Everybody knows that some of the properties of anything you look at
depend on how you look at it. For example, wheter a box is wide and
shallow or deep and narrow depends on what direction you look at it
from. many properties also depend on your state of motion. For example,
whether a coffee cup is staionary or zipping by depends on whether it's
described by the person holding it on a train or a person standing on
the ground.
Despite such differences in how particular things look, Galileo
noticed that the laws of nature (or at least most of them- he wasn't
always consistent)look exactly the same from the point of view of
someone who is 'at rest' and one who is moving steadily. Actually, that
means that there's no real meaning to who is moving and who isn't. They
can use exactly the same laws, treating themselves as stationary, so
there is no test as to who is 'really' stationary, so we might as well
quit thinking that concept has any meaning.
When Maxwell developed the laws of electromagnetism, it became
apparent that they were in conflict with our ideas Galilean invariance.
If you just add velocities when looking at things in different
reference frames, as Galileo told us, then light should travel at a
speed that varies with how fast the observer is moving. In fact, sound
waves do exactly this -- you can catch up with one if you go fast
enough. Maxwell's theory predicted that the speed of light didn't
depend on the observer's motion.
Einstein noticed that Maxwell's laws would work for different
observers, but only if the things which look different depending on
your state of motion included some very surprising features. These
include the lengths of objects and the duration of time intervals
between events! He developed a complete mathematical theory, Special
Relativity, to describe how space and time and other properties depend
on the reference frame in which they are described. When people started
to say that he'd showen that 'everything is relative' he attempted to
change the name of the theory to 'invariants theory', since what he'd
really done was to show that the invariants, the things that come out
the same regardless of how you look, were different from the ones you
initially guess. The speed of light is the most obvious of these
surprising new invariants.
Einstein went on to develop a more general set of ways to change
coordinate systems, General Relativity, in which gravity appears as an
aspect of the geometry of space and time. It still has invariants.
As for E=mc^2, I'm sure we have other answers on that, which you
can find with a search. It's one of the many consequences of Special
Relativity which can be obtained by very simple arguments using only
elementary math.
Mike W.
p.s. In this 100th anniversary of Special Relativity, I'm starting
to feel pretty silly filing this answer under 'new and exciting
physics.'.
Well hey, it's still pretty exciting. But all the other categories are exciting too, in their own ways -- Tom
(published on 10/22/2007)
