Black hole information paradox, 2.2.5
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?
Since neither of the detectors at the two end destinations is activated in the beginning, the entangle variables are still physically-undefined (i.e. in a superposition) at that moment the pair is emitted.
However, while the particles are still on the way, at the moment one of two detectors is first activated, the entangled variables get their physical definitions. The system state is no longer in a superposition state. Instead, it becomes a mixed state. In other words, the system has become a classical system (with respect to those entangled variables).
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?
(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.)
They are correlated only in the statistical sense.
Individual pair of values may be not correlated, but a lot of pairs that have the same superposition (at time of emitting) will form that statistical pattern that is indistinguishable from the one that predicted with the assumption that every pair is correlated.
In analogy, in the double-slit experiment, an individual dot on the final screen cannot tell whether the particle was in a superposition. It is only after a lot of dots forming on the final screen, we can check whether there is an interference pattern. When the interference appears (and we assume that the wave function that governs every particle is the same), we say that every particle is in a superposition state. Or put it more accurately, the system is in the same superposition state before each particle has reached the screen.
Every pair is correlated.
— Me@2022-02-11 12:47:14 AM
2022.02.16 Wednesday (c) All rights reserved by ACHK