9. LORENTZ EXPLANATION
OF THE NEGATIVE RESULTS OF MICHELSON'S EXPERIMENT
The negative results of Michelson's experiment were a great surprise
to all physicists of that time. There were serious doubts about the result,
which is testified to by the persistence with which the experiment was
repeated over many years.
Many physicists of that time tried to explain the reason for the negative
result. Michelson and Morley concluded, on the basis of the experiments,
that the earth, which moves, draws along the ether completely as Stockes's
theory and Hertz electromagnetic theory had stated. But that conclusion
was in contradiction with many experiments, which tried to prove the hypothesis
of the partial drawing of the ether. Lodge, however had shown that the
velocity of light does not change near bodies which move fast, even when
those bodies carry strong electric and magnetic fields.
A special place in explaining and analyzing the negative result of
the experiment, belongs to Lorentz, Fitzgerald and Poincare. Poincare,
for example, was one of the greatest mathematicians and theoretical physicists
of that time. After analyzing the first and simple experiment performed
by Michelson, Lorentz gave a daring and unfounded hypothesis that: "Each
body which has velocity 
is shorter in the direction of motion
for the factor
 |
Actually if instead of the length
in Eq. (5.7) we take 
then the length of the optical paths in both branches of Michelson's interferometer
will be equal, and the expected shift will not occur, as was the case in
the experiment. Fitzgerald and Poincare had the same idea about the shortening.
Therefore the contraction hypothesis is also called the Lorentz - Fitzgerald
contraction hypothesis. The shortening occurs only in the dimension aligned
with the direction of motion, whereas the transversal dimensions do not
change. That shortening cannot allegedly be discovered by any kind of Earthly
observation because each ruler on the earth shortens in the same proportion.
An observer who was at rest position in the ether, and outside earth, would
allegedly be able to see this shortening. The whole earth would look flattened
in the direction of motion and also all its objects.
Thus, according to Lorentz, the objects which move through the ether,
become shorter in the direction of the motion for
the contraction factor 
.
So, if the length of a body is
when it is at rest, then
the length of the body in motion is
|
 |
(9.1) |
is also called proper length.
Now let us take a look at how the theory of relativity looks at the
Lorentz - Fitzgerald's Contraction Hypothesis.
If we connect an unmoving coordinate system to the ether, and a moving
system to the earth, then the measuring system in Michelson's experiment,
was unmoving in the system which moves and all the measurements were done
in that moving system. Accordingly, the shortening of the body originates
in the unmoving system in which observed body is at rest. However, according
to the theory of special relativity there is no shortening of the objects
in the system, in which those objects are at rest. Einstein goes further
and says [6]:
Quotation: "According to the theory of relativity
there is no any privileged coordinate
system which could give a motive for introducing the idea about ether.
Consequently, there is no ethereal wind nor any experiment which could
show that it exists. Here the contraction of bodies in motion follows,
without any particular hypothesis, from both basic principles of the theory.
At that for this contraction, the motion only is not competent. For that
motion is not able to give any sense, but for the motion in relation to
the chosen reference body. Because of this Michelson-Morley's experimental
mirror was not shortened in the relative system which moves together with
the earth, but only in the relative system which is unmoving in relation
to the sun." End of quotation.
As we can see from the quoted text, Einstein did not agree with Lorentz's
explanation of the negative result of Michelson's experiment, that is he
did not accept that the contraction hypothesis could be applied in a system
where the body is at rest, but only in a system where the body is moving.
In conclusion, however, it is necessary to repeat that the Michelson
- Morley measurement could not give the facts about earth's motion through
the ether. Measurements with the new interferometer have also shown that
there is no the earth motion, or more exactly the interferometer motion
relatively to the ether, and that there was not any contraction. This means
that the Lorentz - Fitzgerald contraction hypothesis has no basis, at least
as regards the contraction in connection with Michelson's experiment.
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