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I am reading the book "Emperor's New Mind" and have a question related to time asymmetry in state vector reduction (p.458) in quantum mechanics. Consider the following situation, as presented in the book:

Suppose I have closed room with a lamp L, which emits light in some fixed direction which is to be detected by a photon detector P placed in that direction. Between the photon detector P and the lamp L we have placed a half silvered mirror, which is tilted at an angle of 45 deg. to the path connecting L and P. The mirror reflects some amount of light and transmits some of the light. Whenever a photon is emitted by the lamp L it would be detected by the photon detector P with probability 0.5.

Now suppose we take the reverse time situation:

Suppose the light has reached the photon detector. When we evolve the wavefunction in reverse direction we see that it would bifurcate as it reaches the mirror and would reach L with "amplitude" 1/SQRT(2) and reach the top point B with the same amplitude (figure in attachment). The author then contends that the corresponding probabilities (square of these amplitudes) of 0.5 are the probabilities of following events:

'Given that L registers, what is the probability that P registers?'

'Given that the photon is ejected from wall at B, what is the probability that P registers?'

I do not understand why the above probabilities correspond to these events (above). Since we are considering a time reversed situation where we are assuming that the photon has reached P, shouldn't these probabilities correspond to the following events:

'Given the photon reached P, what is the probability that L registers, i.e. it came from L?'

'Given the photon reached P, what is the probability that it came from B?'

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# Time Asymmetry in Quantum Mechanics

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