Many-worlds versus discrete knowledge

Say that there is some code which will run two instances of you, one where you see a blue light, and one where you see a green light. The code is run, and you see a blue light, and another you sees a green light. The you that sees a blue light gains indexical knowledge about which branch of the code they're in. But there's no need for the code to have a "reality" index parameter to allow them to gain that knowledge. You implicitly have a natural index already: the color of light you saw. I don't see why someone living in a Many-Worlds universe wouldn't be able to do the equivalent thing.

So I guess I would say that in some sense, once you've figured out the rules, measurements don't give you any knowledge about the wave function, they just give you indexical knowledge.

I think in many-worlds you have to say things like "A photon passed through the measurement apparatus, in the branch of the wavefunction where we're speaking."

The more general idea is: you have a fact with a "location tag" of where that fact is true.

In a more everyday example, I can say "The temperature is 29° here". The word "here" tags a time and place.

Or in the other direction, consider "3 quarks can bind together into a proton". This seems to be a universal fact that therefore doesn't need any "location tag".... But is it really? No! In some plausible theories of physics, there are many universes (and this is not related to quantum many-worlds), and they all have different fundamental constants, and in some of these universes, 3 quarks can not bind together into a proton. So you should really say "3 quarks can bind together into a proton (in the universe where I'm speaking)".

So I would just go with the paradigm of "many facts need to come with a 'location tag' specifying where that fact is meant to be valid", and if you're OK with that, quantum many-worlds is fine.

Sorry if I'm misunderstanding your point. I am an expert on QM but not a mathematical and philosophical expert ;-)

I currently disagree with your conclusion about many worlds (I want to take modus tollens where you take modus ponens), but I think this is a really nice conundrum. 

(What is discrete knowledge? It is knowledge that some nontrivial proposition X is definitely true. The sort of knowledge a Bayesian may update on, and the sort of knowledge that logic applies to.)

There is no reason rational agents need to assign 100% probability to anything [LW · GW]. Eliezer rejected it long ago [? · GW], although he seemingly missed the implied rejection of Bayesian updates.

For this reason, I significantly prefer the Bohm interpretation over the many-worlds interpretation

Preferences do not make science. Philosophy, for sure.

Odds are, once mesoscopic quantum effects become accessible to experiment, we will find that none of the interpretational models reflect the observations well. I would put 10:1 odds that the energy difference of entangled states cannot exceed about one Planck mass, a few micrograms. Whether there is a collapse of some sort, hidden variables, superdeterminism, who knows.

Anyway, in general I find this approach peculiar, picking a model based on emotional reasoning like "I like indexicality", or "String theory is pretty". It certainly can serve as a guide of what to put one's efforts in as a promising research area, but it's not a matter of preference, the observations will be the real arbiter.

We model some discrete facts as being known. But Bohm interpretation or Everett, there's still just a bunch of microphysical stuff moving around. To expect the microphysical stuff to be different so that our model of how things are known works seems backwards to me.

Bohmian mechanics is not relativistic and has not been coherently formulated for spin-1/2 or spin 1 fields.

The Copenhagen interpretation is the best (most accurate) interpretation of quantum mechanics, so long as it is understood as a purely "epistemic" interpretation. That is: unlike pre-quantum theories, quantum mechanics does not provide a complete ontology of the world. There are physical properties (the observables) that can take various values, and the theory gives conditional probabilities for these possibilities, but no picture of what happens in between.

Consistent histories, applied to cosmology, is a slight adaptation of Copenhagen, in which one can obtain a probability for an entire history of the universe (specified in terms of observables-taking-values), given a "wavefunction of the universe" and a set of "mutually decoherent histories". However, it is still not ontologically complete, as it is still up to the user to decide when and where in each history, observables shall take values. The only constraint is mutual decoherence, i.e. not violating the uncertainty principle. One might look for a set of maximally specified decoherent histories, as a determining ontological principle, but there's still a very large number of ways to do this.

If simplest physics contradicts epistemology, you should change epistemology - it would be nice to develop some weird quantum knowledge theory without fundamental discrete facts.