Trying to Understand Many-Worlds Interpretation Better

[Alex K]

Surgenator,

It's not really an additional multiplying of particles. The MWI amounts to basically just taking what the Schrödinger equation gives you and running with it. The quantum superpositions of the observer which automatically occur when it is included in the qm state along with the measured system,already give you the many worlds from your perspective. Copenhagen tells you to artificially deviate from Schroedinger after a measurement and project this down to one of the observer states in the superposition. So in a sense its less parsimonious than MWI.

There a two issues with that, how to assign probabilities to the superpositions, and whether some states should be special, but those are technical details.

In this picture, the usual observed quantum interference, eg in the double slit, precisely *is* interference between universes. Interference between very dissimilar universes is ultra suppressed afaik because the wave functions have little overlap.

I'm still having trouble wrapping my head around it. Is there a collapse of the wave function? If there isn't, then we are one solution of enourmous superposition function. How the fuck do you assign a probability if you have to worry about other superposition states your not in interfering with yours? AHHHHHHHHHHHHHHHHHH This is why I'm an experimentalist.

I can't claim to have full understanding here as I'm a measly high energy theorist by training, not a quantum mechanic

My super simple toy example which I told Pickup a few weeks or months ago is like this:

You, the observer, have the three mood states | >, | :| >, | >
and the cat has the states | 8- >, | X- >

The Schrödingers cat system starts out with the tensor product state

Psi1 = 1/sqrt(2) | :| > * ( | 8- > + | X- > )

where your mood is sharp and neutral and the cat is in the superposition dead-alive. Your measurement of looking in the box yields a correlation between your mood state and the cat state, so after the interaction we have

Psi2 = 1/sqrt2 | > * | 8- > + 1/sqrt2 | > * | X- >

So far we have only used the Schrödinger equation for the unitary time evolution from Psi1 to Psi2, no collapse.

In Copenhagen, you would discard one of those halves of the superposition, in MWI, you keep the new state as is. The universe is now a superposition of you happy and cat alive, and you unhappy and cat dead. Those are the two worlds. At no point was there the need to artifically double anything. The prefactors squared give you the propabilities in both cases, i.e. 1/2.

You could recover the copenhagen states corresponding to the two outcomes by projecting e.g. onto your happy state using the operator

| >< | * 1

Of course in this simple 6 state system, there are not enough degrees of freedom to have decoherence, that is implicit in this overly simplistic example. There are some issues as to which states systems decohere to and why, and how to properly define probabilities in these states, which are not at all trivial.