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Quantum Mechanical Conceptual Problems

  1. Apr 21, 2005 #1
    Some straightforward problems I have encountered in QM; i'll post them gradually, otherwise it 'd be a little long, thanks

    1a) Wave/particle Duality: A quantum wave as stated through Dirac and von Neumann is a probability wave expressed by Schrödinger equation and thus here implying a superimposed state. A first conceptual problem I encounter here is that the very being of superposition can never be observed. It can be derived from the interference of for example the double slit experiment. Logically, the superimposed wave function has encountered a "wave collapse" due to a certain form of measurement. Due to this wave collapse, the former probability wave will act as a single vector in Hilbert space, containing finite energy, thus being a point in Hilbert space.
    If we keep on using this definition of the quantum properties, I am very curious what that exactly causes the wave collapse.

    1b) The notion of the "particle"- being of the quantum as a single vector in Hilbert space with finite energy thus implies a major problem explaining classical "rest mass". Thus if a classical observable particle,if being fundamentally different in some way of the quantum vector,is observed, it could never generate an interference pattern (if we do a gedankenexperiment containing two slits and bowling balls), just because the quantum properties of the propability wave needed for interference avoid the classical notion of matter.
    IF! on the other hand you don't make a difference of fundamental level between a single quantum system and a classical system, -what- does then "convert" your theoretical vector in Hilbert space to a classical observable system having a structural rest mass, in which E=mc² must play a major role?

    1c) If indeed, you don't make a fundamental difference between a single quantum state and a "classical" system (as being build up by single quantum states), then what contains the information to collapse the wave function of a whole system, thus creating a logically structured classical system??
     
    Last edited: Apr 21, 2005
  2. jcsd
  3. Apr 21, 2005 #2

    ZapperZ

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    I'm going to risk sounding like a broken record (broken CD?), but here goes.

    The consequences of superposition CAN be observed. When you make a measurement, you are only forcing a definite state only on that corresponding to the commuting observable. It means that the observable that do NOT commute will still be represented by a superposition of states. For example, when you make a measure of Lz, the other two orthorgonal observables, Lx and Ly, REMAINS in indefinite state. Lz do not commute with both Lx and Ly. This means that a measurement of Lz does NOT remove the superposition of states that may be describing Lx and Ly.

    Thus, if something is in a superposition of states, if I can find a non-commuting observable, I can make that measurement and see if so-and-so values reflect the fact that there is some form of superposition going on. This is what has been observed in the Stony Brook/Delft SQUID experiment (I have made repeated references to this here and in my Journal entry).

    Thus, you can still detect the effect of such superposition without causing a total "collapse" of the wavefunction.

    Zz.
     
  4. Apr 21, 2005 #3
    Ok, so according to that paper superposition also is also noted in macroscopic distant states. Thats a clear and straight answer , thanks.

    But that leaves most of my other questions unanswered. I still have conceptual problems on how a dimensionless "energy" vector such as stated by Quantum Mechanics can in some way or another be altered and be converted in a "particle" observable in 3D, and Above all, can be combined in such a way that they form logically structured systems.
    In other words, how a single quantum state can be collapsed in some way or another and form with numerous other similarly collapsed functions a "classical system".

    Thank you
     
  5. Apr 21, 2005 #4

    dlgoff

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    Maybe this will help.

    DECOHERENCE, EINSELECTION,. AND THE
    QUANTUM ORIGINS OF THE CLASSICAL. Wojciech Hubert Zurek.

    arxiv.org/pdf/quant-ph/0105127

    Regards
     
  6. Apr 22, 2005 #5
    There is no wave particle duality.

    The superposition is just a description of the space/time distribution of some of the particle or system's properties.These properties constitute a partial description of the particle and its fields.

    There is no real collapse. There is just redistribution of particle or system properties over space/time.

    juju
     
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