Quantum Entanglement and time travel

[RandallB]

I hate to repeat this for the 100th time or so, but in MWI, there is no genuine non-locality in the EPR situation.

And to reply again for almost as many times: A collection of Multiple Worlds to account for the various outcomes to provide a solution certainly is NOT Local to our classical 3D sense of reality or what is meant by Einstein / Bell Local. As I’ve said before it is acceptable to think of a Non-Local version of “Local” for theories such as MWI, BM, etc.
BUT, The mere idea of Multiple Dimensions or Multiple Worlds converted into a Theory is not sufficient to claim something like MWI or BM kills Bell's theorem. Not without producing some real way of demonstrating that an additional dimension, or in your case at least one of the Many Worlds, actually exists.

I happen to believe in a HVT as did Einsein, but I do not accept those that believe the same so much so, they simply declare Bell to be invalid for some silly reason because they don’t like its results denying a HVT.
Neither of us has the right to declare themselves as Right or that Bell results can be ignored as meaningless; unless verifiable proof is provided.
So do us a favor and identify your MWI theory as a Theory and what it might mean IF it is ever proven, and stop representing it as a given fact.
I’m betting I’ll find a HVT before you can find even one additional “World”. But till one of us does, neither is even a main stream theory let alone worthy of being put forward as fact.

 

[Careful]

I never made a claim for a determinate universe!

Ok, I should have asked in full that I would like to have a reference from Einstein where he explains his position about determinate versus deterministic. Was this so hard to understand from the sentence ``I was clearly asking for a source to establish your claim of a determinate instead of a deterministic universe'' given that just before that we were discussing whether Einstein said determinate in the sense you imply instead of deterministic ?

Just a determinate solution to EPR issues in that at the point of creation of two “entangled” particles determinate HV’s could provide a Local Realist solution to “entanglement” not a problematic (stochastic) one.
That’s why I couldn’t understand your use of stochastic in post #55 or what “a locally stochastic universe” could even mean. Einstein’s HVT takes the view that the problematic (stochastic) solutions to EPR are incomplete and deal with microphysics not the whole or even 'local' universe.

Euh it seems to me that if a determinate theory can cover microphyiscs , it should cover for macrophysics as well. So, for good understanding (because this was not clear from your previous post) : with determinate you mean that the outcome of an experiment is fixed once the HV's are assigned after creation of the entangled pair ?

The quote you gave me (from Prizbram, not Einstein) refers to establishing a determinate explanation to a microphysics problem with very limited boundaries, not the question of a deterministic universe. That is an unfounded extrapolation to the large scope of the whole universe, unjustified by only any conclusions from a limited EPR test.

Why, why would you even want to look for an EPR solution if you cannot extend the same laws to the universe ? This makes no sense at all, since the mere motivation for hidden variables originates from the way macroscopic physics works - given the desire to have one unifying dynamics.

 

[ueit]

Every reputable experiment so far on EPR/entanglement indicates that only non-local solutions will work and strong imply that no truly Local HVT can be possible. So, there is a huge reason to believe this mechanism is non-local.

Bell's theorem states that if the hidden variables do not depend on the detectors' settings the inequality must hold.

There are ways in which this dependence can be enforced in a perfectly local manner, without postulating other dimensions, holograms, backwards causality, etc. I'll give you an example.

We have a source producing entangled particles and two detectors. By "detector" I mean everything that is related to the polarizer, including the device selecting its orientation (randomizer, human, monkey pressing buttons, gamma rays together with the quasar they come from, etc.)

If the proposed LHV theory is deterministic, the orientation of the detectors at any time can be inferred from their state at any previous time.

We have to make the following two assumptions:

1. The state of the detectors is made available at the source location by means of a local field (probably classical EM field would do)

2. The entangled particles are generated as a result of this field (which contains all the information regarding both the time of detection and detector orientation) in accordance with the Malus law.

But there are several different ways to reach a non-local solution, including some that do not require physical interactions taking place faster than the speed of light. Some with a form of extra dimensional part of the items being tested remaining connected even as they separate in our three dimensions. So with so many alternatives like BM MWI etc. in addition to QM theories and no conclusive result on A correct one, just that it does seem to work “Non-Locally”, the issue is NOT something we are "pretty sure about" as GUS may have thought.

I have some doubts regarding the non-locality of Bohm's interpretation. As far as I understand it, the particles are guided by a wave which evolves on its own since big-bang. There is no need for particle A to receive information about what particle B is doing. They both move according to the universal wavefunction and the known local fields.

Although the evidence is strong for non-local, I would agree that there is no reason to stop those that wish to look for a Local solution if they wish. They just need to understand they are going against the majority view, and there is nothing automatically wrong with that. And they need to accept the risk of not making any real progress – and I do accept that risk myself.

I'm not a physicist and I don't know exactly what is the "majority view" but I agree with you that LHV theories are not very high in the physicists' preferences. I'm still puzzled by the wrong interpretation ascribed by many to the EPR experiments.

 

[mgelfan]

Definition of an arrow field : a function from the points of the (spatial) manifold to its tangent space. As you might know a function can have only one image. The arrow of time means that there exists a globally well defined timelike vectorfield such that the motion of every particle is timelike and has positive projection on the field (for signature +---).

I'm not using this model ... rather, just wondering about the connection between expanding wavefronts (local and cosmological) and an arrow of time. In many of the physical problems that I'm confronted with, I've found it useful to begin by thinking in terms of the physical phenomena themselves, rather than using some mathematical model or other at the outset.

In your example there is no direction in which space moves as seen from any point, space just moves outwards from it.

The direction of the arrow of space is away from points of interaction.
In homogenous 3D media, disturbances propagate pretty much isotropically.

Expanding water wavefronts (moving outward from, eg., the interaction of a pool of water with a stone dropped into it) are frequently used as a local example of the radiative arrow of time, aren't they?

In this case the arrow of space is the arrow of time.

So, you might wonder whether expansion somehow relates to an arrow of time. No, it doesn't, ...

I guess I'll have to disagree with you on this then ... at least for the time being.

The fundamental motion of our universe is isotropic expansion, and the fundamental force is the kinetic energy (imparted via the Big Bang) of the expansion. This isotropic expansion on cosmological scales is obviously connected to the radiative arrow of time observed locally. Don't you think so?

... a Friedmann universe which recollapses again also contains an arrow of time, likewise does a Schwarzschild universe which neither expands nor contracts.

But these are just models -- neither of which describes our universe.

 

[Careful]

Expanding water wavefronts (moving outward from, eg., the interaction of a pool of water with a stone dropped into it) are frequently used as a local example of the radiative arrow of time, aren't they?

In this case the arrow of space is the arrow of time.

Your analogy is useless since by throwing in ONE stone you break homogeneity : I have commented on that already and said you can define an arrow of space in this case, but nevertheless this has nothing to do with the arrow of time). One of my objections is about your abuse of the word ``arrow of space'', an arrow is a vector, outwards expansion is a scalar : that is the eigentime derivative of the expansion of a geodesic congruence.

But these are just models -- neither of which describes our universe.

Euh, (a) it is no known wheter a big crunch is excluded or not (b) a Schwarzschild universe is quite a good approximation to a non rotating black hole in the center of some galaxy.

 

[RandallB]

Ok, I should have asked in full that I would like to have a reference from Einstein where he explains his position about determinate versus deterministic. Was this so hard to understand from the sentence ``I was clearly asking for a source to establish your claim of a determinate instead of a deterministic universe'' given that just before that we were discussing whether Einstein said determinate in the sense you imply instead of deterministic ?

Again Einstein did not speak to a “deterministic universe'' but determinate variables. He was certainly smart enough to not jump to global conclusions from a small local event until he at least had the details of how a HV worked to decide if or how it might be applied to a larger perspective. Why would he even consider making such a leap with no information?

I have some doubts regarding the non-locality of Bohm's interpretation. As far as I understand it, the particles are guided by a wave which evolves on its own since big-bang. There is no need for particle A to receive information about what particle B is doing. They both move according to the universal wavefunction and the known local fields.

Until you can show what and exactly where a “BM universal wavefunction” is in strictly Local Terms and how it provides its guide wave function, I’ll consider it NON-Local as do most.

 

[Careful]

Again Einstein did not speak to a “deterministic universe'' but determinate variables. He was certainly smart enough to not jump to global conclusions from a small local event until he at least had the details of how a HV worked to decide if or how it might be applied to a larger perspective. Why would he even consider making such a leap with no information?

You basically did not answer neither my request, nor some questions I had. Euh, Einstein himself made the biggest extrapolation in history on virtually no grounds : he created with GR a theory of the universe. So, why would he refrain himself here (while the logic in both cases appears to be the same to me) ?

 

[RandallB]

You basically did not answer neither my request, nor some questions I had. Euh, Einstein himself made the biggest extrapolation in history on virtually no grounds : he created with GR a theory of the universe. So, why would he refrain himself here (while the logic in both cases appears to be the same to me) ?

The logic is clear to me that it is not the same. GR even has tests to support it, while the HV hasn't even been documented to even consider what it may show related to the larger universe, use a bit of common sense.

And for the third time I do not know how to provide you a referance to something Einstein did not say, by what logic do you think that could be done.
Why haven't you shown a specific Einstein reference to a “deterministic universe'' that is not someones convenient reinterpretation of a determent HV EPR comment, to support something he did not really mean or say.
Without that I see no point in extending this pointless fencing.

 

[Careful]

The logic is clear to me that it is not the same. GR even has tests to support it, while the HV hasn't even been documented to even consider what it may show related to the larger universe, use a bit of common sense.

Things become only real when predictions are supporting some part of a theory, nobody has seen gravitational waves so far, no one knows whether there is a singularity behind the event horizon of a black hole. Oh yes, and let's not forget that our universe seems to square uneasily with it, given the issues of dark matter and energy - GR has only been properly tested in the solar system, seems a tiny place in comparison with our universe. Moreover, I was not saying that any hidden variable theory (suitable for microphysics) immediately needed to be extrapolated to the entire universe ! I said that I would not consider a hidden variable theory which could not.

And for the third time I do not know how to provide you a referance to something Einstein did not say, by what logic do you think that could be done.

You said: ``Einstein said determinate which did not imply deterministic (in his mind)'' while many of us do think he did imply deterministic, so where is your source ? It exists not, fine, so he basically only said that the universe is determinate (in the sense you more or less explained), but my point was that he also saw statistical theories as inadequate (which you acknowledged). So, then I suggested the possibility of a locally stochastic universe (like a random walk, Sorkin and Rideout have made (non local) random walk causal set models). Here, you did not know what I meant (you might want to look up the latter papers - GRW is an example of a non local stochastic collapse theory) ; that caused lot's of confusion with me - since in my mind - only determinstic models are left as a *reasonable* option. But the latter is the very thing you are pointing out to me as being an unnecessary restriction. Therefore, it seems you are talking merely semantics here (which is totally useless); perhaps it would be better if you would present a realistic example of a determinate, but not deterministic hidden variable theory for - say - EPR.

Why haven't you shown a specific Einstein reference to a “deterministic universe'' that is not someones convenient reinterpretation of a determent HV EPR comment, to support something he did not really mean or say.
Without that I see no point in extending this pointless fencing.

Well, you know, I did not make an issue about this one tiny sentence ! Moreover, at one moment I said that Einstein probably considered many options in his life, something which is well known about him. Wolfgang Pauli once made more or less the remark that ``usually a scientist sticks to a direction he chooses for a few years, but Einstein can come up with an entirely new theory in half a year! ´´.

 

[vanesch]

And to reply again for almost as many times: A collection of Multiple Worlds to account for the various outcomes to provide a solution certainly is NOT Local to our classical 3D sense of reality or what is meant by Einstein / Bell Local. As I’ve said before it is acceptable to think of a Non-Local version of “Local” for theories such as MWI, BM, etc.

If you can formulate the theory in a geometrical way (in other words, if its formulation is Lorentz-invariant), then it is "local" enough to me. This is not the case for BM, but it is for MWI. Any genuine projection cannot be written in such a Lorentz-invariant way, and hence violates locality. However, the unitary dynamics can.

BUT, The mere idea of Multiple Dimensions or Multiple Worlds converted into a Theory is not sufficient to claim something like MWI or BM kills Bell's theorem.

What you need, for Bell's theorem to apply, is that there are definite outcomes at Alice and at Bob, because we are talking about probabilities for them to be realized, and it is this probability measure which cannot be set up without simultaneous knowledge of the two polarizer settings. But in MWI, there is no such thing as the unique outcome at Alice and a unique outcome at Bob, so there is no probability measure to be set up in the first place. Hence, Bell's theorem doesn't apply to this case.

Not without producing some real way of demonstrating that an additional dimension, or in your case at least one of the Many Worlds, actually exists.

No, it is a matter of logic. One cannot say that a certain conclusion holds in all cases, when there is demonstrably a counter example - independent of whether that counter example is actually true or not in reality. The conclusion here would be that "physics is non-local", while there is a clear logical construction which reproduces the *observed* probabilities, and which doesn't suffer an explicit non-locality. Even if in the end, this logical construction doesn't correspond to reality, its logical existence proves that the reasoning that lead to the "non-locality" conclusion is erroneous. In the same way as the very construction of BM proves that there CAN be a hidden-variable construction that makes the same predictions as QM, contrary to the "theorem" by von Neumann. The very logical existence of BM makes that the theorem by von Neumann must be false. In the same way, the logical existence of MWI proves that the conclusion of non-locality from EPR is erroneous.

Neither of us has the right to declare themselves as Right or that Bell results can be ignored as meaningless; unless verifiable proof is provided.

Of course Bell's result is not meaningless. Only, his theorem doesn't apply to those cases where his premisses are not valid. Now it seems like such an evident premisse that Alice and Bob "have" a result, but in MWI, that's simply not the case: they both have both results. So Bell's theorem doesn't apply to MWI.

So do us a favor and identify your MWI theory as a Theory and what it might mean IF it is ever proven, and stop representing it as a given fact.
I’m betting I’ll find a HVT before you can find even one additional “World”. But till one of us does, neither is even a main stream theory let alone worthy of being put forward as fact.

MWI, as a logical construction, exists, for a fact. Whether it corresponds to reality is a totally different matter. The same can be said about BM.
Now, MWI is entirely formulated in a lorentz invariant way (which means it is local, to me). So there clearly exists a logical construction which 1) is lorentz-invariant (hence local) and 2) has all the observable predictions of standard QM.
As such, one cannot claim, that ALL thinkable schemes which obey 2) must violate 1), because there's a logical counter example.

 

[Demystifier]

Would that not imply in effect that our destiny is fixed and we can do nothing to change it ?

Not necessarily. It is possible that free will exists, but that it does not act at a specific time. For example, you may decide that tomorrow you will eat ham. But the act of decision does not occur today, nor tomorrow, nor a day after tomorrow. You simply decide it, without attributing a moment of time at which this decision occurs. This is not how this decision is subjectively perceived by your brain, but this is how it really is (in a block universe with a free will).

 

[Demystifier]

Now, MWI is entirely formulated in a lorentz invariant way (which means it is local, to me).

OK, it is local for you. But is it local for itself? Is the whole Universe (the collection of All worlds of mwi) local? Is the split/branching of the Universe in a number of different copies a local event? And if you say that this question is irrelevant, isn't such a view of nature quite antropomorphic?

 

[RandallB]

….., fine, so he basically only said that the universe is determinate (in the sense you more or less explained),

You miss quote me again; I did not explain a “determinate” vs. “deterministic” universe! I said Einstein expected the HV in an EPR to provide “determinate” not problematic solution, and that is all he said. Without actually finding a HV, I’ve seen nothing to suggest that he jumped to the conclusion or opinion that the entire universe was “deterministic” or "determinate", and that all his discoveries and every thought had been predestined from the Big Bang or even earlier. I do not accept that all these posts we fuss over here are meaningless events already set by a predetermined deterministic universe and the idea that Einstein did is balderdash! I don’t care if such a view comes from a PHD, they need to do much better than their interpretation of what Einstein’s comments on EPR might mean for a full universe view of causality. That is their extrapolation not Einstein’s.

…perhaps it would be better if you would present a realistic example of a determinate, but not deterministic hidden variable theory for - say - EPR.

Easy
A photon approaches a PDC at some point (unknown & undeterminable to the photon) ahead. Likewise the PDC cannot know or determine exactly when or it what specific condition all the variables that makeup the EM details of that photon. But when they do interact, all these unknown variables combine to produce two photons. The random direction of one photon within a well defined “cone” of options is perfectly matched by the direction of the second based on conservation laws. Likewise, the polarity of the two photons is set one V the H. These parameters are set at the LOCAL creation of the two photons and remain determinate and unchanging until there interact with something else in each of there unknowable paths. PLUS, going with them on that path is the HV also determinate and unchanging and provides the fixed and unchanging information required to account for “entanglement” correlations.
Now if you can show the exact & complete details of such a HV; only then can you make meaningful judgments to speculate on an interpretation that could define with precision all the unknown details about the PDC and the Photon as it approached, to ultimately generate the two photons. Until that can be done you cannot, and I do not believe Einstein ever presumed, that all the events in the universe that lead up to the conversion of that one photon turning into 2 photons was preset in a “deterministic universe”.
That is an unfair, self-serving, and unsupported claim on Einstein’s real work.
And I do not consider that a small point.

 

[RandallB]

If you can formulate the theory in a geometrical way (in other words, if its formulation is Lorentz-invariant), then it is "local" enough to me.

That only means you have a lower standard for "local" than I do and IMO it is lower than the Einstein/Bell standard.
Also IMO you cannot solve a problem by simply lowering the standards.
AFAIC local to the Einstein/Bell standard is required to confirm a “Local” theory, and adding the need for even one additional “world” beyond the 2D Classical one we seem to see ourselves in, means a Non-Local reality.

As evidence indicates reality is expected to be Non-Local I don’t understand why you don’t want to define MWI a Non-Local. The idea that by playing some game to define a theory as “Local” is enough to presume it as correct is just silly.

As I’ve said you are entitled to your opinion, but please respect the integrity of this forum and stop declaring it as a fact. I do not care to debate the details, of MWI.

 

[vanesch]

That only means you have a lower standard for "local" than I do and IMO it is lower than the Einstein/Bell standard.

What does it mean, local ? Local means that things that are associated with a spacetime point are determined as much as can be by all things that are associated to the past light cone of that spacetime point, and that, once this past lightcone is given, adding or not, any part of the state description outside this lightcone doesn't alter this. A theory which can be written down in a Lorentz-invariant way automatically satisfies this requirement (which is why you cannot write down BM in a Lorentz-invariant way).
The Schroedinger equation (the unitary evolution) satisfies this requirement. As this is the only physical ingredient of MWI, one can say that this version of quantum theory is local in this sense. What makes quantum theory with an explicit projection non-local, is the projection postulate. If you apply a projection on one component, you automatically alter the contributions (by eliminating some of them) of spacelike connected physical systems.

AFAIC local to the Einstein/Bell standard is required to confirm a “Local” theory, and adding the need for even one additional “world” beyond the 2D Classical one we seem to see ourselves in, means a Non-Local reality.

That's a random requirement you postulate. As I said, the Bell requirement is satisfied for MWI: at no point, there is an influence on the part of the state description at event A, by whatever goes on at event B, if B is outside of the past lightcone of A - this is exactly Bell's requirement for locality.
However, in MWI, there are no "outcomes" of experiments independent of the observer that makes them (and for every combination of possible outcomes, there exist observers that have "seen" them). So, what ruins Bell's logic, is that THE observation at A is influenced by THE setting and/or outcome at B, given that at A, both observations take place, in an uninfluenced way by the settings/outcomes at B.

As evidence indicates reality is expected to be Non-Local I don’t understand why you don’t want to define MWI a Non-Local. The idea that by playing some game to define a theory as “Local” is enough to presume it as correct is just silly.

Because the evidence DOESN'T indicate that reality is non-local. It is only if you impose extra conditions on reality that it must turn out to be non-local, and the very logical existence of MWI proves that.

As I’ve said you are entitled to your opinion, but please respect the integrity of this forum and stop declaring it as a fact. I do not care to debate the details, of MWI.

Well, I can understand that you do not want to discuss the logical counter example to the "theorem" you postulate. Again, I'm not claiming that reality corresponds to MWI. I'm only pointing out that there exists a logical counter example to the claim you are making, namely that "evidence indicates that reality is non-local". I have a local theory in every sense of the word (ontological state related to spacetime point A is uninfluenced by whatever is the ontological state related to a spacetime point B which is spacelike connected to A, if we have the ontological state description related to the past light cone of A). It complies with the usual observational predictions of QM. Hence, the usual observational predictions of QM cannot lead logically to the conclusion that nature MUST BE non-local, given the existence of this counter example.

I'm not lowering the standards of "locality" by doing this. If you think I'm doing this, then point out what aspect of the unitary time evolution is NOT respecting locality.

 

[ueit]

Until you can show what and exactly where a “BM universal wavefunction” is in strictly Local Terms and how it provides its guide wave function, I’ll consider it NON-Local as do most.

Think of the universal wave function as a field existing in space or as a curvature of space that particles follow. If the universe is in a stationary state this curvature just is, it doesn't change with time. If not, it changes in a deterministic manner. Either way, no information of any sort is exchanged between the source and detectors in an EPR experiment.

 

[ueit]

As evidence indicates reality is expected to be Non-Local.

I think it doesn't. I've presented you a local mechanism for EPR without any requirement for new dimensions/worlds/etc. I'd like to see what your objections against this mechanism are.

 

[skippedstate]

I am not in the same league as you all, but I do share an interest in your topics. I am humbled by your intellects, and am looking for more understanding. I love reading about this stuff!

One thing I am sure you can correct my logic on, is that, in your post, speaking on memories, you felt that the memories likely would not be there had we gone back to kill our grandpa. Call me naive, but how would our physical body be able to traverse backwards (or to parallels) without our memories, along with every other cell? (praying that it is an answer NOT so elementary... :) )

 

[RandallB]

RB: “ Until you can show what and exactly where a “BM universal wavefunction” is in strictly Local Terms and how it provides its guide wave function, I’ll consider it NON-Local as do most.

Think of the universal wave function as a field existing in space or as a curvature of space that particles follow. If the universe is in a stationary state this curvature just is, it doesn't change with time. If not, it changes in a deterministic manner. Either way, no information of any sort is exchanged between the source and detectors in an EPR experiment.

RB … evidence indicates reality is expected to be Non-Local.

I think it doesn't. I've presented you a local mechanism for EPR without any requirement for new dimensions/worlds/etc. I'd like to see what your objections against this mechanism are.

To just what EVIDENCE do you refer?
Your provided “mechanism” (?) is no evidence. Also, the WHAT, WHERE, AND HOW it gives it well short of being exact in any detail. Plus, as you describe the “state of the universe” (whatever that may be) as stationary or changing deterministically; that “state” you require is well outside the bounds of the “Local” part of EPR. That Non-Local character is similar to MWI selecting an appropriate “world” with its entire surrounding non-local character configured appropriately to justify EPR correlations. I do not ask that you two abandon your opinions as being wrong, just stop demanding that everyone accept you opinion(s) as the correct one!

The two of you cannot both be right, so at least present convincing evidence to each other to demonstrate which is correct BM or MWI. They maybe you will save the entire scientific community that is wasting so much time and effort pursuing so many different things that do not agree with either of you.

I’ll disengage from this debate until I see ueit & vanesch concur on which is correct MWI or BM.
Until then I choose to continue my own individual search for a true Local Theory (I agree, a long shot), without the distraction of these two Non-Local theories claiming to be local.

 

[mgelfan]

Your analogy is useless since by throwing in ONE stone you break homogeneity : I have commented on that already and said you can define an arrow of space in this case, but nevertheless this has nothing to do with the arrow of time). One of my objections is about your abuse of the word ``arrow of space'', an arrow is a vector, outwards expansion is a scalar : that is the eigentime derivative of the expansion of a geodesic congruence.

Maybe we should call it the arrow of motion.
The arrow of motion, any motion (including expansion), has direction and magnitude. My point in addressing this arrow of space and arrow of time thing was that it didn't make much sense to me to talk about an arrow of space as being independent of an arrow of time if space is taken to refer to the material universe, and time is taken to refer to the material universe in motion.

Whether you want to put it in terms of space or in terms of time, there is a fundamental motion underlying all phenomena -- the expansion of the universe. The radiative arrow is fundamental.

... (a) it is no known wheter a big crunch is excluded or not (b) a Schwarzschild universe is quite a good approximation to a non rotating black hole in the center of some galaxy.

The universe is expanding and the energy imparted via the Big Bang is dispersing and dissipating. A Big Crunch would require more energy, not less. So, Big Crunch models can be excluded.

 

[ueit]

Your provided “mechanism” (?) is no evidence. Also, the WHAT, WHERE, AND HOW it gives it well short of being exact in any detail.

It is good evidence against your interpretation of EPR. I only need a logically consistent counterexample, not a TOE.

Plus, as you describe the “state of the universe” (whatever that may be) as stationary or changing deterministically; that “state” you require is well outside the bounds of the “Local” part of EPR.

The experiment is a part of that state and, as a result, it displays the symmetries embedded in that state.

That Non-Local character is similar to MWI selecting an appropriate “world” with its entire surrounding non-local character configured appropriately to justify EPR correlations. I do not ask that you two abandon your opinions as being wrong, just stop demanding that everyone accept you opinion(s) as the correct one!

Look, I think you are redefining the word "local" here. The sea level at your place being similar with the one at my place is hardly a proof for our ftl communication.

I don't demand anything from you but I expect you to back up your claims.
You reject my counterexample for not being detailed enough but this is hardly a reason. What you need to show is that it is either logically inconsistent or it violates accepted physics.

The two of you cannot both be right, so at least present convincing evidence to each other to demonstrate which is correct BM or MWI. They maybe you will save the entire scientific community that is wasting so much time and effort pursuing so many different things that do not agree with either of you.

In fact we are probably both wrong. This doesn't make you right, though.

I’ll disengage from this debate until I see ueit & vanesch concur on which is correct MWI or BM.

I cannot compete with vanesch on this, I'm only trying to understand this stuff.

Until then I choose to continue my own individual search for a true Local Theory (I agree, a long shot), without the distraction of these two Non-Local theories claiming to be local.

Can you provide us with some insight about what you are looking for? Does any of the existing theories/interpretations/hypotheses present any resemblance with your "true Local Theory"?

As far as I remember, your position is that both QM and GR are non-local. Given the fact that these theories are the best we have, can I ask you for what reason do you look for a theory that necessarily denies both of them?

 

[Careful]

You miss quote me again; I did not explain a “determinate” vs. “deterministic” universe! I said Einstein expected the HV in an EPR to provide “determinate” not problematic solution, and that is all he said. Without actually finding a HV, I’ve seen nothing to suggest that he jumped to the conclusion or opinion that the entire universe was “deterministic” or "determinate", and that all his discoveries and every thought had been predestined from the Big Bang or even earlier. I do not accept that all these posts we fuss over here are meaningless events already set by a predetermined deterministic universe and the idea that Einstein did is balderdash!

GR is a determinate theory, and are we not all using it for the entire universe as a good approximation ? It seems YOU are pretty religious about not having determinism.

Easy
A photon approaches a PDC at some point (unknown & undeterminable to the photon) ahead. Likewise the PDC cannot know or determine exactly when or it what specific condition all the variables that makeup the EM details of that photon. But when they do interact, all these unknown variables combine to produce two photons. The random direction of one photon within a well defined “cone” of options is perfectly matched by the direction of the second based on conservation laws. Likewise, the polarity of the two photons is set one V the H. These parameters are set at the LOCAL creation of the two photons and remain determinate and unchanging until there interact with something else in each of there unknowable paths. PLUS, going with them on that path is the HV also determinate and unchanging and provides the fixed and unchanging information required to account for “entanglement” correlations.

Sure that is more or less the most general scenario (in which you could account for conspiration, stochastic theories, as well as faster than light). I asked you for a specific non-deterministic, but determinate example and you did no such thing at all.

Now if you can show the exact & complete details of such a HV; only then can you make meaningful judgments to speculate on an interpretation that could define with precision all the unknown details about the PDC and the Photon as it approached, to ultimately generate the two photons. Until that can be done you cannot, and I do not believe Einstein ever presumed, that all the events in the universe that lead up to the conversion of that one photon turning into 2 photons was preset in a “deterministic universe”.

Why would I need an HV theory of entanglement prior to figuring out a model for a photon ; the latter could very well be found by relying upon well known physics. But again you say, I do not *believe* that Einstein ever presumed a deterministic universe (many people must misread Einstein then, including me, 't Hooft, ..).

That is an unfair, self-serving, and unsupported claim on Einstein’s real work.
And I do not consider that a small point.

Sure, sure, but the point so far is that you did not do anything but pointing out to others what some famous physicist did not say according to you. By the way, what observation is concerned, I guess determinstic theories are indistinguishable from determinate ones; so all this discussion seems to turn around religious tastes.

 

[RandallB]

I don't demand anything from you but I expect you to back up your claims.
In fact we are probably both wrong. This doesn't make you right, though.

Fine that means you think I’m probably right as the ONLY claim I made was it was wrong to consider BM Local or as haven been accepted as “correct”.

GR is a determinate theory, and are we not all using it for the entire universe as a good approximation? It seems YOU are pretty religious about not having determinism.

No not until someone resolves Lee Smolin’s points about GR being background independent. His new book is an OK read but his papers on the subject are easily found and should be understandable by most on this forum.

And I don’t know about religious, but I’m very well convinced that you and I have free will and are not just going though the motions of responding here in accord with some predetermined “deterministic universe”.
The rest of your comments are still so far off the point for me they are “not even wrong” so I can even comment.

Look guys as far as I’m concerned between careful ueit & vanesch I’m seeing three different versions of Non-local theories, each claiming to be “local” and as far as I can see by little more than that claim of being “local” as being the correct theory of reality. None of that has been shown as “accepted physics” in the view of the majority of prominent scientist.

Even at three against one I’ve not changed my mind, as the only thing I think I can agree with you guys on is that showing AND PROVING a local solution would disprove both “entanglement” and “superposition” and “time travel” as well. And that such a proof would displace all non-local theories. BUT AFAIC to do that, the standard for local needs to be much higher that any of you seem to be willing to accept. So allow me to depart this and I’ll stick with my standard for local, even if it might be impossible to satisfy - - that’s my problem.

 

[Careful]

No not until someone resolves Lee Smolin’s points about GR being background independent.

Euhhh, background independence has nothing to do with GR being determinate ! And neither do I consider it to be a crucial ingredient for a future theory of quantum gravity.

And I don’t know about religious, but I’m very well convinced that you and I have free will and are not just going though the motions of responding here in accord with some predetermined “deterministic universe”.

So, that confirms my point.

The rest of your comments are still so far off the point for me they are “not even wrong” so I can even comment.

Look guys as far as I’m concerned between careful ueit & vanesch I’m seeing three different versions of Non-local theories, each claiming to be “local” and as far as I can see by little more than that claim of being “local” as being the correct theory of reality. None of that has been shown as “accepted physics” in the view of the majority of prominent scientist.

You confuse since as long as I am here locality with causality, that's all there is to it. Bell didn't invent the terminology ``local causality'' for nothing you know.

Even at three against one I’ve not changed my mind

Bravo, an heroic act.

BUT AFAIC to do that, the standard for local needs to be much higher that any of you seem to be willing to accept. So allow me to depart this and I’ll stick with my standard for local, even if it might be impossible to satisfy - - that’s my problem.

Perhaps, you should ask wether you can find a local, determinate, realistic theory of photons first, using your notion of locality, such that Maxwell theory is recovered in a suitable limit. You might end up very dissapointed soon.

Careful

 

[vanesch]

That Non-Local character is similar to MWI selecting an appropriate “world” with its entire surrounding non-local character configured appropriately to justify EPR correlations. I do not ask that you two abandon your opinions as being wrong, just stop demanding that everyone accept you opinion(s) as the correct one!

The two of you cannot both be right, so at least present convincing evidence to each other to demonstrate which is correct BM or MWI. They maybe you will save the entire scientific community that is wasting so much time and effort pursuing so many different things that do not agree with either of you.

Both, MWI and BM are "correct" theories in the sense that they set up a logically coherent construction (at least to a level of informal rigor which is usual with physical theories). That's what I'm trying to tell you: logically, these theories exist. Whether they correspond to our universe is another matter of course (probably not !), but that's not the point. The point is that they exist, as theories, and they both agree with the experimental results which are under discussion here (EPR correlations). So their logical existence means that one cannot deduce logically, from these experimental predictions, any property which BM or MWI would not have, given that they logically exist.

von Neumann already committed this error with BM: he claimed that certain predictions of QM could never be obtained with a deterministic HV theory. BM does exactly that, so von Neumann's reasoning must have been wrong, irrespective of whether BM is or isn't "true" in nature.

In exactly the same way, MWI has an entirely local dynamics, and makes the same predictions of observation as does standard QM. As such, any claim that one can deduce, from these observations, that the dynamics must be non-local, is just as erroneous as von Neumann was in his case. Again, irrespective of whether MWI is "true" in nature or not.

So, logically, BM and MWI are both "correct", as is any well-constructed theory. This has nothing to do with whether it is the correct description of nature. Newtonian mechanics is also "correct".

 

[Demystifier]

Vanesch, I would very appreciate if you could answer to my post #82.
Thanks!

 

[vanesch]

OK, it is local for you. But is it local for itself? Is the whole Universe (the collection of All worlds of mwi) local? Is the split/branching of the Universe in a number of different copies a local event? And if you say that this question is irrelevant, isn't such a view of nature quite antropomorphic?

"The whole universe" in MWI is nothing else but the state vector, which evolves under unitary evolution. So the question of locality is related to this unitary evolution. It doesn't need to be so. For instance, the unitary evolution induced by, say, the Coulomb hamiltonian in NR QM certainly doesn't induce a local unitary evolution (in the same way as the Coulomb force in classical phase space doesn't induce a local phase flow, given that there is "action at a distance"). But if the interactions in the hamiltonian (which is the generator of unitary evolution) are local, then the unitary flow in Hilbert space is just as local as the phase space flow in classical mechanics, if the interactions are local. This can easily be verified by the fact that this unitary evolution can be written out in a Lorentz-invariant way.

The "splittings in worlds" in MWI is a pure observer-dependent concept: not for all observers, the universe is "split" in the same way. In fact, this splitting is simply the projection on the different "subspaces of awareness" by the observer (that is, those subspaces of hilbert space which correspond to different "states of awareness", which you can grossly imagine to correspond to different memory states which correspond to "observations"). "Worlds" do not have any objective ontological existence in MWI, independent of an observer.

Look at the wavefunction, where Alice has done a measurement and Bob has done a measurement, but they didn't talk to each other yet:

|psi> = |alice+> (u |bob+> + v|bob->) + |alice->(w |bob+> + x |bob->)

For Alice, there are 2 worlds, one in which she has seen the + outcome, and one in which she has seen the - outcome. Her local state description is |alice+> in one world, and |alice-> in another, and the |alice+> state has an overall weight of u^2 + v^2, while the |alice-> world has an overall weight of w^2 + x^2.
Note that these elements are in no way affected by what happens at Bob, as long as this is a local, unitary evolution. Whatever happens to the "bob" states, the weight of the Alice+ state will always remain u^2 + v^2.

We can re-write the SAME state vector from Bob's PoV:
|psi> = |bob+>(u |alice+> + w |alice-> + |bob-> (v |alice+> + x |alice->)

For Bob, there are also 2 worlds, one in which he has seen the + outcome, and one in which he has seen the - outcome. The bob+ state has an overall weight of u^2 + w^2 and the bob- state has an overall weight of v^2 + x^2.
Again, this local state description of Bob is independent of what happens at Alice: the weights of these two states will remain the same under any unitary transformation at Alice's place.

Note also that Alice's worlds have nothing to do with Bob's worlds.

Now, imagine they come together, and exchange their information. This alters of course the "state of awareness" for both alice and bob, but can only occur when they are in local contact.

We now have an evolved state:
|psi2> = u|bob++> |alice++> + w |bob+->|alice-+> + v|bob-+>|alice+-> + x |bob-->|alice-->

We now have an altered state for alice, which can be in 4 different states:
alice++, alice+-, alice-+ and alice--, with weights respectively u^2, v^2, w^2 and x^2.

This modification of alice's state description came about because of her LOCAL interaction with Bob, when he came to tell her his results. The unitary evolution which did this was local to the place of meeting.

Alice now lives in 4 worlds (and so does bob), and this time the worlds coincide between alice and bob (because they are in local interaction).

Notice the difference with a projection-based (and hence non-local) explanation of this story:
Before Alice or Bob performs a measurement, the state is:
|psi> = |alice0> (|a+>(u |b+> + v|b->) + |a->(w |b+> + x |b->)) |bob0>

(where we introduced the a-states, of the particle at Alice's place,and the b-states, of the particle at Bob's place).

Alice's weight is 1 for her state alice0.
However, the weight for the a+ state (at Alice's place) is (u^2 + v^2) while the weight for the a- state (at Alice's place) is (w^2 + x^2)

Let us first say that Bob performs a measurement, and his outcome is +:
this MODIFIES the statevector by projection:
|psi'> = |alice0> (|a+>(u |bob+>) + |a->(w |bob+>))/sqrt(u^2 + w^2)

and note that this CHANGES the weights of the a-states at Alice:
instead of a weight u^2 + v^2, we now have a weight of u/sqrt(u^2 + w^2) for the a+ state, and a weight w/(sqrt(u^2 + w^2) instead of (w^2+x^2) for the a- state.

So we see here that a state description of something at ALICE has been changed by a remote interaction (Bob's measurement). This is what is non-local in the projection postulate. It is the essence of the EPR effect.

Alice's state description has not been altered however. But of course, as Alice is going to interact locally with a, she will find a different state now than if Bob wouldn't have measured (with projection) on his side.

Alice's measurement will do nothing special to Bob's: imagine she finds +:
|psi"> = |alice+>|bob+>

This interaction doesn't do anything "non-local". Bob's state was +1 with weight 1, and this remains so. The culprit was the first measurement by bob, who ALTERED the state description of the a-particle remotely, by projection. This is the explicit non-local mechanism in "standard" projection-based quantum mechanics. Mind you that what introduces the alteration of the local state description is the projection: the fact of throwing away some terms in the wavefunction for ALL constituents, local or remote. The unitary evolution cannot do such a thing (if the interactions in it are local), because there is conservation of hilbert norm.

 

[Demystifier]

"The whole universe" in MWI is nothing else but the state vector, which evolves under unitary evolution. So the question of locality is related to this unitary evolution. It doesn't need to be so. For instance, the unitary evolution induced by, say, the Coulomb hamiltonian in NR QM certainly doesn't induce a local unitary evolution (in the same way as the Coulomb force in classical phase space doesn't induce a local phase flow, given that there is "action at a distance"). But if the interactions in the hamiltonian (which is the generator of unitary evolution) are local, then the unitary flow in Hilbert space is just as local as the phase space flow in classical mechanics, if the interactions are local. This can easily be verified by the fact that this unitary evolution can be written out in a Lorentz-invariant way.

The "splittings in worlds" in MWI is a pure observer-dependent concept: not for all observers, the universe is "split" in the same way. In fact, this splitting is simply the projection on the different "subspaces of awareness" by the observer (that is, those subspaces of hilbert space which correspond to different "states of awareness", which you can grossly imagine to correspond to different memory states which correspond to "observations"). "Worlds" do not have any objective ontological existence in MWI, independent of an observer.

OK, I am satisfied with the first part in which you explain why it is local.

But I still do not understand the second part, so I will ask you additional questions:
What is "observer"?
Is it necessarily a conscious being?
Can one electron be an observer?
Do observers have objective ontological existence in MWI?
Is the MWI interpretation above essentially the same as Rovelli's relational interpretation?
Is the projection on the different "subspaces of awareness" by the observer - nonlocal at least for that observer (even if there is no objective nonlocality)?
Does MWI misses a satisfying theory of the observer? If yes, does it mean that quantum mechanics is not complete? If yes, could that mean that a satisfying completion would require a sort of nonlocality?

 

[vanesch]

But I still do not understand the second part, so I will ask you additional questions:
What is "observer"?

This is going to turn philosophical again
The ultimate "reason of existence" of physics, and of all studying of nature, and even of all our thinking, is to explain our subjective experiences. Probably
you're not thinking of it that way, but if you give it some reflection, you will find out that all of our intellectual activity comes ultimately down to understanding our subjective experience.

Now, usually we think of that as a secondary problem, because deep down, we are somehow convinced that our subjective experiences are directly derived from our sensory inputs, which correspond to a unique "reality" in an obvious and evident way, and that we can put "ourselves" out of play in the business of describing that outside reality. But this is nothing but hypothesis. It is also possible that the relationship between "reality" and our subjective experience is far more complex than we imagine. (and then maybe not) This is the viewpoint of MWI, and it is essentially inspired by the clash between the obvious quantum description of, say, a human being (which can then be in several places at once, the superposition principle applying to him as well as to anything else), and our daily perception which doesn't allow for such phantasies. There are two ways out: 1) quantum theory doesn't apply to human bodies or 2) our daily perception doesn't correspond to "reality" as a whole. MWI takes on the last stance.

So what's an observer ? It is something having subjective experiences which tries to relate it to an objective world "outside" in this viewpoint. Otherwise, it is just a physical construction as any other.

You might also say: an observer is something which cannot accept being in a quantum superposition because it is convinced that his subjective experiences do not correspond to that.

Is it necessarily a conscious being?

In as far as consciousness is related to "the existence of subjective experience", yes.

Can one electron be an observer?

In as far as an electron has subjective experiences...

It is maybe necessary to make a distinction between "an observer" and a "measuring device". A measuring device is a thing that interacts with a system, and has memory states that correspond to "outcomes of measurement". If you apply quantum theory to a measurement device, there is not really a problem: you will find that the device will end up in a quantum state which is a superposition of "outcomes", in a way which mimicks the original quantum superposition of the system at hand. Nothing goes wrong here. What goes wrong is when we *subjectively observe* such a measurement device, that we only see it in one state. Now, this can be because it truly is in one state (in which case the entire quantum description goes wrong at this level), or, and that is the MWI viewpoint, it is because we are only subjectively aware of one of the states.

Do observers have objective ontological existence in MWI?

The physical structure related to an observer has objective existence in MWI (the "body"). However, the "observer" itself, not really: it are specific body states which "act as observer". You cannot know if a physical structure is "an observer" or not: you just declare it to be so or not. (in fact, in exactly the same way as you cannot really know if a person is conscious or is a zombie) This is the ill-defined part (but as subjective observation is ill-defined in any case, that's not a problem FAPP, but only in principle).

Is the MWI interpretation above essentially the same as Rovelli's relational interpretation?

Personally, I think so ! But others do not agree with me on that point.

Is the projection on the different "subspaces of awareness" by the observer - nonlocal at least for that observer (even if there is no objective nonlocality)?

No, because these subspaces (which identify clearly different bodystates, corresponding to clearly different experiences) are only related to a local bodystate. What an "observer" observes, are his bodystates, and nothing else. So this bodystate is of course local to the body, and observers attached to this body are only "aware" of this bodystate (actually, of components of it). It are bodystate conglomerates which define "different states of awareness" and the corresponding subspaces.

Does MWI misses a satisfying theory of the observer?

yes, on a level of principle. No, FAPP (for all practical purposes). That is to say, our differentiated "states of awareness" are so terribly coarse grained, that their precise definition doesn't really matter. But we bump here into the same difficulty as in Copenhagen QM, with the "quantum-classical" transition. Only, we removed the problem totally out of the "objective physics" part and entirely in the link between objective physics and subjective experience, which is in any case a very fuzzy domain (in principle, but not FAPP).

If yes, does it mean that quantum mechanics is not complete? If yes, could that mean that a satisfying completion would require a sort of nonlocality?

This has nothing to do with it. Concepts such as locality and so on are supposed to reign in the domain of pure physics, which is entirely well-defined in MWI (namely, the Schroedinger equation, period). What is fuzzy, is simply the details of the link between physical reality and subjective experience - which is in any case fuzzy on a very detaillistic level, but which is more than sufficient to talk about observations which have such a clear influence on our "state of awareness" that there is not much discussion - this is what is usually considered as "macroscopic observations".

 

[Demystifier]

Thanks vanesch, now I think I understand MWI (or at least your view of MWI) much better.

But let me also present a critical "summary" of MWI. In MWI, the conscious observer plays an important role. On the other hand, MWI does not contain a theory for that conscious observer.

In comparison, the Bohmian interpretation also does not contain a theory of conscious observers, but they do not play an important role in that interpretation. (Of course, the Bohmian interpretation contains other disadvantages.)

Do you agree?

 

[vanesch]

Thanks vanesch, now I think I understand MWI (or at least your view of MWI) much better.

But let me also present a critical "summary" of MWI. In MWI, the conscious observer plays an important role. On the other hand, MWI does not contain a theory for that conscious observer.

In comparison, the Bohmian interpretation also does not contain a theory of conscious observers, but they do not play an important role in that interpretation. (Of course, the Bohmian interpretation contains other disadvantages.)

Do you agree?

Yes! MWI is a desperate attempt to try to give ontological sense to the quantum formalism, as we know it, in a universal way, while not trying to hide behind "you shouldn't ask that question" kind of rethoric (which Copenhagen does, in a way), and without adding any formal elements. And, as you point out, you are then confronted to the relationship between "subjective experience" and "physical reality". By cleaning out the part of "physical reality" all the fuzzyness has been put in that relationship with "consciousness". One can call it a cop-out, and in a way it is so! But no other view on quantum theory does any better.
Copenhagen, with its "transition into a classical world" needs just as well preferred subspaces which correspond to classical worlds. Statistical views don't even attempt at trying to give any kind of ontological picture, but nevertheless take it for granted that the "projected states" make some kind of sense.
As to Bohmian mechanics, true, it works *slightly* better. What is clear, in BM, is the particle configurations. This is entirely Newtonian, so we "feel at home". However, what one forgets, in BM, is that there is a much fuzzier part to the ontology, namely the wavefunction. As I tried to argue, the wavefunction is an integral part of the dynamical contents of BM (and hence not just a kind of auxilliary variable introduced for convenience, which can be done away with). As, in BM, the wavefunction evolves exactly according to the Schroedinger equation, just as in MWI, part of the interpretational difficulties of MWI are in fact also inherited by BM. Indeed, why should a conscious being only be aware of its "particle" aspect, and not of its "wavefunction" aspect (which contains, remember, also all "worlds" of MWI)?
Granted, this can be solved by a simple postulate: "conscious beings are only aware of their particle positions". I will agree that of all views, BM clearly has the cleanest ontological position (although it is not so clean as one usually presents it). In fact, it is MWI + a token (the particle configuration) in a certain way, where the token indicates "the common world of experience" (namely the particle positions). The difficulty I have with BM is its relativistic non-invariance.

 

[ueit]

As to Bohmian mechanics, true, it works *slightly* better. What is clear, in BM, is the particle configurations. This is entirely Newtonian, so we "feel at home". However, what one forgets, in BM, is that there is a much fuzzier part to the ontology, namely the wavefunction. As I tried to argue, the wavefunction is an integral part of the dynamical contents of BM (and hence not just a kind of auxilliary variable introduced for convenience, which can be done away with). As, in BM, the wavefunction evolves exactly according to the Schroedinger equation, just as in MWI, part of the interpretational difficulties of MWI are in fact also inherited by BM.

I know we've discussed this before but I still do not understand your position. Of course, the quantum force is a part of BM's ontology just like the coulombian, strong or gravitational force. Your point was that it cannot be deduced from the particle configuration only, OK, we need to specify the system energy as well. So what? We have a function relating the quantum potential to some well defined properties of the system evolving in 3d space + time. No need for other worlds/dimensions, no need to ascribe reality to the Hilbert space itself. If we imagine this quantum potential as a kind of space geometry, only this geometry needs to be real in BM, nothing else.
In conclusion, BM's ontology requires, beyond classical parameters, a parameter defining the "space quantum geometry". The details of how we perform the calculation are irrelevant to that ontology. MWI, on the other side, requires that the mathematical formalism maps to some existing reality, BM doesn't need that.

Indeed, why should a conscious being only be aware of its "particle" aspect, and not of its "wavefunction" aspect (which contains, remember, also all "worlds" of MWI)?
Granted, this can be solved by a simple postulate: "conscious beings are only aware of their particle positions".

This is a very strange objection, indeed. We are certainly aware of the quantum potential in the same way we are aware about any other potential, by observing how particles move in its presence. That we cannot directly access this potential is not in any way different from the fact that we cannot observe an electric field without at least a charged object being present. If you maintain that BM needs that postulate then you need to ask classical mechanics to add postulates for the non-observability of every classical potential as well.

I will agree that of all views, BM clearly has the cleanest ontological position (although it is not so clean as one usually presents it). In fact, it is MWI + a token (the particle configuration) in a certain way, where the token indicates "the common world of experience" (namely the particle positions). The difficulty I have with BM is its relativistic non-invariance.

I have some questions related to the relativity issue.

1. BM doesn't look non-local from the point of view of the universal wave-function in the sense that no interaction needs to be transmitted ftl. The quantum potential evolves deterministically, regardless of particles' motion and the particles only interact locally. So, whyle BM requires an absolute reference frame it doesn't seem to conflict directly with relativity (which could be formulated, I think, on an absolute RF).

2. Is there a fully relativistic QFT yet (without the non-local collapse or with the collapse relativistically treated)?

3. Is MWI proven to have a mathematically rigorous relativistic extension? I've read some articles claiming that problems relating to the world splitting could appear.

Thanks.

 

[Rade]

Both, MWI and BM are "correct" theories in the sense that they set up a logically coherent construction (at least to a level of informal rigor which is usual with physical theories)...So, logically, BM and MWI are both "correct", as is any well-constructed theory...

Perhaps, as with the dual particle-wave nature of the photon, quantum reality (whatever it may be) is the union of all the experimentally "correct" theories--that is, there never has been nor will be a "single" correct theory--is what what you are saying here ?

 

[vanesch]

OK, we need to specify the system energy as well. So what? We have a function relating the quantum potential to some well defined properties of the system evolving in 3d space + time. No need for other worlds/dimensions, no need to ascribe reality to the Hilbert space itself. If we imagine this quantum potential as a kind of space geometry, only this geometry needs to be real in BM, nothing else.

But this "geometry" needs the exact wavefunction, and can only be deduced from that wavefunction, so the wavefunction is entirely part of the "ontology" of the theory. Now, you can make extra hypotheses, which come down to specifying a specific wavefunction (like, it must be in the ground state or something), but this limits severely the applicability of BM. In short, you cannot do BM when the initial wavefunction is not given.

You can compare this with the EM field in classical physics. The fact that there are non-trivial vacuum solutions to the EM field, means that these fields have an essential existence of their own. You cannot do electrodynamics without using the EM field (or the vector potential or anything of the kind).
You could get away with it if there were purely a Coulomb interaction, because from the configuration of the charged particles, the Coulomb interaction can be derived. The E-field would then simply be a convenience, but would not be an essential part of the dynamics (and hence, of the ontology). You could, if you wanted to, eliminate the E-field in all calculations.

Even the EM field could be partly eliminated, by using the retarded potential expressions. All EM waves emitted from other charges can be eliminated that way. But what you cannot eliminate, are the initial radiative conditions. There can be initial EM waves, unrelated to any charged source. This dynamical element cannot be eliminated, and hence, the EM field has an essential dynamics to itself, which means that any theory of the EM interaction must consider that there is an ontology to the EM field, and that it is not just an intermediate variable used for convenience.

In the same way, in BM, you NEED the initial wavefunction, because it cannot be derived from the particle positions. It is not an intermediate variable which could be eliminated at leisure. It is an essential component of the dynamical formulation of BM, and hence has an ontological existence.

In conclusion, BM's ontology requires, beyond classical parameters, a parameter defining the "space quantum geometry".

Well, that's an euphemism to say that you need the wavefunction...

The details of how we perform the calculation are irrelevant to that ontology.

Not really. You cannot eliminate it, it is not an intermediate quantity just introduced by convenience but which could be eliminated entirely.

MWI, on the other side, requires that the mathematical formalism maps to some existing reality, BM doesn't need that.

yes, it does so, for exactly the same reason: it is an essential part of the dynamics.

This is a very strange objection, indeed. We are certainly aware of the quantum potential in the same way we are aware about any other potential, by observing how particles move in its presence. That we cannot directly access this potential is not in any way different from the fact that we cannot observe an electric field without at least a charged object being present. If you maintain that BM needs that postulate then you need to ask classical mechanics to add postulates for the non-observability of every classical potential as well.

Well, in classical physics, the ontology consists of particles and fields (both of them). Together they specify the configuration space (or the phase space, if you want). It is hard to say which aspect of the point in conguration space is generating a certain subjective experience: are it purely the particle states, or are it the field states, or both ? Hard to say whether it is the EM field configuration in the brain of a creature living in a classical world which is giving it his memory states, or whether it are the particle configurations ! I would say that it is the entire state which does so. But in a classical setting, this is pretty irrelevant.

1. BM doesn't look non-local from the point of view of the universal wave-function in the sense that no interaction needs to be transmitted ftl. The quantum potential evolves deterministically, regardless of particles' motion and the particles only interact locally.

No, not really. In BM, the potential is function of the wavefunction AND the positions of the remote particles. This is the non-local element: the guiding equation:
$$\frac{dq_k}{dt} = \frac{\hbar}{m_k}\frac{Im\left[ \Psi^* \partial_k \Psi \right]}{\Psi^* \Psi}_{q_1,q_2...,q_N}$$

The presence, in the generalised velocity for the k-th particle, of the generalized coordinates of the other particles at the same moment, makes this an explicitly non-local (and non-lorentz-invariant) expression.

So, whyle BM requires an absolute reference frame it doesn't seem to conflict directly with relativity (which could be formulated, I think, on an absolute RF).

Well, that's a contradiction in terms: any theory requiring an absolute reference frame is in conflict with the fundamental postulate of relativity. It is always possible to make it observationally in agreement with relativity, but it means, in that case, that one has introduced unnecessary elements which break explicit Lorentz invariance. This is the same with an ether theory, or with, say, the coulomb gauge fixing condition in the canonical quantization of QED.

2. Is there a fully relativistic QFT yet (without the non-local collapse or with the collapse relativistically treated)?

You cannot treat the collapse relativistically. What is done in QFT, is the calculation of matrix elements of the unitary evolution operator which transforms initial particle states in final particle states, for "large times". It is very similar to the U(t1,t0) operator which transforms |psi(t_0)> into |psi(t1)>, but taken in the limit where t1 goes to +infinity and t0 goes to -infinity. It is only for that case that there are approximative techniques.
This unitary operator is nothing else but the solution to the schroedinger equation, as usual. These complex numbers, squared, give the transition probabilities of the corresponding initial state in the final state.

Usually, this is done by calculating an approximation to an expression which is called a "path integral". Given that we calculate in this way, the probabilities for the transition from "long ago" into the "far future", this can be interpreted in any way you like. You can continue to consider the superposition of final states (whose coefficients are nothing else but the matrix elements calculated) a la MWI, or you can decide to project one out (in which case you do something non-local), a la Copenhagen.

3. Is MWI proven to have a mathematically rigorous relativistic extension? I've read some articles claiming that problems relating to the world splitting could appear.

The mathematical part of MWI is nothing else but standard unitary quantum theory. QFT is known not to be rigorously correct, but this is just a model as any other.

 

[Demystifier]

Yes! MWI is a desperate attempt to try to give ontological sense to the quantum formalism, as we know it, in a universal way, while not trying to hide behind "you shouldn't ask that question" kind of rethoric (which Copenhagen does, in a way), and without adding any formal elements. And, as you point out, you are then confronted to the relationship between "subjective experience" and "physical reality". By cleaning out the part of "physical reality" all the fuzzyness has been put in that relationship with "consciousness". One can call it a cop-out, and in a way it is so! But no other view on quantum theory does any better.
Copenhagen, with its "transition into a classical world" needs just as well preferred subspaces which correspond to classical worlds. Statistical views don't even attempt at trying to give any kind of ontological picture, but nevertheless take it for granted that the "projected states" make some kind of sense.
As to Bohmian mechanics, true, it works *slightly* better. What is clear, in BM, is the particle configurations. This is entirely Newtonian, so we "feel at home". However, what one forgets, in BM, is that there is a much fuzzier part to the ontology, namely the wavefunction. As I tried to argue, the wavefunction is an integral part of the dynamical contents of BM (and hence not just a kind of auxilliary variable introduced for convenience, which can be done away with). As, in BM, the wavefunction evolves exactly according to the Schroedinger equation, just as in MWI, part of the interpretational difficulties of MWI are in fact also inherited by BM. Indeed, why should a conscious being only be aware of its "particle" aspect, and not of its "wavefunction" aspect (which contains, remember, also all "worlds" of MWI)?
Granted, this can be solved by a simple postulate: "conscious beings are only aware of their particle positions". I will agree that of all views, BM clearly has the cleanest ontological position (although it is not so clean as one usually presents it). In fact, it is MWI + a token (the particle configuration) in a certain way, where the token indicates "the common world of experience" (namely the particle positions). The difficulty I have with BM is its relativistic non-invariance.

I agree with you.
However, what I try to do in my research on Bohmian mechanics, is to use the disadvantages of the Bohmian approach to promote it from an interpretation (which contains negative philosophical connotations) to a physical theory. For example, in some regimes, such relativistic non-invariance might have observable consequences.