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Q. At time t1 = 0, we know the state of our system. Then we send a photon into an atom. Assume the atom absorbs the photon by having an electron move to a di

Q. At time t1 = 0, we know the state of our system. Then we send a photon into an atom. Assume the atom absorbs the photon by having an electron move to a different energy level. Some time later, at time t2, the electron returns to where it was and emits a photon. As I understand, t2 - t1 is random, with exponential distribution, and independent of everything else in the universe. So, at time t2, we cannot recover the state at time t1 or even know just when t1 was. That is, the reversible time evolution equation of state at time t2 can't tell us the random time t2 - t1 or t1 so cannot recover the state at time t1 -- at time t2, we just do not know just when or how we got to the state at time t2. So, the time evolution equation is time reversible but the event of the emission of the photon is not time reversible. This thought experiment seems to conflict with the OP. Where am I going wrong?

evanb 7y ago
The final state wavefunction, which you need to recover the initial state, contains an exponentially decaying distribution of different t2s. The final state wavefunction is not "here's a definite t2"---that requires measurement.
someguy12342 7y ago
It is a bit more difficult to see this because you are describing a continuous time process, however, the answer is that yes you would be able to to figure out the time t1 given you knew had a snapshot of the whole system through the time evolution equation. Perhaps your confusion stems from the fact that the time t2 is observed, and it seems like you can't go back after that. An easier to grasp manifestation of this problem is that if you find Schrodinger's cat dead you can't tell if was always dead or if was dead only after your experiment. The reason is because that's only with the narrow knowledge of that cat being dead (maybe the would call this the cat state subsystem). It might be unsatisfactory to you, but in the theory of quantum mechanics, if you knew the state of everything (say the room, measurement apparatus, and so on), then you would be able to trace back to whether the cat was alive or dead. The moral is that the measurement looks irreversible if you look only at the system you are observing, but overall, people accept that there is a overarching greater space (the "environment, universe" where everything is just a unitary operation in motion according to the time evolution equation [1]). To be clear, the time evolution equation only admits reversible solutions. So with full knowledge, of say, the room and measurement apparatus, it would be possible to deduce the original state of the cat. https://www.quantiki.org/wiki/church-larger-hilbert-space https://www.quantiki.org/wiki/church-larger-hilbert-space
yk 7y ago
You are collapsing the wave function at t1 and t2. At t1 explicitly by stating that the state is known, and by t2 implicitly by defining that you have a defined distance t2- t1. The emission of an photon at an explicit time t2 is not reversible, the emission of an photon according to the wave function of the atom leads to an photon entangled with the atom and the total has a reversible wave function. (For illustrative purposes, when you measure and you find the photon at a distance (t- t2)*c from the atom, then you will also find the atom in a state that has emitted a photon at t2, no Idea if that is especially illustrative.)

evanb 7y ago

The final state wavefunction, which you need to recover the initial state, contains an exponentially decaying distribution of different t2s. The final state wavefunction is not "here's a definite t2"---that requires measurement.

someguy12342 7y ago

It is a bit more difficult to see this because you are describing a continuous time process, however, the answer is that yes you would be able to to figure out the time t1 given you knew had a snapshot of the whole system through the time evolution equation. Perhaps your confusion stems from the fact that the time t2 is observed, and it seems like you can't go back after that. An easier to grasp manifestation of this problem is that if you find Schrodinger's cat dead you can't tell if was always dead or if was dead only after your experiment. The reason is because that's only with the narrow knowledge of that cat being dead (maybe the would call this the cat state subsystem). It might be unsatisfactory to you, but in the theory of quantum mechanics, if you knew the state of everything (say the room, measurement apparatus, and so on), then you would be able to trace back to whether the cat was alive or dead. The moral is that the measurement looks irreversible if you look only at the system you are observing, but overall, people accept that there is a overarching greater space (the "environment, universe" where everything is just a unitary operation in motion according to the time evolution equation [1]). To be clear, the time evolution equation only admits reversible solutions. So with full knowledge, of say, the room and measurement apparatus, it would be possible to deduce the original state of the cat. https://www.quantiki.org/wiki/church-larger-hilbert-space https://www.quantiki.org/wiki/church-larger-hilbert-space

yk 7y ago

You are collapsing the wave function at t1 and t2. At t1 explicitly by stating that the state is known, and by t2 implicitly by defining that you have a defined distance t2- t1. The emission of an photon at an explicit time t2 is not reversible, the emission of an photon according to the wave function of the atom leads to an photon entangled with the atom and the total has a reversible wave function. (For illustrative purposes, when you measure and you find the photon at a distance (t- t2)*c from the atom, then you will also find the atom in a state that has emitted a photon at t2, no Idea if that is especially illustrative.)