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lomidrevo
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- TL;DR Summary
- How conservation of energy works in many-worlds interpretation of QM?
I think I have a rough idea about it, but I am not sure whether it is correct. At least I feel that my understanding is a bit vague. Here it is:
Globally (I mean across all worlds), the energy is conserved because the universal wavefunction evolves strictly according to Schrodinger equation. That is clear. But how is that reflected in observations done by someone living in one of the worlds? Here is my clue:
When the wavefunction branches, the "existence" of new worlds is generally not equal. Instead, each new world (or branch) comes with a weight that is proportional to the amplitude squared (as described by the wavefunction). So if we sum energies of all new branches ##E_i##, the result would be equal to the overall energy of the "parent" world ##E## as it was just before branching. The energies of new branches are indeed the overall energy ##E## multiplied by the corresponding weights ##W_i##:
$$E = \sum{E_i} = \sum{W_i E}$$
Let's say that Alice is going to do some quantum experiment, and just before she manages to measure overall energy of the world ##E##.
After the experiment, the world has branched, and she find herself in a particular new branch where one of the outcomes of the experiment is realized. Now, when she measures the energy of the world it must be again ##E##, (and not ##E_i##) otherwise she would conclude that energy is not conserved. So how should be this interpreted? According to Alice in particular new branch, the measured total energy is still ##E##, but the "real" contribution of this branch to overall energy is only ##W_iE = E_i##?
Am I wrong or do I miss something? If you can correct me or provide any relevant texts on this topic, I would be welcome.
Globally (I mean across all worlds), the energy is conserved because the universal wavefunction evolves strictly according to Schrodinger equation. That is clear. But how is that reflected in observations done by someone living in one of the worlds? Here is my clue:
When the wavefunction branches, the "existence" of new worlds is generally not equal. Instead, each new world (or branch) comes with a weight that is proportional to the amplitude squared (as described by the wavefunction). So if we sum energies of all new branches ##E_i##, the result would be equal to the overall energy of the "parent" world ##E## as it was just before branching. The energies of new branches are indeed the overall energy ##E## multiplied by the corresponding weights ##W_i##:
$$E = \sum{E_i} = \sum{W_i E}$$
Let's say that Alice is going to do some quantum experiment, and just before she manages to measure overall energy of the world ##E##.
After the experiment, the world has branched, and she find herself in a particular new branch where one of the outcomes of the experiment is realized. Now, when she measures the energy of the world it must be again ##E##, (and not ##E_i##) otherwise she would conclude that energy is not conserved. So how should be this interpreted? According to Alice in particular new branch, the measured total energy is still ##E##, but the "real" contribution of this branch to overall energy is only ##W_iE = E_i##?
Am I wrong or do I miss something? If you can correct me or provide any relevant texts on this topic, I would be welcome.