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In light of the uncertainty principle, how can one describe 0, 1, or 2 dimensional entities?

  1. Oct 28, 2014 #1
    Except for associating a statistical mean to a large number of measurements, how can one assign a single point to a particle ? Indeed, how can one assign a size of anything less than the Planck scale? A similar question about strings: how can one talk about one-dimensional objects? A similar question for two-dimensional objects such as a string-world line, or a brane, or an event horizon, etc.
     
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  3. Oct 28, 2014 #2

    phinds

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    Talking about mathematically idealized particles / objects is not constrained by the HUP. I'm not sure if that answers your question or not.
     
  4. Oct 28, 2014 #3
    Thanks for the answer, phinds. I am also not sure if that answers my question. In saying that a real-life particle is associated with an idealized point particle as anything but a statistical mean or as a limit, aren't we saying "the particle is really a point but we just can't measure it as such", which smells of metaphysics?
     
  5. Oct 28, 2014 #4

    Doug Huffman

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    In the Susskind lecture - 'String Theory and M-Theory' - that I watched last night (instead of broadcast TV) he had a lengthy sidebar on 'points' and what attributes they could not have.
     
  6. Oct 28, 2014 #5

    phinds

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    I'm no expert on this but my understanding is that modeling an electron, for example, as point when it is being measured as a particle is what gives the best agreement with reality. I don't think there are ANY "particles" that are actually JUST points because they are all quantum objects and talking about them purely as particles is classical physics and does not match up with reality the way it does when you realize that they are quantum objects (that ACT like particles if you measure them that way and act like waves if you measure them that way).

    I don't think talking about a particle characteristic as a point is metaphysics, it is standard physics in that it is the best model we have. Once, it was the best model we had to say that material stuff is made up of atoms. Then it was the best model to say it was made up of protons/neutrons/electons, now it's known to be MORE correct to say it's made up of quarks and electrons. Is it correct to say that quarks and electrons are a fundamental as it's possible to get? String theorists would likely disagree even though they do not yet have any empirical evidence on their side.
     
  7. Oct 28, 2014 #6
    Thanks for the indication, Doug Huffman. Could you indicate which one of the ten lectures you are referring to? The first one is at , but then it goes on for ten lectures.

    Thanks for your further answer, phinds. The usual formulation of physics as particle theory has 0-dimensional points, but there appears to be a point-less formulation in field theory : http://arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf (for the pure-maths oriented non-physicist, the analogy that comes to mind is the point-less formulation of Category Theory). Perhaps the use of a model with 0-dimension points to approximate a reality without such points used to be the best match in the past, but perhaps the discrepancy means that there is, or at least should be, a better one? If one must have particles, perhaps one needs a formulation whereby they are simply small but not infinitesimal?
     
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