Re: Do baryons generate mesons from the tidal forces around small black holes?
- From: "Jim Black" <tramspap@xxxxxxxxx>
- Date: 22 Nov 2006 18:25:56 -0800
Bill Hobba wrote:
<michalchik@xxxxxxx> wrote in message
news:1164233775.041313.297900@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
It is my understanding that as the quarks in a baryon get pulled apart
in an accelerator collision, the potential energy from the color force
gets converted into a quark anti-quark pair, regenerating the original
baryon and producing a meson. It seems to me that the tidal forces
around a small blackhole (very curved spacetime) could differentially
accelerate the individual quarks and cause the same effect.
What you are talking about is a quantum effect. We only have a quantum
theory of gravity valid to about the plank scale - at energies beyond that
(ie what you seem to be talking about) we don't know.
http://arxiv.org/abs/gr-qc/9512024
Let's do some order-of-magnitude calculations. The maximum force with
which the baryon tries to hold the meson in ought to be about the rest
energy of the meson divided by the radius of the baryon. Using the
rest mass of the lightest meson, the neutral pion, which is
135 MeV/c^2, and the radius of a proton, about .8 femtometers, the
maximum restoring force is about 3*10^4 Newtons. The proton ought to
be able to pull the pion inward at a maximum acceleration of that force
divided by the pion's mass, which would give us c^2/(.8 femtometers),
or 10^32 m/s^2. Divide that by .8 femtometers again and we have an
idea of how much curvature might be required -- around 10^47 s^-2.
Granted, this was a classical calculation in a quantum mechanical
situation, but I would be surprised if quantum-mechanical effects
changed the order-of-magnitude.
Let's put the proton as close to the black hole as possible, which
would be just outside the event horizon. If I recall correctly, the
component of the curvature trying to tear the proton apart is 2GM/r^3,
so if r = 2GM/c^2, we have a curvature of c^2/r^2. That means we need
a black hole about the size of the proton, or smaller. It would be a
very small black hole, but still a lot larger than the Planck scale.
And if the formula at Wikipedia
[http://en.wikipedia.org/wiki/Hawking_radiation#Black_hole_evaporation]
is right, such a black hole would take hundreds of billions of years to
evaporate, so it would be stable for all intents and purposes.
I don't know how throwing quantum mechanics in would affect things, but
my guess would be that it would be possible.
.
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