Re: rest mass/relativistic mass question
- From: John Bell <john.bell@xxxxxxxxxxxxxxxxxx>
- Date: Mon, 20 Feb 2006 02:46:52 +0000 (UTC)
Chalky wrote:
As a thought experiment, suppose, we are accelerating a proton in a
large accelerator (as large as you need it to be). It will continuously
gain mass/energy. Will a time come when it has gained sufficient mass
energy to form a black hole? If not why not?
I am in general agreement with the other respondents on this matter.
However, even though I don't know quite where this is taking me, there
is something about physics in the reference frame of the linearly
accelerating proton, which could be very loosely described as vaguely
analogous to black hole physics (despite also being very clearly
different). I am referring to the well-known fact that an observer
linearly accelerating at 1g, will outrun a photon if given a head start
of about a year. Thus, for the linearly accelerating proton, its source
will have an effective 'temporal event horizon' at about t = c/g.
However, this horizon is never observed from the accelerating reference
frame, because, as that horizon is approached, light from the source
continues to become progressively more red shifted. In other words,
light from the source between time 0 and time t = c/g is observed
progressively more stretched out, from time 0 to infinity, in the
reference frame of the constantly accelerating observer. Clearly,
something very similar happens when we look at light from the
continuously accelerating observer, when viewed in the reference frame
of the source. This consideration alone should help to confirm that the
linearly accelerated proton should never become a black hole relative
to the source, and vice versa.
However, if a cyclotron accelerates the proton, the situation could
become significantly different, because the mean velocity of the proton
remains zero, relative to the earth. I thus agree that it then seems
theoretically possible to 'pump up' the total rest mass of the
system indefinitely, provided sufficient energy can be found to
maintain adequate strength in the containment field, as well as to
maintain acceleration of the particle. So, yes, the system might then
eventually turn into a black hole (theoretically).
If yes, then what happens to an observer who is always at rest relative
to the proton?
The simple answer is that he will probably have been killed by huge
differential centrifugal forces, long before that system becomes a
black hole. In fact, it is difficult to imagine that those centrifugal
forces will not cause the whole system to explode long before that time
too.
To that observer nothing is happening
Not so. Massive experienced forces will become progressively vaster.
but then suddenly
the proton turns into a hole
I don't think so. If he could survive the forces, that observer should
eventually find himself in the same hole as the proton, and nothing is
particularly strange about that.
Hope this helps.
John Bell
.
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- From: Chalky
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