From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of Ken Caviness
Sent: Wed 2/27/2008 4:50 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Invariant mass and relativist mass...
Advantages of using invariant (rest) mass everywhere: Just as the
spacetime interval is the invariant constructed from distances & time
periods by ds^2 = dr^2 - (c dt)^2, (m c^2)^2 = E^2 - (p c)^2. It is
common to use units where c=1 and write ds^2 = dr^2 - dt^2, m^2 = E^2 -
p^2. This parallel reveals (rest) mass as the invariant formed by
energy & momentum: very nice! Also, as I tried to (briefly!) say
earlier, the concept of a single quantity called the relativistic mass
(gamma m) just cannot be used as generally as mass can in Newtonian
physics. Imagine an object having a different effective mass depending
on which way I push! We can decide to use this system but it is awkward
and becomes less intuitive the farther we take it.
The other nice bit of pedagogy that comes from this approach is to write the invariance equation for E and p as E0^2 = E^2 - (pc)^2 and E as E0 + K. At the low speed limit, in order to have K=1/2 mv^2 we must have E0 = mc^2. Students seem to be fascinated by seeing such a familiar result occuring so simply from the concept of invariance. One is certainly able to arrive at the same result through the low speed approximation to relativistic mass, but the assumption of invariance is far more elegant than postulating m = gamma * m0.