Re: rest mass/relativistic mass question
- From: Greg Egan <gregegan@xxxxxxxxxxxxxxxxxxxxx>
- Date: Sun, 19 Feb 2006 05:31:34 +0000 (UTC)
In article <1140282793.633884.228210@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Chalky <utpalchakraborty@xxxxxxxxx> wrote:
thanks everyone for taking the time to reply.-------------------------------------------------------------------------------------
i was pretty sure that a mass moving inertially will not turn into a
black hole (as described in the Baez faq). I understood that much.
However, as I said in my first post the proton is not moving
inertially. It is continuously accelerating.
The acceleration does not make any difference?
Greg Egan Write:
If your proton is in a linear accelerator, I'm sure it-------------------------------------------------------------------------------------
will never become a black hole, because that's basically just changing
the frame of reference.
The kinetic energy of objects *confined* inside a bounded region would
contribute to the total mass-energy in that region -- e.g. a very, very
fast spin could turn the Earth into a black hole (if it was made of
something strong enough) and I guess even a proton moving in a suitably
implausible cyclotron could (along with the energy density of the
magnetic field needed to confine it) turn the cyclotron into a black
hole.
So a linear acceleration of a proton does not turn it into a hole, but
an angular acceleration might?
The proton itself would not turn into a black hole, but it seems possible
to me (in principle, though not with any realistic machine) that the
whole system that was both accelerating and confining the proton -- into
which energy has been poured, via an electric current, and stored, as
kinetic energy and in the electromagnetic field -- might collapse into a
black hole if you could make the energy content high enough. The proton
would be radiating both electromagnetic and gravitational waves, so the
system would also be losing energy, and at the very least the real-world
parameters of the materials used to construct the magnets would surely
make the whole thing vaporise and/or explode long before this point was
reached.
As the FAQ notes, this is a tricky issue, and I certainly can't prove my
hunch. But I'd argue as follows. Suppose we power the cyclotron by
shipping lots of hydrogen and antihydrogen into its neighbourhood. These
are then combined to liberate energy which is somehow captured and used
to generate electricity. From far enough away, the gravitational effects
would be blind to all this interconversion of energy between different
forms; they would just depend on the amount of mass/energy that has
entered the neighbourhood of the cyclotron. The detailed behaviour of
the spacetime curvature close to the cyclotron *would* depend on all
these details, so it might turn out to be much, much harder to form an
event horizon by piping electricity into a cyclotron than by accumulating
a large cloud of cold hydrogen. But it's hard for me to believe that the
difficulty would be *infinitely insurmountable*, that is, no matter how
much electromagnetic and kinetic energy you managed to get into the
cyclotron, a horizon still wouldn't be created. (Of course, the
real-world difficulties would include confining the energy in these forms
in the first place.)
Greg Egan
Email address (remove name of animal and add standard punctuation):
gregegan netspace zebra net au
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