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With regard to the theory that each time a wave function collapses the universe splits so that each possible outcome really exists - where does all the energy required to create all the new universes come from?

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The question you raise is a good one and is precisely the reason why the many world interpretation is flawed... – Killercam Oct 24 '12 at 10:54
@Killercam — you might as well ask where all of the extra matter comes from, which would clearly demonstrate how the OP misunderstands the MWI. The whole point is that the different "worlds" partition the matter and energy of the "parent" worlds from which they spilt, because taken together, they are only terms in a superposition making up the universal wave function. A criticism of MWI must proceed on different grounds. – Niel de Beaudrap Oct 24 '12 at 11:32
Personally, I don't like the interpretation that the law conservation of energy is based on observations within each world and that all observations within each world are consistent with conservation of energy, therefore energy is conserved. This to my mind is weak. Clearly it is based upon conservation of energy in QM being formulated in terms of weighted averages or expectation values. Then by some very basic stance that the energy of the total wavefunction, or any subset of, involves summing over each world, weighted with its probability measure. Hence energy conservation is not violated... – Killercam Oct 24 '12 at 12:30
I have never come accross it expressed like this. Does anybody else have comments on this - to me it seems a type of many-minds interpretation you describe. Thanks for your post... – Killercam Oct 24 '12 at 13:19
@Killercam, nobody argued that "energy conservation is based on observations ..." etc. The only argument for energy conservation is a strictly mathematical one, and that is that the global unitary evolution strictly preserves energy measured as <psi|H|psi>. So no, world splitting does not require energy. And you don't need quantum gravity for that argument either. – A.O.Tell Oct 24 '12 at 13:23

There is no energy required to do that. Unitary evolution preserves energy precisely. The reason is the way energy is calculated in quantum theory, and if that is applied to MWI then each branch only contributes with its squared modulus branch amplitude to the total energy. This is the only consistent way to count energy in quantum theory.

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Thank you for your response A.O.Tell - I am a layman and my question stems from what I have learned from "popular" science books and TV documentaries. Is there a way to explain "unitary evolution" in a way that I might understand ? – hereComesBrod Oct 24 '12 at 12:28
Unitary evolution of a QM system, is the evolution that is described by Schrodinger's equation. At the quantum scale, the state of a system is a superposition of probable states weighted by complex numbers that remain constant in time. If the system remained on the quantum level - were not measured in classical reality where only a single state can be 'real' - both states could be considered equally 'real' - their evolution in time on the quantum level is unitary - as a single entity... – Killercam Oct 24 '12 at 13:03
@hereComesBrod, the many worlds interpretation is derived from taking the Schroedinger equation, which describes the evolution of quantum states, literally. Unitary evolution is a characterization for what the Schroedinger equation does to the quantum state: It preserves its L^2 norm, or the length of the state vector. This kind of evolution has certain mathematical consequences, among them strict conservation of energy in the global quantum state. Since that state contains all the "worlds" or branches, energy is globally conserved and world splitting surprisingly does not require energy. – A.O.Tell Oct 24 '12 at 13:28
@Killercam, it's not very sensible to speak of "probable states" in context of MWI. The relative states approach does not assign probabilities to the wavefunction in the first place, instead it is treated as a real object. The probability interpretation is then supposed to emerge from relative state entanglement between observer and observed object. – A.O.Tell Oct 24 '12 at 14:33
I don't understand A.O. Tell's answer. My understanding is that there are two distinct processes in the evolution of systems under quantum mechanics. The $U$ (unitary evolution) process and the $R$ process (reduction or collapse of the wave function) to use Penrose's notation. But Tell seems to be claiming that $U$ applies at the 'branchings' in the MWI. Certainly these are points at which $R$ is acting. Perhaps you could address this by expanding on your answer? Thanks in advance. – MarkWayne Oct 24 '12 at 18:57

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