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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