| MadSci Network: Physics |
Dear Joshua,
that is a good question. The answer does not depend on which interpretation of Quantum Mechanics you consider. It's more fundamental than the issue of interpretation.
First of all, let me say that a quantum mechanical state is described in terms of a complete set of eigenvectors of some observable or measuring device and probabilities. The probabilities predict the chance that the according eigenvalue is the outcome of a measurement. Quantum Mechanics is not deterministic in the classical sense because the outcome of experiments cannot be predicted for certain, in general. Only probabilities can be given. An important point is that there are exact, unambiguous rules how to compute these probabilities and how they evolve in time. This is determined by the Schrödinger equation.
Let me state it again: The outcome of an experiment can only be predicted in terms of probabilities. BUT the probabilities themselves and their evolution is governed by laws, it is deterministic. Therefore, measurements of different systems may produce the same outcome, but still the laws are deterministic.
Maybe I should say a few words on the many-worlds interpretation. It is some kind trick to handle the probabilities. We live in one of these worlds only, and the other ones only exist in our minds helping us to do our calculations. An experiment can only have one outcome, but many are possible. So for each outcome you create a world, or independent reality. New experiments create new worlds. For example if we consider one experiment with 4 possible outputs and another one with 5, there are 4*5 = 20 parallel worlds. It is a tool to keep track of all possibilities, kind of physicist's incarnation of Musil's "Möglichkeitssinn", sense for what might be possible.
I hope this helps,
best regards, Michael
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