anuttarasammyak said:

may we conclude that the statement “B has ##|b>_B##" is not invariant, but frame-dependent?

You may conclude that that statement, as you make it, is not even well-defined. You didn't specify a time in any frame at which B has that state.

A true statement would be that the time ordering of spacelike separated events is not invariant, but frame-dependent. But specifying an event requires specifying a place and a time in some frame--an event is a point in spacetime.

You are also sweeping under the rug complications that involve quantum mechanics as well as relativity. For example, suppose we say that the measurement on A happens at a particular event--a particular place and time in some chosen frame. You are assuming that the state of B collapses when the measurement on A is made. But at what event does the collapse of B happen? There is no invariant way to specify that--which should be a clue that the intuitive picture of QM you are using is not, in fact, correct--more precisely, it is not relativistic. In relativistic QM, i.e., quantum field theory, the whole idea of "collapse" is much more problematic, because there are no invariant answers to questions like the one I posed just now.

In short, you unfortunately have chosen a bad example to illustrate the relativity of simultaneity.

Thank you @PeterDonis. I should be somewhat satisfied to know that studies are going on.

anuttarasammyak said:

I should be somewhat satisfied to know that studies are going on.

I'm not sure what "studies" you're referring to, but it's certainly true that there have been plenty of experiments testing both relativity of simultaneity and the QM predictions for measurements on entangled particles.

cianfa72 said:

the QM framework provides the answer for the joint probabilities of both Alice and Bob's measurement outcomes.

That's correct.

cianfa72 said:

Therefore, for measurement events spacelike separated, you can think of wavefunction collapsing either way (it first collapses when Alice's measurement takes place or the other way around, that is it collapses first when Bob's measurement takes place).

Not really. See below.

cianfa72 said:

In both cases the joint probabilities are the same.

Yes, but what that means is not that "you can think of the wave function collapsing either way", at least not if you are thinking of the collapse as an actual physical event. (If you're just thinking of it as a mathematical device, sure, go ahead, it doesn't matter.) What the time ordering of the measurements not being invariant means, from the standpoint of relativity, is that you cannot think of the collapse as being a physical event at all, because any physical event would have to be invariant, and there is no invariant that tells you at what event a physical collapse would happen.

PeterDonis said:

(If you're just thinking of it as a mathematical device, sure, go ahead, it doesn't matter.)

Ok, yes.

PeterDonis said:

What the time ordering of the measurements not being invariant means, from the standpoint of relativity, is that you cannot think of the collapse as being a physical event at all, because any physical event would have to be invariant, and there is no invariant that tells you at what event a physical collapse would happen.

Ah, I see. To me this notion of collapsing wavefunction is really an headache

cianfa72 said:

To me this notion of collapsing wavefunction is really an headache

You're certainly not the only one.

PeterDonis said:

You're certainly not the only one.

Have you find any pill as cure ?

cianfa72 said:

Have you find any pill as cure ?

Unfortunately, no. Various patent medicines have been offered in the literature on QM interpretations, but none of them are actual cures.

pervect

pervect said:

Schrödinger's equation is not compatibility with special relativity, and neither is the idea of instantaneous wave function collapse (instantaneous in what frame?).

That's correct. What you are calling "ordinary" QM is a non-relativistic approximation. For relativistically correct QM, you need quantum field theory, as you say. In QFT, in order to compute probabilities, you need to define the specific spacetime events at which measurements take place, and you compute the probabilities from quantum fields that are relativistically covariant. There is no need to apply any "collapse" postulate to the quantum fields, the way you have to with wave functions in non-relativistic QM, so the collapse issue doesn't arise.

anuttarasammyak said:

It seems that this problem cannot be properly understood without mastering relativity.

You don't need to "master" relativity. You just need to understand that one of the lessons relativity teaches us is that physics is contained in invariants. See below.

anuttarasammyak said:

Observers in different inertial frames

You mean, observers in different states of motion. Every observer is "in" every frame; but each observer is at rest in only one of them.

anuttarasammyak said:

present their respective viewpoints

Which are irrelevant since their "viewpoints" as you're using that term don't include any invariants, and all of the actual physics, including all of the actual measurement results, are contained in the invariants.

anuttarasammyak said:

...is that you cannot assign a time to the collapse at all, as I've already said, because there is no invariant that tells you what such a time should be.

PeterDonis said:

In QFT, in order to compute probabilities, you need to define the specific spacetime events at which measurements take place, and you compute the probabilities from quantum fields that are relativistically covariant. There is no need to apply any "collapse" postulate to the quantum fields, the way you have to with wave functions in non-relativistic QM, so the collapse issue doesn't arise.

So basically there is a way out of the collapse of wavefunction. Which are the issues associated with QFT and relativity?

cianfa72 said:

So basically there is a way out of the collapse of wavefunction.

Only in the sense that QFT gives a mechanism for computing probabilities that doesn't have the collapse postulate the way ordinary non-relativistic QM does. QFT doesn't solve the underlying issue of "what is really going on".

cianfa72 said:

Which are the issues associated with QFT and relativity?

I'm not sure what you're asking about here. QFT is consistent with relativity; it's constructed explicitly to be that way.

cianfa72 said:

there is no inconsistency at all between QFT and SR/GR ?

No. You can do QFT in flat or curved spacetime.

anuttarasammyak said:

If not only the concepts of the collapse but also measurement in general are excluded from the theory

What theory are you talking about?

anuttarasammyak said:

Collapse of (entangled) wave functions comes from measurement. If not only the concepts of the collapse but also measurement in general are excluded from the theory, I cannot evaluate how useful it is.

If no theories in the direction I have mentioned have been explored in response to the OP’s question, please excuse my oversight.

anuttarasammyak said:

If no theories in the direction I have mentioned have been explored in response to the OP’s question

I'm still a little confused here. The only theories that have been "explored" at all in this thread are non-relatvistic QM, QFT, and relativity. None of them exclude the concept of measurement.

anuttarasammyak said:

I should appreciate it if you let me know whether all these theories deal with collapse of entangled wave functions as mentioned in OP or not. May I expect that one of them rescue me ?

Rescue you from what? I don't understand what issue you think you need to be "rescued" from. If you mean the scenario you described in your OP, I've already responded to that. What part of my response doesn't satisfy you?

Nugatory said:

collapse is not part of the theory of quantum mechanics as described by the math

More precisely, in non-relativistic QM, there is a collapse postulate, but it is not a postulate about anything that "really happens". It is just a mathematical rule for making predictions about further measurements once you know the result of one measurement. Anything beyond that is interpretation, and you don't need any interpretation to make predictions.

Thank you all. I will think about it further.

PeterDonis said:

There is no need to apply any "collapse" postulate to the quantum fields, the way you have to with wave functions in non-relativistic QM, so the collapse issue doesn't arise.

Interesting. So the issue of collapse is just an artifact of the nonrelativistic approximation?

Herman Trivilino said:

So the issue of collapse is just an artifact of the nonrelativistic approximation?

That depends on what you consider "the issue of collapse" to be. QFT does not have the collapse postulate in the form that non-relativistic QM does, but as I said in the post you quoted part of, it still does not solve the underlying issue of "what is really going on".