High School Does the EPR experiment imply QM is incomplete?

[PeterDonis]

All such correlations are produced by the non-local guidance of the pilot wave, acting simultaneously on all particles with which it is entangled.

The nonlocality in Bohmian Mechanics is in the pilot wave; it "knows" instantaneously what is happening at spacelike separated locations, and guides the particles appropriately to produce the correlations. The "guiding" of the particles by the pilot wave is indeed local; each particle is guided by the wave at its location.

 

[DarMM]

I have the impression you're envisioning this "superliminal signal" as something akin to the way a shadow projected by a laser situated on Earth can appear to dart across the surface of the moon at a faster-than-light velocity.

I'm not picturing it that way, nor am I talking about how it appears or moves in 4D spacetime. I'm talking about signalling in the standard sense used in quantum foundations.

As explained in the link, the phenomenon is real, but no information is transmitted at FTL speeds from (4D spacetime) "point A to point B". That is likewise the case with mutually entangled particles in Bohmian Mechanics. Regardless of how it may appear to occur in our 4D spacetime measurements, no information is conveyed between entangled particles (at any 4D spacetime velocity whatsoever). All such correlations are produced by the non-local guidance of the pilot wave, acting simultaneously on all particles with which it is entangled.

This is true, when in quantum equilibrium. Out of equilibrium information can be transferred.

 

[Lish Lash]

This is true, when in quantum equilibrium. Out of equilibrium information can be transferred.

The Quantum Equilibrium Hypothesis is a postulate specific to Bohmian Mechanics - it is what ensures that BM maintains consistency with the Born Rule (and consequently, reproduces all predications of Quantum Mechanics). I'm not sure whether you're referring to "out of equilibrium information" or instead claiming that "Out of equilibrium, information can be transferred." In either case, such conditions lie outside the domain of Bohmian Mechanics.

 

[DarMM]

The Quantum Equilibrium Hypothesis is a postulate specific to Bohmian Mechanics - it is what ensures that BM maintains consistency with the Borne Rule (and consequently, reproduces all predications of Quantum Mechanics). I'm not sure whether you're referring to "out of equilibrium information" or instead claiming that "Out of equilibrium, information can be transferred." In either case, such conditions lie outside the domain of Bohmian Mechanics.

The latter, "Out of equilibrium, information can be transferred"

From my readings I didn't think Bohmian Mechanics had to assume quantum equilibrium, as a few people have worked on showing it arises dynamically and many still call the theory without it Bohmian Mechanics in their papers.

If this is wrong, what is the more general theory without the assumption called? (Genuine question)

 

[Lish Lash]

I didn't think Bohmian Mechanics had to assume quantum equilibrium, as a few people have worked on showing it arises dynamically and many still call the theory without it Bohmian Mechanics in their papers.

If this is wrong, what is the more general theory without the assumption called? (Genuine question)

Good question, my impression is that relaxing the Born Rule takes Bohmian Mechanics into Multiple Worlds terrritory. However, I can't claim to speak authoritatively on the relation of MWI to the Born Rule.

 

[DarMM]

Good question, my impression is that relaxing the Born Rule takes Bohmian Mechanics into Multiple Worlds terrritory. However, I can't claim to speak authoritatively on the relation of MWI to the Born Rule.

I naively don't think it would. Choosing a different initial epistemic restriction asides from the Quantum Equilibrium can't change the underlying ontology. Or so I would think.

 

[DrChinese]

Regardless of how it may appear to occur in our 4D spacetime measurements, no information is conveyed between entangled particles (at any 4D spacetime velocity whatsoever). All such correlations are produced by the non-local guidance of the pilot wave, acting simultaneously on all particles with which it is entangled.

Presumably, that number of particles is 2. After all, there is monogamy of entanglement in these cases.

Which is interesting, because I don't think the pilot wave itself can be "separated" into a component which applies to the 2 entangled particles, and another component that applies to everything else in the universe. And yet, experimentally it acts that way. When Alice-1 is measured, entangled partner Bob-1 - and only Bob-1 - is affected.

Else the rest of the universe is affected in a way that (I guess) must cancel to a net zero. Which doesn't make sense if there are other entangled pairs hanging around (Alice-2 and Bob-2) since we can't let them be affected by Alice-1 and Bob-1.

 

[bhobba]

Good question, my impression is that relaxing the Born Rule takes Bohmian Mechanics into Multiple Worlds terrritory. However, I can't claim to speak authoritatively on the relation of MWI to the Born Rule.

All interpretations of QM have the so called Born Rule (although it has be pointed out to me historically Born meant something slightly different) which I write as the expectation of the outcome of observing a system with an operator O, E(O) is Trace(OS), where S is a positive operator of unit trace by definition called the state of a system. Since this is a B level threads do not worry about exactly what this means - just know its something every interpretation has and is what on this forum (and in all textbooks I am aware of) we call the Born Rule. For pure states it becomes (again do not worry if you have not seen it before) the way its usually written, and found in more elementary texts, E(O) = <S|O|S>. But these are just technicalities.

Now believe it or not we can actually derive the Born Rule from the other main rule of QM - namely given any observation we can find a Hermiton Operator in some complex vector space (called a Hilbert Space) such that its Eigenvalues are the possible outcomes of those observation. The Born Rule follows from this. In fact as QM - A Modern Approach by Ballentine shows all of QM can basically be derived from just these two main 'axioms' - this is done by what's called Gleason's Theorem:
https://en.wikipedia.org/wiki/Gleason's_theorem

Just as an aside Gelason is an unsung hero of modern math - see attached file.

The only out is what is called contextuality:
https://en.wikipedia.org/wiki/Quantum_contextuality

But since the Born Rule has very strong experimental support, in any interpretation with contextuality it must be true as well - but not provably true like in non-contextual interpretations.

There is some debate on if MW is non-contextual or not, and we have discussed it on this forum a few times, some like me think it is non-contextual, and others are not so sure. The experts even do not agree - Wallace for example in his book the Emergent Multiverse thinks in non-contextual (as do I):
https://www.amazon.com/dp/0198707541/?tag=pfamazon01-20

But its not universally accepted.

Thanks
Bill

 

[DarMM]

Just a small comment on Gleason's theorem and Many Worlds(and thanks bhobba for the reminder that this is B level).

In Quantum Mechanics, unlike Classical Mechanics, the observables like position and momentum don't commute, i.e. if $p$ is momentum and $q$ is position, then $pq \ne qp$. What Gleason showed is that if you want to assign probabilities (in order to estimate the chances of getting various results) to observables that behave like this then you basically have to use the mathematics of Quantum Mechanics, e.g. Hilbert Spaces. Now there are a few ways of assigning probabilities to observables like this, but Quantum Mechanics is the only way that is "non-contextual". Non-contextual means that if I measure $A$ then the chance that $A = 1$, let's say, doesn't depend on what else my device measures along with $A$, e.g. if I measure $A, B$ or $A, C$ in both cases I have the same chance of $A = 1$.

Quantum Mechanic's specific way of assigning probabilities is called the Born Rule. So Gleason's theorem shows that the Born Rule is the only way to assign probabilities to the type of non-commuting observables one sees in microscopic experiments. The Born Rule collects all my chances of seeing observables having various values into one object called "the quantum state".

Now in Many Worlds on the other hand, the quantum state is seen as the main thing. It's not a collection of probabilities, but a physically real "substance". Hence in this case we can't just use Gleason's theorem to explain the success of the Born rule as we're not starting from the observables and finding the state as probabilities on them. Instead we're starting with the state as a physically real thing and in fact the only real thing.

There are many ways to try to derive the Born Rule in Many-Worlds. Wallace's above is the most famous, but I personally found it very confusing and was left with little understanding of why the rule held. Wallace basically says the Born rule arises because, provided the worlds separate in a particular way, it's the only way for a rational agent to predict which world they will find themselves in. There are currently three issues people have with this line of arguing:

1. Do the worlds separate in the way he requires?
2. Is his definition of rational valid? Especially given the way the world works in Many Worlds. Some people have said that if there are multiple worlds there are ways of being rational that Wallace doesn't take into account
3. Even if all this worked, does something being "the best way for agents to bet" really imply it's what you'll see in experiments.

My problem was I couldn't see the physical reason for the Born Rule (so basically 3.)

However a closely related proof by Mateus Araújo (https://arxiv.org/abs/1805.01753) is helpful if you think like myself. Here he shows the Born Rule comes about due to conservation of "world-volume". So there is, from the beginning of time, a continuum of worlds and then a fraction of them get imprinted with one result or another. So my chance to see a particular result (which is what the Born Rule is about) is basically related to how large a fraction of the worlds gets imprinted with that result. "Conserving world volume" just means no new worlds are made.

Araújo has a nice dicussion of how a Many-Worlds theory where the world actually splits and two new worlds are made has a different probability rule than the Born rule. So the Quantum Mechanical Many-Worlds is better thought of as all the worlds already being there.

The real problem with Many-Worlds at the moment is to mathematically prove that 3D semi-classical worlds like the one we experience actually arise. This has not yet been done, so the interpretation cannot be as of yet said to match experiment.

There is some debate on if MW is non-contextual or not, and we have discussed it on this forum a few times, some like me think it is non-contextual, and others are not so sure. The experts even do not agree - Wallace for example in his book the Emergent Multiverse thinks in non-contextual (as do I):
https://www.amazon.com/dp/0198707541/?tag=pfamazon01-20

I would be like yourself and would have thought in noncontextual. I must read the discussions. More so I'm not sure if it really is local. See Travis Norsen's book "Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory" for a discussion of this. In essence in something like the Bell state:
$$\frac{1}{2}\left(|00\rangle + |11\rangle\right)$$
Since Alice will split into a 0 and 1 world, as will Bob, Alice's "0 result" has to know nonlocally it belongs to the same world as Bob's "0 result". Naively you'd think there would be four worlds.

Many Worlds theories supplemented by extra variables beyond the wavefunction don't have this problem as they attach a "charge" to each outcome and only copies of Alice and Bob with the same "charge" can interact. The Parallel lives interpretation is an example. (https://arxiv.org/abs/1709.10016)

 

[DarMM]

Of course the real derivation is that if Many Worlds is true then there is a reality where Max Born rose to power and established an autocratic state over the whole Earth known as "The Born Rule".

 

[bhobba]

The real problem with Many-Worlds at the moment is to mathematically prove that 3D semi-classical worlds like the one we experience actually arise. This has not yet been done, so the interpretation cannot be as of yet said to match experiment.

Some progress has been made in decoherent histories which some like Gell-Mann think is simply MW without the MW:
http://web.physics.ucsb.edu/~quniverse/papers/cop-ext2.pdf

But issues still remain. Some, including a number of very knowledgeable mentors on this forum, think until they are resolved QM is incomplete (ie Einstein was correct - he was anyway because we still have no complete quantum theory of gravity - but most take it to be something a bit different). Others like me think it's basically crossing your t's and dotting your i's. Really it's semantics - either way we are not there yet. Its interesting actually - everyone thought Einstein lost to his good friend Bohr in the Einstein Bohr debates - but here we are today and would say Einstein's intuition did not lead him astray - even here. What the future brings will indeed be interesting - however I may not be around to see what finally emerges. Another interesting thing is just before Einsteins death Bohr came to visit and Einstein would not see him - why - maybe he was too weary of the QM debates - or being so close to death didn't want Bohr to remember hijm like that - who knows - however there is little doubt during their prime they were very good friends - each admiring the other greatly. Bohr never ceased to believe GR was the greatest achievement of the human intellect ever.

Thanks
Bill

 

[vanhees71]

Well, I think nowadays it's pretty obvious that Einstein understood QT way better than Bohr, who was more a philosopher than a physicist after his young years, where he discovered "old quantum mechanics", i.e., did physics in the sense that it described something observable. He also qualitatively got the physical explanation for the chemistry of the periodic table right (to be a bit generous). As we understand QT today, his role in "interpretation" was more towards confusing the subject with quite imprecisely defined philosophical notions like "wave-particle duality" and, even worse, "complementarity". He is topped in obscurity only by Heisenberg ;-))). Of course, Einstein was wrong in thinking that the issue can be "repaired" by the hidden-variable argument, at least when you insist on locality of interactions (as realized in relativistic QFT) and separability, which has been clearly shown by Bell's work on his famous inequality, which brought the philosophical gibberish of EPR and Bohr's response to a clear physical statement which was testable in the lab (as was done by Aspect et al in the 1980ies and later on up to today at ever higher accuracy and with ever more fancy setups to exclude any, if not all!, "loopholes").

Nevertheless, I think that the minimal interpretation is the only thing we need to use the formalism to describe what's seen in Nature. In this sense QT is "complete" as a physical theory, but this completeness is only "for all practical purposes" (FAPP), and as Bell stated, that's not very satisfactory. Indeed, it is very well known that QT as we know it today is for sure incomplete, since there's no quantum description of gravity, and maybe one day some genius finds a solution to this puzzle, which overcomes maybe also the problems with ontology of QT.

For non-relativistic QM, I recently got convinced, that the Bohmian Mechanics, as interpreted and presented by Dürr et al, is an example for such a solution. Unfortunately it seems to be even "less complete" than QT, which also includes a very well working relativistic version in terms of local microcausal relativistic QFT, upon which the all too successful Standard Model of elementary-particle physics is based. So for QT as a whole we still don't have anything better than the FAPP interpretation called "minimal statistical interpretation".

 

[bhobba]

Well, I think nowadays it's pretty obvious that Einstein understood QT way better than Bohr, who was more a philosopher than a physicist after his young years, where he discovered "old quantum mechanics", i.e., did physics in the sense that it described something observable. He also qualitatively got the physical explanation for the chemistry of the periodic table right (to be a bit generous). As we understand QT today, his role in "interpretation" was more towards confusing the subject with quite imprecisely defined philosophical notions like "wave-particle duality" and, even worse, "complementarity". He is topped in obscurity only by Heisenberg ;-))).

First interesting thing about Heisenberg. Bohr's brother, Harald, who was actually a bit more famous in Denmark because he was a bit better soccer player, was a very good mathematician and friend of Hardy. Heisenberg was visiting and Hardy thought he would play a trick on Heisenberg. He said now you are becoming more involved with advanced physics we should develop your math a bit more. He gave him a problem that was then reasonably famous, and just recently solved. To Hardy's astonishment Heisenberg solved it - Hardy thought he had picked the wrong area - he should do math and come to work with him and Littlewood (too young to work with Ramanujan which would have been interesting). Of course he didn't take him up on the offer, but if he did he would have probably ended up working also with Dirac. So yes Heisenberg sometime spoke philosophical 'gibberish', but extremely talented in math and physics he certainly was. Personally I think pretty much everyone in the early days of QM got it wrong except Dirac, and we now know Einstein actually got it right as well - although it took him a while to reach his final view that QM was correct - but incomplete. To give Bohr his due I believe his debates with Einstein helped him in forming his final view even though Bohr was, to be kind, 'subtle' and with his mumble not a good communicator - but neither was Dirac for a different reason.

And yes Bell understood it as well, even though he was at least at the start into BM. To independently basically come up with a cut down version of what was known as a very difficult theorem to prove (Gleason's Theorem - from which Kochen-Speker followed as a simple corollary. Bell independently proved Kochen-Speker), taking one of the best mathematicians at the time, Gleason, to do it. I simply do not know how to categorize someone like that. Same with Feynman and Wilson - they were Putman Fellows - Feynman put on the team at the last minute, and Wilson twice even though he was accepted into Harvard early - 16 I think and was a Putman Fellow at 18 and 19 - but don't hold me to it. Interesting story - when Wilson got his first one he was given a celebration by the math department. He noticed one thing immediately - his father was a professor of Chemistry at Harvard so knew a number other professors. The math professors, while all very good mathematicians, were quite mad

Thanks
Bill

 

[vanhees71]

Sure, there's no question that Heisenberg was an ingenious theoretical physicist. After all he was the first to discover "modern QM" in 1925 in terms of matrix mechanics. The only thing I criticize is part of his "soft skills". In the beginning he fought Schrödinger's wave mechanics to defend his matrix mechanis as the only true quantum mechanics. Of course, this is nonsense given the fact that Schrödinger himself proved very early that both formalisms are equivalent representations.

Indeed of all "founding fathers" of QT, Dirac is the most clear of all, giving the bare formalism without too much interpretational gibberish, but also Schrödinger's paper are marvels in science-writing style, although he didn't have the correct probabilistic interpretation yet, and he was always critical against it until the end of his life. Dirac's textbook is still among the best ever written, but also his papers are not less clear and can be read easily by undergraduate students beginning to learn QT. That I can't say about Heisenberg's most famous Helgoland paper. I never got to understand it completely from scratch, i.e., not using the knowledge about QT I got from other sources. One also shouldn't underestimate the importance of Born, Jordan, and also Pauli, for the success of Heisenberg's matrix mechanics. The two papers by Born and Jordan as well as Born, Jordan, and Heisenberg ("Dreimännerarbeit") are quite well readable (containing even a part on field quantization by Jordan already then, but this one got forgotten, because people found this "too much", i.e., they though one should treat electromagnetism still via classical Maxwell theory, and it had to be reinvented by Dirac some time later to unerstand spontaneous emission). Pauli's contribution was not only the official one, namely the solution of the hydrogen energy-eigenvalue problem within matrix mechanics, using the O(4) symmetry and the associated Runge-Lenz vector from classical mechanics, but also as a "regulator" of Heisenberg's ingenious but not always very clearly stated ideas.

 

[DarMM]

Having read all their papers recently my personal impression was that Bohr and Heisenberg didn't spell out what they meant by phrases like "the electron doesn't exist between measurements". When you know what they mean a good portion of their writings make more sense, but I think they should have just written a summary account of their similar Copenhagen interpretations where they spell everything out.

By "the electron doesn't exist between measurements" they meant "electron" is a conceptual object we use to describe the type of marking "something" else leaves on our equipment. With that something being impossible to describe. It's a bit like how my signature isn't the same thing as me, but if you only have cheque books and your language only speaks of ink and paper, it's the only impression of me you'll have, but the signature doesn't exist between "cheque signing" events/measurements.
The electron is just this ineffable thing's signature on systems we can describe.

You can draw this out from their later papers, but unadorned and often unexplained it sounds like they don't think an independent reality exists.

Also Bohr assumes you've read Kant, many terms are being given their Kantian meaning rather than the everyday reading. Which just makes him even more difficult to understand.

 

[A. Neumaier]

just know its something every interpretation has and is what on this forum (and in all textbooks I am aware of) we call the Born Rule.

Except for my thermal interpretation! The latter says that as a property of measurements, Born's rule is only an approximation, valid only in very simple, idealized systems.
See the thread https://www.physicsforums.com/threads/many-measurements-are-not-covered-by-borns-rule.894095/ where this is argued from well-known cases in the literature.

 

[stevendaryl]

I actually do think that EPR shows that we don't completely understand QM. Whether that means it's incomplete or not is a matter of interpretation.

I don't think that we completely understand what a "measurement" is in QM. There are two competing ways of understanding measurements, and they are at odds. And both come into play in the EPR experiment.

One conception of measurement is that it's passive, at least in principle: When we measure some property of a system, we're just discovering a fact about that system. That's the classical notion of measurement.

A second conception of measurement is that it's active: The result of measurement is not a pre-existing quantity that you just become aware of, but is brought into existence through the participation and interaction of both the system being measured and the measuring device. The act of measuring disturbs the system being measured.

Both conceptions come into play in EPR. When it comes to measuring the polarization of a single photon, we can actually prove (at least in a one-world ontology) that the measurement disturbs the state of the photon being measured. The way that we measure a photon's polarization is by using a polarizing filter: If the photon passes through the filter, then its polarization is aligned with the orientation of the filter. If the photon is absorbed, then its polarization is perpendicular to the filter's orientation. To see that the filter is actually changing the state of the photon (as opposed to just filtering out photons of the wrong polarization), you can do the following:

• Send photons through one filter. The photons that come through will have a specific polarization.
• Have those that pass through go through a second filter, oriented at angle $\theta$ relative to the first.
• Have those that pass through the second filter go through a third.
• Etc.

With enough intermediate filters (actually, just three is enough, with a relative angle of 45^o between the orientations of successive filters), you can get photons coming through oriented 90^o away from the orientation they had after the first filter. It's obvious in this case that the filters have twisted the photons' polarizations, rather than simply passing those that had the wrong polarization. So the act of measurement of a photon's polarization actually does something to the photon. The fact that the photon coming out of the filter is polarization in a particular direction doesn't say anything definite about what it's polarization was before it went through.

In EPR, we have two correlated photons measured by Alice and Bob. Alice measures the polarization of one photon, and whatever answer she gets, she immediately knows the polarization of Bob's photon. Unless you allow for faster-than-light influences, Alice's measurement can't disturb Bob's photon. So if you disbelieve in FTL influences, you have to think of Alice's measurement as simply updating her information about Bob's photon, rather than changing Bob's photon.

But how can both be the case? When Alice measure's her own photon's polarization, her photon is interacting with her filter, and the state of her photon is affected by the filter. The fact that her photon comes through the filter polarized along a particular direction does not imply that the photon had the polarization prior to its passing through. But Alice can use the polarization of her photon after passing through the filter to deduce Bob's photon's polarization. How can that be possible? The disturbance model of measurement is justified in the case of Alice measuring her own photon, while the passive update model of measurement is justified in the case of Alice deducing something about Bob's photon.

 

[Mentz114]

I actually do think that EPR shows that we don't completely understand QM. Whether that means it's incomplete or not is a matter of interpretation.[].

About entangled photons QT says the the probability of a coincidence between A's and B's results is $\cos(\alpha-\beta)^2$ and no-one misunderstands that.

You are concerned about the things that QT does not tell us. The fact that it says so little could mean it is incomplete, but who cares anyway except philosophers

 

[DarMM]

Nice way of looking at EPR stevendaryl, I never thought of it like that.

Just a small thing, since the EPR correlations can be simulated by a local classical model, would maybe a Bell situation be better? I think your main point carries over without change.

There you would have the frustration between the active and passive view, but without the easy "out" that QM is incomplete due to the existence of a local classical model to simulate the correlations.

 

[Lish Lash]

When Alice measure's her own photon's polarization, her photon is interacting with her filter, and the state of her photon is affected by the filter. The fact that her photon comes through the filter polarized along a particular direction does not imply that the photon had the polarization prior to its passing through. But Alice can use the polarization of her photon after passing through the filter to deduce Bob's photon's polarization. How can that be possible?

Here's how this experiment is interpreted in Bohmian Mechanics: The photons detected by Alice and Bob are particles that each possesses just one (hidden) property: their actual position in 3D space at the point in time they are measured. All other quantum properties, such as polarization, are properties of the pilot wave with which these particles are entangled. When Alice measures the polarization of her photon, the wave function of her measuring device becomes entangled with the wave function of the photon. It is the pilot wave of the entangled photon/measuring device system that produces the measured outcome. So long as Bob's photon remains entangled with Alice's photon, its polarization will be correlated with the outcome of Alice's measurement.

 

[zonde]

Here's how this experiment is interpreted in Bohmian Mechanics: The photons detected by Alice and Bob are particles that each possesses just one (hidden) property: their actual position in 3D space at the point in time they are measured. All other quantum properties, such as polarization, are properties of the pilot wave with which these particles are entangled. When Alice measures the polarization of her photon, the wave function of her measuring device becomes entangled with the wave function of the photon. It is the pilot wave of the entangled photon/measuring device system that produces the measured outcome. So long as Bob's photon remains entangled with Alice's photon, its polarization will be correlated with the outcome of Alice's measurement.

You are explaining entanglement with a help of entanglement. It's circular explanation, don't you see?

 

[stevendaryl]

About entangled photons QT says the the probability of a coincidence between A's and B's results is $\cos(\alpha-\beta)^2$ and no-one misunderstands that.

You are concerned about the things that QT does not tell us. The fact that it says so little could mean it is incomplete, but who cares anyway except philosophers

I actually don't think that it "says so little". I think that what it does (quantum mechanics in the usual rule of thumb) is actually inconsistent, but it's a "soft" inconsistency. I've said before the reason I think that:

• You have the Born rule, which says that when a measuring device interacts with a system to measure some property of that system, then you get a result that is an eigenvalue of the corresponding operator with probabilities given by the squares of the relevant amplitudes.
• Getting a particular result means that the measuring device is in some definite configuration.
• However, if you treat the measuring device as a quantum system, then the interaction of the measuring device with the system it's measuring doesn't produce a single result, but produces a superposition of all possible results.

So on the one hand, you have a prediction from quantum mechanics (Schrodinger's equation) that the measurement device will be described by one state, a superposition of various possible macroscopic results. This prediction is deterministic. On the other hand, you have a prediction from quantum mechanics (Born's rule) that the measurement device will be described by one or another state, where each has a definite macroscopic result. Those are two different, and contradictory, predictions, both made by quantum mechanics.

I call that a "soft" contradiction, because nobody actually computes the state of a macroscopic device by treating it as a quantum-mechanical system and applying Schrodinger's equation. It's too complex to do that. They treat the device classically, or semi-classically, and only consider the Born prediction. But I think that it's actually inconsistent, logically. Maybe only philosophers care about inconsistencies, if there is a work-around.

 

[stevendaryl]

Here's how this experiment is interpreted in Bohmian Mechanics: The photons detected by Alice and Bob are particles that each possesses just one (hidden) property: their actual position in 3D space at the point in time they are measured. All other quantum properties, such as polarization, are properties of the pilot wave with which these particles are entangled. When Alice measures the polarization of her photon, the wave function of her measuring device becomes entangled with the wave function of the photon. It is the pilot wave of the entangled photon/measuring device system that produces the measured outcome. So long as Bob's photon remains entangled with Alice's photon, its polarization will be correlated with the outcome of Alice's measurement.

Yes, Bohmian mechanics doesn't actually treat measurements according to the Born rule, but instead, only uses the Born rule to give probabilities of various locations in configuration space (the position space for all particles involved). So the two aspects of measurement don't directly come into play.

 

[Mentz114]

[..]
So on the one hand, you have a prediction from quantum mechanics (Schrodinger's equation) that the measurement device will be described by one state, a superposition of various possible macroscopic results.
[..]

We've been here. I don't think macroscopic superpositions are possible. The SE does not assert that. People interpreting the SE say that.

 

[stevendaryl]

We've been here. I don't think macroscopic superpositions are possible. The SE does not assert that.

I don't agree. Quantum mechanics certainly has no criterion for when a system is too large to be described by the Schrodinger equation. And if it is really the case that sufficiently large systems are no longer described by the Schrodinger equation, then that would definitely mean that quantum mechanics is incomplete. (It would actually mean that it is false, but only an approximation good for small systems.)

 

[Mentz114]

I don't agree. Quantum mechanics certainly has no criterion for when a system is too large to be described by the Schrodinger equation. And if it is really the case that sufficiently large systems are no longer described by the Schrodinger equation, then that would definitely mean that quantum mechanics is incomplete. (It would actually mean that it is false, but only an approximation good for small systems.)

I am not saying that the SE cannot describe a macroscopic object. I'm objecting to the assumption of superpositions of solutions.
They are mathematically valid but so what. Not every solution to a set of constraints necessarily has a real counterpart.

 

[zonde]

So on the one hand, you have a prediction from quantum mechanics (Schrodinger's equation) that the measurement device will be described by one state, a superposition of various possible macroscopic results. This prediction is deterministic. On the other hand, you have a prediction from quantum mechanics (Born's rule) that the measurement device will be described by one or another state, where each has a definite macroscopic result. Those are two different, and contradictory, predictions, both made by quantum mechanics.

These two predictions are contradictory only if you consider QM complete.
If QM is incomplete there is no contradiction, because the state that is associated with different macroscopic configurations describes only one property of these configurations. That property is the same while other properties are different.

 

[PeterDonis]

I am not saying that the SE cannot describe a macroscopic object. I'm objecting to the assumption of superpositions of solutions.

These two statements are inconsistent. The SE gives you "superpositions of solutions" just by time evolution. You can't arbitrarily exclude "superpositions of solutions" and still use the SE at all.

 

[Mentz114]

These two statements are inconsistent. The SE gives you "superpositions of solutions" just by time evolution. You can't arbitrarily exclude "superpositions of solutions" and still use the SE at all.

I could be wrong but I thought

$\hat{H}=\sum c_n|E_n\rangle\langle E_n|$, so that $\hat{H}E_n\rangle =c_n |E_n \rangle$

The evolution is driven by $e^{\hat{H}t}$ but $\hat{H}$ is idempotent so I think my point below stands.

i.e. an eigenvalue cannot evolve to a superposition ? And a superposition can only evolve to a superposition.

 

[PeterDonis]

an eigenvalue cannot evolve to a superposition ?

An eigenstate of the Hamiltonian will stay an eigenstate of the Hamiltonian, yes. But an eigenstate of the Hamiltonian has no interactions whatever--nothing ever happens to it. So no real object is ever in an eigenstate of the Hamiltonian. Any state that is a reasonable candidate to describe a real object will change under time evolution; and any state that, at some instant of time, happens to look like a reasonable classical state of a classical object, will not stay that way; it will evolve into a "Schrodinger's Cat" type state that does not describe anything like a classical state of a classical object.