Muhammed- We're getting to expect these challenging questions from you.
As often happens, I'll give an answer that may be only partially
satisfying.
The impossibility of travel faster than the speed of light follows
directly from the form of the laws of Special Relativity. A special
speed enters into these laws, which describe how to transform between
the apparent coordinates used by two observers travelling at a consatnt
velocity with respect to each other. It turns out that If anything were
to travel above that speed, according to any observer, it would have to
have infinite energy. That's not esy to get. There are some other
limits too. If some conserved quantity, like electrical charge, were to
travel faster than that speed according to some observer, then
according to other observers it wouldn't always be conserved.
This special speed turns out to be the only speed something can
travel at if it doesn't have any 'rest mass'. Light seems to be one
such rest-mass-free entity, so it travels at this special speed.
Furthermore, there is a problem with causality if objects can
travel faster than light. Events only seem to be able to have
consequences in the future -- so far we have not been able to change
what happened in the past. Travel faster than the speed of light would
allow a traveler to reappear at an earlier time in a similar position,
making him able to shake his own hand and create paradoxical
situations, such as killing himself before he is able to go on the
journey in the first place. This is related to the conservation laws
problem -- if the traveler is electrically charged, say, the charge
will appear to vanish from everywhere in the universe for some times,
and be present twice for other times.
OK, you want to know why Special Relativity should have such weird
laws. All I can say (maybe somebody else could give a deeper answer) is
that the laws for transforming between different reference frames
actually are logically consistent and not very mathematically
complicated. We latched on to an over-simplified version classical
physics) because it worked well enough for most practical purposes.
Time inervals between events may depend on reference frame, but an
ancestor who never thought about that possibility while chasing an
antelope would not have lost any advantage to one who knew it. In fact,
the simple-minded ancestor would probably have an easier time. So it's
not surprising we have very strong gut feelings that time and space do
not depend on refernce frames.
Mike W. (with Tom)
(published on 10/22/2007)
