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Planck Length Paradox?

  1. Oct 10, 2012 #1
    Assuming that a planck length is the smallest unit of distance, I propose this:

    Assume there was a circle of radius r and had an area of A. If I would increase this circle's area by 1 planck length^2, would the radius change? The radius would theoretically change by less than a planck length, but would the radius actually change?

    Another would be if I increased this circle's diameter by 1 planck length. Would the radius increase?

    Are these true paradoxes, something that just happens at this level or do they not hold any water?
     
  2. jcsd
  3. Oct 10, 2012 #2
    I am certainly not an expert in Planck measurements (and I really doubt there is such a thing as a Planck expert), but I'm fairly certain there are 2 different measurements called Planck Length and Planck Area. Planck Area is a smaller unit than Planck length for the exact reason you are bringing up. There is also Planck Volume and I believe other similar measurements for higher dimensions, though I'm not sure how many of these have an established value as of yet.
     
  4. Oct 11, 2012 #3

    mathman

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    You seem to be mixing mathematics and physics. Planck length is a physics concept and the question you are raising is mathematical. In mathematics there is no smallest unit of distance.
     
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