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Wave Function of the Universe

  1. Apr 22, 2012 #1
    I have not started studying quantum mechanics in depth (so I don't know too much of the math behind it). But I read about the Schrodinger's wave equation and how it can be applied to a system when there are more than one particle (for example, hydrogen atom, a molecule etc). However, if the events in the whole universe was concerned, then wouldn't every single particle in the universe have to be in the equation? Then would the final wave function be the complete description of the whole universe?

    I have another part to the question concerning the double split experiment. I read that if a detector is placed then the wave nature of the particle disappears apparently because the device is measuring the position of the particle. However, what is the definition of measurement in this case? What is the exact interaction in the device with the particle that collapses the wave function. (and how could that be possible if the explanation for the whole universe is just one gigantic wave function?) Is it a photon just hitting an electron (if that is the particle used) that collapses the wave function?

    Finally, if the wave function of the whole universe is known (or at least a wave function of all the particles involved in the experiment), then when the device is placed at the slits, wouldn't the wave function perfectly predict the way the electron will hit the screen (just one strip of dots where electrons hit instead of interference)?
     
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  3. Apr 23, 2012 #2

    Jano L.

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    PSarkar,

    your questions are very hard. There is no agreement among physicists on how to answer them. Various points of view are possible, and are sometimes called " interpretations of quantum theory ", but they are so much different that I'd say they are different theories. If you are new to these questions and want to plunge into further study, there are some related advanced discussions on this forum, but I should warn you, it will be difficult and probably will cause you headaches. There is no clear accepted view on these things. Be careful before believing any claims!

    But it is a fascinating study too. You can read on quantum theory from the original authors, I recommend mainly these

    Old theory of quantum jumps: Bohr (Quantum theory of line spectra); Bohr,Kramers, Slater; Einstein (both Quantum theory of radiation), Kramers, Heisenberg (papers in book by van der Waerden, Sources of Quantum Mechanics).

    Wave mechanics: Schroedinger, book Papers on wave mechanics.

    Orthodox interpretation: Niels Bohr (papers on complementarity), David Bohm (book Quantum theory)

    Critique of the orthodox theory: de Broglie, Einstein, Schroedinger

    Theory of hidden variables: David Bohm (papers on his hidden variable theory)

    Questions of locality: Bell inequalities (John Bell)


    Sorry if this is not the answer you wanted. Hope it helps anyway.

    J.
     
  4. Apr 23, 2012 #3

    ZapperZ

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    Back off a bit. Just because one can write a wavefunction for a Hydrogen atom, doesn't mean one can write it for any number of particles AND have a meaningful, solvable solution to it!

    In condensed matter physics, we deal with a gazillion particle that make up materials, such as your conductor. Here, there is no way for anyone to solve for the wavefunction of such a system. It is impossible to do. Thus, one has to make approximations, such as the mean-field approximation, to solve many of these problems.

    So the notion of having a wavefunction that ".. be the complete description of the whole universe" is a fallacy considering that we don't even have an analytic wavefunction for complex atoms or solids!

    Zz.
     
  5. Apr 23, 2012 #4
    Yes, it's also worth noting that when people like Hawking, Gibbons, Hartle etc use the term "wave function of the universe", they are often refering to a wavefunction on minisuperspace - a low dimensional configuration space of highly symmetric solutions of Einstein's equations.
     
  6. Apr 23, 2012 #5
    Einstein's equations are related to General Relativity, which is a classical (non-quantum) theory. Therefore, it has nothing to do with wavefunctions, being an artifice of Quantum Theory.
     
  7. Apr 23, 2012 #6
    Its not the detector that's changing the outcome of the experiment Its the "knowing" of what the particles did/travelled.
     
  8. Apr 23, 2012 #7
    Yeah, I know the schrodinger wave equation cannot be solved even for helium. However, just because you cannot find the wave function in terms of elementary functions does not mean that the solution does not exist. It simply means we cannot get the exact analytic solution but we can of course get the approximations. But, I wasn't even concerned with getting approximate solutions. I was just thinking that since the laws of physics apply to the whole universe, if one was to a description of the universe then wouldn't quantum mechanics have to be applied to all the particles at once using the wave equation (of course ignoring gravity and many other factors which would complicate things even more). Kind of like the N-body problem for gravity where all particles have to be considered but thats of course without quantum mechanics or relativity.

    Now I was just wondering how you can talk about wavefunctions of individual particles if they are all part of a bigger system? If you are doing the double slit experiment, why would you say that the electrons wave function collapsed? Isn't it theoretically more correct to talk about the wavefunction of the entire system? (techniqally the whole universe but to symplify everything, just considering the whole system as everything in the experiment including the particles that make up the slit, the detector, and all the electrons) I know its not feasible but if one were to find this wave function of the entire system for the experiment, then can't you find the probabilities for where the electrons will hit on the screen? And shouldn't this probability match the experiment where it is just a strip instead of an interference since there is a detector. I am asking this since if this is the case then you don't really have to talk about wave function collapse of an electron. Also, if the wave function without the detector is found then shouldn't the probabilities of where the electrons will hit go back to the interference pattern?

    Also to micky_gta: What do you mean by "knowing"?. You don't mean that a conscious person has to measure do you? I thought it works without anything or anyone in the room except the detector. So the measurement by the dector should be causing this according to most articles on the web. Then which exact interaction is considered a measurement?

    To Jano L: So is it really possible that all those interpretations are right or is there one absolute right one but no one knows?

    Thanks for the quick replies by the way.
     
  9. Apr 23, 2012 #8

    Thats the old, very old way of thinking. The most recent tests performed 1990-2012 can have the detectors on and no interference pattern when the data ( "knowing" ) was cut off before someone can see/record 'the numbers' or measurement. I have seen and read too many articles on that so to me its a fact. =)
     
  10. Apr 23, 2012 #9
  11. Apr 24, 2012 #10

    mfb

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    This idea leads you to the many-worlds interpretation (MWI), or, if you add particles, to the de-Broglie-Bohm-theory.
    This is a valid way to interpret quantum mechanics, and it does not need any "collapse" of the wave function.


    You would get a correlation between the measurement at the "slit detector" and the "screen detector". Once you influence the photon at one side in a way that you can detect it, you get decoherence between the two photon path's, and therefore you cannot see interference any more. With MWI, you get a lot of different branches of the wave function, which do not interact (in a significant way) any more after your experiment. With collapse interpretations, only one of these branches exists, and the other branches somehow vanish.


    There are extensions of QM which could make predictions, and could therefore be tested. However, most interpretations just give the same results everywhere.
     
  12. Apr 24, 2012 #11
    TO micky_gta: I still don't think consciousness is causing the collapse but the fact that measurement is being made and the electron or photon's information exists. In the video it showed that when the informations was destroyed, the interference pattern came back (even if the informations was destroyed after the other photon went through the slits). It would be interesting to see what happens if the delay is extended by increasing the distance travelled by the second photon before going through the polarizer.

    To mfb: Your answer cleared up many of the questions I had. Thanks
    I guess I'll learn more about this stuff later on since I am going to University of Toronto starting this September. :)
     
  13. Apr 24, 2012 #12
    Dude its very understandable "In the video it showed that when the informations was destroyed, the interference pattern came back (even if the informations was destroyed after the other photon went through the slits)."

    Its called entanglement.
     
  14. Apr 24, 2012 #13
    Yeah, I know, I read about it. I understood what they did in the video. I was just saying that I still don't think its consciousness that causing the wavefunction collapse. I think it was happening as long as the information existed. When the information was destroyed even after the photon went throught the slits, the interference was back.
     
  15. Apr 24, 2012 #14
    If the information 'exists' and is not retrievable to prove objectively then its an interference pattern.
     
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  19. Jun 4, 2012 #18

    A. Neumaier

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    One can talk about the density matrix of a subsystem, which is obtained by tracing out the rest of the universe. In general, the density matrix is a mixture, and indeed, in quantum optics one needs to consider this mixture to get accurate predictions. For elementary textbook examples, one can idealize and pretend that the mixture has rank 1 and hence is a pure state - then and only then one can talk about the wave function of the subsystem.

    In some cases, namely when the subsystem has only very few degrees of freedom (such as a few spins or a few polarizations), one can prepare pure states to a good approximation, and thus implement good approximations to the ideal textbook scenarios. This is indeed done to test fundamental questions of quantum mechanics, as in tests of Bell inequalities and the like. But even in this case one needs the more accurate description by density matrices to assess the accuracy of the results.
     
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