B What are Lorentz Factors?

The ratio between the clock rates of an observer at rest in an inertial frame and an observer moving at constant speed. Also the ratio of ruler lengths, if the rulers are pointing in the direction of motion.

 

Here is the Euclidean analogue: cos(theta).
Given two unit vectors, cos(theta) is the dot product of those two vectors. What it means is that, generally you don't get all of a vector pointing along one of your coordinate axes... You get components... And they involve that cosine factor. In special relativity, that is the hyperbolic cosine... which is often called ##\gamma## (and hyperbolic sine is ##\beta\gamma##).

 

Also, Google for "light clock". You can derive the Lorentz transforms (including the Lorentz factor, ##\gamma##) with no maths beyond Pythagoras' Theorem.

 

I spent the summer after high school trying to figure that out from scratch. I finally got it, but doing the whole thing with just a generic linear transformation (x = ax' + bt', t = ft' + gx') a year later was much more satisfying.

 

There was also Edward Lorenz, a mathematician and meteorologist, famous for his pioneering contributions to chaos theory.