History of Lorentz Transformations - Larmor (1897, 1900)

Larmor (1897, 1900)

Larmor in 1897 and 1900 presented the transformations in two parts. Similar to Lorentz, he considered first the transformation from a rest system (x, y, z, t) to a moving system (x′, y′, z′, t′)

This transformation is just the Galilean transformation for the x, y, z coordinates but contains Lorentz’s "local time". Larmor knew that the Michelson–Morley experiment was accurate enough to detect an effect of motion depending on the factor v²/c², and so he sought the transformations which were "accurate to second order" (as he put it). Thus he wrote the final transformations (where x* = x − vt) as:

Larmor showed that Maxwell's equations were invariant under this two-step transformation, "to second order in v/c", as he put it. Larmor noted that if it is assumed that the constitution of molecules is electrical then the Fitzgerald-Lorentz contraction is a consequence of this transformation. It's notable that Larmor was the first who recognized that some sort of time dilation is a consequence of this transformation as well, because individual electrons describe corresponding parts of their orbits in times shorter for the system in the ratio 1/γ.