"MWI having a fixed phase space that doesn't actually increase in size over time."
(1) That assumes we are already simulating the entire universe from the Big Bang forward, which is already preposterously infeasible (not to mention that we don't know the starting state).
(2) It doesn't model the central events in QM, namely the nondeterministic events which in MWI are interpreted as which "world" we "find ourselves" in.
Of course in real QM work simulations are what they are, independently of interpretations, they evolve the wavefunction, or a computationally more efficient but less accurate version of same, to the desired elaboration (which is radically different for different applications). For output they often either graph the whole wavefunction (relying on the viewer of the graph to understand that such a graph corresponds to the results of a very large number of repeated experiments, not to a particular observable outcome) or do a Monte Carlo or Markov simulation of the nondeterministic events which are central to QM. But I've never seen a Monte Carlo or Markov simulation of QM that simulates the events that supposedly occur in "other worlds" that we can never observe -- it would indeed be exponentially (at least) more wasteful in time and memory, yet utterly pointless, for the same reasons that the interpretation itself is wasteful and pointless. You'd think that a good interpretation, even if it can't produce any novel experimental predictions, could at least provide ideas for more efficient modeling of the theory, but MWI suggests quite the opposite, gratuitously inefficient ways to simulate a theory that is already extraordinarily expensive to simulate.
Objective collapse, OTOH, continually prunes the possibilities of the phase space and thus suggests exponential improvements in simulation time and memory usage. Indeed, some versions of objective collapse are bone fide new theories of QM, making experimental predictions that distinguish it from the model of perpetual elaboration of a wavefunction. Penrose for example bases his theory on a quantum gravity theory and several experiments have been proposed to test his theory.
That's an easy one -- objective collapse QM predicts that with astronomically^astronomically^astronomically high probability objects large enough to be seen at that distance (or even objects merely the size of ourselves) don't cease to exist. Like everything else they continue to follow the laws of objective collapse QM whether we observe them or not.
The hypo is radically different from believing in an infinitely expanding infinity of parallel "worlds", none of which we have ever observed, either directly or indirectly, and none of which are necessary for a coherent and objective QM theory.
"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.
It doesn't matter whether branching occurs at a point of or at during some blob of time, probabilistic or otherwise, it's a central part of MWI and you need an equation to describe when it happens. And that equation should agree with the Born probabilities up to our observational limits. Likewise for collapse in theories that invoke collapse. Otherwise it's just hand-waving not science.
"Imagine a universe containing an infinite line of apples."
If we did I would imagine it, but we don't. In QM we don't observe infinite anything, we observe discrete events. That some of the math to model this involves infinities may be merely a matter of convenience to deal with a universe that may merely have a very large but finite number of voxels (or similar), as suggested by Planck length and similar ideas.
"It's reasonable to assume run time is important, but problematic to formalize."
Run time complexity theory (and also memory space complexity, which also grows at least exponentially in MWI) is much easier to apply than Kolmogorov complexity in this context. Kolmogorov complexity only makes sense as an order of magnitude (i.e. O(f(x) not equal to merely a constant), because choice of language adds an (often large) constant to program length. So from Kolmogorov theory it doesn't much matter than one adds a small extra constant amount of bits to one's theory, making it problematic to invoke Kolmogorov theory to distinguish between different interpretations and equations that each add only a small constant amount of bits.
(Besides the fact that QM is really wavefunction + nondeterministic Born probability, not merely the nominally deterministic wave function on which MWI folks focus, and everybody needs some "collapse"/"world split" rule for when the nondeterministic event happens, so there really is not even any clear constant factor equation description length parsimony to MWI).
OTOH, MWI clearly adds at least an exponential (and perhaps worse, infinitely expanding at every step!) amount of run time, and a similar amount of required memory, not merely a small constant amount. As for the ability to formalize this there's a big literature of run-time complexity that is similar to, but older and more mature than, the literature on Kolmogorov complexity.
Every interpretation is "adding something." Just because interpreters choose to bundle their extra mechanisms in vague English language “interpretations” rather than mathematical models does not mean they aren’t extra mechanisms. Copenhagen adds an incoherent and subjective entity called "the observer." MWI adds a preposterous amount of mechanism involving an infinite and ever-exponentially-expanding number of completely unobservable clone universes. Copenhagen grossly violates objectivity and MWI grossly violates Occam's Razor. Also, MWI needs a way to determine when a "world" splits, or to shove the issue under the rug, every bit as much as collapse theories need to figure out or ignore when collapse occurs. If as many "interpreters" like to claim QM itself is just the wavefunction, then collapse and world-splits are both extra mechanisms.
But QM is not just the wavefunction. QM is also the Born probabilities. The wavefunction predicts nothing if we do not square it to find the probabilities of the events we actually observe. Of all the interpretations, objective collapse adds the least to quantum mechanics as it is actually practiced. Everybody who uses QM for practical purposes uses the Born probabilities or the direct consequences thereof (e.g. spectra). Thus -- despite the many who shudder at the nondeterminism of the universe and thus come up with interpretations like Copenhagen and MWI to try to turn inherent nondeterminism into mere subjective ignorance -- the nondeterministic quantum event whereby a superposition of eigenvectors reduces to a single eigenvector (and the various other isomorphic ways this can be mathematically represented) is every bit as central to QM as the nominally deterministic wavefunction. The Born probabilities are not in any way "extra mechanism" they are central to QM. Even more central than the wavefunction, because all that we observe directly are the Born random events. The wavefunction we never observe directly, but only infer it as defining the probability distribution of the nondeterministic events we do observe.
Thus any interpretation of QM as it is actually practiced must take the Born probabilities as being at least as objective and physical as the wavefunction. If the Born probabilities are objective, we have objective collapse, and neither Copenhagen nor MWI are true.
Wikipedia has a bare-bones description of objective collapse:
http://en.wikipedia.org/wiki/Objective_collapse_theory
Further experimental evidence: if the Born probabilities do not represent an objective and physical randomness that is inherent to the universe, then the EPR/Bell/Aspect/et,. al. work tells us that FTL signaling (and more importantly a variety of related paradoxes, FTL signaling not itself being paradoxical in QM) is possible. QM is not special relativity. Special relativity can't explain the small scale or even certain macroscale effects like diffraction that QM explains. Special relativity is just an emergent large-scale special case of QM (specifically of QFT), it is QM that is fundamental. QM itself, in the EPR/et. al. line of work, tells is that it is the objective and physical randomness inherent in the universe, not causal locality, that stands in the way of FTL signaling and its associated paradoxes.
Emphasize the "almost". I'm advocating objective collapse, not Copenhagen.
"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.
Let me join all those observing that these are great explanations of QM. But I don't get why we need to invoke MWI and the Ebborians. If the wavefunction evolves into
(Human-LEFT Sensor-LEFT Atom-LEFT) + (Human-RIGHT Sensor-RIGHT Atom-RIGHT)
but we only observe
(Human-LEFT Sensor-LEFT Atom-LEFT)
then it makes far more sense to me that, rather than conjuring up a completely unobservable universe with clones of ourselves where (Human-RIGHT Sensor-RIGHT Atom-RIGHT) happened, a far more empirical explanation is that it simply didn't happen. Half of the wavefunction disappears, nondeterministically. Why, as Occam might say, multiply trees beyond necessity? Prune them instead. Multiple "worlds" strike me as no more necessary than the aether or absolute space.
BTW, it's MWI that adds extra postulates. In both MWI and collapse, parts of the wavefunction effectively disappear from the observable universe (or as MWI folks like to say "the world I find myself in.") MWI adds the extra and completely gratuitous postulate that this portion of the wave function magically re-appears in another, imaginary, completely unobservable "world", on top of the gratuitous extra postulate that these new worlds are magically created, and all of us magically cloned, such that the copy of myself I experience finds me in one "world" but not another. And all that just to explain why we observe a nondeterministic event, one random eigenstate out of the infinity of eigenstates derived from the wavefunction and operator, instead of observing all of them.
Why not just admit that quantum events are objectively nondeterministic and be done with it? What's so hard about that?