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Re: [Phys-l] Rest mass again?

Derek McKenzie wrote on Wed, October 20, 2010 6:42:13 PM

The term 'rest mass' seems to be quite misleading to me because although we may
choose to view a lump of matter as 'at rest' in a particular frame, it >is made
up of many moving constituents in that same frame...

Yes, so what? A "particular frame" is unambiguously defined as a frame in which
the net momentum of a system is zero. It is a rest frame of a system.
Similarly, the rest (invariant) mass is defined as the norm of a 4-momentum of
a system. Applying this to the rest frame of the system where the system's
3-momentum, by above definition, is zero, you get the rest mass. And since it
does not matter what system you use for calculating an invariant characteristic,
the invariant mass and the rest mass are synonyms. What is so misleading about
it?

>...and what one person calls 'rest mass' could equally well be called a
sum of relativistic masses of its constituents.

Yes, so what? If we have one photon, we usually call it massless. I do
it myself, unfortunately, just to pay tribute to what is "customary". But if one
insists that there is no mass other than the rest mass, then the term "massless"
for a photon becomes misleading, for a very simple reason. Add another photon
with the opposite momentum of the same magnitude. Now you have a system of two
photons which (the system) has a rest frame and a non-zero rest mass. In my
view, it is more convenient to say that this rest mass comes from the
relativistic masses of constituents than to say that it is rest energy of the
system divided by c^2. The first possibility avoids any necessity to explain the
students (without invoking energy, which is a different property of an
object), why is each photon separately massless but the system of both is
massive.
The first possibility DOES NOT deny the second one. But those who discard the
first one, should explain their students how come that energy/c^2 determines
mass in one special reference frame, but does not determine anything meaningful
in all other frames. This would single out that one frame as something really
special, quite in the spirit of pre-Galilean physics, and totally against
relativity.

Moses Fayngold,
NJIT

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