[Ghoulish Delight]

Okay, I sent this to someone after they said they were interested in learning my above tidbit about relativity. He suggested I actually post it here. So, um, here you go...Einstein's Special Theory of Relativity 101 (surprisingly intuitive!)

First, the Assumptions
1) The observer has no acceleration. That's what makes this the "Special" theory as opposed to the "general" theory. Acceleration seriously complicates things. We're talking situations where the environments are at constant velocity. (in our example, we'll be talking about 1 person standing still, and 1 person on a train moving at constant velocity)

2) The speed of light is constant, no matter how the observer is moving relative to it. So, unlike other matter, there are no "related rates". You know how if a car is going 60 miles per hour, and you are going 20 miles per hour in the same direction, then the car, from your point of view is going 40 miles per hour? Not so with light. From everyone's perspective, at any speed, in any direction, light moves at the speed of light. Crazy, but true (been proven experimentally).

The Setup
Imagine a clock. This is a REALLY big clock. It looks something like this...

---------
----|
----|
----|
--------
----^

The blue dealy is a light emitter/sensor. The red lines is the path of the emitted light. The top is a mirror. The mirror at the top is spaced such that it takes exactly 1 second for a photom emitted from the emitter to go up, reflect off the mirror, and return to the sensor (call the total distance traveled up and back N).

Now, place this clock on a moving train.

The payoff

Okay, so, there's someone on the train watching this clock. He sees the photon travel from the bottom, reflect off the top and return to the sensor. It travels a distance of N, as we've already determined. It does this at the speed of light, so it takes 1 second (N/speed of light = 1 second). Fair enough, we've already agreed that this is how the clock is designed.

Now, the train car is made of glass, and there's someone standing still outside of the train observing this. Here's the path of the photon that this observer sees.

---------------
----------|
-------|-----|
----|-----------|
---- ------------ ----
----^-----------^

It's emitted from the bottom. By the time it reaches the mirror at the top (we know it reaches it and hits it in the middle beause that's what the observer on the train sees), that mirror has moved with the train. It reflects, and by the time it returns to the sensor at the bottom, the bottom has moved again. So the path is a basically a triangle (minus one side).

Now, some basic trig proves that that path is longer than N. And we're assuming that the speed of light is constant, no matter where the observer is. So, the light has now traveled a distance greater than N, at the same speed. That means it must take longer than 1 second. (N+x/speed of light > 1 second)

So voila, you have two people observing the exact same event, and seeing it take 2 different ammounts of times. Relativity.

More than you ever cared to know, I'm sure, but I love explaining it because once you accept the very simple assumption that the speed of light is constant, the rest is VERY intuitive, most people are susprised at how much sense it makes.