[FOM] why should we, in computer science, be excited about the possibility of speeds exceeding speed of light

[Kreinovich, Vladik]

Sorry for not explaining these details. Here is a brief description of why motions faster than speed of light lead to potential time travel. For details see Thorne's book that I mentioned in my original email. Thorne is one of the world leading astrophysicist and a good writer. 

Contrary to what the journalists say, special relativity as it is understood now, does not automatically imply that all velocities must be limited by the speed of light, it simply implies that all the processes must be invariant with respect to Lorentz transformations -- transformations that preserve the speed of light. Consistent relativistic theories have been developed for describing particle moving faster than speed of light, called tachyons, these particles have never been experimentally detected before. 

In Minkowski space-time (described by special relativity theory) motion starting with a single event with a constant velocity is described by a straight half-line (ray) starting at this event. Half-lines corresponding to motion with speeds smaller than the speed of light are located inside the so-called future cone. The fact that in special relativity, motion is relative (hence the name relativity theory) is reflected in the following mathematical fact: for every two half-lines inside the future cone can be transformed into each other by an appropriate Lorentz transformation. In other words, we have a frame of reference in which the corresponding object is stationary, and all the physical laws are the same in this frame of reference as in the original frame. 

Half-lines corresponding to velocities larger than the speed of light are outside future cone and past cone. For these half-lines, there is a similar result: that for every two such half-lines, there is a Lorentz transformation transforming one of them into another one. Thus, if one such motion is possible, then, according to relativity theory, all other such motions are possible as well, in particular, half-lines for which the time coordinate decreases, i.e., which go into the past. By combining two such half-lines, we can then send communication to our own past. 

This is the gist of the argument made in some popular books that in special relativity, all the processes happen with a speed not exceeding speed of light: because otherwise, we would have time travel to the past. 

-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of meskew at math.uci.edu
Sent: Tuesday, November 22, 2011 2:07 PM
To: Foundations of Mathematics
Subject: Re: [FOM] why should we, in computer science, be excited about the possibility of speeds exceeding speed of light

This is probably just my ignorance about physics, but why would these
experimental results say anything about time travel or "acausal
processes"?  It is my understanding that if the experimental results are
valid, then relativity will have to be fundamentally rewritten.  In this
case, from what theory would you be deducing time travel?  Or are you
saying that general relativity can hold true in the face of the results,
with the explanation that closed-timelike curves were influencing the
experiments?

Best,
Monroe