# What are Lorentz Factors?

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

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.

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robphy
Homework Helper
Gold Member
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##).

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

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

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.

Mister T