24 The Michelson Experiment
259
for the change in running times differences of the interfering wave trains before and
after rotation, according to (310). I.e.
δ = t π
2
− t =
1
2
τ .
Moving
interferometer
(311)
Due to this result, δ = τ /2, a total displacement of the bands should be observed.
Nevertheless, nothing occurs: Neither during the first experiment in 1881, nor
during any other experiment anytime, anyplace.
Lorentz’ [62] simple explanation is: ‘We are therefore led to suppose that the
influence of a translation on the dimension (of the separate electrons and of a ponderable body as a whole) is confined to those that have the direction of the motion,
these becoming k times smaller than they are in the state of rest’, where k is the factor
k =
1 − v 2 /c
2
L .
Indeed, replacing the length of the arm l 1 with l 1
1 − v 2 /c
2
L in (307) and the
length of the arm l 2 with l 2
1 − v 2 /c
2
L in (308), we receive t = t π
2
, so that
according to δ = 0 no change of the interference figure can be expected.