I'm way out of my depth here, but I'll point out that Philip Morrison (MIT)
in his Ring of Truth series talks about this. He says we should consider
Einstein's equation to be just E = M, 'call it energy, call it mass as you
will, these are just two aspects of the same thing.' (a close paraphrasing)
He certainly talks about changing mass as we expend energy, about a spring
gaining mass when wound. Seems to me this is more a question of focus or
perhaps style. Usually in intro courses and for everyday objects we like to
separate out the energies of motion and position (concepts we have made
up--remember) from the rest-mass energy of the object. It is useful to do
so, but wouldn't it be fair to simply consider the total energy (a.k.a.
mass) of the object as well. By the time one is dealing with protons and
electrons (or any of the rest of the particle menagerie) it becomes more
useful to just consider the energy. Thirty years ago, I worked in low
energy nuclear physics and we of course used energy units (MeV) to measure
energies and/or masses.
JD indicates (I think) that this doesn't work in all possible cases--maybe
not--but I really don't think we are going to give up moving clocks run
slow, moving lengths contract, and moving mass increases in our intro books
for space-time geometry. Many of those books are for the seriously math
challenged students (ones who can't figure the Carnot Efficiency of an ideal
heat engine running between 600 and 300 Kelvin or the amount of work that a
1000 J input produces in a 25% efficient engine). The 'standard test book'
descriptions of the phenomena seem to function OK without somehow totally
distorting whatever the 'reality' is--at least many think so.
Of course, my vote only counts when I buy the textbooks! ;-)
Rick
Richard W. Tarara
Professor of Physics
Department of Chemistry & Physics
Saint Mary's College
Notre Dame, IN 46556
----- Original Message -----
From: "Moses Fayngold" <moshfarlan@yahoo.com>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Sunday, June 28, 2009 3:44 PM
Subject: Re: [Phys-l] velocity-dependent mass (or not)
--- On Sun, 6/28/09, John Denker <jsd@av8n.com> wrote:
"It doesn't "come from" anywhere. You shouldn't assume it needs to
"come from" anywhere. Asking where it comes from has no physical
significance, because mass is not conserved. There is no reason
why it should be."
It comes from the past. If an isolated system
(e.g. positronium) had a certain rest mass before reaction (e.g.,
before annihilation), it has the same rest mass after reaction. In case of
annihilation, the system of emerging two photons has the rest mass
exactly equal to the initial mas of positronium. The system has changed
beyond recognition, but its rest mass remains as before. The rest mass
of the new state comes from the rest mass of the initial state. This is
what conservation means.
.
" Energy is conserved. Rest energy (by itself) is not conserved. There is no
reason why it should be".
The reason is that the rest energy is also energy. Would you deny this?
" I don't have a problem with non-conserved mass."
This is YOUR problem, then. And many others, too, unfortunately, who read
uncritically the textbooks' statement to this effect. What these statements
actually mean is that the rest mass is NOT additive. Non-additivity has
nothing to do with non-conservation.
"There is plenty of evidence (including the "extreme" example cited above)
to tell us that mass is not in fact conserved."
I am curious to see references to any experimental or other scientific
evidence (not just statements like the one right above) that the rest mass
of the two-photon system resulting from positronium annihilation is not
conserved. Could you tell what is this new rest mass equal to, then? And
could you answer the question which is reverse to *where the new rest mass
come from*: namely, if the rest mass here does not conserve, where does the
rest mass of positronium go to after the annihilation? Disappears into thin
air?
"Mass is Lorentz invariant. That means it is invariant with respect
to Lorentz transformations. That does *not* mean it is invariant
with respect to all imaginable transformations (such as annihilation
reactions)."
Since when the Lorentz transformations started denying conservation laws?
Also many decades ago?
"I apologize to the list members who think I am belaboring the obvious".