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Why does math describe physics so perfectly?

  1. May 27, 2013 #1
    How is it that the numbers we get for our equations describe the laws of physics so cleanly? As a good example, take the equation for gravitational attraction.

    The strength of the gravitational attraction is divided by the distance squared, AKA the distance x the distance itself.

    But r^2 seems like too perfect of a coincidence. Why wouldnt it be to the power of some random non whole number that reflected the randomness of the universe?
    i.e.

    r^2.02934

    This means there must be something special and fundamental about whole number exponentials, but im not sure what it is or why it is.

    So why exactly is it that the distance is multiplied by itself exactly once in that equation, and many others?
     
  2. jcsd
  3. May 27, 2013 #2

    Vanadium 50

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    In the case you mention, it's because we live in 3.00000 dimensional space, and that power is d-1.
     
  4. May 27, 2013 #3

    Fredrik

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    1/r2 has the nice property that the orbit of a planet is an ellipse (if we neglect the influence of the other planets).

    General relativity predicts that the orbits are not exactly ellipses. If I remember correctly, it predicts a result that corresponds to what we'd get from Newtonian mechanics with terms proportional to 1/r2, 1/r3, 1/r4, and so on in the formula for the gravitational force.
     
  5. May 27, 2013 #4
    Ahh, i didnt expect an answer relating to the dimensionality of space, that's very interesting, and makes perfect sense.

    Unfortunately, i have no idea why it makes perfect sense, and don't understand the logic of the relationship between number of dimensions and degree of exponents.

    Dare i ask why? Or would that be too complicated?

    Also, that d-1 rule applies as a blanket for any dimensional space? Does that mean that a 9 dimensional space would have r^8?
     
  6. May 27, 2013 #5

    Vanadium 50

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    In this case, the strength of the field in N dimensions is inversely related to the surface of an N-sphere or radius r. In 3 dimensions, the area is 4pi r^2, and there is your 1/r^2. In 9 dimensions, the area of a 9-sphere is something like 32pi^4/105 r^8, so there you get a 1/r^8 field.
     
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