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## Main Question or Discussion Point

So, this is a simple question that's been bugging me for a while. Let's consider a particularly simple universe (and its wavefunction): a single qubit. This might be in a superposed state, wrt the computational basis ([itex]\lbrace |0\rangle, |1\rangle\rbrace[/itex]), such as [itex]|\psi\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)[/itex]. Now, measurement in this basis yields with 50% probability either 0 or 1. Naively, in a many-worlds picture, one might thus consider this as 'two worlds', one in which the qubit is 0, and the other in which it is 1.

However, measuring the same qubit in the [itex]\lbrace |+\rangle, |-\rangle \rbrace[/itex] basis, we get '+' with certainty (since [itex]|+\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)[/itex], so we'd be inclined to consider this as 'one world'. More generally, any wavefunction in an eigenstate wrt some observable can be written as a superposition of eigenstates of some other observable.

Now, ordinarily, perhaps the environment, or some scientist (who's after all part of the environment) decides the basis to 'measure' in. Or, perhaps the canonical answer in the many-worlds picture is that world-splitting happens only upon decoherence, when some thermodynamically irreversible interaction occurs.

This is fine for everyday systems, but it runs into problems when the whole universe is considered: there's neither an environment to account for decoherence (the universe being, you know, all there is), nor is there an experimenter to do measurements (unless, I suppose, you count God, but let's just not go there). So, is the wave function of the universe in a superposition, or not? In what sense are there then 'many worlds' as opposed to just one, defined by whatever observable the universal wavefunction happens to be an eigenstate of? Or is my whole thinking just muddled?

However, measuring the same qubit in the [itex]\lbrace |+\rangle, |-\rangle \rbrace[/itex] basis, we get '+' with certainty (since [itex]|+\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)[/itex], so we'd be inclined to consider this as 'one world'. More generally, any wavefunction in an eigenstate wrt some observable can be written as a superposition of eigenstates of some other observable.

Now, ordinarily, perhaps the environment, or some scientist (who's after all part of the environment) decides the basis to 'measure' in. Or, perhaps the canonical answer in the many-worlds picture is that world-splitting happens only upon decoherence, when some thermodynamically irreversible interaction occurs.

This is fine for everyday systems, but it runs into problems when the whole universe is considered: there's neither an environment to account for decoherence (the universe being, you know, all there is), nor is there an experimenter to do measurements (unless, I suppose, you count God, but let's just not go there). So, is the wave function of the universe in a superposition, or not? In what sense are there then 'many worlds' as opposed to just one, defined by whatever observable the universal wavefunction happens to be an eigenstate of? Or is my whole thinking just muddled?