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Schroedinger's Cat and Uncertainty

  1. Dec 26, 2008 #1
    Any study of modern physics inevitably brings one to the Heisenburg Uncertainty Principle, and usually to the Schroedinger's Cat paradox. Pop articles on the subject usually give such a cursory and dumbed-down overview that the reader really doesn't gain a good understanding of the topics.

    I was reading a book, published in 2007, called 50 Physics Ideas You Really Need To Know, which brings the reader to the Uncertainty Principle, and then the Copenhagen Interpretation of the Uncertainty Principle, and then Schroedinger's Cat.

    As I was reading these articles, I was thinking of what seemed to me to be rather straight-forward answers to the seemingly-paradoxical nature of these concepts. Given that this book was published so recently, I was surprised that these "paradoxes" didn't seem outdated. I thought that surely my retorts to these questions must have been thought of by other people before me. Perhaps the knowledge of the author of the book was a little lacking. I want present my thoughts on the subject and learn if these ideas have already made the rounds in the scientific community, and I want to have the ideas critiqued.

    Firstly, relating to the Schroedinger's Cat paradox, I think that the crux of the problem relates to what one consider's an "observer". The root of the paradox comes from thing that an "observer" must be a conscious entity--which seems to be a completely unfounded presumption. In this situation, the Geiger counter would be the observer, thus its observation would cause the cat to be either definitely alive, or definitely dead before any human inspects the situation.

    But going deeper, into the nature of Uncertainty, as it relates to the Copenhagen Interpretation, the collapsing of wave functions, and wave-particle duality, I have the following thoughts. The Copenhagen Interpretation states that basically that, at the quantum level, phenomena are not deterministic, and position and momentum are fixed when they are measured. This is distinct from the notion that Uncertainty just stems from the way that we measure position and momentum with photons.

    I would propose that the position and momentum of a *particle* do indeed arise from our measurement. However, this is due to the fact that a particle is really nothing more than an interpretation of data---that data being the way that our measurement systems and and the measured entity(ies) interact. The particle position and/or momentum, according to this line of thought, are just abstractions that we, as humans, make about the interactions between the wave(s) that we are measuring, and the wave(s) that we use to measure them. With this explanation, the seeming indeterminancy (of particles) goes away, as particles do not really exist in the first place. There are only waves, which I would think have momentum, but no exact position, as they are not volume-less entities.

    Is there anything in these ideas that have not made the rounds in scientific and science-oriented communities? Are there any counter-arguments to or flaws in what I have just presented.

    I should probably mention that my formal education in physics is limited to 2 semesters of college physics, which dealt a lot with electromagnetism, but just barely touched quantum physics (and Relativity).
     
  2. jcsd
  3. Dec 26, 2008 #2

    jambaugh

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    At the pragmatic level it suffices to interpret quantum mechanics' predictions about what happens at the points of observation. Since "what is real" between observations is by definition outside the domain of empirical confirmation we needn't ever worry about it from a scientific point of view. The various "interpertations" trying to address these issues are academic philosophical exercises which cannot really contribute to the physics unless they as models lead to empirical predictions beyond those of QM.

    Let me also mention that the quantum "particle" is neither wave nor particle. Both waves (defined by amplitudes and phase over all points in a region of space) and particles (with well defined count, positions, and velocity/momentum) are classical entities. Quanta are dynamic processes which have components which may be resolved in one or the other of these classical paradigms. We can resolve the phase of a stream of electrons passing through a Josephson junction, we can resolve the number and positions of electrons striking a florescent screen.
     
  4. Dec 26, 2008 #3
    The correct understanding of Heisenberg Uncertainty Principle is the following:

    Momentum by definition is a product of velocity. Velocity can be defined as a rate of change of position. Therefore momentum is really a product of the rate of change of position. This means to measure the momentum of a system, you need to measure how it's position is changing in time and the resultant momentum will be associated with a multitude of positions not a single one. Similarly, measuring a single position will not tell you what the momentum is, since you still have a wide range of possible ways in which the position might have been changing the instant before or after your measurement.


    Mathematically speaking, "position" is a Fourier transform of the "momentum" and vice versa. The uncertainty principle simply says that the more concentrated a function is, the more spread out its Fourier transform. It is not possible to arbitrarily concentrate both a function and its Fourier transform.

    The HUP has nothing to do with the Copenhagen interpretation.
     
    Last edited: Dec 26, 2008
  5. Dec 26, 2008 #4
    The Cat's paradox is indeed one of the deepest ones.

    Sorry (others) for repeating it over and over :)

    1. Forget about Copenhagen interpretation, duality, collapses etc.
    2. There is no such thing as 'collapse'. Instead there is: http://en.wikipedia.org/wiki/Quantum_decoherence
    QD does not involve consciousness, magic properties of 'measurement' etc.
    3. After reading #2, more advanced form of Shroedinger Cat's paradox, called Wigner's Friend (http://en.wikipedia.org/wiki/Wigner's_friend) will be a piece of cake for you.
     
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