#### BELIEVE ME NOT! **-** **-** A SKEPTICs GUIDE

** Next:** The Luminiferous Æther
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The problem is, *it doesn't work for light*.
Without any *stuff* with respect to which
to measure relative velocity, one person's vacuum
looks exactly the same as another's,
even though they may be moving past each other at enormous velocity!
If so, then MAXWELL'S EQUATIONS tell *both* observers
that they should "see" the light go past them at *c*, even though
one *observer* might be moving at
relative to the other!

The only way to make such a description *self-consistent*
(not to say reasonable) is to allow *length* and *duration*
to be different for observers moving relative to one another.
That is, *x*' and *t*' must differ from *x* and *t*
*not only* by additive constants but also by a
*multiplicative factor*.

For æsthetic reasons I will reproduce here the equations
that provide such coordinate transformations;
the derivation will come later.

Note that the "prime" is on the *right-hand side*
of the velocity transformation and we have assumed (for simplicity)
that
and
are both in the
direction
(the same as ). The ubiquitous factor
is equal to 1 for vanishingly small relative velocity *u*
and grows without limit as .
In fact, if *u*
ever got as big as *c* then
would "blow up"
(become infinite) and then (worse yet) become *imaginary*
for *u* > *c*.

** Next:** The Luminiferous Æther
** Up:** The Special Theory of Relativity
** Previous:** Galilean Transformations
*Jess H. Brewer *

1999-03-19