Re: Tracking

MajorOz wrote:

The bad guy is chasing the good guy. The GG jumps to warp speed and
disappearss. The BG says to his near by tekke: "track them using the
_________ trail that they are leaving."

Given the premise of FTL, what possible "trail" could there be?

Photons. A charged particle moving faster than light in the medium through which it's travelling emits Cherenkov radiation, which is simply photons.

This is quite neat since it's a real effect (it can observed in pools of water surrounding fission cores as an eerie blue glow). However, the photons are emitted in a forward-facing cone around the particle track; the angle theta is related to the refractive index of the medium n and the speed of the particle v by

cos theta = 1/(n beta) = c/(n v).

You can then write n as c/c_medium if you wish (it's the ratio of the speed of light in vacuum to the speed of light in the medium). For a tachyon travelling through vacuum, c_medium = c and n = 1, so

cos theta = 1/beta = c/v.

For a tachyon with a speed v just barely over c, c/v ~= 1, so theta ~= 0. In other words, the Cherenkov radiation is radiated away at a very shallow angle relative to the particle, and so can be only detected if the particle is moving very nearly toward you.

For a tachyon with very large v, c/v ~= 0, so theta ~= pi/2. So very a very fast tachyon, the Cherenkov radiation is emitted nearly perpendicular to the particle's path. Taking the limit as v -> oo, theta -> pi/2. So the faster it goes, the more easily detectable it will be to observers not directly in its line of travel.

Now the only problem with all that is that we know that charged tachyons can't exist because they lead to paradoxes (they'd be emitting Cherenkov radiation in some frames but not others, which makes no logical sense). But with handwaving it probably could be used in a story for your purposes.

--
Erik Max Francis && max@xxxxxxxxxxx && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis
Time is a storm in which we are all lost.
-- George Bernard Shaw
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