Chapter 24
The MICHELSON Experiment
We here describe the simple idea of the Michelson experiment as illustrated below.
A source S emits a wave train which arrives at a semi silver-coated glass plate P.
There the wave train is split into two coherent wave trains moving along the arms l 1
and l 2 of Michelson’s interferometer. The waves were reflected at the ends l 1 and l 2
by the mirrors M 1 and M 2 , respectively, and finally give rise to an interference figure
observed at P.
Let us assume that the speed of light c L has the same amount in an arbitrary
direction if it is measured in the preferred frame o . There is also another reference
system
that has the velocity v with respect to o .
We firstly consider the case where Michelson’s interferometer is at rest in o ,
cf. Fig. 24.1. The propagation of the wave trains is isotropic in o . Hence, the time
needed for the wave trains to traverse the distance along the arms l 1 and l 2 and
back are t
o
1 = 2l 1 /c L and t
o
2 = 2l 2 /c L , respectively. The interference figure at P is
determined by the difference t
o in the running times,
t
o
= t
o
2 − t
o
1 =
2l 1
c L
−
2l 2
c L
.
(301)
The idea of the experiment is to rotate the interferometer by π/2, cf. Fig. 24.1b.
Taking the isotropy of light propagation in o into account, the difference t
o
π
2
in
the running times t
o
1,
π
2
and t
o
2,
π
2
does not change during this rotation,
t
o
π
2
= t
o
2,
π
2
− t
o
1,
π
2
=
2l 2
c L
−
2l 1
c L
= t
o
.
(302)
Let us define a quantity δ as the difference between the running time differences
of the coherent wave trains before and after rotation of the interferometer,
δ := t π
2
− t .
(303)
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_24
255
The MICHELSON Experiment
We here describe the simple idea of the Michelson experiment as illustrated below.
A source S emits a wave train which arrives at a semi silver-coated glass plate P.
There the wave train is split into two coherent wave trains moving along the arms l 1
and l 2 of Michelson’s interferometer. The waves were reflected at the ends l 1 and l 2
by the mirrors M 1 and M 2 , respectively, and finally give rise to an interference figure
observed at P.
Let us assume that the speed of light c L has the same amount in an arbitrary
direction if it is measured in the preferred frame o . There is also another reference
system
that has the velocity v with respect to o .
We firstly consider the case where Michelson’s interferometer is at rest in o ,
cf. Fig. 24.1. The propagation of the wave trains is isotropic in o . Hence, the time
needed for the wave trains to traverse the distance along the arms l 1 and l 2 and
back are t
o
1 = 2l 1 /c L and t
o
2 = 2l 2 /c L , respectively. The interference figure at P is
determined by the difference t
o in the running times,
t
o
= t
o
2 − t
o
1 =
2l 1
c L
−
2l 2
c L
.
(301)
The idea of the experiment is to rotate the interferometer by π/2, cf. Fig. 24.1b.
Taking the isotropy of light propagation in o into account, the difference t
o
π
2
in
the running times t
o
1,
π
2
and t
o
2,
π
2
does not change during this rotation,
t
o
π
2
= t
o
2,
π
2
− t
o
1,
π
2
=
2l 2
c L
−
2l 1
c L
= t
o
.
(302)
Let us define a quantity δ as the difference between the running time differences
of the coherent wave trains before and after rotation of the interferometer,
δ := t π
2
− t .
(303)
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_24
255