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It seems to me, that Schrodinger's Equation implies that the universe is deterministic, given an initial state. Now I know people will talk a lot about measurements, and wave function collapses as being probabilistic, but when you consider a closed quantum system, then given an initial state, it will evolve according to Schrodinger's equation in a predictable way.

When we talk about wave function collapse, we are really talking about two interacting quantum systems, the thing being measured and the thing doing the measuring. We treat the thing being measured as completely separable from the thing doing the measuring, that is ψ=ψ

_{A}+ψ

_{B}where A is the system we want to measure, and B is the thing doing the measuring (and the rest of the universe). We in general take ψ=ψ

_{A}and evolve that with Shrodinger's equation, until we measure it and the wave function collapses into an eigenstate (with the appropriate probability). From this we say that quantum mechanics is a probabilistic theory, where we can only say what the answer will be with a given probability if we try to measure something.

But isn't this just an illusion? I mean, the real wave function must still evolve according to Schrodinger's equation, and the "collapse" of the wave function of the thing we measure is actually just a result of two interacting quantum systems, where some information must be transferred to the quantum system that is doing the measuring (which includes the rest of the universe). I guess what I am trying to say is that if the universe is a closed quantum system, then its time evolution must be given by Shrodinger's equation, and if we knew the initial state of the universe (not likely since its got infinite degrees of freedom, but that's another topic) we would know the state for all eternity. Hence, Shrodinger's equation implies fate.

What do you all think?