Re: OT: Helen Keller & Whorf-Sapir

On Mon, Aug 16, 2004 at 04:43:34PM -0500, Mark P. Line wrote:
> The equations seem to be saying that nothing material can be observed to
> travel relative to the observer faster than the speed of light.
Right.  This stuff all falls naturally out of some observations
and assumptions whose implications Dr. Einstein wasn't afraid to
examine:

1. There can be no absolute location or motion, because there is no
   fixed frame of reference.  All motion is relative, and can be
   described in different but equivalent ways based on vantage
   (e.g. it is just as correct to say that the Earth is moving around
   the Sun as it is to say that the Sun is moving around the Earth;
   this discounts the *cause* of the motion, which is of course not
   relative and rather heliocentric :)).

2. That implies that motion alone cannot change the laws of physics.
   Any two observers will each observe the universe obeying the same
   rules, right down to the fundamental constants, no matter how they
   are moving relative to each other.  Otherwise, the laws of physics
   aren't universal, so what's the point? :)

3. The speed of light in a vacuum is such a fundamental constant.

If you're travelling through space relative to the Earth at, say, half
the speed of light, and then you turn on your flashlight, the naive,
non-relativistic assumption is that you would measure the speed of the
light relative to you as c, while an observer on earth would measure it
relative to them as 1.5c.    But that violates rule 3, above, which says
that the speed of light is a constant and must therefore be the same for
all observers.  And analogous experiments have demonstrated that, in
fact, both observers measure the light travelling at c.

To borrow a line from Douglas Adams: "This, you say, is clearly impossible."
According to our pre-relativistic understanding of motion, yes.  But it
turns out that our pre-relativistic understanding of motion was wrong,
or was, at least, a good approximation to the truth only for motion that
is very slow relative to the speed of light.

The upshot is: the speed of light is a constant.  Speed is distance over
time.  The only way to keep the speed constant in the face of varying
conditions is to vary time and distance.  That is: my meter and second
are not necessarily the same as your meter and second; only if we're not
moving relative to each other is that true.  Nevertheless, all the laws
of physics hold when measured by each of us according to our own
instruments' idea of what a meter and a second is.

Also, velocities don't really add.  If someone starts moving away from
the Earth at 0.9c, and someone else starts moving away from the Earth in
the exact opposite direction at 0.9c, and they measure their velocity
relative to each other, they won't get 1.8c.   Instead they'll get
something that is greater than 0.9c but still less than c.  This
same rule applies all the time; it's just that for velocities slow
enough relative to c, the difference between straight addition and
the actual result is negligible.

-Marcos