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I The units for Planks Constant and the Uncertainty Principle

  1. Feb 10, 2017 #1
    The unit for Planks Constant is Joule-Sec/cycle. Another way to view it is Joule/Hertz.

    I have a hunch and I would like to test it out on some of the members of this forum.

    Momentum*position (p*λ) also has the units of Planks Constant. Similarly Energy*Time(E*t) has the same unit as Planks Constant.

    Based entirely on the observation that momentum*position (or Energy*Time) have the same units as planks constant..I am going to make the conclusion that both of those quantities can only take on values that is some multiple of planks constant.

    In equation form...

    p*λ = n*h, where h is planks constant, p is momentum and n is some integer >= 1

    If n = 1 we get DeBroglie's formula.

    Because it is the quantity p*λ that is quantized, and not the individual constituents (p or λ) we cannot consider either of those parameters separately. It is as if the parameters are entangled (as opposed to two particles being entangled)

    We can measure the quantity momentum*position but we cannot measure momentum and position.

    A similar analysis would be true for Energy*Time.

    Reasoning this way, the complementary nature of momentum and position or energy and time becomes sensible to me, the respective parameters are pieces of a quantized quantity.

    I think I carry this a bit further.

    Here are two formulations of the uncertainty principle

    ΔP*ΔX ≥ ħ/2 and ΔE*ΔT ≥ ħ/2

    I recently realized that the following equation follows from those two formulations

    ΔP*ΔX = ΔE*ΔT

    Taking the limits of the above equation and re-arranging yields the following differential equation.

    ∂E/∂X = ∂P/∂T (the gradient of Energy Field = derivative of the momentum with respect to time)

    As I read over this I realize it might not be clear. But if I get some questions I think I can clarify what am trying to say.
     
    Last edited: Feb 10, 2017
  2. jcsd
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