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

[David Bowman <David_Bowman@georgetowncollege.edu>]

Regarding John M's comments:

> 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.

Actually, the whole point of having that 2nd postulate (of the nonexistence of instantaneous interaction at a distance) is *precisely* to prohibit the option of having an infinite value for c.  Without such a special 2nd postulate there is nothing to distinguish the case of SR from the case of Galilean/Newtonian physics.

> The result is the Galilean transformation laws and the  
> corresponding possibility of instantaneous interaction at a
> distance.

Exactly.  But since nature seems to insist on effects being retarded in time from their spatially separated causes with a finite bounded speed limit we would like to insist that that actually be the case.

> 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?

The brute experimental fact of retarded causation is precisely stipulated by the imposition of the second postulate.  OTOH, if we did not observe retarded causation in nature with a finite bounded speed limit we would have to change the 2nd postulate to one that insists on c being infinite.  This is accomplished by replacing the 2nd postulate of the nonexistence of instantaneous interaction at a distance by the alternate 2nd postulate that the time interval between any two distinct fixed events is always the same regardless of which inertial reference frame they are observed from.  This alterative 2nd postulate of time intervals being independent of reference frame has the effect of forbidding a finite value for c, and it requires that instantaneus interactions at a distance be a fact.  A universe with the alternate 2nd postulate of universal time intervals is a Galilean/Newtonian world that requires that the coordinates of the events of spacetime be transformed among the members of the equivalence class of inertial reference frames via Galilean transformations.  But a universe with the 2nd postulate forbidding instantaneous interaction at a distance is a SR world with a finite value for c that transforms the events among the inertial frames via Lorentz/Poincaré transformations having a specifically *finite* value for c.  Since our world is one with effects being retarded from their causes by a bounded speed limit I think we should take the 2nd postulate as the one I proposed.  If we didn't impose either version of the 2nd postulate then we would not be able to distinguish a SR world from a Galilean/Newtonian one, and both kinds of causation would be live possibilities with no theoretical way of choosing which is the case.

> John Mallinckrodt
> Cal Poly Pomona

David Bowman