Trying to Understand Many-Worlds Interpretation Better

[Anomalocaris]

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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.

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Thanks Alex. I got more of an idea of what it is. It still bothers me because it destroys the concept of what is real. For example, the superposition of the dead and alive cat becomes two distinct answer. The "real" answer dependends on which "universe" you split into.

Since you have no means of perceiving much less communicating with any other other universes, it's presence does not produce any implication on what is real that you can test.