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shminux comments on Yet more "stupid" questions - Less Wrong Discussion
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This is quite misleading. Since collapse is experimentally compatible with "shut up and calculate", which is the minimal non-interpretation of QM, and it describes our world, where energy is mostly conserved, energy is also conserved in the collapse-based interpretations.
That's wrong, as far as I understand. The math works out perfectly. Objective collapse models have other issues (EPR-related), but conservation of energy is not one of them.
Links? I suspect that whatever you mean by energy conservation here is not the standard definition.
When isn't it? (This is another Stupid Question.)
One example is that in an expanding universe (like ours) total energy is not even defined. Also note that the dark energy component of whatever can possibly be defined as energy increases with time in an expanding universe. And if some day we manage to convert it into a usable energy source, we'll have something like a perpetuum mobile. A silly example: connect two receding galaxies to an electric motor in the middle with really long and strong ropes and use the relative pull to spin the motor.
What is conserved, however, according to general relativity, anyway, is the local stress-energy-momentum tensor field at each point in spacetime.
Read the first section of this paper. Conservation of energy absolutely is a problem for objective collapse theories.
The definition of conservation being employed in the paper is this: The probability distribution of the eigenvalues of a conserved quantity must remain constant. If this condition isn't satisfied, it's hard to see why one should consider the quantity conserved.
ETA: I can also give you a non-technical heuristic argument against conservation of energy during collapse. When a particle's position-space wavefunction collapses, its momentum-space wavefunction must spread out in accord with the uncertainty principle. In the aggregate, this corresponds to increase in the average squared momentum, which in turn corresponds to an increase in kinetic energy. So collapse produces an increase in energy out of nowhere.
I have skimmed through the paper, but I don't see any mention of how such a hypothetical violation can be detected experimentally.
Yeah, the paper I linked doesn't have anything on experimental detection of the violation. I offered it as support for my claim that the math for energy conservation doesn't work out in collapse interpretations. Do you agree that it shows that this claim is true? Anyway, here's a paper that does discuss experimental consequences.
Again, my point only applies to objective collapse theories, not instrumentalist theories that use collapse as a calculational device (like the original Copenhagen interpretation). The big difference between these two types of theories is that in the former there is a specified size threshold or interaction type which triggers collapse. Instrumentalist theories involve no such specification. This is why objective collapse theories are empirically distinct from MWI but instrumentalist theories are not.
... and is isomorphic to MWI...
Doesn't seem like it. You have an initial state which is some ensemble of energy eigenstates. You do measurements, and thereby lose some of them. Looks like energy went somewhere to me. Of course under non-ontological collapse you can say 'we're isomorphic to QM! Without interpretation!' but when you come across a statement 'we're conserving this quantity we just changed!', something needs interpretation here.
If your interpretation is that the other parts of the wavefunction are still out there and that's how it's still conserved... well... guess what you just did. If you have any other solutions, I'm willing to hear them -- but I think you've been using the MWI all along, you just don't admit it.
... or any other interpretation...
I guess our disagreement is whether "something needs interpretation here". I hold all models with the same consequences as isomorphic, with people being free to use what works best for them for a given problem. I also don't give any stock to Occam's razor arguments to argue for one of several mathematically equivalent approaches.
If you have any arguments why one of the many untestables is better than the rest, I'm willing to hear them -- but I think you've been using "shut-up-and-calculate" all along, you just don't admit it.
I totally do admit it. MWI just happens to be what I call it. You're the one who's been saying it's different.