OK, they claim that the only meaningful conservation of energy in quantum mechanics is the conservation of the expectation value of the Hamiltonian; that this is violated; that this violation can be arbitrarily large; that this violation cannot be attributed to the energy of the observer or the apparatus; and that the "many-worlds interpretation" makes all these questions more controllable. Each of the five statements is absolutely and fundamentally wrong.Okay, I don't need to belabor the point. Obviously Carroll is not going to be making any perpetual motion machines. I just want to comment on how Carroll believes in Many-Worlds, and that everything makes more sense there. He says:
In the Many-Worlds formulation of quantum mechanics, the energy of the wave function of the universe is perfectly conserved. It doesn’t “require energy to make new universes,” so that is not a respectable objection to Many-Worlds. ...The way he sees it, energy might be lost to our universe, and slip into a parallel universe so that the total evergy is conserved. Millions of new parallel universes are created all around you every second, but these do not require any additional energy, so again, energy is conserved.
The first point here is well-accepted and completely obvious to anyone who understands Many-Worlds.
This stuff doesn't make any sense. Sure, it is obvious that energy is not used to create new universes, because no new universes are created, and it doesn't even make sense to talk about unobservable universes. But now he says that energy is needed in the new universe to make up for energy losses in our universe? I give up. It makes no sense to me.