From: aephraim@physics.Berkeley.EDU (Aephraim M. Steinberg)
Newsgroups: sci.physics
Subject: Re: FTL
Date: 28 Aug 1992 23:59:33 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: physics.berkeley.edu

In article <1992Aug18.085010.24910@syma.sussex.ac.uk> mppu3@syma.sussex.ac.uk (Conor McMenamin) writes:
>Nir.Oren@f54.n7101.z5.fidonet.org (Nir Oren) writes:
>: Using the uncertanty principle, is it possible to travel faster than 
>: the speed of light: A particles exact speed can't be mesured 
>: ks>|for an exact period of time, therefore, could one not exceed 
>: the speed of light, if he were then to slow down below it for an 
>: equal ( or slightly greater) amount of time?
>: Chow
>: Nir
>: --  
>
>	Some people don't know when to leave it. I'm one. How's about

Apparently I'm another.  (Read on...)

>this. The uncertainty principle states that there is a degree of
>uncertainty in position and velocity such that the product of the two
>uncertainties is greater than or equal to something with a h in it and
>probably some 2 pi's and stuff. (Less chance of being flamed if I keep
>it vague). If something is going at speeds near c, where is it? Try
>pointing at it. Therefore delta x is BIG. And delta v is correspondingly
>small.
>	But the basic result is, if you're dealing with things in terms
>of the uncertainty principle, you're never going to observe it, so why
>does it matter?
>
>	Conor


If you're going to talk about objects moving near the speed of light,
you should really go to relativistic QM, i.e., quantum field theory.
The uncertainty principle in this case doesn't exist in the same sense
as in nonrel. QM, since x and p are no longer operators.  It does exist
as a statement about Fourier transforms, like the "energy-time uncertainty
relation" in nonrel. QM.
If you try, in the context of the Dirac equation, to measure velocity,
you find its only eigenvalues along any given axis are +/- c, oddly
enough, so not only does nothing travel faster than light, nothing travels
slower either!  (Hence "Zitterbewegung," the supposed jitterbug electrons
are constantly performing within... oh, perhaps John Baez will remind me
whether it's the Compton wavelength or the classical radius, though I'm
always embarassed to have an uncertainty of more than two orders of
magnitude... of its approximate (nonrelativistic) trajectory)

I think more in the spirit of the question, however, is an experiment
where you measure a position at two different times, and divide distance
by time to get velocity.  In field theory, you might say you "create"
(creation operator) a particle at one point in space-time and then
see what happens when you try to "annihilate" (annihilation operator) it
at another.  Sarfatti's postings aside, the fact that spacelike-separated
(i.e., separated by d > ct) operators commute means that the amplitude
for the above event is zero-- it never happens.

There may be a subtlety here beyond my ken, however, and the above may only
apply in first-order perturbation theory... or maybe it's just that at
non-zero temperatures it breaks down.  Someone has mentioned to me 
something about the possibility for an electron-positron pair to be
created "across the light cone" (sort of like Hawking radiation, I gather)
in such a way that a positron annihiliates with the electron I've sent out,
and its corresponding electron is not in my forward light cone, so it
does look like an electron has travelled faster than light.  If there were
real pair-creation going on, somehow that wouldn't bother me so much,
but the claim I heard (and please don't think I understand it!) was that
the pair-creation could be a virtual event, and thus happen even in the
zero-temp. vacuum.

Does someone know anything about this?
Isn't the commutation an exact relation, though, meaning this process could
not possibly happen?

Happily making a rather simple question even more confusing than before,
aephraim


-- 
Aephraim M. Steinberg                    | "WHY must I treat the measuring
UCB Physics                              | device classically??  What will
aephraim@physics.berkeley.edu            | happen to me if I don't??"
                                         |       -- Eugene Wigner