Jim, list,
 
Oops, erratum: I wrote: "Darned if I know what it'd mean for a particle to go at lightspeed -- tau zero -- in a circle and thus coincide with itself indefinitely many times all at once.)."
 
I was thinking of the particle's "own" viewpoint.  (Technically, it doesn't even have one -- a lightspeed particle has no rest frame of reference. One does speak of "tau zero" even though maybe technically one should say that rest mass and proper time are "meaningless" rather than "zero" for lightspeed particles. "Tau" (sometimes spelt out informally in Roman characters instead of expressed by the Greek letter; I just discovered that gmane doesn't keep the Symbol font formatting, and I can't use the Unicode character without causing problems) is a system's proper time, its time in its own rest frame.)  In any case, the circling lightspeed particle would not coincide with itself indefinitely many times or even once.  At Dtau=0, it's still traveling at the quite non-zero and positive Dd/Dt = 1, even though, if by a miracle it were sentient, then it would experience no passage of time (that's why photons and the like don't age -- there's no such thing as "old" light -- the Doppler shift is something else -- lightspeed particles are pristine, agelessly young, the angelic ambassadors of morning, etc.)  Sorry about that! -- Ben
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