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I Planck length confusion

  1. Feb 28, 2017 #1
    If I understand correctly, the Planck length, or maybe a tenth of it, is considered the point at which quantum effects mess up any attempt to apply our present physical laws, and so one could not even in theory make a dependable measurement of something smaller. However, I was wondering what would be wrong with the following simpler argument; it must be wrong somewhere because my answer is too big.

    Suppose we had some slit of width d . To measure it would require a photon with a wavelength of d/2 or smaller, that is, an Energy of at least 2hc/d, the equivalent rest mass of 2h/(cd). If we try to get the photon into the slit of width d, d will have to be bigger than the Schwarzchild radius r = 2GM/c2 = 4Gh/(c3d) . That is, d>4Gh/(c3d), or d>2√(Gh/c3) , but that is a factor of 2√(2π) too big, as the Planck length is √(Għ/c3). What is wrong? Thanks.
     
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  3. Feb 28, 2017 #2

    Vanadium 50

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    You're reading into terms of order one when you only have an order of magnitude estimate.
     
    Last edited: Feb 28, 2017
  4. Feb 28, 2017 #3
    Thanks for the reply, Vanadium 50. I ask forgiveness for my own density (hopefully less than that needed to collapse into a black hole), but I am afraid that I don't quite understand your comment. What are you saying that I am estimating?
     
  5. Feb 28, 2017 #4

    Nugatory

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    Not "at which quantum effects mess up...." but "around which, give or take a factor of ten or thereabouts, quantum effects must mess up...."

    The statement isn't precise enough to worry about a factor of ##2\sqrt{\pi}##
     
  6. Feb 28, 2017 #5
    Thanks, Nugatory. Ah. So the Planck length is a rather fuzzy border?
     
  7. Feb 28, 2017 #6

    Vanadium 50

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    The Planck length is very well defined. The size where you have to worry about quantum gravity is fuzzy - just like the size where you have to worry about everything else. Are you making a 10% measurement? A 1% measurement? A 0.00000001% measurement?
     
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