The Lorentz transformation

We have already stated that the Galilean transformation from frame S to frame S' does not give the same value for the speed of a bullet, and neither will it give the same value for the speed of light. The transformation which preserves the value of the speed of light in both frames of reference is named in recognition of the Dutch physicist Hendrik Anton Lorentz (1853-1928).

It is simplest to reverse the logical order of the argument by stating the equations of the Lorentz transformation, and later showing that they satisfy the requirement that the speed of light remain constant for all unaccelerated observers.

The basic difference between the Galilean transformation and the Lorentz transformation is that the measure of time is not the same in the two frames (t' ^ t).

Verifying that the Lorentz transformation satisfies Equation (15.3)

Using x' and t' from above, we substitute into Equation (15.3)

1 c2

f

2 ^

f

2

1 —

v

+ c 2t2

1 —

T2

V

y

V

0 0

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