Speed, distance, time - Reply

Chris asked, and, unless the mail system here has gone nuts again,
no-one
has yet replied to it:

> I heard something about speed of light in relation to time That once
you
approach 'c', you become more dense and time slows. Help me out on this
if
you could. Is that right? <

Yes. According to Special Relativity, at high sub-light speeds, your
mass
increases and time slows down relative to a body moving more slowly.
Also, the
universe seems to shrink in the direction that you're moving (described
delightfully by Larry Niven as having someone heavy sit on the
universe). I won't
quote the exact equations here -- mail me if you want them. The
important point
that makes c the upper limit for speed is that your mass goes to
infinity _at_ c.
Also, time stops and distances shrink to zero.

>And, the fourth dimension is? Could that be time? <

Again, yes, although it's important to realise just what people who
blithely talk
about the 4th dimension really mean (or _should_ mean). Most people are
familiar with the 3 spacial dimensions (call 'em x,y and z); but when
you
introduce time into the equations (to deal with that thing we call
"space-time"),
there is the problem that time is a different quantity to length, which
is how we
quantify the 3 spacial dimensions. _But_, by introducing a fundamental
quantity
(a constant) like the speed of light in a vacuum (our old friendly
enemy, c), you
can treat the mathematics of space-time as a problem in 4 similar
dimensions, all measured as lengths: x,y,z and "ct". Which is what
Einstein
did, and what led to things like the Lorenz contraction (someone sitting
on the
universe) and other non-obvious results of relativity. The thing is, it
seems to
work!

However, why we perceive time as a different quantity to length, and why
movement in time is not readily performed as it is in space (and all the
important
results that follow from that, like the second law of thermodynamics),
is
something that we still don't know.

It's interesting to note that it has been worked out that if you re-do
special
relativity in _5_ dimensions (and no, I don't know what the 5th could
be) for a
charged particle, the maximum speed obtainable by said particle (or
larger
body) -- the equivalent to c in 4D SR -- depends on the charge-to-mass
ratio.
For a "typical spaceship", anything up to about 1000c could be possible
(Warp
Factor 10 from the original Star Trek, anyone?). Electrons can zip
around at
10^21 c, which should do for communications systems. All we have to do
is
come up with this 5th dimension. Makes all the old SF versions of
hyperspace
take on a whole new lease of life...

Phil
-------------------------------------------------------------
 Gravity is a Downer... So let's go flying!
   -- so sayeth Phil Atcliffe (p-atclif@uwe.ac.uk)