Re: What Hath Einstein Writ?

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

> Hmm?  Well let's see.  What is it we need mass for?   We need a
> proportionality constant between momentum and velocity, and we need
> something to be proportional to the total energy of a particle.
> In neither case will the rest mass suffice so we are sort of stuck with
> the relativistic mass.   That said, I must admit that the concept of the
> rest mass is useful in the theory in an way that is analogous to the
> usefulness of the proper time.                      WBN

While we're waiting for the heavyweights to weigh in on this topic,
let's try some preliminary thoughts. Mass as a property of matter is
something one should be able to measure, right? But if a mass is
moving, how do we measure that mass? I contend that we cannot measure
it directly, but must be content to measure its momentum, and use
that value to calculate a mass. In relativity, the momentum can be
found from p=(gamma)mv, and so the mass to be found will be
m=p/(gamma)v. If we then recover the object (assuming that nothing
funny has been done to it between the measurements, and measure its
mass now that its at rest we should obtain the same result, because
we all recognize that what I calculated is what some introductory
texts still call the "rest mass." We can do the same thing with
energy, and will find that, as long as we try to calculate the mass
by moving everything that doesn't involve the mass directly to the
other side of the equation, we will find that the mass we calculate
dynamically is just that thing we call the "rest mass." So why bother
with the idea of rest mass at all? It is really redundant, and once I
have used the idea is a couple of simple-minded approaches to derive
the expression E=mc^2, I try never to use the idea of rest mass
again. If I was in a position in my class to do a more rigorous
derivation of E=mc^2, I would never use any kind of relativistic mass
at all, and if someone shows me a derivation that will be
understandable to high school juniors, I will avoid the idea even
there.

But E=mc^2 does permit mass to be converted to energy, and that, of
course, is the whole point of nuclear physics. The energy that binds
the nucleons together comes from the masses of the nucleons
themselves. And those nuclei that prove to be radioactive are those
for which there is another possible "daughter" nucleus whose mass is
less than the parent nucleus less the radioactive particles emitted.
Systems always tend to the lowest available energy state. One can get
a lot of mileage out of that idea in discussing nuclei. And nowhere
do we ever use "relativistic mass."

So if we don't need it, why use it? I have to come down on the side
of the professional relativists who have not used the term for years,
if not longer.

Hugh


Hugh Haskell
<mailto://hhaskell@mindspring.com>

Let's face it. People use a Mac because they want to, Windows because they
have to..
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