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I Does the Uncertainty Principle imply a linear cosmology?

  1. Jun 14, 2018 #1
    If the uncertainty in the age of the Universe is ##\Delta t## then the Uncertainty Principle implies that it has an uncertainty in its energy ##\Delta E## given by
    $$\Delta E \ \Delta t \sim h.\tag{1}$$
    If this energy fluctuation excites the zero-point electromagnetic field of the vacuum then a photon is created with energy ##\Delta E## and wavelength ##\lambda## given by
    $$\Delta E \sim h \frac{c}{\lambda}.\tag{2}$$
    Combining Equations ##(1)## and ##(2)## we find that
    $$\lambda \sim c\ \Delta t.\tag{3}$$
    Now as this characteristic length ##\lambda## is the wavelength of a photon it is a proper length that expands with the Universal scale factor ##a(t)## so that
    $$\lambda \sim a(t).\tag{4}$$
    Combining Equations ##(3)## and ##(4)##, and taking ##\Delta t \sim t##, we arrive at a unique linear cosmology with the normalized scale factor ##a## given by
    $$a(t) = \frac{t}{t_0}.$$
    where ##t_0## is the current age of the Universe.
     
    Last edited: Jun 14, 2018
  2. jcsd
  3. Jun 14, 2018 #2

    phinds

    User Avatar
    Gold Member

    I'll leave it to more knowledgeable folks to weight in, but what I think is that you have extrapolated the HUP to WAY outside of it's domain of relevance.
     
  4. Jun 14, 2018 #3

    PeterDonis

    Staff: Mentor

    You can't apply the uncertainty principle to the universe as a whole since there is no way to make an external measurement on it, and the uncertainty principle applies to external measurements.

    Also, there is no "energy-time" uncertainty principle as you are using it. See, for example, here:

    http://math.ucr.edu/home/baez/uncertainty.html

    So your post is based on at least two incorrect premises.
     
  5. Jun 14, 2018 #4

    PeterDonis

    Staff: Mentor

    Correction, three incorrect premises. The universe as a whole doesn't have "energy fluctuations" in this sense.
     
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