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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

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

$$- \gamma \beta \, x \; + \; \gamma \, c t$$ 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.