Energy in Everett's Many-worlds Interpretation

In summary, the energy in a superposition is not necessarily the energy of the constituent states, and the conservation of energy expectation value is 0 only for states that are eigenstates.
  • #1
jxcs
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Hi,

Is anybody able to explain how energy is "distributed" in the many-worlds interpretation. I'm using scare quotes as I think this may be the wrong line of thought. It's tempting to imagine energy being distributed amongst subsequent branches as the wave function evolves but I'm not certain that is a true picture? In this sense, energy would be proportional to the number of branches, at which point it all just starts to sound very fuzzy!
 
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  • #2
jxcs said:
Hi,

Is anybody able to explain how energy is "distributed" in the many-worlds interpretation. I'm using scare quotes as I think this may be the wrong line of thought. It's tempting to imagine energy being distributed amongst subsequent branches as the wave function evolves but I'm not certain that is a true picture? In this sense, energy would be proportional to the number of branches, at which point it all just starts to sound very fuzzy!

The various "worlds" in Many-Worlds are different branches of the universal wave function. The branching is just a way of writing the universal wave function as a superposition of wave functions. So in the simplest nontrivial case (two branches), the wave function ##\psi(t)## can be written as a superposition ##\alpha \psi_1(t) + \beta \psi_2(t)##. The energy of the universe is a weighted average of the energy of the branches. So splitting into two branches doesn't mean each branch has half the energy; each branch will have (approximately) the same energy as before the split.
 
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  • #3
Hi
Thanks so much for getting back to me. Ok, so one might naively conclude that the energy in a superposition might somehow sum to the energy of its constituents but I guess the "energy" of a state that is not an energy eigenstate is not *defined* and we can only consider energy in a state once it's in an eigenstate?
Could you also point me in the direction of an explanation of how the conservation of energy expectation value is 0?

Thanks!
 

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