meekerdb wrote:
ISTM there are two ways of looking at it. In one you say before the event there were several possibilities x,y,z,... with probabilites a,b,c,... and one of them, x, happened. The energy before x was the same as after x, so energy is conserved. In the other you say x happened with probability a in the multiverse, y happened with probability b in the multiverse, z happened with probability c in the multiverse,... And in each of x,y,z energy was conserved and since a+b+c+...=1 energy is conserved in the multiverse. Non-conservation only appears when you use these two pictures inconsistently.
This seems to be the same as the renormalization that Wilczek talks about -- you essentially re-weight energies in the same way as you re-weight probabilities.
From an instrumentalist viewpoint (which I think can be useful) "energy" is just the conjugate variable of "time". We want our theories to apply at all times so we seek formulations of energy and time that do this as simply as possible. Having a conserved quantity called "energy" is a consequence of having theories that apply uniformly in time.
Without local energy conservation QM, on which MWI is based, is in real trouble.
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