What is Many Worlds? What isn't Many Worlds?

[SU3SU2U1]

Your basis is just a mathematical tool, not a physical property of the system.

I agree- this means for many worlds to make predictions, we need very much for the number of 'branches' (I shall try and consistently use branches from now on, as opposed to blobs, or worlds,etc),however we define them, to be basis-independent. So I was asking- is it?

I shall answer my own question- if you have large objects that can cause decoherence (i.e. density matrices evolve until they are diagonal) then yes- branches are independent, as I've defined them. It is in this sense that decoherence solves the preferred basis problem.

HOWEVER- you aren't guaranteed to ever form those initial decoherent objects. Barvinsky and Kamenschchik (Physical Review D 52, 743-757, I apologize its behind a paywall) showed something neat- if you don't pick specific initial conditions for your universal wavefunction, then you may never get any 'classical' branches of the wavefunction. For other choices of initial condition, branches can evolve from 'classical' to not, very quickly. The non-classical branches ARE basis dependent, and this is problematic- without a unique decomposition, we can't make consistent predictions!

This is very much related to the initial conditions issue in Bohm's theory- which shouldn't be surprising since both interpretations strive to match the same set of predictions (standard quantum).

The only interpretations that avoid this particularly weird issue are ensemble and collapse interpretations (see GRW or one of the many other objective/stochastic collapse theories). In ensembles, this is because the wavefunction isn't "real" in the same way, and we use it only to predict probability distributions. In collapse, this is because collapse is guaranteed to create a diagonal (one entry) density matrix.

Something new

I did try earlier in the thread to move on from the multiplicity of worlds arguments, but then people asked more questions.

[doogly]

Come now, that's not true. Superluminal effects that don't allow superluminal information transfer are still quite compatible with physics.

What does the word "effect" mean to you? An "effect" which is not causal does not seem like something I would use the word "effect" for, and all causality is subluminal.

[mfb]

And mfb, you misunderstand. Switching from a spin-x to spin-y is not something you'd expect to change the number of branches. Going from spin-x to position or momentum, hmm?

How are spin and [position or momentum] related here?

if you don't pick specific initial conditions for your universal wavefunction, then you may never get any 'classical' branches of the wavefunction. For other choices of initial condition, branches can evolve from 'classical' to not, very quickly

This is an interesting point. Can you quote the requirements for the initial conditions?
Thinking a bit about it, exploring the initial conditions in our universe could be really tricky without some quantum gravity or a better explanation of the big bang.

In collapse, this is because collapse is guaranteed to create a diagonal (one entry) density matrix.

But if a collapse changes this problem, the collapse cuts away things which are not independent (in other branches for MWI), otherwise I don't understand why a collapse can remove "unphysical" parts of an initial wave function.
Or do the initial conditions just require (for MWI) something similar to "the initial wave function is a set of blobs"?

[doogly]

And mfb, you misunderstand. Switching from a spin-x to spin-y is not something you'd expect to change the number of branches. Going from spin-x to position or momentum, hmm?

How are spin and [position or momentum] related here?

They're not. To repeat, the idea is that choice of basis is very much independent of the evolution of the wavefunction. Evolution of the wavefunction is the only thing happening in MWI. The number of branches seems to be determined by choice of basis though. "Qua?" we say.

[Sizik]

This type of argument only works because of the nice numbers that pop out of an even probability measure like what fair dice provide.

Instead, take my thought experiment from before - set up 6 identical experiments, each with a 90% chance of producing an "A" on their detector, and 1% each chance of producing the digits 0-9 on their detector. (Assume that the difference in the 11 outcomes is due to a single quantum variable, for simplicity.) Run them all.

Basic probability says that you have a hair over 50% chance to see 6 As, and the chance of seeing 6 digits (of any kind) is 1 in a million. If you count worlds, though, there are about 1.7million worlds, in which 1 million of them (a bit over 50%) see 6 digits. Only *one* world sees six As. The two situations have *completely* reversed - now "most" observers see the most unlikely events.

The problem goes away if you if you describe the experiment correctly. Say you have a wheel with 100 equal-sized sectors, 90 of which are labeled A and the remaining 10 are labelled 0-9. One of the sectors is chosen through some random process that has an even probability distribution (quantum darts, quantum roulette, quantum wheel-of-fortune...).

Like this, 53% of the worlds get 6 As, and only 0.0001% of them get 6 digits.

[Xanthir]

Why is it "correct" to describe the problem that way?

(This seems closer to the "infinite worlds" formulation, where there are an infinity of worlds, and the amplitude describes what proportion of that infinity has a particular result.)