What is more difficult to understand is the non-classical part:

`What if, instead of turning on a detector before the time of emitting, we turn it on after the pair is emitted but before either of them has reached its destination?`

In the common (but inaccurate) language, the action of activating a detector has collapsed the wave function of the system.

`Would the pair of (such as) spin values be correlated?`

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(Me@2022-02-16 12:07:25 AM: I think I have the answer now. I plan to publish it soon. But I keep the following as a record of thoughts.)

There are 2 possibilities.

(I do not know which of them is true, because I have not yet found an actual experiment that has tested against them.)

[guess]

1.

They are correlated only in the statistical sense.

2.

Every pair is correlated.

This is stranger than the first case, because if the two detectors are several light-years apart, the whole system exists across those light-years. The strangeness is the fact that even for a system-across-light-years, operations at one end can influence the probability of an event at the other end.

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For the time being, I guess that the second case is the true one.

Even if the first case is the true one, it is still strange because it implies that an action at one part of the system influences the statistical properties of another part, which may be several light-years away.

[guess]

Even in this stranger case, all experimental results are still consistent with special relativity (aka causality), because wave functions are not physical quantities. Instead, they are mathematical quantities for calculating probabilities, which themselves are also mathematical quantities, for predicting experimental results.

— Me@2022-02-11 12:47:14 AM

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Bug fixes:

1.1  It is not the particle’s state that is in a superposition or not, but the system’s state.

2.1  We need to specify which observer that the wave function is with respect to.

A wave function is for an observer to calculate the probabilities of different possible results in an experiment.

2.2  There is no “god’s eye view” in physics.

Every physical event must be described with respect to an observer. Every physical event, even if the event is “to compare observation results”, must be described with respect to an observer. — Me@2017-05-10 07:45:36 AM

2.3  A wave function is mathematical, not physical.

It is a mathematical function for an observer to calculate the probabilities. It is not something existing in physical spacetime. Thus superposition is also not something existing in physical spacetime. So it is meaningless to ask if the system state is in a superposition at a particular time.

Instead, whether a system is in superposition or not (with respect to a particular variable) is an intrinsic property of your experimental setup design, which includes not just objects and devices, but also operations.

“Wave function collapse” is not a physical event that happens during the operation of the experiment. Instead, it “happens” when you replace one experiment design with another.

— Me@2022-02-16 10:45:01 AM

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