From: [t little] at [bruny.cc.utas.edu.au] (Timothy Little)
Newsgroups: rec.games.frp.advocacy
Subject: Re: Realistic FTL?
Date: 30 Sep 1993 03:46:42 GMT

[Nick Janow] at [mindlink.bc.ca] (Nick Janow) writes:

>[m--th--w] at [mantis.co.uk] (mathew) writes:

>> The main difficulty is that any sort of FTL at all, no matter how you
>> explain it, will completely ruin causality.  It will (for example) be
>> possible to send a message to someone and receive his reply before you sent
>> the original message.
>
>Does it ruin causality?  If our universe has a so far undiscovered FTL
>communication phenomenon, then the original message will arrive (via FTL)
>before the reply can be sent.  Causality still holds true, but for the FTL
>speed as the limiting speed of the universe, not the speed of light.

`c' in relativity is not *only* a limiting speed.  That arises almost as
a byproduct of its much more fundamental role.  Most people hear the word
`relativity' and think "E=mc^2" and "Nothing can go faster than light".
Both are partially correct, and partially wrong.

(E=mc^2 holds only for an object at rest.  The real equation is 
 E^2 = p^2 c^2 + m^2 c^4,
where `p' is the momentum.  In terms of speed,
 p = mv/sqrt(1-v^2/c^2).
I'll give you one guess why the incomplete formula caught on.)

I'll go into the second part a little more deeply.  The principle of
relativity implies that the no matter how fast you yourself are moving,
the speed of light (in vacuum) that you measure will be the same.  This
is not true of sound.  One consequence of this is that a massive object
(in the sense that it has mass) accelerating to the speed of light 
increases in energy without bound.  Another is that any massless object
has zero energy except at the speed of light.  So, objects with mass
can't pass the speed of light, objects without can't change speed.  But
what about objects that might *always* be moving faster than light?
Their rest mass would be a complex number (hence escaping both categories
above), which is reasonable since they're never at rest.

Now, back to the original point.  Causality.
Another consequence of relativity is that events that look simultaneous
to one observer, may not look simultaneous to another.  In general, any
events that cannot be connected by something travelling slower than light,
are ambiguous to the question "which came first?".  So, if something
travels FTL from Earth to some other star, it will look like it arrived
before it left, to someone on a spaceship travelling at a high enough speed
(in the right direction) relative to Earth.  This may not seem so bad.  
After all, it's just another point of view; surely nothing *real*.

Now, suppose that this other spacecraft is hanging around the far star.
And, that it *also* has FTL equipment.  As soon as the first FTL thing
arrives, the spaceship uses its FTL equipment to send something back
to Earth.  Now, by the symmetry of the situation, an observer on Earth
will also measure the time of arrival to be earlier than the departure
time of the fast-moving spaceship's FTL signal.  Fitting these two
observations together, the second signal arrived at Earth before the
original one left.

It's very difficult to explain in ASCII without diagrams and formulas,
but if anyone wants a more technical explanation, try reading some
articles from `rec.arts.sf.science'.  It comes up in that group rather
frequently.

In short:  `c' is more than just a speed.  It is a conversion between
space and time.

--
Tim Little