# How can the quantum state of the universe decohere

Decoherence explains how a classical state appears once quantum information in a quantum state leaks out. But presumably that environment has its own quantum state which then leaks out to a larger environment.

Does this mean that decoherence can only be understood locally, and not globally? For example if the entire universe is encoded in a quantum state how can it decohere?

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Welcome to the Everett Interpretation of quantum mechanics. –  Peter Shor Jul 31 at 2:57
You'll have to define what you mean by the quantum state of the universe. I wish you luck - no-one else knows what it means or even if the concept makes sense. –  John Rennie Jul 31 at 7:33
@Rennie: I'm not even going to try...! –  Mozibur Ullah Jul 31 at 11:32

As mentioned in the comments, there's no guarantee that the quantum state of the universe is a concept that even makes sense.

Assuming the universe is describable by quantum mechanics, and assuming it's a quantum system with nothing to interact with ever, and (most importantly) assuming all interactions and evolutions happening inside are unitary (even though there's no guarantee any of these assumptions are the least bit plausible); then no, it probably can't decohere.

Decoherence, as in a pure state becoming mixed, can only happen in unitary QM when the system entangles with something else and you insist on looking only at the system. It's easy to see this case is excluded by the assumptions.

Note however, that the unitary assumption is very much not plausible - it is incompatible with measurement collapse, and let's not even get started on relativity. And without it the answer would be: yeah sure, whatever you want. =)

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An interesting state (thermofield state) is :

$$|\psi\rangle = \sum_n e^{- \frac{\beta}{2} E_n}|E_n\rangle_1|E_n\rangle_2$$

where $1$ and $2$ are regions separated by a space-like interval.

When you make a measurement in the region $1$, you will have to perform a partial trace on $2$, and you get a thermal state $\rho_1 = e^{-\beta E}$

So, even if the evolution of the universe is unitary (for instance with an entangled state), practically measurements are done locally

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