
 
In 1095, Einstein released his Special Theory of Relativity. In this theory,
our ideas about what space and time were had to be changed. Say you're on a
stationary space station in deep space, nothing around you. A spaceship coasts
toward you with no rockets on at a velocity of 9/10 the speed of light. In order
to confirm the identity of the ship, you carefully measure its lengh (by say bouncing
lasers off the front and back and measuring their return times) and you find that
the ship is shorter than it was a week ago when it was docked at your station.
You look at the top of the ship, which happens to have a giant clock on it, and you
notice that the clock is running slower than your clocks. Then you get a message from
the ship's captain saying, "Your station's a little flat today, commander. Maybe
it's because you're all takin' it easy and movin' real slow today." You laugh
at the captain's joke, but aren't surprised that each of you measures the same thing
about the other, because ever since the 1900s, people had heard of these phenomena
and some, like you, even knew the cause and could accurately calculate the effect.
What your encounter reminds you most of is that these things happen not because
something changes about their rulers or clocks, but because space and time
themselves are different than people used to think.

 
Newton's Laws look the same to any observer in any
inertial reference frame. This is the principle of
Gallilean Invariance or Gallilean Relativity. After
Maxell's Equations were formulated to describe electrisity
and magnetism, people noticed that these equations do not look the same to
observers in different reference frames. It seemed like there was only one
frame where they would be valid, and in every other frame, they would have
to be modified slightly. Since one of the predictions of
Maxell's Equations is the radiation of electromagnetic
waves, it seemed like there was some medium throughout space that was doing
the waving, which the called the aether. Just like sound waves propogate
through air, and they are best analysed in the special frame where the air
is, on average, standing still, it was thought that
Maxell's Equations were only perfectly valid in the frame
of the aether. Experiments were done to measure the movement of Earth through
this aether, the most famous being the
Michelson Morley Experiment
that used light (an electromagnetic wave) to measure the difference between
propogation in the direction of the moving Earth and perpendicular to the direction.
What Michelson and Morley found was that their experiment wasn't moving through
the aether at all. People tried to explain this result by saying the earth was
dragging along the aether, and just like like a car drags along the air inside
of it so that sound from a radio acts the same within the car as it does in within
a house, the experiment is in a local bubble of aether being dragged along.
Einstein came up with a radically different solution. He got rid of the concept
of the aether by extending Gallilean Relativity to include
electromagnetic phenomena. He claimed that all laws of physics,
including the laws of electromagnetism are the same for
observers in any inertial reference frame. One of the predictions of
Maxell's Equations is that the speed of light is
a constant . Einstein's proposal meant that this
speed would be measured to be the same in all reference frames  a very
strange prediction given that our intuition and the laws of
Gallilean Relativity would predict that if you fire a
burst of light from a space station and chase after it with a rocket moving
at half the speed of light, people in the rocket would see it moving away from them
at only half the speed of light. These two principles  that the laws of
physics and the speed of light are the same in all reference frames  mean
that Newton's Laws of Mechanics and our very ideas of space
and time need modification, most drastically in cases where things are moving
near the speed of light.

 
Taking the historical approach and motivating relativity by
Maxell's Equations the way Einstein was motivated would
require knowledge of electromagnetism and some vector calculus. The
modern approach, and the approach that's best to take as a beginner, is
to start with the two basic principles of special relativity and use
only simple thought experiments and simple algebra to derive the classic
and unintuitive effects of NonSimultineity,
Time Dialation, and Length Contraction.
Then sum these up in Lorentz Transformations and
the Invarient Interval. After that, discuss
Relivistic Kinematics, and the Relativity of Electromagnetism.
In fact, one approach to electromagnetism is to combine the laws of electrostatics
and magnetostatics with the laws of special relativity to get the laws of electrodynamics.

 
These seemingly reasonable assumptions lead to some amazing results.
For example, a ruler moving with respect to you will be shorter
along the direction it's moving, which is
called Length Contraction.
A clock moving with respect to you will run slower, which is called
Time Dialation. Also,
events that are simultanious to one observer are not simultanious
to another observer moving with respect to the first, which is
referred to as NonSimultaneity

