# Time Asymmetry in Quantum Mechanics

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1. Nov 14, 2015

### klen

Hi all,
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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2. Nov 19, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?