By Lieber L.R.
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Additional resources for The Einstein Theory of Relativity
Which is That the remaining two equations = y and z' z also hold, y' Einstein shows as follows: = K and Let /C' each have a cylinder of radius r, when at rest relatively to each other, and whose axes coincide with the Now, unless / = y and z = z, K and K would each claim that X (X ) axis/ 7 r f own his We cylinder is OUTSIDE the other fellow's! thus see that the Lorentz transformation was derived by Einstein (quite independently of Lorentz), as a set of empirical equations NOT 49 devoid of physical meaning, but, on the contrary, as a result of most rational change a in our ideas regarding the measurement of the fundamental quantities length and time.
We should be able to determine v. But FACT this contradicts (1), according to which it is IMPOSSIBLE Thus it to determine v. APPEARS that FACT (2) requires the velocity of light MOVING EARTH RELATIVELY TO THE to be v (see diagram on p. * re-stated as follows: light A MOVING (For example, an observer on the moving earth) must be it NOT c vt for otherwise, he would be able to find v which is contrary to fact. , 38 OBSERVER And so the two facts contradict each other! Or, If, stating it another way: one second, moves from E in the earth to E' while a ray of light, goes from the earth to L , then FACT(1) E'/.
Substituting in (10) this value of a and the value we x' which the is first ay from (13), 0x - |8vf /3(x-rt) = = x' or = fee get (18) of the set of equations on page 19! of the Lorenti transformation Furthermore, from (1 = = x 8) and / \x' we get = = ct' or t' Or, since t = ct ct' - vt) - vt/c). P(ct /3(t x/c, t' = /3(t - 2 vx/c ), (19) another of the equations of the Lorentz transformation! which is That the remaining two equations = y and z' z also hold, y' Einstein shows as follows: = K and Let /C' each have a cylinder of radius r, when at rest relatively to each other, and whose axes coincide with the Now, unless / = y and z = z, K and K would each claim that X (X ) axis/ 7 r f own his We cylinder is OUTSIDE the other fellow's!