Time Asymmetry in Quantum Mechanics

[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?'

 

[eljose79]

Thank you for your question about time asymmetry in state vector reduction in quantum mechanics. This is a fascinating topic and one that has been the subject of much debate and research in the scientific community.

To answer your question, let's first review the scenario described in the book. We have a closed room with a lamp L, emitting light in a fixed direction towards a photon detector P. Between L and P, there is a half-silvered mirror tilted at a 45-degree angle. When a photon is emitted from L, it has a 50% chance of being detected by P, and a 50% chance of being reflected by the mirror and reaching the top point B.

Now, let's consider the reverse time situation where the light has already reached P. In this case, we are evolving the wavefunction in the opposite direction, from P back to L. As the wavefunction approaches the mirror, it will bifurcate, with one part of the wavefunction reaching L with an amplitude of 1/sqrt(2), and the other part reaching B with the same amplitude. This means that the probability of the photon reaching L is 0.5, and the probability of it reaching B is also 0.5.

The probabilities mentioned by the author in the book correspond to the following events:
- Given that L registers, what is the probability that P registers? This corresponds to the probability of the photon reaching L, and then being detected by P. This is 0.5 x 0.5 = 0.25.
- Given that the photon is ejected from wall at B, what is the probability that P registers? This corresponds to the probability of the photon reaching B, and then being detected by P. Again, this is 0.5 x 0.5 = 0.25.

So, these probabilities do indeed correspond to the events mentioned by the author. The reason for this is that in the reverse time scenario, we are considering the probability of the photon reaching P, given that it has already reached either L or B. This is different from the probabilities you suggested, which would correspond to the probability of the photon coming from either L or B, given that it has already reached P. These probabilities would be different, and would not take into account the wavefunction bifurcating when it reaches the mirror.

I hope this helps to clarify the situation. If you have any further questions,