn't mean energy isn't conserved; it means that the energy goes into the Universe's expansion itself, in the form of work. And if the Universe ever reverses the expansion and contracts again, that work will be done in reverse, and will go right back into the photons inside.

Negative. By equivocating negative existence with non-existence I'm using only one well-established meaning for 'negation' as defined in formal logic (propositional or first-order). This definition is unproblematic ontologically (i.e. when applied to real world objects). However, the notion of 'negative energy' mathematically employs another definition of negation (i.e. less than zero) and it doesn't translate as comfortably into real world objects and phenomena. Hence this whole debate.

(By the way, negative absolute temperatures may not be the best example about something that cannot exist, because they absolutely do and are technologically very useful. All you need is a system with a bounded upper energy and a population inversion. A laser is a good example of a situation where this happens.

A system with a truly negative temperature on the Kelvin scale is hotter than any system with a positive temperature. If a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system.[2][3] A standard example of such a system is population inversion in laser physics.

I think there is a semantic confusion here. At zero kelvin (minus 273 degrees Celsius) particles stop moving. Thus, nothing can be colder than absolute zero on the Kelvin scale in the sense of particles behaving as less-than-stationary, an evident absurdity which highlights the very issue of this debate.

On the subject of inflation, we don't think of theories as being proved or unproven, but rather supported or unsupported by evidence. Is inflation supported by evidence? You bet. Trying to say that warp drive is on shaky ground because inflation is supposedly on shaky ground also "proves too much".

That's not what I was trying to say. I was merely correcting the false statement that cosmic inflation is an observation, and that as a theory it's uncontested. For every set of observations you will always have multiple mutually inconsistent theories consistent with the same set of observations. Being 'supported' by evidence is therefore not a scientifically particularly interesting statement, but rather, which theory generates better, more accurate and more useful predictions.

I told you before, people think they ARE understanding others posts. Surely their interpretation of "your" words is the superior interpretation because they are always right.

I'm sorry, but it's not "poor reading comprehension" to have a difficult time decoding fringe vocabulary and needlessly complex syntax about a topic that is already confusing enough as it is.

If so, we should cease forthwith discussing the topic using human logic and simply resign to uncritically accepting as brute fact that aliens are supernatural beings operating beyond all known rules of reason and observable reality. How anthropomorphic of us to rely on human logic and observation!

You would get marked down, because the language you're using is getting in the way of your message. If you tried to publish a scientific paper with this wording, you'd be told to edit and simplify during review. If your reader has to do any extra labor to decode your message, the issue isn't their reading comprehension, it's your writing.

Saying that mass and matter are "forms of energy" really makes about as much sense as saying they're each "forms of velocity". Energy is a quantity that is conserved (in some circumstances) which usefully constrains the time evolution of physical states, enabling us to make conclusions without needing to solve the full equations of motion. Matter is not congealed energy, electric charge is not congealed energy. Both of those are category error -- energy is a number. When you see stuff out there, stuff with mass, electric fields and what not you add an entry to the balance sheet of the universe. To real objects there corresponds an amount of energy. But it makes little sense to declare objects to "be" energy, regardless of the poetic language Einstein may have used. Feynman's lectures Vol. I, Chapter 4 (freely available online) contain a useful discussion.

I'm sure. If you go through the usual Noether's theorem argument in general relativity and jump through some hoops you get a conservation equation, but the conserved charge is identically zero.

To compute a divergence, we need to compare quantities (here vectors) on opposite faces. Using parallel transport for this leads to the covariant divergence. This is well-defined, because we're dealing with an infinitesimal hypervolume. But to add up fluxes all over a finite-sized hypervolume (as in the contemplated extension of Gauss's theorem) runs smack into the dependence on transportation path. So the flux integral is not well-defined, and we have no analogue for Gauss's theorem.

One way to get round this is to pick one coordinate system, and transport vectors so their components stay constant. Partial derivatives replace covariant derivatives, and Gauss's theorem is restored. The energy pseudo-tensors take this approach (at least some of them do). If you can mangle Equation 3 (covariant_div(T) = 0) into the form:

coord_div(Theta) = 0

then you can get an "energy conservation law" in integral form.

However, this "conservation law" is toothless. As I mentioned previously, conservation of energy is a constraint; states with energy E must go into states of energy E. If all states have the same energy 0, there are no constraints, which means there's no useful sense in which it can be said that energy is conserved. One can make up all sorts of stories like "the energy becomes gravitational energy" based on how the terms in this equation happen to be arranged, but because (see Baez's explanation above) that story is dependent on the coordinate system -- i.e., on how we choose to describe the system -- it has no legitimate physical meaning. It's just a story.

(It is possible to define quantities that are analogous to a conserved energy in GR in some restricted circumstances but this is the general case).

Negative. By equivocating negative existence with non-existence I'm using only one well-established meaning for 'negation' as defined in formal logic (propositional or first-order). This definition is unproblematic ontologically (i.e. when applied to real world objects). However, the notion of 'negative energy' mathematically employs another definition of negation (i.e. less than zero)

Those are the two unrelated meanings for the word 'negative' I was referring to. This is a linguistic accident and can't really have anything useful to tell us about physics.

Temperature as a "measure of the amount of random motion" is not the fundamental definition of temperature, just a simpler way of thinking about it that works for most everyday substances like typical gases/liquids/solids. Temperature is defined as the partial derivative of energy with respect to entropy, which means that if you're in a physical situation where energy decreases with increasing entropy (such as if there's an upper bound to energy), temperature can be negative in the absolute Kelvin scale.

Thus, nothing can be colder than absolute zero on the Kelvin scale in the sense of particles behaving as less-than-stationary, an evident absurdity which highlights the very issue of this debate.

I didn't say colder -- I said negative. Negative temperatures are 'hotter' than any positive temperature. In a sense, the more fundamental quantity is not temperature, but rather the "coldness" 1/kT. Zero coldness corresponds to infinite temperature, and infinite coldness to absolute zero (from the positive side). In some situations coldness can be negative, and objects with negative coldness cede heat to objects with positive coldness. It always works.

This is illustrative: the linguistic accidents that led to things having "positive" or "negative" connotations couldn't possibly have had any bearing on the matter because temperature wasn't even the right quantity to think about to begin with.

That's not what I was trying to say. I was merely correcting the false statement that cosmic inflation is an observation, and that as a theory it's uncontested. For every set of observations you will always have multiple mutually inconsistent theories consistent with the same set of observations. Being 'supported' by evidence is therefore not a scientifically particularly interesting statement, but rather, which theory generates better, more accurate and more useful predictions.

"Supported by evidence" and "generates better, more accurate, and more useful predictions" are essentially two ways of saying the same thing in this context. No theory is "uncontested", but it's important to avoid the perception that there's intense debate about whether or not there was an inflationary period in the early universe. Rejection of this is decidedly a minority/fringe position. This is for good reason: no other theory explains the available data as well as inflation does, even if we don't understand the precise mechanism. You seemed to be suggesting back there that inflationary cosmology is not "real" physics, and, whether or not that was the intended meaning, I wanted to make sure to clarify that's not the case.

Only if such discussions are fruitful. A rationalistic attempt to make physics predictions based on some simple syllogisms derived from connotations that happen to exist in some natural language, I think, is not very fruitful.

Those are the two unrelated meanings for the word 'negative' I was referring to. This is a linguistic accident and can't really have anything useful to tell us about physics.

A rationalistic attempt to make physics predictions based on some simple syllogisms derived from connotations that happen to exist in some natural language, I think, is not very fruitful.

Apart from a couple of valid counterpoints (to be addressed below), the following four consistent issues in your response(s) to my argument don’t sit particularly well with me.

(1) Declarative statements, contested by known and acclaimed physicists, which appeal to your own anonymous authority as a physicist whilst seemingly expecting uncritical assent from the ‘dilettante’, instead of addressing accurately and exactly the specific counterpoints raised by the dilettante.

In our little echo chamber of MB, there's the psychological risk that a resident theoretical physicist becomes unnecessarily emboldened by other dilettantes like Mendel who are always shopping for any ‘authority’ to agree with his preferred position without putting much independent and impartial thought into the matter at hand, and sincerely searching for the most plausible explanation which may or may not agree with his initial position.

(2) Espousal of a fringe (amongst physicists) instrumentalist (non-realist) philosophy of science which either deliberately or unwittingly conflates mathematical descriptions of reality with the real things being described. Your superbly controversial claim ‘energy is a number’ is a case in point.

(3) The seeming assumption that a verbose technical elaboration of your point adds to the credence of your argument irrespective of the not-too-subtle errors in your underlying reasoning and assumptions which is the stuff I’m addressing.

(4) Constant encroachment into philosophy, common to many theoretical physicists, whilst unaware of doing so and mistaking your unwitting philosophically easily challengeable encroachments for uncontestable physics facts or expertise.

(This response showcases issues 1 and 4 outlined at the start of this post.)

Not if Einstein is right about the energy-mass equivalence. Mass and energy are "different manifestations of the same thing", whatever that thing is. To broadly call that 'thing' energy is not arbitrary, trivial nor unreasonable. However, it does broaden the classical conception of energy whereby energy was viewed to be something essentially different from mass.

Article:

"It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing -- a somewhat unfamiliar conception for the average mind. Furthermore, the equation E is equal to m c-squared, in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned above. This was demonstrated by Cockcroft and Walton in 1932, experimentally." - Albert Einstein

Calling mass and matter "forms of velocity" would be equally reasonable as calling them "forms of energy" only if mass and velocity were demonstrated to be similarly equivalent as mass and energy. Hence, I wrote to you earlier that the key difference is in one predicate (energy) better describing a fundamental property of mass than the other (velocity). If mass-energy equivalence is true, energy qualifies as a total cause of mass (i.e. the cause of the very existence of mass) whilst velocity qualifies as merely a partial cause of mass (i.e. the cause of a particular behaviour, namely motion, of mass). Energy therefore wins as a more fundamental property of mass in accordance with Einstein equation. If I had to choose his authority against yours (disclaimer: a simplistic and blind choice which I'm not actually making), the choice would be obvious.

Energy is a quantity that is conserved (in some circumstances) which usefully constrains the time evolution of physical states, enabling us to make conclusions without needing to solve the full equations of motion. Matter is not congealed energy, electric charge is not congealed energy. Both of those are category error -- energy is a number.

(This response showcases the issue 2 outlined at the start of this post.)

A category mistake. Energy is a quantitatively measurable property in the universe, not just a mere arithmetic value or mathematical unit (number) used to measure that property.

Due to mass–energy equivalence, any object that has mass when stationary (called rest mass) also has an equivalent amount of energy whose form is called rest energy, and any additional energy (of any form) acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy.

When you see stuff out there, stuff with mass, electric fields and what not you add an entry to the balance sheet of the universe. To real objects there corresponds an amount of energy. But it makes little sense to declare objects to "be" energy, regardless of the poetic language Einstein may have used. Feynman's lectures Vol. I, Chapter 4 (freely available online) contain a useful discussion.

I'm sure. If you go through the usual Noether's theorem argument in general relativity and jump through some hoops you get a conservation equation, but the conserved charge is identically zero.

To compute a divergence, we need to compare quantities (here vectors) on opposite faces. Using parallel transport for this leads to the covariant divergence. This is well-defined, because we're dealing with an infinitesimal hypervolume. But to add up fluxes all over a finite-sized hypervolume (as in the contemplated extension of Gauss's theorem) runs smack into the dependence on transportation path. So the flux integral is not well-defined, and we have no analogue for Gauss's theorem.

One way to get round this is to pick one coordinate system, and transport vectors so their components stay constant. Partial derivatives replace covariant derivatives, and Gauss's theorem is restored. The energy pseudo-tensors take this approach (at least some of them do). If you can mangle Equation 3 (covariant_div(T) = 0) into the form:

coord_div(Theta) = 0

then you can get an "energy conservation law" in integral form.

However, this "conservation law" is toothless. As I mentioned previously, conservation of energy is a constraint; states with energy E must go into states of energy E. If all states have the same energy 0, there are no constraints, which means there's no useful sense in which it can be said that energy is conserved. One can make up all sorts of stories like "the energy becomes gravitational energy" based on how the terms in this equation happen to be arranged, but because (see Baez's explanation above) that story is dependent on the coordinate system -- i.e., on how we choose to describe the system -- it has no legitimate physical meaning. It's just a story.

(It is possible to define quantities that are analogous to a conserved energy in GR in some restricted circumstances but this is the general case).

Those are the two unrelated meanings for the word 'negative' I was referring to. This is a linguistic accident and can't really have anything useful to tell us about physics.

Temperature as a "measure of the amount of random motion" is not the fundamental definition of temperature, just a simpler way of thinking about it that works for most everyday substances like typical gases/liquids/solids. Temperature is defined as the partial derivative of energy with respect to entropy, which means that if you're in a physical situation where energy decreases with increasing entropy (such as if there's an upper bound to energy), temperature can be negative in the absolute Kelvin scale.

(This response showcases the issue 2 outlined at the start of this post.)

Yet even the so-called negative thermodynamic temperature (which can be expressed as a negative quantity on the Kelvin scale) is not ontologically negative in the sense of being less-than-stationary, which was the explicit point I made and you ignored. When you increase energy in a bounded phase space, entropy is obviously decreased after a peak, which measures as subzero on a Kelvin scale, while in actual fact the temperature increases. Nothing amazing or baffling there.

Article:

A system with bounded phase space necessarily has a peak in the entropy as energy is increased. For energies exceeding the value where the peak occurs, the entropy decreases as energy increases, and high-energy states necessarily have negative Boltzmann temperature. . .

The existence of negative temperature, let alone negative temperature representing "hotter" systems than positive temperature, would seem paradoxical in this interpretation. The paradox is resolved by considering the more rigorous definition of thermodynamic temperature as the tradeoff between internal energy and entropy contained in the system, with "coldness", the reciprocal of temperature, being the more fundamental quantity.

"Supported by evidence" and "generates better, more accurate, and more useful predictions" are essentially two ways of saying the same thing in this context. No theory is "uncontested", but it's important to avoid the perception that there's intense debate about whether or not there was an inflationary period in the early universe.

That's not what I said. There is an intense debate about whether inflation (accelerated expansion) continues / has resumed after the initial slow-down following the inflation of the early universe. Plus it seems that even the early inflation is disputed by "a substantial minority" which is a separate discussion entirely and a notion which I don't personally subscribe to.

Article:

The basic inflationary paradigm is accepted by most physicists, as a number of inflation model predictions have been confirmed by observation;[a] however, a substantial minority of scientists dissent from this position.[5][6][7]

Article:

The Inflation Debate

Is the theory at the heart of modern cosmology deeply flawed?

The notion that the current expansion of the universe is accelerating is not data-driven but grand theory-driven, attempting to preserve a faith-based doctrine of the cosmological constant which assumes that the universe is homogeneous and isotropic. Majority practice or not, a grand theory-driven science is generally bad science and more akin to religion.

As Subir Sarkar says, the only direct evidence for dark energy is that it is 'supposed' to be causing a currently accelerating expansion -- the latter being a claim in and of itself for which we do not currently have strong empirical support. If the expansion of the universe is actually accelerating, we can measure it by measuring the velocity of expansion today and ten years from now using the ELT in Chile whereby we can actually monitor the redshift of the object and see it changing in time. This has yet to be observed and may, indeed, successfully demonstrate an accelerating expansion. But we're not quite there yet.

According to Sarkar, the most "direct" evidence claimed for a currently accelerating expansion is based on a measurement of distant supernovae made in the late 1990s. This measurement was interpreted to demonstrate that the distant supernovae are 30 % further away than expected had the universe been slowing down. Sarkar asks, what if the supernovae had just become 30 % less bright? And even if not, according to him, the data of the 1990s study was made public only in 2016 which he had a closer look at with his team. They discovered that the statistical analysis had allowed arbitrarily large uncertainties on each measurement, meaning you can fit any model into the data. Which they did. The evidence is not particularly strong when applying more rigorous statistical methods. The apparent acceleration is not the same in every direction and indeed seems to be the highest in the bulk flow (a cosmic wave of galaxies) in which we and our nearby galaxies are located. This creates an observer error of acceleration and has nothing to do with dark energy. Sarkar concludes:

"It's simply an artifact of our being located in a bulk flow. Dark energy is an artifact of not taking account of this fact that we are not typical observers."

I'd say the debate is still very much ongoing and the counter-arguments propounded are reasonable and plausible, quite irrespective of who's in the minority and who's not. There's no such fact as dark energy, let alone negative mass. Only speculation.

"Some vegan meals are quite tasty."
"Give me an example then, in my experience they all contain tofu and I hate tofu."
"All right, here's an example of a tasty meal without tofu."
"Yeah ...uh, no thanks. This recipe was made by vegans, and in my experience they all use tofu."

"Some vegan meals are quite tasty."
"Give me an example then, in my experience they all contain tofu and I hate tofu."
"All right, here's an example of a tasty meal without tofu."
"Yeah ...uh, no thanks. This recipe was made by vegans, and in my experience they all use tofu."