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Re: Increasing Mass of Particles



I want to check out my response to a student question related to the
increase in mass of a particle moving at a high speed. The student asked
if the density of the particle changes or if there is an actual change in
the volume of the particle. I told him that I thought there was no
evidence for a change in volume and that I was unsure about density.
Rather, the increased mass was tied up in the energy of the particle.
Would a few of you care to expand on this puzzle and I will send comments
on to this curious student?

According to modern convention the mass of a particle does not increase
with speed. Mass is, according to this new enlightenment, a relativistic
invariant. "Mass" now refers to what we used to call "proper mass" or
"rest mass". In my youth it meant "inertial mass", that is, the ratio of
force to acceleration. Such is no longer acceptable, I'm told.

The particle is presumably affected by Lorentz contraction, so its mass
density transforms as gamma (according to the new convention) or gamma
squared (according to the old convention). I can't think that this has
any physicality to it, however; it doesn't mean anything. For example,
at some critical density the disk should collapse gravitationally into
a black hole if the density is meaningful. It is claer that such a
collapse cannot be frame dependent, so what is the meaning of density
at high speed?

It is also the case that charge is not uniformly distributed in
particles. No one has any idea what the charge distribution might be
in electrons. They are pointlike down to the shortest length scales
accessible to experiment. Protons, on the other hand, are lumpy; they
have nonuniform charge density and do not act like Coulomb scatterers
when electrons approach them sufficiently closely (Robert Hofstadter
got the Nobel Prize for discovering that, and many Nobel prizes have
followed for refining the idea).

I think there is some value in pointing out to students that some of
their questions are, perhaps, syntactically reasonable, but they have
no real physical content. This should be done tactfully, of course,
but I think many teachers treat all such questions as equally valid -
and they aren't! A thoughtful question which has an already conceived
followup question is of much greater value.

Leigh