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Constant comments on On Being Decoherent - Less Wrong
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"Eliezer's argument is that multiple worlds require no additions to the length of the theory if it was formally expressed, whereas a 'deleting worlds' function is additional. It's also unclear where it would kick in, what 'counts' as a sufficiently fixed function to chop off the other bit."
Run time is at least as important as length. If we want to simulate evolution of the wavefunction on a computer, do we get a more accurate answer of more phenomena by computing an exploding tree of alternatives that don't actually significantly influence anything that we can ever observe, or does the algorithm explain more by pruning these irrelevant branches and elaborating the branches that actually make an observable difference? We save exponential time and thus explain exponentially more by pruning the branches.
"It's not clear from your post if you think the other half's chopped off because we haven't observed it, or we don't observe it because it's chopped off!"
Neither. QM is objective and the other half is chopped off because decoherence created a mutually exclusive alternative. This presents no more problem for my interpretation (which might be called "quantum randomness is objective" or "God plays dice, get over it") than it does for MWI (when does a "world" branch off?) It's the sorities paradox either way.
"The other point is that if we are 'Human-LEFT' then we don't expect the other part of the wave function to be observable to us. Does that mean we delete it from what is real?"
Yes, for the same reason we delete other imagined but unobserved things like Santa Claus, absolute space, and the aether from what we consider real. If we don't observe them and they are unnecessary for explaining the world we do see, they don't belong in science.
You're almost exactly playing the part of Huve Erett in this dialog:
http://lesswrong.com/lw/q7/if_manyworlds_had_come_first/
Emphasize the "almost". I'm advocating objective collapse, not Copenhagen.
It sure seems to me as though Huve Erett advocates objective collapse. Maybe you can explain what part of the dialog convinces you that Huve Erett can't be talking about objective collapse.
"This happens when, way up at the macroscopic level, we 'measure' something."
vs. in objective collapse, when the collapse occurs has no necessary relationship to measurement. "Measurement" is a Copenhagen thing.
"So the wavefunction knows when we 'measure' it. What exactly is a 'measurement'? How does the wavefunction know we're here? What happened before humans were around to measure things?"
Again, this describes Copenhagen (or even Conscious Collapse, which is even worse). Objective collapse depends on neither measurements nor measurers.
Much of the rest of this parody might be characterized as a preposterously unfair roast of collapse theories, objective or otherwise, but the trouble is all the valid criticisms also apply to MWI. For example "the only law in all of quantum mechanics that is non-linear, non-unitary, non-differentiable and discontinuous" also applies to the law that is necessary for any actually scientific account of MWI, but that MWI people sweep under the rug with incoherent talk about "decoherence", namely when "worlds" "split" such that we "find ourselves" in one but not the other. AFAIK, no MWI proponent has ever proposed a linear, unitary, or differentiable function that predicts such a split that is consistent with what we actually observe in QM. And they couldn't, because "world split" is nearly isomorphic with "collapse" -- it's just an excessive way of saying the same thing. If MWI came up with an objective "world branch" function it would serve equallywell, or even better given Occam's Razor, as an objective collapse function. In both MWI and collapse part of the wave function effectively disappears from the observable universe -- MWI only adds a gratuitous extra mechanism, that it re-appears in another, imaginary, unobservable "world."
BTW, the standard way that QM treats the nondeterministic event predicted probabilistically by the wavefunction and the Born probabilities (whether you choose to call such event "collapse", "decoherence", "branching worlds", or otherwise) is completely non-linear, non-unitary, non-differentiable and discontinuous, and worst of all, nondeterminstic (horrors!). In the matrix model, the "collapse", if you will forgive the phrase, of a large (often infinite) set of possible eigenvalues and corresponding eigenvectors to one, the one we actually observe, according to the Born probabilities. No matter how much "interpreters" try to sweep this under the rug this nondeterminstic disappearance of all eigenvectors (or their isomorphs in other algebras) save one is central to real-world QM math and if it weren't so it wouldn't predict the quantum events we actually observe. So the dispute here is with QM itself, not with collapse theories.
Well, I don't agree with the "vs", but let that pass, since then the dialog quickly continues:
That occurs as early as one fourth of the way through the dialog, so that leaves three fourths of the dialog addressing what you are apparently calling an objective collapse theory.