# Time in the Lorentz transformation

where does t=(t-vx/c^2)/(1-v^2/c^2)^1/2 come from?

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asdf1 said:
where does t=(t-vx/c^2)/(1-v^2/c^2)^1/2 come from?
From
$$\left( \begin{array}{c} x' \\ t' \end{array} \right) = \left( \begin{array}{cc} cosh(\theta) & -sinh(\theta) \\ sinh(\theta) & cosh(\theta) \end{array} \right) \left( \begin{array}{c} x \\ t \end{array} \right)$$

where $$v = tanh(\theta)$$ and c is taken to be 1.

asdf1 said:
where does t`=(t-vx/c^2)/(1-v^2/c^2)^1/2 come from?
There are many elegant ways to derive the Lorentz transformation:

http://www.everythingimportant.org/relativity/
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000043000005000434000001 [Broken]
http://arxiv.org/PS_cache/physics/pdf/0302/0302045.pdf [Broken]

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robphy
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It should be $$+\sinh(\theta)$$.
(The determinant has to be 1.)

learningphysics
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robphy said:
It should be $$+\sinh(\theta)$$.
(The determinant has to be 1.)
Or rather they should both be $$-\sinh(\theta)$$ I believe.

robphy
Or rather they should both be $$-\sinh(\theta)$$ I believe.