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If we know the state of the universe at a certain point in time, is the future set? There have been quite a few similar questions on here and some of the answers were quite useful to me. But there is still some confusion on my part since there seem to be 2 different kinds of answers to this question:

  • The Schrödinger equation is deterministic. The indeterminism comes from the collapse of the wavefunction when a measurement is made. So the future is not set.
  • A wavefunction only appears to collapse if your quantum system doesn't describe your measuring apparatus as well. A measurement involves entangling the measured system and the measuring system, and in the process simply spreads the coherence from the initial state over both systems. There is no loss of information, it's hard to unentangle the two systems, but theoretically it's possible. So 'knowing the state of the universe at a certain point in time' would be equivalent to knowing the wave function of the universe at a certain point in time, which will then evolve deterministically. So to me this would seem to imply that the future is set.

There have also been some answers saying it depends on the interpretation of quantum mechanics and hence the above question doesn't really have an answer rooted in physics. So my question: Does physics provide an answer to the above question and if so, which of the above answers (if any) is correct?

Milan
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  • @Tesseract That's one of the questions I'm referencing to in my question. It has different answers, so I'm asking for some clarity. – Milan Nov 05 '19 at 23:59
  • If you want more clarity on an existing question, don't start a new question on the same topic. –  Nov 06 '19 at 05:42
  • @BenCrowell Will do! But this question was mainly to ask about the concept of the "wavefunction of the universe", which the above question doesn't have anything to with. – Milan Nov 06 '19 at 13:20

2 Answers2

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If the measuring apparatus and the system being measured are both described by wavefunctions, there is no loss of information -- and you end up with the Many Worlds view. In the Many Worlds view, the equations are deterministic, but the equations describe the relative probability of an infinity of possible futures.

Because you are a measurement apparatus that - in each possible world - can only perceive itself in one state at any moment in time, your history will appear to you (when examined in close detail) to include a series of "wave collapse" events, but (according to the Many Worlds view) actually those events mark branches in the wavefunction describing the world. Looking backward in time, you only see the path you remember experiencing. Those alternative "you"s on other branches will also see only those paths they remember experiencing, all the way back to where your paths diverged from theirs.

The jury is still out on whether the Many Worlds view is truly the correct interpretation of quantum mechanics. I'll keep my own opinion to myself for the time being.

S. McGrew
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According to currently accepted physics we are not able to perfectly predict the future, even if we had complete knowledge of the present state of the universe. QM can only give probabilistic predictions.

Many worlds interpretation (MWI) also needs to postulate Born's rule. The probabilistic predictions that are obtained from this interpretation in a natural way (counting branches) are wrong. The problem is that it does not seem to be any physical justification for introducing Born's rule in MWI so I don't think it is a valid option.

It is certainly possible that QM is not a fundamental theory, but a statistical approximation of a fundamental theory that could be either deterministic or non-deterministic. In order to decide which is more probable we need to go back to the EPR's reality criterion:

"If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity."

We know that, given a pair of two entangled particles, if we measure, say the Z spin of particle A we can predict with certainty the Z-spin of the particle B, even if A and B are very far from each other. If the measurements are performed at the same time and we assume locality is true it follows that "there exists an element of reality " corresponding to the Z-spin of particle B. In other words, the Z-spin of particle B was determined before any measurement took place.

We have strong evidence that locality is true, so, according to the above argument, we also have strong evidence that QM is a statistical approximation of a fundamentally deterministic theory.

In conclusion, we do not have a rock-solid proof that the universe is deterministic but we have good evidence that it is. So, more likely than not, the future is set.

Andrei
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