Re: Relativity

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Tue, 19 Mar 2002, David Abineri wrote:

> If a stationary positron (in some frame of reference) is
> struck by an electron moving relativisticly, is there perfect
> conversion of the mass into energy considering that, from the
> point of view of the positron, the electron has more mass than
> the positron.

First of all, the modern viewpoint is *not* that the relativistic
electron has more mass, it simply has more momentum and energy
than you would get using *classical* formulas for the energy and
momentum of an electron moving at that speed. Furthermore it is
misleading to talk about mass being converted into energy
"perfectly" or otherwise.  It is enough simply to require that
energy and momentum be conserved.

The initial energy of the two particle system is (gamma+1)*m*c^2
and the initial momentum is gamma*m*v where m is *the* mass of an
electron (or positron), beta = v/c, and gamma = 1/sqrt(1-beta^2).

After anhilation, we could be left with lots of different things
depending on the total energy.  One possibility (and the *only*
one at low enough energy) is two photons.  Whatever is produced,
however, it is subject to the constraints of many conservation
laws including, to name just two, those of energy and momentum.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm