Re: [Phys-l] Relativisitic mass vs Invariant mass

[John Mallinckrodt <ajm@csupomona.edu>]

Moses Fayngold wrote:

>  John Mallinckrodt wrote:
>
> > "The fact that that object appears to another observer to 
> > asymptotically approach the speed of light is the "observer's" 
> > problem"
>
> According to Relativity, all observers enjoy equal rights and
> may deserve equal attention.

Actually, that's not quite true.  Comoving observers DO enjoy a few 
minor special rights and may, in some cases, deserve a little more 
attention.

> If we engage into dismissing something as an observer's problem, we 
> should not do Physics.

Point taken.  If it wasn't clear that I was purposefully overspeaking 
a bit with the conscious intent of being provocative, I apologize and 
affirm that I was.

Later, in referring to my solution of his electron positron 
annihilation problem, Moses writes:

> The system of the two photons moving in the opposite directions has 
> a nonzero invariant mass. John determines this mass referring to 
> pre-existing electron-positron system. This is perfectly OK, but 
> what if I do not know about prehistory?

No problem.  Just measure the momenta of the two photons and then 
DISCOVER for yourself that the invariant mass of the two photon 
system has a numerical value that is equal to twice the invariant 
mass of an electron.  It matters not at all whether or not the two 
photons were produced in an annihilation event (but I must say that 
the appearance of two photons 1) hacing equal and opposite momenta, 
2) moving away from each other along the same line, and 3) having 
energies equal to that of an electron and a positron at rest IS VERY 
highly suggestive!)

> I may only detect the produced photons themselves, and
> it is reasonably then to express the rest mass of the two-photon
> system in terms of the constituting photons only, without any
> reference to prehistory.

Absolutely.  See the above.

> In this case John's description only illustrates limitations of the 
> concept of invariant mass alone.  The only way to remove these 
> limitations is to invoke the concept of relativistic mass.

I disagree.  John Denker has also fully addressed this objection.