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# Re: [Phys-l] Why is the photon massless?

If mass is defined in terms of a rest frame, and you require definitions to be empirically meaningful (your requirement below), then surely a photon does not have a mass of zero, but rather an UNDEFINED mass. A limiting procedure is surely unreliable in 'singular-limit' cases like this - as discussed recently in another thread.

What makes us choose a value of zero rather than undefined?

Derek

Date: Mon, 4 Oct 2010 07:26:08 -0700
From: moshfarlan@yahoo.com
To: phys-l@carnot.physics.buffalo.edu
Subject: Re: [Phys-l] Why is the photon massless?

Derek McKenzie wrote on Sun, October 3, 2010 11:20:13 PM

The question 'Why must massive particles travel at subluminar (or non-invariant)
speeds?' gets replaced by 'Why must massive particles have comoving >(inertial)
frames?'. I'm not sure that the latter is more self-evident than the former.

This is a question of DEFINITION rather than self-evidence. The non-zero rest
mass is DEFINED as mass at rest, so the corresponding particle has a rest frame.
Trying to apply this to a massless (m = 0) particle would take us to a
hypothetical frame in which ANY attempt to measure particle's mass gives zero,
in other words, we find nothing (no particle) there. This is another way of
saying that such particle does not have a rest frame.
We could also say that the rest mass is DEFINED as the invariant norm of
particle's 4-momentum (hence its second name - the invariant mass), which does
not require any reference to its rest frame. This is true, but if we insist on
measuring m from (E/c)^2 - p^2 = (mc)^2, the measurements of E and p must be
increasingly accurate for increasingly smaller m or increasingly higher energies
since m in this case would come out as a small difference between two big
numbers, and in principle we could face the fact that any achievable accuracy is
not sufficient to get a reliable result. After all, Physics is (and, I think,
will remain) an experimental science, and inasmuch as we are talking about a
measurable physical characteristic, it must admit, apart from any abstract
definition in terms of other characteristics, also a direct measurement. If we
accept this, it takes us back to the first definition of the rest mass.

Answer number 2 assumes more about the structure of matter than I would like. I
suspect an answer can be given that relies much more on the >concepts of
spacetime and mass than on the quantum features of matter. Well, I hope so at
least ;-)

I probably did not emphasize as strongly as I should that quantum features of
matter are, perhaps, themselves consequence of relativity. The fact that E and p
(particle characteristics) undergo exactly the same Lorentz transformation as w
and k (wave characteristics) is a strong indication that they are intimately
linked together (E/w = p/k (= Plank's const)); in other words, de Broglie's
postulates are actually the corollaries of the relativity postulates. I would
say that Relativity is begging, if not demanding, for Quantum Mechanics which
is, in fact, intrinsically relativistic.

Moses Fayngold,
NJIT

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