On 2008-04-15, Wayne Throop <throopw@[EMAIL PROTECTED]
> wrote:
> Yet, cosmic rays hit "stationary" particles all the time, right?
Sure, and the products have a resulting velocity which is certainly
not less than Earth's escape velocity.
> And sometimes with many times the energy of a CERN particle, right?
Yes, occasionally.
> So... choose a frame in which the "stationary" particle is moving
> with the same speed as the cosmic ray, in the opposite direction.
> This is always possible, and just as valid as any other frame. And
> you'll *still* have a collision energy in that frame higher than
> CERN's.
Not necessarily. Kinetic energy is not just halved when you transform
to center-of-mass frame. This is a surprising result of the way that
relativistic velocities add. It's also why the highest energy
experiments are designed with opposing beams rather than stationary
targets.
The center-of-mass energy for a proton meeting another proton head-on
at 0.99999c is about 800 GeV. In the center-of-mass frame for a
0.99999c proton hitting a stationary proton, the velocity is about
0.9955c for an energy of about 20 GeV. At higher energies, the ratio
is even worse.
> Not sure what "the same in the other two axes" means, but it seems
> clear that since "axes" are an artifact of the coordinate system
In this particular case, we have a special coordinate system: one in
which the Earth is at rest. Black holes with a high momentum in this
frame will just leave the Earth's vicinity and never come back.
In order to create a black hole that can drop into the Earth and
slowly eat it away, it needs both lots of energy to create it, and
less than 0.00004c velocity along all axes relative to Earth. Even if
the distribution of final velocities relative to Earth was uniformly
random with a sphere of radius c, the chance would be less than 1 in
10^12. It's actually astronomically less likely than that because the
speed distribution is really massively weighted toward c.
And even that is assuming two high-energy cosmic rays very near Earth
happen to hit *each other* coming in opposite directions.
- Tim
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