# B What are Lorentz Factors?

1. Apr 27, 2016

### Fuinne

Hi, I was wondering what Lorenz Factors are. Can someone give me a simple definition?

2. Apr 27, 2016

### Ibix

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.

Last edited by a moderator: Apr 27, 2016
3. Apr 27, 2016

### robphy

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 $\beta\gamma$).

4. Apr 27, 2016

### Staff: Mentor

"Lorentz" not "Lorenz"..... Not all spelling mistakes matter but this one does because Ludwig Lorenz and Hendrik Lorentz are different people.

You'll often see the Lorentz factor represented with the symbol $\gamma$, a convenient shorthand for the longer $1/\sqrt{1-\frac{v^2}{c^2}}$.

The wikipedia article is worth reading if you haven't https://en.wikipedia.org/wiki/Lorentz_factor

Last edited by a moderator: Apr 27, 2016
5. Apr 27, 2016

### Ibix

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

6. Apr 28, 2016

### Battlemage!

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.

7. Apr 28, 2016

### Mister T

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