EPR revisited

[anuttarasammyak]

Observers in different inertial frames who were making observations in the vicinity of measurement at A hold a meeting and present their respective viewpoints. It turns out that each of them is making a rational judgment. As a conclusion of the meeting, they adopt the earliest possible reading of B’s clock, T−L/c where L is distanbe between A and B, as the common consensus. This is because B’s behavior corresponding to clock readings between T−L/c and T+L/c is unknown, and measurement at B may occur during this interval. The only choice consistent with this possibility is the earliest time, T−L/c.

Here, I assume that all inertial frames agree that the collapse occurs when the reading of clock B is the smallest, namely at T−L/c.
This is consistent with the viewpoint of each inertial frame in the sense that, in every frame, B is in the collapsed state only afterward (although the observation itself is performed at A).

Next, let us consider the situation from B toward A.
If we take the collapsed state of B as the starting point, then, due to the relativity of simultaneity, in some inertial frames the state of A appears to have collapsed at a time earlier than the observation. The earliest such time is when the reading of clock A is T−2L/c. Let us again assume that this is accepted by all inertial frames as well.

If we continue this kind of reasoning back and forth between A and B, tracing further and further into the past, we arrive at the conclusion that, ever since the moment when A and B were at the same location for the purpose of generating quantum entanglement, the states of A and B had in fact already collapsed.
What was regarded as an entangled state up until the observation by A is, after the observation, reinterpreted as having been a collapsed state extending retroactively into the past, back to the time of entanglement generation.
In this way, it seems that there is no longer any need to worry about spooky long-distance correlations.

[EDIT]
What has been described here can also be regarded as an exchange of signals at the speed of light, directed toward the past between A and B.

What is described here represents the viewpoint of A and of all observers in inertial frames located in the neighborhood of A. After the observation has concluded with a result consistent with the entangled quantum state, the past history is reinterpreted.

This viewpoint can be propagated to the surrounding region at the speed of light together with the observation result.

 

[PeterDonis]

If we continue this kind of reasoning

We can't because it's giving you contradictions. First you assume the collapse takes place at a certain event on B's worldline; then you assume that the collapse takes place at a certain event on A's worldline; and then you conclude that the collapse takes place at a different event on B's worldline. What that tells you is that "this kind of reasoning" is not valid. As I already pointed out to you in post #14.

 

[Nugatory]

What was regarded as an entangled state up until the observation by A is, after the observation, reinterpreted as having been a collapsed state extending retroactively into the past, back to the time of entanglement generation.

The collapsed state is a mixture of $|+-\rangle$ and $|-+\rangle$; the uncollapsed state is a pure superposition of the two. These are different states that behave differently in experiments designed to expose the difference. What does it mean to “interpret” one as the other?

 

[PeterDonis]

The collapsed state is a mixture of $|+-\rangle$ and $|-+\rangle$

I would say that the collapsed state is either $\ket{+-}$ or $\ket{- +}$, whichever corresponds to the measured results. We don't use the mixture state to predict further measurements; we use whichever of the two kets corresponds to the result that was measured. That's what the collapse postulate says to do.

 

[anuttarasammyak]

We can't because it's giving you contradictions. First you assume the collapse takes place at a certain event on B's worldline; then you assume that the collapse takes place at a certain event on A's worldline; and then you conclude that the collapse takes place at a different event on B's worldline. What that tells you is that "this kind of reasoning" is not valid. As I already pointed out to you in post #14.

If B performs a measurement, there is no doubt that this constitutes an event. However, in the situation under consideration, B does not perform any measurement, and the collapse of B’s state is only attributions made by A and all the observers of A's measurement nearby in oher IFRs. Therefore, it is not clear whether the collapse of B’s state should be regarded as an “event” in the sense used in relativity theory. What should we make of this?

 

[Nugatory]

Therefore, it is not clear whether the collapse of B’s state should be regarded as an “event” in the sense used in relativity theory.

From the very first post in this thread: “the moment when B has $|b>_B$” is specifying an event.

 

[PeterDonis]

it is not clear whether the collapse of B’s state should be regarded as an “event” in the sense used in relativity theory. What should we make of this?

I already told you in post #14: there is nothing that can be made of it as far as relativity theory is concerned; there is no invariant that corresponds to "the collapse of B's state". And there is also nothing according to standard QM that can be made of it: if B is not measured, standard QM says you can't apply the collapse postulate to B's state. Any claim about that is interpretation dependent as far as QM is concerned.

 

[anuttarasammyak]

This is my conjecture about QFT that I learned from this thread and some othre readngs:

In quantum field theory (QFT), measurement is not treated as a special kind of dynamics. It is described as an interaction of fields, including the measuring apparatus itself. Due to decoherence, the probabilities of obtaining particular measurement outcomes are determined within purely unitary time evolution.

QFT provides probabilities as the absolute square of amplitudes, and for practical purposes this is sufficient.

QFT is indifferent to the “measurement problem,” including the question of whether it truly exists. Those who are concerned with the measurement problem—or with the question “why do we experience a single outcome?”—must look for answers outside QFT. From the standpoint of those who regard QFT as complete, such interpretational issues are not part of physics.

QFT denies causal influence between two spacelike separated points, but it does not deny the existence of correlations between them.

 

[Nugatory]

This is my conjecture about QFT that I learned from this thread and some othre readngs:

In quantum field theory (QFT), measurement is not treated as a special kind of dynamics. It is described as an interaction of fields, including the measuring apparatus itself. Due to decoherence, the probabilities of obtaining particular measurement outcomes are determined within purely unitary time evolution.

QFT provides probabilities as the absolute square of amplitudes, and for practical purposes this is sufficient.

QFT is indifferent to the “measurement problem,” including the question of whether it truly exists. Those who are concerned with the measurement problem—or with the question “why do we experience a single outcome?”—must look for answers outside QFT. From the standpoint of those who regard QFT as complete, such interpretational issues are not part of physics.

QFT denies causal influence between two spacelike separated points, but it does not deny the existence of correlations between them.

You are conflating a bunch of different things here. Much of what you mention above (probability as squared amplitudes, role of decoherence, indifference to single outcome question, interaction with the measuring apparatus) is part of ordinary non-relativistic QM as well - although often glossed over in first-year intro-to-QM classes which stress computation over foundation/interpretation.

To get a better sense of how QFT differs from the intro stuff, you might try the first chapter of Srednicki (that's through page 30 of the online draft version - the water gets deeper very quickly after that point) or Lancaster and Blundell's "Quantum Field Theory for the gifted amateur". Either will be a better starting point than your conjectures.