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Re: [Phys-l] velocity-dependent mass (or not)

--- On Sun, 6/28/09, John Denker <> 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
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".

I join you in this.

Moses Fayngold,

Forum for Physics Educators