# The form of the lorentz transformations

#### Identity

In a lecture on special relativity online, the form

$$x'=x\cosh{\omega}-ct\sinh{\omega}$$

$$t'=-x\sinh{\omega}+ct\cosh{\omega}$$

is used for the lorentz transformations, where the velocity is $$v=\frac{c\sinh{\omega}}{\cosh{\omega}}$$.

However, I'm wondering, couldn't you also do

$$x'=x\sec{\omega}-ct\tan{\omega}$$

$$t'=-x\tan{\omega}+ct\sec{\omega}$$

(or even the similar thing with $$\csc{\omega}$$ and $$\cot{\omega}$$)

With $$v=\frac{c\tan{\omega}}{\sec{\omega}}$$

Since this also reproduces the lorentz transformations

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#### bcrowell

Staff Emeritus
Gold Member
When you use the hyperbolic functions the parameter $\omega$, called the rapidity, becomes additive. See http://www.lightandmatter.com/html_books/genrel/ch02/ch02.html#Section2.3 [Broken] , subsection 2.3.1.

Last edited by a moderator:

Cool, thanks

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