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Next: Proper Time and Lorentz Invariants Up: A Rotational Analogy Previous: Rotation in Two Dimensions

Rotating Space into Time

If we now look at just the  x  and  t  part of the LORENTZ TRANSFORMATION [leaving out the y and z parts, which don't do much anyway], we have

x' = $\displaystyle \gamma \, x \; - \; \gamma \beta \, c t$ (23.4)
c t' = $\displaystyle - \gamma \beta \, x \; + \; \gamma \, c t$ (23.5)

-- i.e., the LORENTZ TRANSFORMATION "sort of" rotates the space and time axes in much the same way as a normal rotation of x and y. I have used  ct  as the time axis to keep the units explicitly the same; if we use "natural units" (c = 1) then we can just drop  c  out of the equations completely and the analogy becomes obvious.


Jess H. Brewer