what’s all this nonsense about Bell’s theorem and supposed non-locality?He is right, and he cites a Gell-Mann video in agreement, but most of the comments don't.
If I go to the Scholarpedia entry for Bell’s theorem, I’m told that:
Bell’s theorem asserts that if certain predictions of quantum theory are correct then our world is non-local.but I don’t see this at all. As far as I can tell, for all the experiments that come up in discussions of Bell’s theorem, if you do a local measurement you get a local result, and only if you do a non-local measurement can you get a non-local result. Yes, Bell’s theorem tells you that if you try and replace the extremely simple quantum mechanical description of a spin 1/2 degree of freedom by a vastly more complicated and ugly description, it’s going to have to be non-local. But why would you want to do that anyway?
In short, Bell proved in about 1965 a nice theorem showing the difference between quantum mechanics and classical theories. He showed that assuming local hidden variables leads to different conclusions.
In later years, Bell convinced many people that the assumption of hidden variables was not necessary. They are wrong, and most respectable physicists, textbooks, and Wikipedia articles say so. Some say that he would have deserved a Nobel Prize if he had been right, but he got no such prize.
Lee Smolin responds:
I have made what I hope is a strong case for taking seriously what we might call the “John Bell point of view” in my recent book Einstein’s Unfinished Revolution, and find myself mostly in agreement with Eric Dennis and Marko. I would very briefly underline a few points:This is so wrong that I am tempted to cite Lubos Motl's opinion of Smolin.
-This is not a debate resting on confusions of words. Nor is there, to my knowledge, confusion among experts about the direct implications of the experimental results that test the Bell inequalities. The main non-trivial assumption leading to those inequalities is a statement that is usually labeled “Bell-locality”. Roughly this says (given the usual set up) that the “choice of device setting at A cannot influence the same-time output at B”.
Nothing from either quantum mechanics nor classical mechanics is assumed. The experiments test “Bell-locality” and the experimental results are (after careful examination of loop-holes etc.) that the inequality is cleanly and convincingly violated in nature. Therefor “Bell-locality” is false in nature.
-The conclusion that “Bell-locality” is false in nature is an objective fact. It does not depend on what view you may hold on the ultimate correctness, completeness or incompleteness of QM. Bohmians, Copenhagenists,Everetians etc all come to the same conclusion.
There is no experiment where the choice of device setting at A influences the same-time output at B. The Bell experiments only show that the choice of device setting at A influences how we go about making predictions at B, but it never affects the output at B.
There is a big difference. One is spooky action-at-a-distance, and one is not.
It is amazing that Smolin could write a book in this subject, and get this simple point wrong.
I added this comment, but it was deleted:
As Wikipedia says: Cornell solid-state physicist David Mermin has described the appraisals of the importance of Bell's theorem in the physics community as ranging from "indifference" to "wild extravagance".Motl posted his explanation.
Bell assumed local hidden variables. If you believe that the theory of everything should be based on hidden variables, then Bell's theorem is a big deal. If you believe in QM as a perfectly good non-hidden-variable theory, then Bell's theorem has no importance.
As Peter says, "systems don’t have simultaneous well-defined values for non-commuting observables." That is another way of saying that Bell's assumption of hidden variables is violated.
You would need non-locality in a classical theory to fake the quantum results. But that doesn't mean that our Universe is non-local because your classical theory – and any classical theory – is just wrong. In particular, the correct theory – quantum mechanics – says that the wave function is not an actual observable. It means that its collapse isn't an "objective phenomenon" that could cause some non-local influences. Instead, it may always be interpreted as the observer's learning of some new information.One comment cited Travis Norsen to support Bell. I explained his errors in this 2015 post.
Peter Shor comments:
First: quantum mechanics doesn’t just break classical probability theory (as Bell demonstrated); it breaks classical computational complexity theory and classical information theory as well. This is why there are a number of computer scientists who are convinced that quantum computers can’t possibly work.Those computer scientists might be right.
The Bell test experiments were done by physicists with a belief that they would disprove quantum mechanics, and overthrow 50 years of conventional wisdom. All they did was to confirm what the textbooks said.
Most of the XX century was without any firm opinion that quantum mechanics breaks classical computational complexity theory and classical information theory. That opinion developed in the last 30 years, just as experiments were being done. While experiments have confirmed aspects of quantum mechanics that Bell doubted, the jury is still out on quantum computing.
So basically are you stating that this article is wrong:ReplyDelete
Do you think that this article is wrong: "Measurements of physical properties such as position, momentum, spin, and polarization, performed on entangled particles are found to be correlated. For example, if a pair of particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, the spin of the other particle, measured on the same axis, will be found to be counterclockwise, as is to be expected due to their entanglement. However, this behavior gives rise to seemingly paradoxical effects: any measurement of a property of a particle performs an irreversible collapse on that particle and will change the original quantum state. In the case of entangled particles, such a measurement will be on the entangled system as a whole."
Also, is this page wrong?
Is this book wrong?
Is Tim Maudlin wrong?
Is anyone other than Woit right about quantum entanglment?
The WP article is correct that measurements on entangled particles are correlated. Also that the wave function collapses in the Copenhagen interpretation. The SEP article is mostly correct, but is wrong where it tries to restate the hidden variables assumption as a causality assumption. Maudlin makes similar mistakes. I don't know about the Quantum Enigma book. The reviews say that it presents various points of view. As cited above, Gell-Mann is correct about entanglement.ReplyDelete
Do you agree that the wavefunction is nonlocal? Over time as a photon propagates through space, do you agree that its wavefunction expands?ReplyDelete
Suppose a single photon passes through two slits at the same time. Would you argue that the photon is entirely local, or does it have nonlocal properties?ReplyDelete
Do you also consider Murray Gell-Mann to be an expert on particle physics: https://www.youtube.com/watch?v=hgldeDEr3DA Do you also agree with Murray that Superstring Theory is wonderful?ReplyDelete
You write, "There is no experiment where the choice of device setting at A influences the same-time output at B. The Bell experiments only show that the choice of device setting at A influences how we go about making predictions at B, but it never affects the output at B."ReplyDelete
Are you saying that Alain Aspect's experiments and his conclusions were wrong?
"Aspect's experiments unambiguously confirmed the violation, as predicted the Copenhagen interpretation of quantum physics, thus undermining Einstein's local realistic outlook on quantum mechanics and local hidden variable scenarios. In addition to being confirmed, the violation was confirmed in the exact way predicted by quantum mechanics, with a statistical agreement of up to 40 standard deviation."
Will you and Woit be updating the Aspect Wikipedia page to reflect your "correct" views? After that, there are hundreds more wikipedia pages to be updated, as well as thousands of papers and books and articles. Do you plan on attempting this correction?
Yes, the wave function expands, but the wave function is not observable. The expansion reflects our lack of knowledge.ReplyDelete
Yes, Gell-Mann was an expert on particle physics. He may have had opinions with which I disagree. He even changed his mind about quarks.
The WP article correctly says that Aspect's experiments rule out local hidden variables. The experiments do not rule out locality, but only a certain class of local classical theories. They confirmed the conventional wisdom of the last 90 years. I have no quarrel with that 90-year-old understanding.
You write, "Yes, the wave function expands, but the wave function is not observable. The expansion reflects our lack of knowledge."ReplyDelete
Can you please cite the text that states thusly, and present the equation that shows that as a wavefunction expands, our lack of knowledge also expands? I have never seen this, and, in fact, see that quantum mechanics states something quite different/
Also, how do you know that a wavefunction expands if it is not observable? Are you stating that the wavefunction has NO physical reality whatsoever and is not a part of physics?
The purpose of Aspect's experiments were NOT to rule out local hidden variables, but rather to demonstrate the existence of nonlocality, which they did. Are you stating that Aspect's experiments did NOT demonstrate nonlocality?
Again you wrote, "There is no experiment where the choice of device setting at A influences the same-time output at B. The Bell experiments only show that the choice of device setting at A influences how we go about There making predictions at B, but it never affects the output at B."
You never answered the question about your statement, as you probably see your error now, as the Bell experiments DEMONSTRATE that the choice of the setting at A instantaneously (faster than light) influences the output at B. That is what the Bell experiments, and many others, have demonstrated.
1. The Schrodinger formalism involves IAD (instantaneous action at a distance) for both V and \Psi. Changes in \Psi, in particular, occur with IAD. By Born's rule, therefore, the probability distribution too undergoes instantaneous changes everywhere. Thus QM is basically, and most generally, non-local.
2. Scenario 1: Consider an isolated system containing only two atoms of the same element separated by a distance L. Assume the initial state has atom A in an excited state, and atom B in the ground state. Suppose atom A undergoes a quantum jump down to the ground-state in a time interval \Delta t. It may be said to emit a photon. Since the system is isolated, the atom B must take a quantum jump up. This change will be called the absorption of the same photon.
It is possible in the Schrodinger formalism that both emission and absorption begin at the same time t0 and complete at t1 = t0 + \Delta t. This is transfer of photon at a speed v = (\Delta t)/L.
Now, the point is that you can always arrange for L to be large enough that v exceeds c, the speed of light. Thus, QM is essentially non-local.
3. Einstein didn't consider Scenario 1. He considered, essentially, something like the one below:
Scenario 2: The entire universe forms the system under consideration, out of which 3 atoms are picked up for consideration. Suppose the atom A undergoes a PDC jump, emitting two entangled photons. The atom B (regarded as detector D1) is at a distance L from A. It absorbs one of the photons. The atom C (regarded as detector D2) again lies the distance L away from A. Thus B and C are equidistant from A. The distance between B and C is large enough, say L2.
Suppose the atom A emits the two photons at time t = t0. Suppose the atom B absorbs one of them at t1 such that t1 = (L/c) + t0, thereby preserving Special Relativity in our QM experiment (though, as seen above, this is not strictly necessary). The atom C may or may not absorb the second photon exactly at t1. (Practically speaking, we may allow some small tolerance in time beyond t1 for this event to occur.)
Suppose the atom C indeed absorbs the second photon at t1. If so, we may conclude that it must be the same photon as the one which came from the atom A.
In this case, the quantum properties of the two photons are found to be entangled.
4. Scenario 2 allows you to say that QM is local. But that's only because the description has deliberately been arranged in such a way that c is not violated. However, going by the actual formalism (tested well), Scenario 1 is a better description of what QM is like, in general.
5. If so, why do you say that QM is local? (Am I making any error? Please feel free to point out.)
Do you and Woit even understand the difference between classical probabilities and quantum probabilities?ReplyDelete
I quote from Quantum Enigma: Physics Encounters Consciousness (p. 83). Oxford University Press. Kindle Edition. :
There is, however, a crucial difference between the classical probability illustrated by the shell game and quantum probability represented by waviness. Classical probability is a statement of one’s knowledge. In the shell game, your not knowing at all which shell covered the pea means that for you the probability of it being under each shell was 1/2. The shell-game operator likely had better knowledge. For him the probability was different. Classical probability represents someone’s knowledge of a situation. It is not the whole story. Something physical is presumed to exist in addition to that knowledge, something it was the probability of. There was a real pea under one of the shells. If someone peeked and saw the pea under the left-hand shell, the probability would collapse to a certainty, to 1, for her. But it could still be 1/2 for each shell for her friend. Classical probability is subjective. Quantum probability, waviness, on the other hand, is mysteriously objective; it’s the same for everyone. The wavefunction is the whole story: The standard quantum description has no atom in addition to the wave-function of the atom. As a leading quantum physics text would have it, the term “the wavefunction of the atom” is a synonym for “the atom.”"
--from Rosenblum, Bruce. Quantum Enigma: Physics Encounters Consciousness (p. 83). Oxford University Press. Kindle Edition.
So it is that you stating that the wave-function simply represents our "lack of knowledge" is wrong.
Quantum mechanics is different from playing the "which shell is the pea under" game which you are conflating quantum mechanics with.
It seems you and Woit have quite a lot of work to do in "correcting" all the journal articles, wikipedia pages, books, and youtube videos which demonstrate that physical reality is nonlocal.
But before you start, do you really think that the wave function is entirely local?
Above you state "Yes it expands," when you're asked if the wavefunction is nonlocal.
You write, "Yes, the wave function expands."
So are you saying "Yes the wave function is nonlocal."?
Do you really believe that the wave function of a photon passing through two slits at the same time is entirely local?
Golden: The book is saying that classical probability is subjective while quantum probability is objective. It is not clear that the authors are committed to this view, as it is in a section titled "the accepted view of waviness".ReplyDelete
I don't think it is the accepted view. Bayesian statisticians argue that classical probability is subjective, but there are other views. Bohr would not have agreed that quantum probability is objective.
To answer your question, the only probability I accept is Kolmogorov probability. And it applies to classical and quantum settings the same way. So no, there is no difference between classical and quantum probability.
Ajit: In scenario 1, the energy is carried by a photon from atom A to atom B. The photon travels at the speed of light, and the energy transfer is not instantaneous. There is no experiment showing an instantaneous effect over a distance.
But the Schrodinger formalism permits scenario 1, doesn't it? The reason is this.
The energy is _not_ carried by the photon. (That is some vestige of a purely particles-view of the photon.) The energy is carried by the spatial region of the isolated system as a whole.
Like so many other differential equations, Schrodinger's equation is formulated in the so-called Eulerian framework (i.e. one in which a system is defined in reference to a control _volume_, i.e. a region of space). It is not formulated in the alternative, Lagrangian framework (in which a system is defined in reference to a control ``_mass_'', i.e. a portion of matter). The CV vs. CM distinction is very well known to mechanical engineers (right from Fluid Mechanics-1 course), but perhaps not to electrical engineers. So I explained.
The convenience of using an isolated system is that the system-energy remains all the time contained within the spatial region defining the system---it doesn't get exchanged with environment.
The photon refers to a pair of emission and absorption events (quantum jumps). In Scenario 1, the energy stays constant; it's just that its pattern undergoes a change, all within the system, as the system eigenfunction changes---from the initial state to the final state which is degenerate.
The shift in the two local neighbourhoods near the two nuclei indeed occurs simultaneously, i.e. instantaneously. This is exactly like, in classical Fourier theory of heat conduction, a source loses thermal energy and a distant sink gains it, with both processes occurring at the same time. Such a process may be regarded, from a higher-level point-of-view, as an instantaneous transfer of thermal energy. But then, it's not really IAD, because only energy is changing at two points at the same time---there is no transport of mass with infinite speed between the source and the sink.
Too long, but hope it helps clarify how I am viewing these matters.
You write, "Bohr would not have agreed that quantum probability is objective." Where in the literature did Bohr ever state this?ReplyDelete
Where in the literature did Bohr, Fermi, Dirac, Planck, Einstein, Born, or any other famous quantum theorist ever cite "Bayesian statisticians"?
As you must admit, Bayesian statisticians are entirely irrelevant to the formulation of quantum mechanics. Why are you bringing them into this? More straw men?
You write, "To answer your question, the only probability I accept is Kolmogorov probability."
Are you and/or Kolmogorov relevant to quantum mechanics? Have you and Kolmogorov taken quantum mechanics beyond Bohr, Shcrodinger, Fermi, Dirac, Planck, Einstein, Born, et al.?
Could we please discuss the quantum mechanics of Bohr, Schrodinger, Fermi, Dirac, Planck, Einstein, Born, et al. instead of your bizarre Kolmogorov versions?
Please let us know what you and Kolmogorov have contributed to quantum mechanics. If it is nothing, as it seems to be, then we probably don't need your opinions. Correct?
Golden: Light is not composed of classical particles. Thinking of photons as classical particles will lead you astray. No particle is ever in two places at the same time. A light wave can go thru two slits at once. Light has entirely local properties.ReplyDelete
Did you get a Ph.D. in physics by any chance?
Have you ever read any of the foundational papers on quantum mechanics?
You write, "Thinking of photons as classical particles will lead you astray."
Where did I ever state that a photon is a classical particle?
Again, you erect strawmen in your head, without any of the founding papers on quantum mechanics backing it up, and then you conclude that "Light has entirely local properties," which is a vast falsehood.
At any rate, as it seems you are on a crusade to "correct" Wikipedia, I wish you all the best in adding your sentence "Light has entirely local properties" here:
As your statement is so important and revolutionary, I imagine that you will be able to add it as the very first line in the article, citing all your published papers on the topic of course.
Please let us know how it goes! Best wishes!
Perhaps you can cite Woit's research too?
I seem to have gotten some comments out of order.ReplyDelete
Golden: Probability, logic, statistics, and Bayesianism are all mathematical concepts. Those physicists had nothing to add to those concepts. I mention Kolmogorov probability because you asked about the difference between classical and quantum probability.
Bohr believed in things that are observable. Probability is not directly observable.
I guess you could say that the wavefunction is nonlocal as it represents spatially distinct points at the same time.
The quantum mechanics under discussion was settled about 90 years ago. No, I have not contributed to the theory, and neither has Bell or anyone alive today. The positions I am taking here are entirely consistent with the dominant understanding of the last 90 years. You haven't shown me any textbook or Wikipedia page that says I am wrong.
Golden: I am not on a crusade to correct Wikipedia. The Wikipedia articles mostly agree with me, and disagree with Bell, Maudlin, and Smolin. The photon article already says "photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles." That is essentially the same as what I have said here. Even the article on quantum nonlocality agrees with what I have said here.ReplyDelete
Roger, you write, "Bohr believed in things that are observable. Probability is not directly observable."ReplyDelete
What do you mean by DIRECTLY observable?
Are stars directly observable, in your opinion?
Or do we only ever observe the photons when they hit our detectors or eyes?
And even then, are you one of those who argues that we don't actually observe the photon, but rather we observe the elctrochemical reaction on our retina?
again, you write, "Bohr believed in things that are observable. Probability is not directly observable."
So are you saying that Bohr did NOT believe in quantum probabilities?
Are you going to update Bohr's wikipedia page with "Bohr did NOT believe in quantum probabilities, as nobody has ever observed probabilities in the realm of quantum mechanics, and Bohr ONLY believed in things one could observe."
Have you ever read Bohr's papers? Do you have a favorite?
Golden: I don't get the point of all your comments about probability. The Wikipedia page on Niels Bohr doesn't even mention any of his views on probability. Bohr was a physicist, not a mathematician or statistician.ReplyDelete
Stars, starlight, and retinas are physically observable things.
You write, "I don't get the point of all your comments about probability. The Wikipedia page on Niels Bohr doesn't even mention any of his views on probability. Bohr was a physicist, not a mathematician or statistician."
My comments were not responding to Bohr, but rather to you, who wrote: "Bohr believed in things that are observable. Probability is not directly observable."
You are trying to make the case that Bohr did NOT believe in quantum probabilities.
This is you saying thusly. Not Bohr, as Bohr never said this.
I don't believe Bohr ever said that there is a quantum probability that is different from ordinary probability. But even if he did, probability is a mathematical concept and Bohr was a physicist, so I don't know why anyone would care about Bohr's mathematical opinions.ReplyDelete