History of Lorentz Transformations - Lorentz (1899, 1904)

Lorentz (1899, 1904)

Also Lorentz, by extending his theorem of corresponding states, derived in 1899 the complete transformations. However, he used the undetermined factor l as an arbitrary function of v. Like Larmor, in 1899 also Lorentz noticed some sort of time dilation effect, and he wrote that for the frequency of oscillating electrons "that in S the time of vibrations be kl times as great as in S₀", where S₀ is the ether frame,

and l is an undetermined factor. This factor was set to unity by him in 1904, so Lorentz's equations now assumed the same form as Larmor's (as mentioned above x* must be replaced by x − vt):

In connection with this he also derived the correct formulas for the velocity dependence of mass. He concluded, that this transformation must apply to all forces of nature, not only electrical ones and therefore length contraction is a consequence of this transformation.