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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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    $\begingroup$ @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. $\endgroup$ Oct 24, 2012 at 11:32
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    $\begingroup$ @Killercam, MWI is surely criticizable for a few things, like the dependence of branches on the level of coarse graining or the failure to produce the right event statistic from just counting events, but conservation laws are not an issue. The global evolution is unitary and all conservation laws are exact. The only possible criticism could be based on the fact that for one observer the branching may break conservation laws subjectively, but that effect has a vanishing expectation value. $\endgroup$
    – A.O.Tell
    Oct 24, 2012 at 12:03
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    $\begingroup$ 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... $\endgroup$
    – MoonKnight
    Oct 24, 2012 at 12:30
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    $\begingroup$ 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... $\endgroup$
    – MoonKnight
    Oct 24, 2012 at 13:19
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    $\begingroup$ @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. $\endgroup$
    – A.O.Tell
    Oct 24, 2012 at 13:23

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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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  • $\begingroup$ 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 ? $\endgroup$ Oct 24, 2012 at 12:28
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    $\begingroup$ @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. $\endgroup$
    – A.O.Tell
    Oct 24, 2012 at 14:33
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    $\begingroup$ 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. $\endgroup$
    – MarkWayne
    Oct 24, 2012 at 18:57
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    $\begingroup$ @MarkWayne - The point of MWI is that the projective dynamic is regarded as non-fundamental and instead derived as subjective feature of a global unitary evolution that entangles the observer with the observed system in a way that correlates an observed property with the system state possessing that property. So in an MWI context the objective evolution is unitary, always. $\endgroup$
    – A.O.Tell
    Oct 24, 2012 at 19:58
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    $\begingroup$ The primary confusion in this thread seems to be in thinking that many-world postulates a new discrete process that generates new worlds/structures instead of just being about unitary evolution of a single state vector. Here are some links to further reading that folks may find useful: arxiv.org/abs/gr-qc/9410006 frankwilczek.com/2013/multiverseEnergy01.pdf blog.jessriedel.com/2015/08/23/… arxiv.org/abs/1609.05041 $\endgroup$ Dec 10, 2017 at 18:12
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There is no need for extra energy. The energy of all-worlds-together is conserved, and the energy within each-world is conserved on-average (which is what energy-conservation means in quantum theory).

Consider a collection of identical quantum systems, where each can be in two states - we can mark the states as state $|1\rangle$ and state $|2\rangle$. Each state may have its own energy associated with it, $E_1$ and $E_2$.

As part of the way quantum mechanics is built up mathematically, this means that each system can also be in a "superposition" state, i.e. a weighted sum like $\sqrt{\frac{1}{3}} |1\rangle+\sqrt{\frac{2}{3}}|2\rangle$. Let us consider the systems to initially all be in this state.

Now, some device comes along and measures the system's energy. What happens?

First, consider things from the standard, no-multiple-world, (Copenhagen) interpretation. On this view the systems will "collapse" to state $|1\rangle$ with energy $E_1$ 1/3 of the time, and to state $|2\rangle$ with energy $E_2$ 2/3 of the time. So on average we will receive that this kind of system has energy $1/3 E_1 + 2/3 E_2$. And this is the same amount of energy the system "had" before we measured it (e.g. it would cost us this amount of energy to prepare these systems). So there is a "conservation of energy" in the sense that on average energy is conserved. This is how conservation of energy works in QM.

Now, let us consider the measurement from the many-worlds-interpretation. Consider a single system in the above superposition state. In this case you get that reality "splits" into infinitely many worlds, so that 1/3 of them include the system in state $|1\rangle$ with energy $E_1$ and 2/3 in state $|2\rangle$ and energy $E_2$. So if we repeat this experiment again and again (measuring the whole collection of systems we considered under Copenhagen), we will again receive that on average energy is conserved.

And as a bonus, if we consider the whole collection of worlds from the many-worlds-interpretation, then it has the same energy as that average.

So if you take just one system in a superposition, you will find that in each world it has a different energy (what scientists call "quantum fluctuations") but that on average the system has the same energy it initially had, and you will also find that the total collection of worlds is still in this superposition state (there is no collapse) and hence still has the same initial energy.

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