Does many-worlds violate conservation of energy?
First, the law conservation of energy is based on observations within each world. All observations within each world are consistent with conservation of energy, therefore energy is conserved. Second, and more precisely, conservation of energy, in QM, is formulated in terms of weighted averages or expectation values. Conservation of energy is expressed by saying that the time derivative of the expected energy of a closed system vanishes. This statement can be scaled up to include the whole universe. Each world has an approximate energy, but the energy of the total wavefunction, or any subset of, involves summing over each world, weighted with its probability measure. This weighted sum is a constant. So energy is conserved within each world and also across the totality of worlds. One way of viewing this result – that observed conserved quantities are conserved across the totality of worlds – is to note that new worlds are not created by the action of the wave equation, rather existing wo
