The Time Symmetry Debate in Quantum Theory

[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...

 

[T0mr]

This last property is not a problem, because everybody knows that classical statistical physics is not some basic theory from which we would like to derive deterministic models. Everybody knows it is the other way around: the classical statistical physics is built upon already available deterministic classical mechanics and probability theory.

Thank you Jano for your views, I feel you are right on with your observations. Good observation about the use of classical equations of motion for alpha particles in Rutherford experiment too.

My main problem with the QM is that it claims these probabilities are fundamental. Take the hydrogen atom in ground state. The probability distribution gives a spherically symmetric pattern where probabilities are concentrated around the Bohr radius. But at the Bohr radius there is a spherical shell were the probability of finding an electron at any position on the shell is completely random. You have the same chance of finding the electron anywhere on that spherical shell. The same goes for any spherical shell at radius greater or less than the Bohr radius.

In my mind two interpretations of the electron can be given at this point:

1.) If you interpret the electron position to be described only by probabilities at any instant, then it must be the case that to maintain equal probabilities over individual shells over some period of time, the electron position must be discontinuous in space.

2.) If instead you interpret the electron path to be continuous then the particle must not be more fundamentally described by a probability distribution which could only acts as a statistical analysis. Since we have assumed the particle has a set path whether we can observe that path or not.

Both 1 and 2 assume that one particle is always one particle and that the particle must exist somewhere in space at all times. With these assumptions we can observe that the particle must either follow a continuous path or be discontinuous in space.

Option 1 has obvious problems such as the infinite velocity required for the electron to make discontinuous jumps through space. So QM could not logically say that what these probability distributions really represent are particle positions in time. Then what do the probability distributions represent? We are only left with option 2 in which the paths of particles are always continuous through space and so cannot have been actually represented by spatial probability distributions. In the case of an orbiting electron at the Bohr radius, the electron must move from one point in space to adjacent points and can never move to points not adjacent to its current position. So, a probability distribution tells us nothing about the particles actual path and yet we must assume that continuous path through space exists. Therefore the probability distribution for a particle can only represent the state of our knowledge about where the particle can be not being aware of its path which is exactly how a statistical approach works.

Then the question becomes what is deciding the path the electron is taking. It cannot be the probability distribution because by 1 that will necessarily cause the path to be discontinuous. So we are forced to conclude, at least I am, that we are missing something that would explain the continuous path a particle must have.

So what is the only thing that we have that can represent a continuous path through space? This leaves me to think there must be deterministic functions governing the path of particles. Otherwise we must violate one or more of the above assumptions: that one particle is always one particle, the particle must always exist in space, and the particle cannot move instantaneously through space.

By assuming QM is the final theory we are forced to propose things like by the measurement of a particle the particle becomes real and/or the wave function collapses or multiple universes must exist etc. and so on and on. The existence of such propositions as legitimate theories is a big hint that something is fundamentally wrong with QM.

 

[DrChinese]

...

By assuming QM is the final theory we are forced to propose things like by the measurement of a particle the particle becomes real and/or the wave function collapses or multiple universes must exist etc. and so on and on. The existence of such propositions as legitimate theories is a big hint that something is fundamentally wrong with QM.

But that is precisely the point as far as I am concerned. There is nothing wrong with the theory other than you don't care for the philosophical implications. The kind of quantum (non-continuous) leaps you refer to do appear to occur. Such quantum non-locality is evidenced in many ways, and there are hundreds of papers documenting such.

http://arxiv.org/find/all/1/ti:+EXACT+non_locality/0/1/0/all/0/1?per_page=100
http://arxiv.org/find/all/1/AND+abs:+EXACT+non_locality+abs:+experiment/0/1/0/all/0/1?per_page=100

So I see it as hinting at the correctness of QM, not that QM is wrong! In fact, I would say that anyone wanting a strictly local (and presumably realistic) version of QM is the one missing hints . Except that experimental evidence is much stronger than a hint. There are no experimental misses at this point on the predictions of QM.

 

[Jano L.]

1.) If you interpret the electron position to be described only by probabilities at any instant, then it must be the case that to maintain equal probabilities over individual shells over some period of time, the electron position must be discontinuous in space.

I am not sure what you mean by " the electron position must be discontinuous in space." The electron jumping instantaneously from one point to another? If so, I do not see how it follows from the probabilistic description. In the theory of the Brownian motion, the particle can have similar probability distribution, but its motion is continuous.

 

[T0mr]

There is nothing wrong with the theory other than you don't care for the philosophical implications. The kind of quantum (non-continuous) leaps you refer to do appear to occur. Such quantum non-locality is evidenced in many ways, and there are hundreds of papers documenting such.

I never said that entanglement does not violate locality. It certainly appears to be the case. The question is now why can't a deterministic theory be used to explain the instantaneous determination in entangled particle properties. It is not really necessary that we limit our set of laws to describe the interactions between billiard balls. That is a very simplistic view. Why can't the instantaneous determination of spin of entangled particles be based in deterministic law?

I am not sure what you mean by " the electron position must be discontinuous in space." The electron jumping instantaneously from one point to another? If so, I do not see how it follows from the probabilistic description. In the theory of the Brownian motion, the particle can have similar probability distribution, but its motion is continuous.

I was thinking about the probability distribution as a whole but if you only consider adjacent points in space as possibilities around the electron then you could come up with something similar to Brownian motion. I guess that should have been option 3. Is that how these paths are interpreted to behave or should we determine points based on the entire distribution at any point in time regardless of where the particle might be located?

Now that you say that. I think I have to fall back from the original argument to another position. How can probability determine positions at all? What is it to be governed by probability and how can concrete positions or continuous paths be determined completely by probability? For the case similar to Brownian motion, what is picking the next position in the chain of positions if all we are given is probability. You need some kind of selection process to determine points and if everything that interacts with a particle is governed by probability how is it possible to construct a path? Or what is picking the next point in the path of an electron whose position is described by a probability distribution. Essentially what I am saying is that probabilities cannot pick points only deterministic functions can.

 

[bhobba]

I never said that entanglement does not violate locality. It certainly appears to be the case. The question is now why can't a deterministic theory be used to explain the instantaneous determination in entangled particle properties.

Well it can eg Bohmian Mechanics. But as far as the formalism of QM goes it is unnatural being contextual ie the outcome depends on what else you are measuring at the same time. Why exactly do you want to make assumptions that are a bit kludgey? That's got nothing to do if BM is correct or not (that is a matter for experiment and until experiment can decide there is no way to tell what nature chose), the issue though is why is determinism more appealing than contextuality?

Determinism is simply a special case of probabilistic theories - the only allowed probabilities are zero and one. Some fairly basic considerations indicate there are really only two basic ways to model physical systems - standard probability theory and QM:
http://arxiv.org/pdf/0911.0695v1.pdf

And QM is the only one that allows entanglement.

Thanks
Bill

 

[bhobba]

I am not sure what you mean by " the electron position must be discontinuous in space." The electron jumping instantaneously from one point to another?

Indeed. Exactly what electrons are doing when not being observed is a matter of interpretation - many interpretations say it has no property unless observed so thinking it jumps from one point to another, instantaneously or otherwise, is rather meaningless.

Thanks
Bill

 

[TrickyDicky]

My main problem with the QM is that it claims these probabilities are fundamental. Take the hydrogen atom in ground state. The probability distribution gives a spherically symmetric pattern where probabilities are concentrated around the Bohr radius. But at the Bohr radius there is a spherical shell were the probability of finding an electron at any position on the shell is completely random. You have the same chance of finding the electron anywhere on that spherical shell. The same goes for any spherical shell at radius greater or less than the Bohr radius.

In my mind two interpretations of the electron can be given at this point:

1.) If you interpret the electron position to be described only by probabilities at any instant, then it must be the case that to maintain equal probabilities over individual shells over some period of time, the electron position must be discontinuous in space.

2.) If instead you interpret the electron path to be continuous then the particle must not be more fundamentally described by a probability distribution which could only acts as a statistical analysis. Since we have assumed the particle has a set path whether we can observe that path or not.

Both 1 and 2 assume that one particle is always one particle and that the particle must exist somewhere in space at all times. With these assumptions we can observe that the particle must either follow a continuous path or be discontinuous in space.

Option 1 has obvious problems such as the infinite velocity required for the electron to make discontinuous jumps through space. So QM could not logically say that what these probability distributions really represent are particle positions in time. Then what do the probability distributions represent? We are only left with option 2 in which the paths of particles are always continuous through space and so cannot have been actually represented by spatial probability distributions. In the case of an orbiting electron at the Bohr radius, the electron must move from one point in space to adjacent points and can never move to points not adjacent to its current position. So, a probability distribution tells us nothing about the particles actual path and yet we must assume that continuous path through space exists. Therefore the probability distribution for a particle can only represent the state of our knowledge about where the particle can be not being aware of its path which is exactly how a statistical approach works.

Then the question becomes what is deciding the path the electron is taking. It cannot be the probability distribution because by 1 that will necessarily cause the path to be discontinuous. So we are forced to conclude, at least I am, that we are missing something that would explain the continuous path a particle must have.

So what is the only thing that we have that can represent a continuous path through space? This leaves me to think there must be deterministic functions governing the path of particles. Otherwise we must violate one or more of the above assumptions: that one particle is always one particle, the particle must always exist in space, and the particle cannot move instantaneously through space.

By assuming QM is the final theory we are forced to propose things like by the measurement of a particle the particle becomes real and/or the wave function collapses or multiple universes must exist etc. and so on and on. The existence of such propositions as legitimate theories is a big hint that something is fundamentally wrong with QM.

I never said that entanglement does not violate locality. It certainly appears to be the case. The question is now why can't a deterministic theory be used to explain the instantaneous determination in entangled particle properties. It is not really necessary that we limit our set of laws to describe the interactions between billiard balls. That is a very simplistic view. Why can't the instantaneous determination of spin of entangled particles be based in deterministic law?



I was thinking about the probability distribution as a whole but if you only consider adjacent points in space as possibilities around the electron then you could come up with something similar to Brownian motion. I guess that should have been option 3. Is that how these paths are interpreted to behave or should we determine points based on the entire distribution at any point in time regardless of where the particle might be located?

Now that you say that. I think I have to fall back from the original argument to another position. How can probability determine positions at all? What is it to be governed by probability and how can concrete positions or continuous paths be determined completely by probability? For the case similar to Brownian motion, what is picking the next position in the chain of positions if all we are given is probability. You need some kind of selection process to determine points and if everything that interacts with a particle is governed by probability how is it possible to construct a path? Or what is picking the next point in the path of an electron whose position is described by a probability distribution. Essentially what I am saying is that probabilities cannot pick points only deterministic functions can.

As I have insisted in previous posts but apparently nobody noticed this argument (maybe it deserves a thread of its own but I think it is quite related to QM incompleteness issues), it seems to me like the measurement problem and the probabilistic uncertainties associated to QM (and I'm concentrating here on NRQM since everybody seems to be referring to it anyway) all rest on holding on to the particle picture as fundamental. Why should the wave function be describing both the position and momentum of a quantum as if it was a classical particle? why an equation that has features of a wave equation but even more clearly of a diffusion equation should be interpreted as fundamentally related to a classical particle behaviour rather than to a field? Do we think in terms of heat particles when dealing with the heat equation? Doesn't it make more sesnse to think in terms of relativistic quantum fields whose localized behaviour is subject to probabilistic analysis?

 

[bhobba]

As I have insisted in previous posts but apparently nobody noticed this argument (maybe it deserves a thread of its own but I think it is quite related to QM incompleteness issues), it seems to me like the measurement problem and the probabilistic uncertainties associated to QM (and I'm concentrating here on NRQM since everybody seems to be referring to it anyway) all rest on holding on to the particle picture as fundamental. Why should the wave function be describing both the position and momentum of a quantum as if it was a classical particle? why an equation that has features of a wave equation but even more clearly of a diffusion equation should be interpreted as fundamentally related to a classical particle behaviour rather than to a field? Do we think in terms of heat particles when dealing with the heat equation? Doesn't it make more sesnse to think in terms of relativistic quantum fields whose localized behaviour is subject to probabilistic analysis?

I think you need to read chapter 3 of Ballentine - Quantum Mechanics - A Modern Development. It's got nothing to do with a particle picture other than position as an observable exists (which is an indisputable experimental fact) but symmetries.

Thanks
Bill

 

[TrickyDicky]

I think you need to read chapter 3 of Ballentine - Quantum Mechanics - A Modern Development. It's got nothing to do with a particle picture other than position as an observable exists (which is an indisputable experimental fact) but symmetries.

Thanks
Bill

I don't have it handy. Can you give the basic points where Ballentine argues that puzzlement about QM not giving deterministic trajectories but amplitude probabilities has nothing to do with insisting about classical particle behaviour?

Besides, observavility of fields interactions positions is not what I mean by classical particle behaviour.

 

[bhobba]

I don't have it handy. Can you give the basic points where Ballentine argues that puzzlement about QM not giving deterministic trajectories but amplitude probabilities has nothing to do with insisting about classical particle behaviour?

Purely from the Principle Of Relativity that the laws of physics are the same in all inertial reference frames you can derive - not assume - but derive Schrodinger's equation, the definition and existence of the momentum operator and all the stuff that other textbooks assume. This is because of the symmetries implied by the POR. Its the exact analogue of the least action formulation of classical mechanics. As you will find in Landau - Classical Mechanics that is the case there as well - the existence of momentum, Newtons laws etc all follow from symmetry.

If you haven't read Landau read it:
http://ia601205.us.archive.org/11/items/Mechanics_541/LandauLifgarbagez-Mechanics.pdf
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

'If physicists could weep, they would weep over this book. The book is devastingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages. I first came across Landau's mechanics many years ago as a brash undergrad. My prof at the time had given me this book but warned me that it's the kind of book that ages like wine. I've read this book several times since and I have found that indeed, each time is more rewarding than the last.

The reason for the brevity is that, as pointed out by previous reviewers, Landau derives mechanics from symmetry. Historically, it was long after the main bulk of mechanics was developed that Emmy Noether proved that symmetries underly every important quantity in physics. So instead of starting from concrete mechanical case-studies and generalising to the formal machinery of the Hamilton equations, Landau starts out from the most generic symmetry and dervies the mechanics. The 2nd laws of mechanics, for example, is derived as a consequence of the uniqueness of trajectories in the Lagragian. For some, this may seem too "mathematical" but in reality, it is a sign of sophisitication in physics if one can identify the underlying symmetries in a mechanical system. Thus this book represents the height of theoretical sophistication in that symmetries are used to derive so many physical results.

The difficulty with this approach, and the reason why this book is not a beginner's book, is that to the follow symmetric arguments, one really has to have already mastered vector calculus. Ideally, you should be able to transform coordinate in your sleep, perform integrals without missing a beat, whether they be line, area, or path, and differentiate functions in many dimensions. The arguments are not sloppy, as some have claimed - it only seems so if you have not mastered vector calculus.

Tradition says that in Plato's academy was engraved the phrase, "Let no one ignorant of geometry enter here", so should the modern theoretical physicist, with Landau's bible in hand, march under the arches engraved with the words "Let no one ignorant of symmetry enter here".'

After reading that read Ballentine. You will see its got nothing to do with a particle picture but symmetries. These force the equations on us purely from the fact position is an observable.

When you understand this you will wonder what the connection is - answer - Feynman's path integral approach. This is why classical mechanics is as it is - and both are deeply, no very deeply, determined by symmetry. This is unbelievably beautiful mathematically and once I understood it it revolutionized my view of nature - as I think it will for anyone exposed to it.

Also get Susskinds new book:
https://www.amazon.com/dp/046502811X/?tag=pfamazon01-20

At a more basic mathematical level in the sense he develops the math as you go along he explains the same stuff as Landau. Like Euclid Landau and Susskind looked on physical beauty bare - once you understand it so will you.

Enough said - end of rant.

Thanks
Bill