Lorentz and Fitzgerald picked up the MMX equation and developed the length contraction hypothesis to explain the failure of MMX. Lorentz transformation quation surface first time in history.

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RESURRECTION OF THE MMX –
LENGTH CONTRACTION

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Community Shocked
As soon as Michelson
announced the null results, the
physicists were utterly
shocked. The scientific
community found it hard to
assimilate the failure of MMX
to get the expected results.
The first thing of the failed
MMX did was to whirl the
science world into great chaos.

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Salvaging the Aether
There was a rush of efforts among the scientists to look for what was actually
going wrong. Numerous attempts were made to explain the experiment so as
to salvage the endangered aether postulate.

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Aether Drag Proposal
Michelson himself also
proposed that the aether
near the earth might have
been affected by the earth
and move along with the
earth. This aether flow
would have carried the light
along with it and jeopardize
the results.

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Aether Drag – Partial & Complete
There were existing theories of
two modes by which aether
was being dragged along.
The first one was proposed by
Augustin-Jean Fresnel in 1818.
He thought that the aether is
almost stationary and is
‘partially’ entrained by matter.
This phenomenon was
‘apparently’ confirmed by the
Fizeau experiment in 1851.
Another theory was proposed
by George Stokes in 1845. He
believed that the aether is
‘completely’ entrained within
or in the vicinity of matter. This
proposal was apparently
confirmed by the Michelson–
Morley experiment in 1881
and finally in 1887.

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Contraction Theory
This contradictive situation
form of aether dragging was
later banished by the
contraction theory proposed
independently by George
Fitzgerald (1851-1901) in
1889 and Hendrik Lorentz
(1853-1928) in 1895.
Hendrik Lorentz-
1853-1928
George Fitzgerald
1851-1901

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Lorentz-Fitzgerald
contraction
Both of them try to explain the
experiment by way of length
contraction to an amount
according to their proposed
equation. So the proposals
were called Lorentz-Fitzgerald
contraction.
However it was Lorentz who
put the theory in exact
mathematical form, so the
formulation is also called
Lorentz contraction.
Lorentz-Fitzgerald contraction

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Encumbered Proposal
Of course there were also
others theories proposed
besides the contraction
theory. Only the Lorentz
hypothesis was quoted
because the transformation
equation contained therein
bored special relation to the
development of a
supposedly better theory
that was to come.
𝑙 = 𝑙 𝑜 1 − 𝑣2/𝑐2
𝑙 𝑜 is the length at
absolute rest
𝑙 is the shrunken
length on the move
𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑚𝑜𝑡𝑖𝑜𝑛 𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝐿𝑖𝑔ℎ𝑡

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Hendrik Lorentz said in
1906:
“In order to explain this
absence of any effect of the
Earth's translation (in the
Michelson-Morley
experiment), I have ventured
the hypothesis, that the
dimensions of a solid body
undergo slight change, of
the order of 𝑣2
/𝑐2
, when it
moves through the ether. . .

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Lorentz continued: “From this
point of view it is natural to suppose
that, just like the electromagnetic
forces, the molecular attractions and
repulsions are somewhat modified by
a translation imparted to the body,
and this may very well result in a
change of dimensions. The electrons
themselves become flattened
ellipsoids. . . This would enable us to
predict that no experiment made
with a terrestrial source of light will
ever show us an influence of the
Earth's motion.”
10% the speed of light
85% the speed of light
99% the speed of light
99.99% the speed of light

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Beam A under focus
We go to the details first by
considering Beam A which is
aligned with the movement of
the earth and thus reversely
with the aether wind.
Beam B
Beam A
Light Source
Beam B
Beam A
Light Source

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Shrinkage along Motion
The setup contracted along
the direction of motion.
Lorentz considered this
length contraction as a real
physical change in the
material object that depends
on its motion relative to
absolute space.
Beam A

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BeamB
Beam A
Viewer
Light Path Geometry
Since the apparatus set-up
in the experiment contracted
in a certain amount in the
direction of the aether wind,
light would take less time to
travel along such a path
than that along the path
perpendicular to the wind.
Diagram
showing over
emphasized
contraction
Shorter
path thus
less time

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The Data from Michelson
𝐵𝑒𝑎𝑚 𝐴 𝑃𝑟𝑒𝑠𝑒𝑡 𝑃𝑎𝑡ℎ 𝑙𝑒𝑛𝑔𝑡ℎ
2𝑙 𝑜
𝐵𝑒𝑎𝑚 𝐴 𝑇𝑖𝑚𝑖𝑛𝑔
=
2𝑙 𝑜
𝑐 1 − 𝑣2/𝑐2
* 1 − 𝑣2
/𝑐2
𝐵𝑒𝑎𝑚 𝐵 𝑃𝑟𝑒𝑠𝑒𝑡 𝑃𝑎𝑡ℎ 𝐿𝑒𝑛𝑔𝑡ℎ
2𝑙 𝑜
𝐵𝑒𝑎𝑚 𝐵 𝑇𝑖𝑚𝑖𝑛𝑔
=
2𝑙 𝑜
𝑐 1 − 𝑣2/𝑐2
** 1 − 𝑣2/𝑐2

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Transformation
Applying the equation to Beam A:
𝐵𝑒𝑎𝑚 𝐴 𝑇𝑖𝑚𝑖𝑛𝑔
=
2𝑙 𝑜
𝑐 1 − 𝑣2/𝑐2
× 1 − 𝑣2/𝑐2
=
2𝑙 𝑜
𝑐 1 − 𝑣2/𝑐2
𝐵𝑒𝑎𝑚 𝐵 𝑇𝑖𝑚𝑖𝑛𝑔
=
2𝑙 𝑜
𝑐 1 − 𝑣2/𝑐2
Then the two timings are the
same

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Length Contraction
Lorentz has two choices: either
there is a dilation in time or a
contraction in length. Time in
classical physics is a ratio and
has nothing to be changed. So
it may be length because it is
made up of the solid chunk of
stone material. So he assigned
the change to the length
instead of to time as a whole.
Beam A Timing
Shrinkage applied to timing:
=
2𝑙 𝑜
𝑐 1 − 𝑣2/𝑐2
× 1 − 𝑣2/𝑐2
Shrinkage applied to length:
=
2𝑙 𝑜 × 1 − 𝑣2/𝑐2
𝑐 1 − 𝑣2/𝑐2

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Shrinkage Explained MMX
The shortening in path thus
permitted the beam to catch
up with the other beam and
arrive at the viewer at the
same time. In other words,
the contraction was there just
enough to make light to
retain its constancy without
being affected by the way the
apparatus is orientated.
BeamB
Beam A
Viewer
Diagram
showing over
emphasized
contraction
Shorter
path thus
less time

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Application to MMX
By doing the length
contraction, the two timings in
MMX matched perfectly.
𝐵𝑒𝑎𝑚 𝐴 𝑇𝑖𝑚𝑖𝑛𝑔
=
2𝑙 𝑜 × 1 − 𝑣2/𝑐2
𝑐 1 − 𝑣2/𝑐2
=
2𝑙 𝑜
𝑐 1 − 𝑣2/𝑐2
𝐵𝑒𝑎𝑚 𝐵 𝑇𝑖𝑚𝑖𝑛𝑔
=
2𝑙 𝑜
𝑐 1 − 𝑣2/𝑐2

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The Mysterious Factor
The most wonderful thing
is that a very unusual
factor sprung up.
Although Lorentz and
Fitzgerald used it to
explain MMX, they did not
derived the equation. In
fact, you simply have no
explanation to it because it
had come from a basically
wrong concept.
1 − 𝑣2/𝑐2

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Contraction theory
not acceptable
The contraction of material
bodies by itself puzzled the
physicists. It seemed to them
that the phenomenon is out
of this world and did not
appeal to their senses.
?
*
*

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Shrinking - Unfathomable
Phenomenon
It appeared to the scientists
of the day that this way of
thinking about nature is
unfathomable. They
wondered if it was worth to
go to such an extraordinary
length just to prevent the
aether from being detected.
So the contraction theory
was finally not favoured.

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Return of the Dead
We saw the deaths of two
theories:
1. The MMX aether theory by
Maxwell and Michelson.
2. The proposed Length
Contraction postulate by
Fitzgerald and Lorentz.

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𝜸 =
𝟏
𝟏−
𝒗 𝟐
𝒄 𝟐
WAS BORN
But in such a way

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THE REBIRTH OF 𝜸 IN RELATIVITY
To be continued in Episode 3.01