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

I agree with David (for the most part, see below) and I regret opining earlier today that one needed at least to assume that Maxwell's equations are laws of physics to obtain special relativity. Along the lines that David pursues, several authors (e.g., Jean‐Marc Lévy‐Leblond, "One more derivation of the Lorentz transformation," AJP, 44, 271, 1976 and N. David Mermin, "Relativity without light," AJP, 52, 119, 1984) have shown that under only a few very general assumptions about the homogeneity and isotropy of space and time one arrives at the Lorentz transformations and finds that they depend on a single, theoretically undetermined constant (call it, say, c) having the dimensions of velocity and which can be interpreted as a maximum observable speed.

The only reason I say that David is right for the most part is that it seems to me that his second postulate (that there is no such thing as instantaneous interaction at a distance) is neither necessary nor even proper. There is nothing that prohibits an infinite value for c. The result is the Galilean transformation laws and the corresponding possibility of instantaneous interaction at a distance.

AFAIK, the fact that c is *not* infinite must still be taken as an experimental fact and not a prediction of theory. Am I wrong?

John Mallinckrodt
Cal Poly Pomona

On Oct 1, 2010, at 11:21 AM, David Bowman wrote:

I don't think putting all the laws of nature into a hodgepodge that one calls the first postulate is a good idea. To my mind the postulates are supposed to be meta-laws that the observed laws of are to obey. This means that we ought not assume Maxwell's equations a priori before we get the meta-laws down. The way I see it Maxwell's equations *depend on* the Lorentz invariance of SR; they don't dictate that invariance *to* SR (contrary to the formulations of SR that one often sees that takes the constancy of the speed of light as the 2nd postulate of SR).

The way I see things is that SR's Lorentz transformations and the Lorentz invariance of the laws of nature (or a local version of such invariance if we want to accommodate a curved spacetime for GR later) depends on the following two postulates:

P1) The laws of physics (whatever they happen to be, and regardless of which particles may or may not be massless) are form-invariant under transformations among the equivalence class of (local) inertial reference frames.

P2) There is no such thing as instantaneous-interaction-at-a-distance.