The Time Symmetry Debate in Quantum Theory

[audioloop]

There is one important difference between incompleteness of Newtonian mechanics (NM) and incompleteness of quantum mechanics (QM).

We know that NM is incomplete because there are EXPERIMENTS which demonstrate so. But there is nothing in the Newtonian THEORY itself suggesting that it should be incomplete on the basis of internal theoretical inconsistencies.

The situation with QM is exactly the opposite. There no is [STRIKE]experiments demonstrating [/STRIKE]incompleteness of QM. But there are serious theoretical arguments suggesting that something important must be missing in the standard version of quantum theory.

Information Paradox.

and:

Is quantum linear superposition an exact principle of nature?
http://arxiv.org/abs/1212.0135

 

[kith]

Jano L., just to make sure I understand your line of reasoning: you don't think QM tells us how classical mechanics emerges because in all derivations, expectation values and probabilities are involved. QM is a theory of the behaviour of individual quantum objects. If it is a fundamental theory, we should be able to recover a theory of individual classical objects from it. Instead, we get a theory of an ensemble of such objects. In other words, we don't get classical mechanics but classical statistical mechanics.

 

[kith]

Is quantum linear superposition an exact principle of nature?
http://arxiv.org/abs/1212.0135

I haven't read the paper but I don't think that a "stochastic nonlinear theory" answers the question of the transition from QM to classical mechanics better than QM itself. Such a theory is a theory about ensembles and QM already explains how the classical world emerges for ensembles (decoherence). Controversy arises only if we try to say something about individual systems.

 

[audioloop]

I haven't read the paper but I don't think that a "stochastic nonlinear theory" answers the question of the transition from QM to classical mechanics better than QM itself. Such a theory is a theory about ensembles and QM already explains how the classical world emerges for ensembles (decoherence). Controversy arises only if we try to say something about individual systems.

Decoherence is not enough to explain classicality.

 

[DevilsAvocado]

Well LastManStanding, I must say you did a pretty decent job, misinterpreting almost everything I said, putting words in my mouth never spoken, in this debate-battle-warzone...

No, they don't. They make very specific claims about specific axiomatic systems—those that describe the properties of the natural numbers. To naively carry this over into axiomatized physics models is to assume, with no justification, that every statement about the natural numbers has an analogous physical statement (i.e. a statement about a physically realizable state in terms of elementary processes). What physical process is a reflection of, e.g., the Goldbach conjecture? Fermat's Last Theorem? If you look at the Gödel statements used in the theorems, the suggestion that they have physical analogues is even sillier. Plus, there's a fundamental difference between choosing axioms for the natural numbers and choosing axioms for physics: the latter have empirical consequences. This wishy-washy pop sci idea that Gödel's incomplete theorems have anything to do with scientific models is just as unfounded (and annoying) as New Agers saying, "Quantum mechanics says anything you can imagine is possible!" Mathematical theorems are precisely worded for a reason: if you start running off with vague assertions based on out-of-context generalizations, you're going to say a lot of very incorrect things.

[my bolding]

I must be missing something... because to me this looks like a wishy-washy contradiction... you seem to be saying that Gödel has nothing to do with real physics, “it’s just silly”. Then you point out that mathematics is indeed needed in physics – not to say a lot of very incorrect things, with vague assertions based on out-of-context generalizations.

I think I agree on that very last statement...

And this is supposed to count against the theory somehow?

Did I really say anywhere that there is anything wrong about quantum mechanics, really??

I think I made it pretty clear:

Quantum mechanics is the most accurate theory we have so far.

That is precisely why we use the mathematical models: they take us where our intuition can't.

And this is precisely why I mentioned Gödel, which you somehow refute as “silly wishy-washy pop sci idea”. Which is pretty interesting as it is...

This, and nearly everything else in this paragraph, is wrong.

Thanks, great news.

There is no mystery as to how the equations of classical mechanics emerge from various limiting cases of quantum mechanics; disagreements about the nature of quantum states has absolutely no bearing on that fact.

This is even greater news. You have solved the measurement problem!? If you could provide a link to the peer reviewed paper, I will see to it that Nobel Committee for Physics gets a copy immediately!

And since you seem to have closed the divine book of QM completeness – could you please describe exactly what entanglement is and how it works? If it’s okay with you, I’ll send the answer to Anton Zeilinger (he doesn’t know either). Phew! Finally a clear answer on the main feature of quantum mechanics:

I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.
— Erwin Schrödinger (1935)

Nothing you've said has anything to do with the 'completeness' of QM, by any standard definition of the word.

Please, I can’t wait – what’s the standard definition of the word [in relation to QM]??

You're apparently confusing 'incomplete' with 'makes me uncomfortable'.

Confused seems to be the word of the day. You’re obviously reading stuff that isn’t there. Above my imagination how the phrase “it’s a weird world out there... and I love it!” could ever be coupled to “makes me uncomfortable”... but I guess you have some ‘complete interpretation’ on the shelf for that too...

The only thing I tried to say was – let’s not pretend QM is the [complete and] ultimate truth and the final chapter of science. I hope you agree this is not how science works, right? This could be the methodology for the Vatican, but not for scientist, right? History has told us that when one question is answered, two new arises at the horizon. And isn’t that freaking great!? What an utterly boring place this would be if “the heavenly completeness” has answered every question there is to ask... could we even bear to live in a “Lego-universe” where everything is “small plastic bricks of completeness”... stacked on one another? And superfluous questions are to be sent to the CEO Jørgen Vig Knudstorp??

Does this mean QM is wrong??

I sure hope everybody understand that’s not what I’m saying. However, this endeavor for ultimate completeness/truth looks more like some sort of religion than science, or maybe something for a New-Age-Brahmaputra-Guru type of guy.

What about “mystery” then?

First, I never used the word – it’s pretty superfluous if you ask me. One could make everything into a “mystery”, and if you are religious even the wind could be a “mysterious” sign of “something greater” (even if science tells us otherwise). Since “something greater” never interested me, mystery goes the same way – it’s pretty great as it is.

Finally: The mandatory question – What if I’m wrong!?

Could be, however with the consolation – I’m in pretty darned good company:

I think I can safely say that nobody understands quantum mechanics.
— Richard Feynman, The Character of Physical Law (1965)


We always have had a great deal of difficulty in understanding the world view that quantum mechanics represents. At least I do, because I'm an old enough man that I haven't got to the point that this stuff is obvious to me. Okay, I still get nervous with it. And therefore, some of the younger students... you know how it always is, every new idea, it takes a generation or two until it becomes obvious that there's no real problem. It has not yet become obvious to me that there's no real problem. I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem.
— Richard Feynman, Simulating physics with computers (1982)


The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you accept Nature as She is — absurd.
— Richard Feynman, QED: The Strange Theory of Light and Matter (1985)


I don’t feel frightened by not knowing things, by being lost in a mysterious universe without having any purpose, which is the way it really is, as far as I can tell, possibly. It doesn’t frighten me.
— Richard Feynman, The Pleasure of Finding Things Out (1999)

 

[Jano L.]

Kith, what you say is quite close to my view. I might add that the probabilistic description of evolution of configuration could in principle be satisfactory, if its implications in the physical space would be close to autonomous behaviour known from the models of classical physics.

For example, if the calculation of the function $\psi$*or some other quantum theoretical procedure lead to well localized probability distribution of electron's position in physical space moving closely to the trajectory described by the Newton-Lorentz equations, one could say that the classical description has been recovered from the quantum theory, the classical position being the centroid of the quantum probability distribution, thus leaving the details of the actual fluctuations negligible.

However, ordinary quantum theory happens in abstract many-dimensional configuration space. The implicated probability distribution in physical space does not seem to lead to such central localized packets naturally, except perhaps for a particle in harmonic potential. Typically, one expects rather that the probability distributions will have more unconnected maxima at distant positions and spread out in time.

Instead, we get a theory of an ensemble of such objects. In other words, we don't get classical mechanics but classical statistical mechanics.

We get a theory giving probability distributions. I do not know whether the classical statistical physics can be derived from the quantum theory, there may be some problems, but the basic point is right: the classical mechanics is not a statistical theory.

 

[kith]

Decoherence is not enough to explain classicality.

For ensembles of systems, it is.

 

[VantagePoint72]

Perhaps the last statement was true:-) Please send us some reference to such computation, it seems interesting. I am curious how the trajectory is actually recovered in such an approach, since in ordinary quantum theory, we do not have position unless we measure it and no autonomous motion governed by the differential equation if we do.

Any reasonably complete textbook on QM will introduce the path integral approach. Then take take a classically sized object and put in a well-localized position and momentum state (which is possible because its large enough and massive enough that the uncertainty principle requires a very small uncertainty relative to the overall size and position). The position and momentum of the object can be described by, e.g., extremely narrow—narrower than any reasonable measurement precision—Gaussians. Then a quick application of the path integral formulation shows that the expectation values of the position and momentum follow those predicted by the classical equations of motion, whatever your potential looks like. Since both the position and momentum wavefunctions are extremely well localized around this expectation value, the experimental predictions of quantum mechanics are identical to those of classical mechanics. To essentially arbitrary precision, you have a particle whose position and momentum evolves according to the equations of classical mechanics. This, in a nutshell, is the correspondence principle.

 

[kith]

For example, if the calculation of the function $\psi$*or some other quantum theoretical procedure lead to well localized probability distribution of electron's position in physical space moving closely to the trajectory described by the Newton-Lorentz equations, one could say that the classical description has been recovered from the quantum theory, the classical position being the centroid of the quantum probability distribution, thus leaving the details of the actual fluctuations negligible.

Thanks for your comment. Do you think such a description is likely within the framework of a more fundamental theory? Personally, I doubt this because I don't think that a more fundamental theory will be able to explain entanglement in more classical terms than QM.

 

[Jano L.]

Then take a classically sized object ...

Does a dust grain with mass $10^{-15}$ kg qualify ? How do you describe it - as one havy particle, or as a collection of many particles? Such are very hard to analyze.

To essentially arbitrary precision, you have a particle whose position and momentum evolves according to the equations of classical mechanics.

For how long? Does not the probability distribution spread out eventually?

What about the electron beams? Does the path integral lead to the Newton-Lorentz equations for a persistently peaked probability distribution ?

 

[VantagePoint72]

I must be missing something... because to me this looks like a wishy-washy contradiction... you seem to be saying that Gödel has nothing to do with real physics, “it’s just silly”. Then you point out that mathematics is indeed needed in physics – not to say a lot of very incorrect things, with vague assertions based on out-of-context generalizations.

The entire point of that part of the comment was explaining why, just because mathematics is used in physics, there's no reason to expect the completeness of mathematics has any bearing on the completeness of a physical theory. Physics is not the study of the natural numbers. The fact that certain statements about the natural numbers are undecidable in number theory has no bearing on whether there are undecidable statements in physics. Obviously a combined "physical theory and mathematical formalism" would trivially be incomplete because number theoretic statements would exist within its language and some of them would be undecidable. That has no bearing on whether the physical statements in its language would be undecidable.

Did I really say anywhere that there is anything wrong about quantum mechanics, really??

Yes, a great deal, particularly with respect to the classical limit of QM.

This is even greater news. You have solved the measurement problem!? If you could provide a link to the peer reviewed paper, I will see to it that Nobel Committee for Physics gets a copy immediately!

The measurement problem as zero to do with whether QM reproduces the empirical claims of classical mechanics in the latter's domain of validity. Nothing. Zip. It is a largely philosophical problem that is irrelevant for the experimental predictions of QM's formalism. As a purely side note, I happen to find the Everettian interpretation of QM compelling, according to which there is no measurement problem, but that is not relevant to this discussion. Quantum formalism is agnostic about the ontological status of measurement and the wavefunction—going as far as allowing a purely instrumentalist view for those who prefer to avoid philosophy altogether—and the fact that its predictions for what we consider classical systems are indistinguishable from those of classical systems is just a mathematical fact.

And since you seem to have closed the divine book of QM completeness – could you please describe exactly what entanglement is and how it works? If it’s okay with you, I’ll send the answer to Anton Zeilinger (he doesn’t know either). Phew! Finally a clear answer on the main feature of quantum mechanics:

You are, as I said in my first post, confused about the difference between intuition and formalism. The fact that we lack intuition for these has no bearing on the strength of the theory. It's entirely possible that as we go along we will come to understand quantum theory better. That isn't quantum theory changing and becoming 'closer to complete'; that's us changing. Of course, I'm not suggesting the theory itself is immune to corrections. Any theory in physics may be altered if necessary. I'm saying that our lack of intuition for concepts like entanglement is not a reason why it needs to.

The only thing I tried to say was – let’s not pretend QM is the [complete and] ultimate truth and the final chapter of science. I hope you agree this is not how science works, right?

I certainly do. I just disagree that any of your reasons for this are any good. Rather, I think all of them suggest that, to varying degrees, you don't understand how quantum mechanics as it is currently formulated works. Quantum theory may altered if necessary on the basis of experiment; it doesn't need to be altered on the basis of your incorrect claims about its alleged problems with the classical limit. There are no such problems.

Finally: The mandatory question – What if I’m wrong!?

Nothing happens. I'm not sure exactly what you're expecting. I don't believe your issues with quantum mechanics are some kind of life or death issue. You're welcome to continue believing wrong things about QM if you like.

Could be, however with the consolation – I’m in pretty darned good company:

In all your quotations—particularly the second and the third—Feynman is discussing the exact point I'm making: that our inability to intuit quantum mechanics (necessitating a reliance on the formalism) is not a problem for the theory. It just means we don't—and possibly can't—understand what it means. However, the theory doesn't care whether or not a bunch of hairless apes who evolved in a classical world understand it. For one thing, I don't see how the third quote doesn't strike you as contradictory to your view that quantum mechanics can't account for the classical behaviour of every day physics. That would constitute an experimental contradiction.

The validity of a physical theory is determined solely by its ability to make good experimental predictions. The extent to which we can make sense of its formalism with our very limited intuition says nothing about how 'complete' it is. "No one understands quantum mechanics," isn't a comment on quantum mechanics; it's a comment on physicists.

 

[VantagePoint72]

Does a dust grain with mass $10^{-15}$ kg qualify ? How do you describe it - as one havy particle, or as a collection of many particles? Such are very hard to analyze.

Whatever is big enough to display classical behaviour experimentally qualifies. This is what I meant about putting the cart before the horse. You may treat it either in aggregate or as a complex system; and, yes, the latter is extremely difficult. Treating a bouncing ball quantumly was given as an example by someone else earlier. That is why we just make the observation the correspondence principle (e.g. Ehrenfest's theorem, etc.) guarantees the process will always work and skip right to the classical equations as an approximation. When you prove a theorem, you don't need to check cases any more.

For how long? Does not the probability distribution spread out eventually?

According to a quick back-of-the-envelope calculation on an easy studied classical system, a standard baseball thrown in a ball game would have to be in motion for over a million years before the uncertainty in its position became comparable to its size due to quantum effects. I think we'll be safe in using classical mechanics to describe its trajectory without doing quantum theory an injustice.

What about the electron beams? Does the path integral lead to the Newton-Lorentz equations for a persistently peaked probability distribution ?

Again, an electron beam is a quantum object. It is capable of interference. Why do you continue to insist that quantum mechanics should predict classical behaviour for things that don't behave classically?

 

[Jano L.]

It just means we don't—and possibly can't—understand what it means. However, the theory doesn't care whether or not a bunch of hairless apes who evolved in a classical world understand it.

The theory cannot care, because it is a theory, i.e. artificial construction.

The validity of a physical theory is determined solely by its ability to make good experimental predictions.

This was debunked already by Kepler and Newton in their theories of planetary motion. Did you know how good predictions were made by the epicycle theory? The epicycles were very accurate in describing apparent motions on the sky. But perhaps the epicycles were ugly because there was a lot of them - dozens, and people may have had scratched their heads, "are these additional epicycles necessary? what the hell do they mean ? What is really going on in the heavens? Isn't there something simpler, better ?" And then the Newton's physics brought light.

"No one understands quantum mechanics," isn't a comment on quantum mechanics; it's a comment on physicists.

If it was few physicists, it would be comment on physicists. But Feynman said no one. If the theory cannot be understood by anybody, isn't it worthy of critical reconsideration ? After all, it is only a creation of humans, and such are superable. Wouldn't it be better to have a theory that is more acceptable to people? Wouldn't it make them more happy and achieve more?

 

[VantagePoint72]

The theory cannot care, because it is a theory, i.e. artificial construction.

As we've reached the point where you treating as literal what any reasonable person would immediately see is a figure of speech, it's clear I'm at an impasse with you and there's no sense in continuing. I've answered every single objection you've put forward, in most cases repeatedly.

(PS: when I said things like "according to quantum mechanics" earlier, I wasn't implying quantum mechanics was a living entity capable of articulating opinions. Just want to be clear, since apparently metaphorical language is difficult for you.)

 

[Jano L.]

The example with the baseball is not very convincing, because the Schroedinger equation does not describe balls as heavy particles. It describes them as a collection of many light particles.

That is why we just make the observation the correspondence principle (e.g. Ehrenfest's theorem, etc.) guarantees the process will always work and skip right to the classical equations as an approximation. When you prove a theorem, you don't need to check cases any more.

This sounds like a belief to me. What do you mean by "correspondence principle" ? That the classical mechanics is a limiting case of quantum mechanics? Is that an assumption, or a derived fact?

If it does not work for one light particle, why do you expect it will for system composed of many such particles?

Why do you continue to insist that quantum mechanics should predict classical behaviour for things that don't behave classically?

Let me repeat myself:

The trajectories computed from the Lorentz-Newton differential equations for electrons are often within the domain of their validity, since they are used successfully to construct such devices as cyclotrons, CRT displays, electron microscopes and mass spectrometers.

Do you agree these are within the domain of the mentioned equations ?

 

[Jano L.]

LastOneStanding, I think you are being too feisty. I am not trying to prove you wrong by showing your statements are wrong when taken literally. They are wrong semantically. You suggested that it does not matter that nobody understands a theory, that the theory can be nevertheless right, independently of humans.

Now, I do not believe that can be supported. When I said that theory cannot care, it was said figuratively as well; I meant that only humans can decide whether the theory is sound or not. If nobody can understand it, it is most probably wrong somewhere.

I would be interested in what you think of the examples I repeated in my last post. Do you recognize them?

 

[DennisN]

In my opinion, it's experiments which ultimately decides whether a theory needs to be corrected or replaced. Our understanding has nothing to do with this. Nature decides. We observe. And we try to understand what nature is telling us. If/when there will come an experiment that disagrees with QM, it will become famous, no doubt about it.

 

[DevilsAvocado]

The entire point of that part of the comment was explaining why, just because mathematics is used in physics, there's no reason to expect the completeness of mathematics has any bearing on the completeness of a physical theory. Physics is not the study of the natural numbers. The fact that certain statements about the natural numbers are undecidable in number theory has no bearing on whether there are undecidable statements in physics. Obviously a combined "physical theory and mathematical formalism" would trivially be incomplete because number theoretic statements would exist within its language and some of them would be undecidable. That has no bearing on whether the physical statements in its language would be undecidable.

Undecidable? You are confused about Gödel's incompleteness theorems, which are about the inherent limitations of all axiomatic systems capable of doing arithmetic – the consistency of arithmetic is provably impossible.

Yes, a great deal, particularly with respect to the classical limit of QM.

You seem to have some hiccup about the classical limit. I think I wrote one line about your beloved classical limit.

The measurement problem as zero to do with whether QM reproduces the empirical claims of classical mechanics in the latter's domain of validity. Nothing. Zip. It is a largely philosophical problem that is irrelevant for the experimental predictions of QM's formalism.

More classical hiccup... but let me ask you this: The Schrödinger wavefunction is deterministic, right? Why can we not predict precise results for QM measurements, if the measuring apparatus itself is described by the deterministic wavefunction? Do you really think that’s a totally irrelevant philosophical problem?? Wow...

As a purely side note, I happen to find the Everettian interpretation of QM compelling,

Now we’re talking totally irrelevant philosophical problems, and I don't see how this doesn't strike you as contradictory to your distaste for mystery cults?

according to which there is no measurement problem,

Gosh, why am I not surprised...?

You are, as I said in my first post, confused about the difference between intuition and formalism. The fact that we lack intuition for these has no bearing on the strength of the theory. [...] Of course, I'm not suggesting the theory itself is immune to corrections. Any theory in physics may be altered if necessary. I'm saying that our lack of intuition for concepts like entanglement is not a reason why it needs to.

So you are saying that a complete mathematical description of entanglement is right now available in QM theory, i.e. a complete description that will undoubtedly tell us if the world is non-local or/and non-real? And if it’s non-local, there’s a mathematical description that exactly explains instantaneous casual effects across the entire universe. It’s just because the lack of human intuition that we haven’t seen this mathematical description yet?

Did I get that right?

It's entirely possible that as we go along we will come to understand quantum theory better. That isn't quantum theory changing and becoming 'closer to complete'; that's us changing.

Wow, that’s really interesting. Schrödinger and those guys had no idea what they were doing, right? They created a kind of “QM Monster” that lives its own life, right? And if we are lucky the “QM Monster” will take us to the “QM Cave” and show us things that we never knew existed, right?

Please tell me it’s a joke? Humans create scientific theories, period. The opposite rarely happens, and if it does – it’s only in mystery cults and the wishy-washy New-Age-Brahmaputra domain.

it doesn't need to be altered on the basis of your incorrect claims about its alleged problems with the classical limit. There are no such problems.

Seriously, I get the very strong feeling that you are talking about the “problems with the classical limit” 10 times more than I do?? And all other issues are dismissed as “philosophical problems”? I do think we have problem here, but I’m not sure it’s classical...

In all your quotations—particularly the second and the third—Feynman is discussing the exact point I'm making: that our inability to intuit quantum mechanics (necessitating a reliance on the formalism) is not a problem for the theory. It just means we don't—and possibly can't—understand what it means. However, the theory doesn't care whether or not a bunch of hairless apes who evolved in a classical world understand it.

Here we go again – the “QM Monster” has now turned into a superior philosopher...

For one thing, I don't see how the third quote doesn't strike you as contradictory to your view that quantum mechanics can't account for the classical behaviour of every day physics.

Gee, I’m about to sign out... more classical hiccup... seriously, this is what I wrote about your BIG fixation:

Where exact is the border between microscopic QM fields/particles and classical macroscopic objects (if any)? Could two elephants be entangled? No one knows for sure...

I do hope you noticed --> (if any) <-- ??

But okay, I’ll give you something to chew on:

Could two elephants be entangled? If not, why? If yes, where can I go to see them?

And maybe you could also elaborate on what happens to classical (elephant) gravity at the quantum level?

This will probably keep you occupied for a couple of hours...

 

[TrickyDicky]

Even though I was trying to avoid this kind of polarized debate I understand the OP theme was probably ripe for it.
LastOneStanding, IMO the way you present your point emerges as somewhat caricature like or exaggerated. Such maximalist positions are usually wrong in science.

 

[DevilsAvocado]

TrickyDicky, agree 100%.

And I’m sorry if the ‘preposterous’ debate between me and LastOne almost hijacked this thread... promise to be a brief and good guy... ;)

 

[lugita15]

Undecidable? You are confused about Gödel's incompleteness theorems, which are about the inherent limitations of all axiomatic systems capable of doing arithmetic

Yes, but it's about the inherent *arithmetical* limitations of axiomatic systems capable of doing Peano arithmetic. First of all, it's not clear why a physical theory would need to be capable of doing Peano arithmetic. And even if there were such a theory, Godel's theorem would not prevent you from using the theory to predict the position and momentum of all the particles in the universe, for all time. So Godel's theorem doesn't really place physical limitations on a physical theory.

the consistency of arithmetic is provably impossible.

Sorry, did you mean that the consistency of arithmetic is provably impossible to prove?

 

[audioloop]

In my opinion,
it's experiments which ultimately decides whether a theory needs to be corrected or replaced. Our understanding has nothing to do with this.
Nature decides.
We observe. And we try to understand what nature is telling us. If/when there will come an experiment that disagrees with QM, it will become famous, no doubt about it.

welll said.

Observation of a kilogram-scale oscillator near
its quantum ground state.
New Journal of Physics 11 (7): 073032
Abbott, B. et al.
http://eprints.gla.ac.uk/32707/1/ID32707.pdf

Quantum Upsizing
Aspelmeyer, Schwab, Zeilinger.
http://fqxi.org/data/articles/Schwab_Asp_Zeil.pdf


.

 

[DevilsAvocado]

Godel's theorem would not prevent you from using the theory to predict the position and momentum of all the particles in the universe, for all time. So Godel's theorem doesn't really place physical limitations on a physical theory.

Of course not, Gödel doesn’t prevent you from calculating anything; I could count the number of sheep in the universe and that would be perfectly doable. But the reason I mentioned Gödel was in relation to the completeness of QM (but now I regret it), and AFAIK the foundation of physics rest on mathematics.

Any formal system that is strong enough to formulate its own absence of axiomatic contradiction can prove its own consistency if – and only if – it is inconsistent. Since theorems are derived from a set of axioms, to be embodied in some general principle that makes it part of a larger theory – it looks like Gödel has something to say about this enchilada... when it comes to completeness.

But what do I know...

Maybe Professor Mark Colyvan can explain it better:

KURT GÖDEL AND THE LIMITS OF MATHEMATICS - Professor Mark Colyvan
https://www.youtube.com/watch?v=92Gdhr7dd_I

Sorry, did you mean that the consistency of arithmetic is provably impossible to prove?

I think so; it is not possible to find a totally adequate set of axioms for arithmetic:
http://math.mind-crafts.com/godels_incompleteness_theorems.php


... I feel guilty, this is not what OP asked about and this will be my last comment on this ...

 

[TrickyDicky]

... I feel guilty, this is not what OP asked about and this will be my last comment on this ...

Hey, no problem, I actually agree with your take on Godel and find your comments pertinent.

 

[audioloop]

Steve Giddings
http://www.edge.org/response-detail/23857

"These principles clash when pushed to the extreme—the sharpest version of the problem arises when we collide two particles at sufficient energy to form a black hole. Here, we encounter the famed black hole information problem: if the incoming particles start in a pure quantum state, Hawking's calculation predicts that the black hole evaporates into a mixed, thermal-like final state, with a massive loss of quantum information. This would violate—and thus doom—quantum mechanics."

 

[DevilsAvocado]

Hey, no problem, I actually agree with your take on Godel and find your comments pertinent.

Thanks! Well, fasten your seatbelt, here we go!

Sir Roger Penrose held a talk at GoogleTechTalks about conscious understanding, where he discussed Gödel’s theorem, quantum mechanics and the human brain. Very interesting!

It’s quite long so I fixed direct links to different parts. Notice that Penrose claim QM “is wrong in some sense”, but I think he really mean “not the whole story”... his view is that there has to be a radical new way of looking at quantum mechanics which will make almost no difference (hence QM is correct but not complete) in the same way general relativity makes almost no difference to Newtonian physics but it’s a completely different framework, and this is what Penrose suspects will happen also to QM.

Who knows...

Conscious Understanding: What is its Physical Basis?
https://www.youtube.com/watch?v=f477FnTe1M0

• @19:09 – Gödel’s theorem
• @39:40 – Something non-computational in mathematical understanding & physical laws
• @43:10 – A non-computable toy model universe
• @48:49 – Computable classical physics & (non-)computable quantum mechanics
• @55:31 – The measurement problem; a sign quantum mechanics is not right at all levels
• @57:34 – Non-computable quantum processes in the human brain (microtubules)
• @1:10:00 – Q&A
• @1:15:25 – Quantum mechanics is incomplete

Regarding Gödel, @1:53:53 Penrose get a question on discrete computation and continues computation and the human spectrum between true/false, and then mention his colleague Professor Tim Palmer who works with stochastic physics and climate modeling and furthermore has put forward a quite interesting hypothesis, the Invariant Set Postulate: A New Geometric Framework for the Foundations of Quantum Theory and the Role Played by Gravity (which of course is not a rigorous physical theory at this stage but still very interesting), which seems to satisfy both Bohr and Einstein, and the key feature of this idea is that it is not a new interpretation – like a ‘QM overcoat’ – but a new ‘backbone’ that QM could rest on; the hypothesis suggests the existence of a state space, within which a smaller (fractal) subset of state space is embedded. There’s an introduction on Phys.org and the paper is published on Proceedings of the Royal Society A and arXiv.org.

Click to watch the zoom sequence

Tim Palmer: "The invariant set hypothesis"
https://www.youtube.com/watch?v=Ciduvyv7ToE

 

[bhobba]

Notice that Penrose claim QM “is wrong in some sense”, but I think he really mean “not the whole story”... his view is that there has to be a radical new way of looking at quantum mechanics which will make almost no difference (hence QM is correct but not complete) in the same way general relativity makes almost no difference to Newtonian physics but it’s a completely different framework, and this is what Penrose suspects will happen also to QM. Who knows...

First thanks for posting that - very enjoyable.

Its the same view Einstein had (it's wrong to think Einstein disagreed with QM - he thought it merely incomplete - not incorrect - many people seem to forget that - possibly because his views changed a bit from, his early struggles with Bohr, to the publishing of the EPR paradox) and I think Weinberg holds to it as well.

There is no doubt Rogers views are very interesting and thought provoking - I have read many of his books such as the Emperors New Mind. I even held to his view about the literal existence of the Platonic realm for a while to explain issues in Wigner's famous essay:
http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

But was ultimately swayed by Murray Gell-Manns View:
http://www.ted.com/talks/murray_gell_mann_on_beauty_and_truth_in_physics.html

My personal view for what its worth is QM is complete and its simply one of two possible probabilistic theories that follow from some very reasonable assumptions:
http://arxiv.org/pdf/0911.0695v1.pdf

It would seem that there are only two reasonable alternatives - standard probability theory and QM. The difference is entanglement or having continuous transformations between the outcomes of observations (the so called pure states). You can't do either with standard probability theory.

Still - who knows what the future will bring.

Thanks
Bill

 

[DevilsAvocado]

First thanks for posting that - very enjoyable.

You are welcome, glad you liked it!

Its the same view Einstein had (it's wrong to think Einstein disagreed with QM - he thought it merely incomplete - not incorrect - many people seem to forget that - possibly because his views changed a bit from, his early struggles with Bohr, to the publishing of the EPR paradox) and I think Weinberg holds to it as well.

Agreed, there seems to be some confusion regarding Einstein’s later ideas.

There is no doubt Rogers views are very interesting and thought provoking - I have read many of his books such as the Emperors New Mind. I even held to his view about the literal existence of the Platonic realm for a while to explain issues in Wigner's famous essay:
http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

But was ultimately swayed by Murray Gell-Manns View:
http://www.ted.com/talks/murray_gell_mann_on_beauty_and_truth_in_physics.html

Thank you for the links, Murray Gell-Mann is just splendid! And of course he is right – you have to be blind not to see the “mysterious” link between nature and mathematics. The questions is: Is mathematics a fundamental part of nature (at the deepest level), or are we just incredible lucky to have invented this marvelous “nature-compatible-tool”?

I have absolutely no idea... but if mathematics is a fundamental part of nature and Gödel is right – then nature must be inconsistent!

And maybe she is...

My very personal thoughts on this, goes something like this: The human brain obeys the laws of nature. Humans are undoubtedly inconsistent. Something in the laws of nature must allow human thinking to be inconsistent, even if the laws themselves are perfectly consistent. When humans think about nature they utilize the laws of nature, and that fact will strongly influence what ideas humans could have about the laws of nature. Humans are not prefect but very creative. When humans invented the tool of mathematics (which at a later stage helped us understand physics) it was a mix of inconsistency, creativity and the laws of nature – but it was not perfect/complete!

And this explains some of the ‘situation’ today... maybe... perhaps... what do I know...

Agreed, Penrose is ‘provocative’, but brilliant as he is, linking his ideas to people like Anirban Bandyopadhyay (microtubules) could turn out to be a mistake. I’m only a layman, but flashy videos and no papers don’t really convince me Bandyopadhyay has found something exceptionally extraordinary...

It would seem that there are only two reasonable alternatives - standard probability theory and QM. The difference is entanglement or having continuous transformations between the outcomes of observations (the so called pure states). You can't do either with standard probability theory.

Sounds reasonable, the thing that has interested me is the words of Bell:

For me then this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and fundamental relativity. That is to say, we have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory...

I.e. we have two great contemporary theories, that are empirically tested – and they don’t match!?

So, what’s going on here...?

If you (and maybe TrickyDicky) are interested in the background to Gödel’s theorems, here’s the full lecture by Professor Mark Colyvan:

Key thinkers: Kurt Gödel and the Limits of Mathematics. Mark Colyvan (p1)
https://www.youtube.com/watch?v=bYpSVSGBxis


Key Thinkers: Kurt Gödel and the Limits of Mathematics. Mark Colyvan (p2)
https://www.youtube.com/watch?v=CCac2oP4XB8



P.S: Isn’t this just amazing... David Hilbert who wanted mathematics to be formulated on a solid and complete logical foundation – the same man who introduced the concept of a Hilbert space, an indispensable tool in quantum mechanics – was crushed by Kurt Gödel, whom later become a very close friend of Einstein... what a thriller! ;)

 

[bhobba]

Regarding the incompatibility between relativity and GR:

we have two great contemporary theories, that are empirically tested – and they don’t match!? So, what’s going on here...?

Yea - I suspect Bell wasn't aware of the latest developments in the area, in particular that EFT shows QM and Relativity are not incompatible:
http://arxiv.org/abs/1209.3511

Thanks
Bill

 

[DevilsAvocado]

Yea - I suspect Bell wasn't aware of the latest developments in the area, in particular that EFT shows QM and Relativity are not incompatible:

Thanks, very interesting, but it’s not the final answer is it?

http://arxiv.org/abs/1209.3511]The[/PLAIN] effective field theory has limits to its validity, most notably it is limited to scales below the Planck energy, and does not resolve all of the issues of quantum gravity. However, effective field theory has shown that general relativity and quantum mechanics do in fact go together fine at ordinary scales where both are valid. GR behaves like an ordinary field theory over those scales. This is important progress. We still have work to do in order to understand gravity and the other interactions at extreme scales.

I think that Bell’s primary concern was not gravity but that his theorem established an essential conflict between the well-tested empirical predictions of quantum theory and Relativistic Local Causality (i.e. SR).

Okay, you can ‘escape’ this problem by accepting either the Many Worlds Interpretation or Superdeterminism (=absence of free will), but neither feels like a tasty final answer...