Talk:Joseph Larmor

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[edit] contributions to Lorent transformations to add

The following has been removed from relativity of simultaneity and some of it could be used here (keeping in mind that some of it already is in lorentz transformations):

Development of the final Lorentz Transformations

Larmor knew that the Michelson-Morley experiment was accurate enough to detect an effect of motion depending on the factor v2 / c2, yet no such effect was detected. He sought, therefore, the transformations which were "accurate to second order" (as he put it). His solution was to modify the first order transformations in two ways:

  • he included the Fitzgerald contraction (already known to account for the Michelson-Morley result and already in Lorentz's first version of the transformation) and
  • he introduced (or predicted) the revolutionary idea of time dilation, at least for particles whose motion was determined by electromagnetic forces.

Thus he wrote the final transformations as

x' = \epsilon^{1/2} x^*= \epsilon^{1/2} \left(x-vt\right)\,
y' = y\,
z' = z\,
t' = \epsilon^{-1/2}t^* = \epsilon^{-1/2}t - \epsilon^{1/2}vx^*/c^2 = \epsilon^{-1/2}t - \epsilon^{1/2}\left(x-vt\right)/c^2,\,

from which it can be seen that lengths x' = ε1 / 2x * are shorter by the factor ε1 / 2 = γ and time t' = \epsilon^{-\frac{1}{2}}t^* is longer by the factor ε − 1 / 2 = 1 / γ for the moving system.

Larmor showed that Maxwell's equations were invariant under this two-step transformation, "to second order in v / c", as he put it. His transformations did more than this since a little algebra shows that the relation between \left(x',\, y',\, z',\, t' \right)\, and \left(x,\,y,\,z,\,t\right)\, is

x' = \gamma (x - v t)\,
y' = y\,
z' = z\,
t' = \gamma \left(t - v x/c^{2} \right)

which are the Lorentz transformations, for which we know Maxwell's equations are invariant to any order in v / c. Einstein (1905) and Poincaré (1905) wrote the transformations in this form. It was Poincaré (1905) who named them as the Lorentz Transformations. Lorentz (1899) and (1904) had published the transformations in a similar form to Larmor (as above), and Poincaré was apparently unaware of Larmor's (1897) previous publication.

It is worth repeating the first published prediction of time dilation:

"... individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio ε − 1 / 2" (Larmor 1897)

Larmor probably would have thought of this as a dynamical prediction from Maxwell's equations rather than a general statement about the nature of time.

  • Larmor, J. (1897) "On a dynamical theory of the electric and luminiferous medium", Phil. Trans. Roy. Soc. 190, 205-300 (third and last in a series of papers with the same name).
  • Larmor, J. (1900) Aether and Matter, Cambridge University Press

Harald88 12:33, 1 October 2006 (UTC)