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

• From: John Denker <jsd@av8n.com>
• Date: Fri, 01 Oct 2010 12:41:10 -0400

Bob Sciamanda wrote:

Yes, but that approach simply substitutes the validity of Maxwell's
Equations as the second postulate!"

On 10/01/2010 12:16 PM, Spagna Jr., George replied:

I suggest that they are included under "all laws of physics" in the first postulate!

(I love these conversations! We can get deeper insights into both
the physics itself and physics pedagogy by learning from the group's
collective wisdom.)

I vote with Bob.

In my book, questioning the mass of the photon is nothing more or
less than questioning Maxwell's equations.

As I wrote previously, if we needed to reclassify the photon into
the category of massive particles, implementing the reclassification
would not be hard. We know what the equations would look like.

In outline: The equation for an electromagnetic wave in a waveguide
is indistinguishable from the "massive scalar Klein-Gordon equation".
The k-vector in the transverse direction plays the role of the mass;
the waveguide cutoff frequency plays the role of the "mass gap" in
the dispersion relation for the massive particle.

So basically all you need to do is imagine an Nth dimension and
give every EM wave a little bit of k-vector in that direction.

(The same trick works in reverse for massive particles.)

Remember Feynman's dictum: The same equations have the same solutions.

There are other ways of obtaining a mass gap. For example, propagation
on a _lattice_ will have gaps. The high-momentum behavior is not what
you would expect for an ordinary massive particle, but the low-momentum
behavior is just what you would expect, good to second order.

=====================================

On 10/01/2010 09:16 AM, Rauber, Joel wrote:

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.

That's well said. I have not much to add except to underline how
important that is.

As another way of seeing the importance, consider that the instantaneously
comoving inertial frame is where the _correspondence principle_ applies.
You get to use all of classical physics in that frame.