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Proof that micro black holes can't exist?

  1. Aug 7, 2011 #1
    I was playing around with some equations and I found a reason why I think micro black holes cannot exist. This proof requires a few assumptions which I have tended to find to be a scientific consensus. They are the following.

    1) The smallest mass a black hole can have is the planck mass which by definition will give the schwarchilds radius of the black hole the planck length.
    2) The smallest meaningful increment of time in the universe is the planck time.

    Lets start with the uncertainty principle.

    ΔXΔP <= h / 4π

    This can also being written as.

    ΔEΔT <= h / 4π
    ΔE <= h / 4πΔT

    This tells us that the amount of energy uncertainty created from the vacuum is inversely proportional to the time. Now let us change our units of energy to mass by dividing the equation by c^2

    Mtotal <= h / 4πΔTc^2

    The maximum amount of mass that can be created from nothing out of the uncertainty of the vacuum can now be written as the following.

    Mtotal = h / 4π(Tplanck)c^2
    Mtotal = (6.626 * 10^-34) / ((4π)(5.39 * 10^-44)(299792458)^2)
    Mtotal = 1.088 * 10^-8 kg

    The planck mass is 2.17 * 10^-8 kg. So it turns out the maximum amount of mass that can be created from nothing for 10^-44 seconds is exactly half the planck mass. Am I missing a factor of two anywhere? Or is it just planck masses and micro black holes cannot be created from the uncertainty principle? Thanks
  2. jcsd
  3. Aug 8, 2011 #2
    Well, what if you have a black hole moving at relativistic speeds? (so E =/= mc^2) :P

    I don't know quite enough about QM to comment about anything else...
  4. Aug 8, 2011 #3
    Well, at least you tried.
  5. Aug 8, 2011 #4
    You just go in the reference where it is at rest (which exist becausse [itex]M_{BH} > 0[/itex])

    Well, first you need to reverse all the inequalities: It's [itex]\Delta X \Delta P \geq \hbar[/itex] and [itex]\Delta E \Delta t \geq \hbar[/itex].
    Last edited: Aug 8, 2011
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