starship-design: The speed of now

[wharton@physics.ucla.edu (Ken Wharton)]

Jim writes:

>Now I know that this is'nt quite the same
>thing, but, could these causality violations just a result of limited
>sensing ability, ie, our sensors work only a light speed, but our 
(ships,
>torpedoes, comm systems) work FTL.  Kind of like seeing an explosion
>before you hear it.  Help me out here.

Read Gravity's Rainbow lately?

Actually, these relativity issues aren't a result of only learning about 
things after the fact, via our light-speed information constraint.  As 
others have pointed out, you can go back and reconstruct what ACTUALLY 
happened (from our perspective), and even after you do that, relavistic 
effects still do happen.

But, in a sense, you're still right.  Think about it this way: light 
travels at an infinite speed.  If you were a photon, you would cross the 
entire universe in no time at all.  So why does c appear finite to us?  
Because of the link between space and time; our idea of what is "now" 
and what is "1 second from now" is spatially-dependant.  You can think 
of this as a perceptual problem, but the analogy is not between the 
speed of sound and light, but rather between the speed of sound and the 
speed of "now".  

It's a tough concept, but think of a 15-minute delayed signal travelling 
from Mars to Earth.  If it arrives at Earth "now", we naturally consider 
"now" on Mars to be 15 minutes after the light left Mars, from which we 
can calculate a finite speed of light.  But imagine that what we 
consider "now" at Mars is a confused notion, brought about by the large 
distance, and the real "now" on Mars is actually 15 minutes ago, when 
the light left in the first place.  Think of ripples of "now-ness" 
propagating out through space, making our perception of simultaneity not 
reflect what is "really" one instant.  In that sense, you are right: 
relativistic effects are only a result of our perception of a more 
fundamental reality.

If you can manage to imagine this, that's the heart of relativity.  What 
we consider simultaneousness is only our perception, not some absolute 
objective reality.  

The bottom line: Light appears to travel at a finite speed (from our 
perspective, or frame) but you could say it "actually" travels at an 
infinite speed.

When looked at this way, the link between FTL and Time-Travel is 
obvious.  Going FTL means travelling faster than an infinite speed.  The 
only way to get somewhere faster than instenantously is to get there 
BEFORE you leave.  Thus FTL = travel backwards in time.

Now, from our perspective, things don't always look that way.  An FTL 
Journey can APPEAR (to certain observers) to move forwards in time and 
still be faster than light, because to us light appears to be finite.  
But to other observers, the FTL journey will seem to go backwards in 
time.  If you're asking what "really" happens, in a frame where "now" is 
not frame-dependant, the only way to be sure is to look at a value that 
doesn't change from frame to frame.  We need to look at a measure of 
space-time distance that is independant of perspective.

That value is D = [t ^ 2  -  x ^ 2].  The distance between any two 
events, measured in terms of D (where t is the time-separation in 
seconds and x is the distance separation in light-seconds) will be 
identical in all frames.  

For light, D=0.  Thus my assertion that light "really" travels 
infinitely fast.  

For STL, D>0.  The time is always larger than the distance.

But for FTL, D<0.  You also get D<0 for local time travel; set x=0 (you 
don't go anywhere) and set t<0 (you go back in time).  Therefore the D 
associated with time travel is equivalent with the D associated with 
FTL.  It's very simple to take two FTL journeys, one out and one back, 
that gets you to return before you left.  

Just another way of thinking about it, I guess.  Which, of course, was 
probably more confusing than illuminating...

Ken