What is the current perspective on quantum interpretation?

[vanhees71]

That's what I just did: The state of the universe factors into the state of local regions, and the state of local regions evolves in a way that depends only on neighboring regions.

The state does not factor into the state of local regions (whatever you mean by this) as the possibility of entanglement for far distant parts (i.e., parts measured at far distant places) of a quantum system shows. Within relativistic local QFT the interactions are local though. There's no faster-than light signal propagation and the linked-cluster principle holds (see Weinberg, Quantum theory of fields vol. 1).

 

[vanhees71]

I don't see how it wouldn't be a problem, since "frame-dependent" is inconsistent with "relativistically invariant".
This state is, as you say, frame-dependent, and therefore not relativistically invariant. So I am totally confused as to how you can say this isn't a problem for consistency with relativistic invariance.

The electromagnetic field is not frame dependent. It's a 2nd-rank antisymmetric tensor field!

 

[martinbn]

Ok, I am late for the discussion but I am still confused. Following @stevendaryl by locality we mean that to understand what is going on in a small region we only need the information from near by. But how is the usual Alice and Bob scenario any different? The results are probabilistic, and the predictions can only be probabilistic. Alice doesn't need anything from Bob in order to make her predictions. So how is there anything that is not local? Let me put it this way. If they make repeated predictions and measurements on an equally prepared pair of entangled particles. And if Alice measures hers a moment later than Bob, and Bob can decide whether to measure or not, she cannot tell if he did it or not. For me this is convincing that Bob's actions have no causal effect on Alice's particle.

 

[martinbn]

I think I answered this already. Given an inertial coordinate system, there is a notion of global state that changes with time. If the laws of physics are "separable" in the sense that I'm talking about, then the laws for the evolution of the global state factors into laws for how each small region evolves. If it's not separable, then it means that the laws governing the evolution of the local states are not sufficient to determine the evolution of the global state.

Unless I misunderstood you, then GR is nonseparable, but I wouldn't call it nonlocal.

Some people say that we should interpret "local" to mean the impossibility of FTL communication. I don't think that captures the notion of "local" very well. I gave the counter-example of a hypothetical pair of coins such that the $n^{th}$ flip of one coin always returns the opposite result of the $n^{th}$ flip of the other coin, no matter how far away they are from each other (but are otherwise random--there is no way to predict which will be "heads" and which will be "tails"). Such a pair of coins could not be used for FTL communication, but such a correlation is certainly non-local, intuitively.

I agree with this, but there is nothing in nature that behaves that way. For entangled pairs you can make only one measurement. If you did $n$ on the same pair it wouldn't be like that. But I object more to the insistance (not by you) to say that all this (the EPR case) implies action at a distance i.e. Bob causes something to happen at Alice's.

 

[vanhees71]

Entanglement does not imply action at a distance, because local relativistic QFT is an example for a QT, which of course allows entanglement but is at the same time a theory where you have only local interactions by construction.

 

[martinbn]

Entanglement does not imply action at a distance, because local relativistic QFT is an example for a QT, which of course allows entanglement but is at the same time a theory where you have only local interactions by construction.

Yes, but the question is should one still say that space-like events can be cause/effect related? I am not convinced that EPR, Bell and all that implies that one should.

 

[Tendex]

The electromagnetic field is not frame dependent. It's a 2nd-rank antisymmetric tensor field!

Sure, the tensor is local, what I think they mean by frame-dependent state is a supposed "global" state. But I'm not clear if this is trivial mathematical fact or something else.

 

[Tendex]

I think going back to the local vs nonlocal debates leads nowhere, it is much better going by Bell's distinction between classic correlations versus quantum correlations and their probabilities(although ironically it also helped introduce following the EPR article all this word salad philosophical debates about locality, causality, realism, determinism, action at a distance, ftl influence, etc).
It is also not very useful to still be going about the causal vs ftl influence(in whatever form) debate. By definition any theory that makes "predictions" is causal and doesn't allow ftl signaling or whatever one may like to call it, otherwise it couldn't claim to make "predictions", or to be a scientific theory for that matter and I find it a bit silly to still be using classically unexplained quantum correlations to speculate about spookiness, and ftl.
On the other hand, regardless of its making precise and accurate predictions a theory might be doubted in its mathematical completeness or rigor and correction, and in that sense the theory that is worse off is the generalization of nonrelativistic QM: QFT.

 

[atyy]

Entanglement does not imply action at a distance, because local relativistic QFT is an example for a QT, which of course allows entanglement but is at the same time a theory where you have only local interactions by construction.

Since you have used the unobservable definition of no superluminal signaling, QT is not local since it allows superluminal signaling in the form of collapse intrpreted physically. By using the unobservable definition, you promote quantum nonlocality.

 

[stevendaryl]

Unless I misunderstood you, then GR is nonseparable, but I wouldn't call it nonlocal.

Well, I am a little bit uncertain about that, but I specifically restricted my discussion to flat spacetime because I wasn't prepared to discuss GR in these terms.

 

[stevendaryl]

Entanglement does not imply action at a distance, because local relativistic QFT is an example for a QT, which of course allows entanglement but is at the same time a theory where you have only local interactions by construction.

There are two aspects to quantum theory (including QFT). One is the recipe for the evolution of the quantum state (Schrodinger's equation for QM and the differential equations governing the evolution of the field operators in QFT). The second is the recipe that says that when one performs a measurement, one gets an eigenvalue of the corresponding operator, with a probability calculated from the quantum state.

The issue with nonlocality is about the second aspect. When you say "you have only local interactions by construction", you're not including the measurement process itself.

 

[stevendaryl]

I agree with this, but there is nothing in nature that behaves that way.

The point of the example is to show that local is not the same thing as lack of FTL communication. Local implies no FTL but the converse isn't true.

 

[stevendaryl]

Ok, I am late for the discussion but I am still confused. Following @stevendaryl by locality we mean that to understand what is going on in a small region we only need the information from near by. But how is the usual Alice and Bob scenario any different?

If Bob has already measured his particle's spin along the z-axis, then Alice's result for a measurement along the z-axis is already determined, even if she hasn't performed the measurement yet. It's not probabilistic in the sense of a stochastic process. It's still probabilistic in the sense of lack of knowledge---anybody who is unaware of Bob's result will assign a 50/50 subjective probability to Alice's result.

So the strangeness of EPR (and maybe QM in general) is how probability shifts from being intrinsic probability to being subjective probability. If you believe that intrinsic probability is an objective property, then such a shift seems to be a change in Alice's situation that happens FTL when Bob performs his measurement.

If you don't believe that probability is intrinsic, but is always subjective, then that seems to be suggesting either hidden variables or superdeterminism. If there was no change for Alice due to Bob's measurement, and after Bob's measurement it is 100% certain that Alice will measure spin-up, then it seems that it must have been 100% certain before Bob's measurement.

 

[vanhees71]

Yes, but the question is should one still say that space-like events can be cause/effect related? I am not convinced that EPR, Bell and all that implies that one should.

No, space-like events cannot be cause-effect related by construction (microcausality constraint on local operators).

 

[vanhees71]

The point of the example is to show that local is not the same thing as lack of FTL communication. Local implies no FTL but the converse isn't true.

You still did no clearly define, what you mean by "local". The usual definition is that the Hamilton density is a local operator and that all local operators commute with it at space-like distances (micro-causality constraint). This excludes the possibility of space-like separated cause-effect related events, i.e., it excludes faster-than-light signal propagation. Other conclusions follow from that: the unitarity of and the cluster-decomposition principle of the S-matrix, the CPT symmetry, and the usual spin-statistics relation.

 

[stevendaryl]

No, space-like events cannot be cause-effect related by construction (microcausality constraint on local operators).

You keep saying that, but it completely misses the point. The microcausality constraint is on the field operators. But as you keep saying yourself, the only meaning to quantum theory is the predictions it makes about measurement results. Measurement results produce a SINGLE outcome from a set of possible outcomes. That is not described by the evolution of the field operators.

 

[stevendaryl]

You still did no clearly define, what you mean by "local".

Yes, I did. Local means that the conditions in one region of space evolve over a period of time $\Delta t$ in a way that is independent of the evolution of conditions in regions of space that are farther than $c \Delta t$ away (once you take into account information in the common backwards lightcone). In the EPR experiment, that is not true.

Alice in one region is measuring the z-component of spin for one particle from an anti-correlated pair.

Far, far away, Bob is measuring the z-component for the other particle.

The evolution of those two regions is not independent, and the dependency is not removed by looking at information in the common backwards lightcone.

 

[PeterDonis]

The electromagnetic field is not frame dependent.

Its value at a particular point is not. But @stevendaryl meant by "state" a global set of values for the EM field "at an instant of time". That is not invariant because "an instant of time" is not; it's frame-dependent.

 

[PeterDonis]

The evolution of those two regions is not independent, and the dependency is not removed by looking at information in the common backwards lightcone.

This is just another way of saying "the correlations violate the Bell inequalities". Which is, IMO, a much better way of saying it, since it doesn't require any questionable notion of "evolution" or "state". It's just a testable statement about the correlations.

 

[stevendaryl]

This is just another way of saying "the correlations violate the Bell inequalities".

It's not another way of saying it. There is quite a lot of work needed to go from things being local in the sense that I'm talking about to Bell's inequalities being satisfied. But it is true that every local system in my sense obeys Bell's inequalites.

 

[vanhees71]

Yes, I did. Local means that the conditions in one region of space evolve over a period of time $\Delta t$ in a way that is independent of the evolution of conditions in regions of space that are farther than $c \Delta t$ away (once you take into account information in the common backwards lightcone). In the EPR experiment, that is not true.

Alice in one region is measuring the z-component of spin for one particle from an anti-correlated pair.

Far, far away, Bob is measuring the z-component for the other particle.

The evolution of those two regions is not independent, and the dependency is not removed by looking at information in the common backwards lightcone.

This is an empty definition in the case of quantum theory. What do you mean by "conditions in one region of space"? In quantum theory what evolves are probabilities (and quantities derived from them like expectation values).

Your concrete example of course makes sense, but what you describe there is no non-locality but inseparability. There are correlations between far-distant measurements described by entanglement, but there is no non-local causal effect from one local measurement at A on the measurement at B and vice versa, because the interactions between the photons with the detectors at the places A and B are local, i.e., they fulfill the microcausality constraint such that there cannot be any instantaneous influence between the detectors at the far distant places through the measured object (in this case the two photons).

 

[stevendaryl]

This is just another way of saying "the correlations violate the Bell inequalities". Which is, IMO, a much better way of saying it, since it doesn't require any questionable notion of "evolution" or "state". It's just a testable statement about the correlations.

I realize now that what I'm sketching out is basically what Bell laid out in his "Theory of Local Beables":

https://cds.cern.ch/record/980036/files/197508125.pdf

 

[Tendex]

The point of the example is to show that local is not the same thing as lack of FTL communication. Local implies no FTL but the converse isn't true.

It would help if you clarified in what sense you are talking about FTL, in the gallilean or classical pre-Einstein-Lorentz sense where it can still be causal since there was no speed limit or in the modern (Einstein relativistic) more fundamental sense.

 

[vanhees71]

I think we should discuss within relativistic theory only, and since the only really working relativistic QT is local relativistic QFT, maybe also restrict ourselves to this.

There is also of course no problem with actions at a distance in non-relativistic physics (to the contrary it's the usual model of interactions as Newton's theory of the gravitational interaction). There's of course also no microcausality condition in non-relativistic QFT. It couldn't even be sensibly defined there.

 

[Tendex]

I think so too. That's why I wanted for stevendaryl to clarify, since he himself made a classification of qm interpretations with 2 catrgories: wrong and nonsense. My point is that talking about FTL is mathematically sound but physically wrong with the galilean mindset, and pure nonsense with the modern fundamental mindset so maybe it's better to leave it out.

 

[stevendaryl]

It would help if you clarified in what sense you are talking about FTL, in the gallilean or classical pre-Einstein-Lorentz sense where it can still be causal since there was no speed limit or in the modern (Einstein relativistic) more fundamental sense.

The issue is whether QM obeys Einsteinian relativity, when one takes into account the measurement process. As I explained in a different post, quantum mechanics has two pieces: (1) the smooth deterministic evolution of the quantum state, and (2) the nondeterministic production of a measurement result. In QFT, it's pretty clear that (1) is relativistically invariant, but it's much less clear whether (2) is. According to some interpretations of QM, relativity is only approximately true, for macroscopic measurements, but fails at a microscopic level.

In any case, I don't agree with you that you need to assume Einsteinian or Galilean relativity in order to say what FTL means. It is enough that there is a single frame in which light travels at its characteristic speed. Then relative to that choice of a frame, you can ask whether or not there are FTL influences.

 

[Tendex]

The issue is whether QM obeys Einsteinian relativity.

That's not so hard, Non-relativistic QM doesn't obey it, while its generalization RQFT does. This doesn't necessarily mean the whole construct of QFT as a mathematical theory is correct, if that's what you are suggesting.

In any case, I don't agree with you that you need to assume Einsteinian or Galilean relativity in order to say what FTL means. It is enough that there is a single frame in which light travels at its characteristic speed. Then relative to that choice of a frame, you can ask whether or not there are FTL influences.

I didn't talk about assuming anything, I asked you a simple question that you seem to refuse to answer and that's your privilege. But when you say there is a single frame in which light travel at it's characteristic speed and you mention FTL in relation with it, it is relevant to know if you are referring to frames in Galilean or Einsteinian relativity because it is not the same thing and it helps to clarify which to judge the argument adequately.

 

[stevendaryl]

That's not so hard, Non-relativistic QM doesn't obey it, while its generalization RQFT does.

The latter is just not clear.

 

[stevendaryl]

I didn't talk about assuming anything, I asked you a simple question that you seem to refuse to answer and that's your privilege.

I don't understand what your question means. Whether something is FTL doesn't depend on whether we're talking galilean or einsteinian relativity. It doesn't depend on relativity (galilean or einsteinian), since I'm only talking about a single frame. Relativity is about the relationship between two DIFFERENT frames. Within a single frame, relativity is not relevant.

Maybe it would be better to say "coordinate system" rather than frame?

 

[Tendex]

The latter is just not clear.

As I said its formulation has serious mathematical issues, but the "FTL influence" is a physical problem it does not have, it makes perfectly causal predictions.

 

[Tendex]

I don't understand what your question means. Whether something is FTL doesn't depend on whether we're talking galilean or einsteinian relativity. It doesn't depend on relativity (galilean or einsteinian), since I'm only talking about a single frame. Relativity is about the relationship between two DIFFERENT frames. Within a single frame, relativity is not relevant.

Maybe it would be better to say "coordinate system" rather than frame?

FTL might not depend on it, that's what I'm saying in a way, but you must have some idea of what you intend for your single frame when it relates with other frame. Single frame physics is not really so useful as in NRQM for quantum fields theories.

 

[stevendaryl]

As I said its formulation has serious mathematical issues, but the "FTL influence" is a physical problem it does not have, it makes perfectly causal predictions.

Oh, my god. I HATE Physics Forums discussions.

I agree that

1. In relativistic quantum field theory, the quantum state evolves according to local equations.
2. RQFT does not allow FTL signal transmission.

The issue is whether 1&2 imply that it is local. 1 by itself is not enough, because the smooth evolution does not include the measurement process by which a single outcome is selected out of a set of several possibilities. 2 is not enough, either, because although Local implies no FTL, no FTL does not imply local.

 

[atyy]

You still did no clearly define, what you mean by "local". The usual definition is that the Hamilton density is a local operator and that all local operators commute with it at space-like distances (micro-causality constraint). This excludes the possibility of space-like separated cause-effect related events, i.e., it excludes faster-than-light signal propagation. Other conclusions follow from that: the unitarity of and the cluster-decomposition principle of the S-matrix, the CPT symmetry, and the usual spin-statistics relation.

If one uses your definition of "local" in post #90, then relativistic quantum field theory is not local. So we don't have to use another person's definition, we just use yours.

If you accept that collapse interpreted as physical is "local" since it does not allow "faster-than-light signal propagation", then relativistic quantum field theory is "local".

If you reject that collapse interpreted as physical is "local" since allows "faster-than-light signal propagation", then relativistic quantum field theory is "nonlocal".

 

[stevendaryl]

If one uses your definition of "local" in post #90, then relativistic quantum field theory is not local. So we don't have to use another person's definition, we just use yours.

If you accept that collapse interpreted as physical is "local" since it does not allow "faster-than-light signal propagation", then relativistic quantum field theory is "local".

If you reject that collapse interpreted as physical is "local" since allows "faster-than-light signal propagation", then relativistic quantum field theory is "nonlocal".

Truly, I don't understand how what some people say about "collapse" isn't complete nonsense.

In an EPR experiment, with anti-correlated spin-1/2 particles, Alice and Bob agree to measure spin along the z-axis. Immediately before Alice's measurement she would say that there is a 50/50 chance that Bob will measure spin-up. Immediately after Alice's measurement, if she gets spin-up, the probability that Bob will measure spin-up changes to 0. How can you account for that sudden change? It seems to me that there are several possibilities:

1. Alice's measurement caused a physical change that affected Bob's measurement. Well, we have to rule this out because it involves FTL influences.
2. Alice's measurement, like a classical measurement, only changed Alice's knowledge about Bob. It didn't change anything physical on Bob's end. But let's think about this. If after Alice's measurement, she knows that it is 100% certain that Bob will measure spin-down, and if Alice's measurement didn't change anything about Bob, then it means that before Alice's measurement, it must have already been true that Bob would measure spin-down (only Alice didn't know it). Well, we have to reject this, too, because it involves hidden variables (the value of Bob's measurement before he makes it).
3. Umm, maybe there are two versions of the universe: One in which Alice measures spin-up and Bob measures spin-down, and another version in which Alice measures spin-down and Bob measures spin-up. Well, this would be a many-worlds interpretation, which is fanciful nonsense, and should be ruled out.

Any of those three seem like weird, unappealing choices: Unobservable FTL influences, unobservable hidden variables, unobservable alternate universes. But to reject all three seems like nonsense. Or at best, it amounts to saying: "I have no idea".

 

[RUTA]

Here is a paper that might be of interest:

M. Schlosshauer, J. Kofler, and A. Zeilinger, ``A snapshot of foundational attitudes toward quantum mechanics,'' Studies in the History and Philosophy of Modern Physics 44, 222–230 (2013).

https://arxiv.org/abs/1301.1069