Re: [Phys-l] Absolute four-momentum of massless particles

["Rauber, Joel" <Joel.Rauber@SDSTATE.EDU>]

One reference frame that is useful to have in the calculation tool box is the Instantaneously co-moving reference frame (some authors say momentarily co-moving reference frame MCRF.)  These have lots of calculational uses, one being that a sequence of these reference frames can be used to handle acceleration calculations within the framework of SR.  Even as a conceptual idea they are a nice handy thing for use when you hear people who suggest that SR can not handle kinematics of accelerating particles and then claim that you need GR for such objects.

_________________________

Joel Rauber, Ph.D 
Professor and Head of Physics
Department of Physics
South Dakota State University
Brookings, SD 57007
Joel.Rauber@sdstate.edu 
605.688.5428 (w)
605.688.5878 (fax) 


> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
> Sent: Thursday, September 30, 2010 11:49 PM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] Absolute four-momentum of massless particles
>
> On 09/30/2010 08:23 PM, Derek McKenzie wrote:
> > Now this thread has got me wondering about a fact that I think is
> > supposed to obvious, but isn't (to me). Massless particles must
> > travel at the speed of light. Everybody assumes it, but what is/are
> > the strongest argument/s for this assumption?
> >
> > One that comes to mind, given the arguments put forward in this
> > thread, is that if a massless particle didn't travel at the speed of
> > light, then its four momentum would have to be zero by virtue of the
> > (now well-defined formula) P = mU, and conservation of four momentum
> > would fail (I think). But this is a pretty weak argument because I
> > can always declare that the formula P = mU only holds for massive
> > particles (which is actually what we end up doing, in fact). There
> > must be something really silly (i.e. inconsistent) about the very
> > idea of a sub-luminal massless particle that I'm just not seeing.
> > Which usually means I'm looking at things the wrong way...
>
> You can prove that the massless particle (moving at
> less than the speed of light) has zero energy and
> zero momentum in all frames.  You can prove this in
> about two lines, without assuming P = m U.
>
> Hint:  What are the components of P in the rest frame
> of the particle?
>
> Take-home message:  There is a style of doing relativity
> calculations that goes like this:  Calculate something
> in a frame where it is easy to calculate, then express
> it in a frame-independent way, whereupon it can be used
> in other frames.  A serious calculation may switch back
> and forth many times, switching from frame-based to frame-
> independent representations, using several different frames
> along the way, including the lab frame, the CM frame, et
> cetera.
>
> Knowing how to express things in a frame-independent way
> is important, but it is not the only tool in the toolbox.
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