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Fate and Schrodinger's Equation

  1. Nov 14, 2011 #1
    Now, I have put a lot of thought into the following idea, and at different times in my life I held completely opposite views on it.

    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=ψAB 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=ψA 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 thats another topic) we would know the state for all eternity. Hence, Shrodinger's equation implies fate.

    What do you all think?
     
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  3. Nov 14, 2011 #2

    Ken G

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    What you are saying involves choosing an interpretation to quantum mechanics, which means you are using quantum mechanics to do more than make statistical predictions (which is the only aspect of quantum mechanics we can actually test). The interpretation you have chosen sounds a lot like what is called "many worlds", and is originally due to Everett but now has proponents like Deutsch you can read up about. The fundamental premise is just what you say-- the universe is ruled by a "universal wave function", which evolves via the Schroedinger equation, and is thus entirely deterministic.

    Now, it is certainly true that quantum mechanics works by saying that systems that can be described by a wave function and are subject to a Hamiltonian operator evolve via the Schroedinger equation. The problem is, we don't actually know the limits of this claim. Other interpretations, like the Copenhagen interpretation, hold that the wave function is not a physically real entity, should not be taken literally, and the "universe" does not have one. They might also argue that there is no meaningful "Hamiltonian operator" for the whole universe, as a typical Hamiltonian operator that we would use in quantum mechanics involves a lot of idealizations (in particular around isolation from macroscopic measuring devices, during intervals when the Schroedinger equation is being applied). So it is not at all clear if the wave function of a universe really exists, or if it really evolves according to the Schroedinger equation.

    Another issue that crops up is general relativity, which we need to talk about what the universe is doing, but which has never been unified with quantum mechanics. The two theories really seem to be at loggerheads, they adopt very different fundamental philosophies about the dynamics of systems, and seem to completely part company at the Planck scale. If the universe is to have a "universal wave function", it must work at the tiny Planck scale, as well as at the huge scale of dark energy and so on. We really have no idea how to use quantum mechanical language in these kinds of situations, the theories just don't yet exist.

    On the topic of many worlds, you should know before you choose that interpretation that it comes with a kind of "poison pill" that many find hard to swallow-- if the whole universe evolves deterministically according to the Schroedinger equation, then it has no way to pick out a particular outcome of an experiment like the measurement of the linear polarization of an initially circularly polarized photon. The universe as a whole is equally vested in both outcomes of that experiment, and deterministic evolution must therefore produce both outcomes of that experiment-- we just only perceive a part of the "many worlds", so we think that only one outcome occured. So we live in a kind of tiny island of the whole truth of that universal wave function. Some see this view as liberating, others see it as wholly unacceptable for any scientific theory to assert.

    And one final point. Some, like Hawking, like to imagine that when you account for the kinetic energy, mass energy, and gravity of the universe, the total energy comes out zero. But if there is a universal wave function, and it evolves by the Schroedinger equation, then the evolution is "unitary". Unitary evolution of a state with definite energy (here zero energy) means that the state never changes at all. The universe has no concept of time, no concept of evolution, no kind of change of any kind that isn't pure illusion stemming from the fact that we don't really observe the whole enchilada. Thus the Big Bang is a kind of artifact of our limited ability to perceive, stemming from our need to get a definite outcome from an observation, rather than the complete range of possibilities that actually occur every time. It is certainly a rather weird way to view reality, so there's a high philosophical cost to pay for the many-worlds interpretation, but not everyone rejects it on those grounds-- and I would note that the ancient Greek philosopher Parmenides, about 25 centuries ago, reached a similar conclusion from what he felt was pure logic that all change must be an illusion.
     
  4. Nov 14, 2011 #3
    I'm no expert but I think you have the right idea.

    Suppose we know the wave equation of a particle perfectly, including how that wave equation evolves over time for all time. There would be an infinite amount of information in that. Would it be enough to predict the fate of the entire universe? I don't think so, but it might.

    But I don't believe it will ever be possible to know a wave equation for any particle perfectly. There are several reasons. The first thing is that the whole idea of real numbers is unrealistic. The whole idea of measuring anything to infinite accuracy seems impossible. Our universe doesn't allow it. The second is that it seems to me that particles don't really have an identity. If two identical particles collide then after the collision we don't know which is which. It seems to me that the universe doesn't know which is which either.

    Then there is the issue of interpretations of quantum physics. Does the wave function collapse and the other possibilities disappear? Or do those possibilities remain unchanged somewhere where we can't access them? I don't know, and don't spend much time worrying about it. What is more profitable might be to consider that in quantum mechanics only do we know the future probabilistically, we also know the past probabilistically. Indeed, we know everything probabilistically.

    If there is determinism, as far as we are concerned it involves so many choices -- illusory or not -- that it is for all practical purposes non-deterministic.
     
  5. Nov 16, 2011 #4
    It certainly implies only allowable physical situations can occur. But I wouldn't go so far as saying that the perceived world (i.e. a collapsed wave function) is deterministic - (which as far as I'm concerned, is the only world that needs worrying about)
     
    Last edited: Nov 16, 2011
  6. Nov 17, 2011 #5

    ZapperZ

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    Closed pending moderation.

    Zz.
     
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