Michelson investigated the aether with his famous MM experiment. But no result was found. Explanation required.

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THE MICHELSON-MORLEY EXPERIMENT
Cosmic Adventure Episode 2.06

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Shifted Positions
When the system moves
with the earth, the situation
is different.
Before the beams are able to
reach the reflectors, the
reflectors will have been
moved by the earth’s motion
a distance equal to 𝑣𝑡. The
beams have to move further
to reach these new positions.
New position
New position
Beam 1
Beam 2
𝑣𝑡
𝑣𝑡

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Beam 1 Forward Trip
Upwind Speed:
𝑐 − 𝑣
Upwind Time :
𝑡1𝑎 =
𝑙 𝑜
𝑐 − 𝑣
Beam 1
Beam 2

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Beam 1 Return Trip
But when he returns, he is
aided by the aether wind and
ended up in gaining speed,
that is:
Downwind Speed:
𝑐 + 𝑣
Downwind Time:
𝑡1𝑏 =
𝑙 𝑜
𝑐 + 𝑣
Beam 1
𝑣𝑡

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Timing for Beam 1
The total time taken by Beam 1 is:
𝑡 𝐵𝑒𝑎𝑚 1 𝐹𝑜𝑟𝑤𝑎𝑟𝑑 + 𝑡 𝐵𝑒𝑎𝑚 1 𝑟𝑒𝑡𝑢𝑟𝑛
=
𝑙 𝑜
𝑐 − 𝑣
+
𝑙 𝑜
𝑐 + 𝑣
=
2𝑙 𝑜
𝑐 𝑐2 − 𝑣2
As if it has not suffered any
deviation.
Beam 1

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Beam 2
For Beam 2, the situation is
a bit more complicated. To
reached the new position of
the reflector, Beam 2 has to
bend towards it.
Michelson explained.
New position
Beam 2
𝑣𝑡

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So now the beam shoots at a
slanting angle to its original
path 𝑙 𝑜.
By the Pythagoras theorem:
𝑙 𝑜
2
= 𝑐2
𝑡2
2
− 𝑣2
𝑡2
2
= 𝑡2
2
𝑐2
− 𝑣2
𝑡2
2
=
𝑙 𝑜
2
𝑐2 − 𝑣2
𝑡2 =
𝑙 𝑜
𝑐 1 − 𝑣2/𝑐2
𝑣𝑡
𝑐𝑡
𝑙 𝑜
𝑙 𝑜
𝑣𝑡
𝑐𝑡

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Complete Trip Time
Doubling the trip:
𝑇𝑖𝑚𝑒 = 2𝑡2
=
2𝑙 𝑜
𝑐 1 − 𝑣2/𝑐2
𝑐𝑡
𝑙 𝑜
𝑣𝑡

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Comparison
𝑇𝑖𝑚𝑒 𝑓𝑜𝑟 𝐵𝑒𝑎𝑚 1
=
2𝑙 𝑜
𝑐 𝑐2 − 𝑣2
𝑇𝑖𝑚𝑒 𝑓𝑜𝑟 𝐵𝑒𝑎𝑚 2
=
2𝑙 𝑜
𝑐 𝑐2 − 𝑣2
Now we can have a complete information of the times used by the two
reflected beams. The difference is obvious. Beam 2 will take a longer
time than Beam 1 to complete the round trip.

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Analysing the Beams
The returned beams
recombined by respectively
transmission and reflection
at the beam splitter. They
will be collected by the
telescope or observer.
Since there are differences in
the path lengths, there
should be interferences and
fringes would came out.
Waves not in
phase.
Fringes appears.
Beam 1 Beam 2

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Interference Fringes
Like every other objects in the universe, the earth is moving through the
aether at a velocity of 30 miles a second. So the aether winds thus created
should be equal to the earth’s speed in orbit.
The ratio of earth’s velocity to light speed is 𝑣/𝑐 and is about 1/10,000, so
𝑣²/𝑐² is about 1/100,000,000.
This means the time delay between the pulses is about one-hundred-
millionth of a few millionths of a second.

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Interference Fringes
It seems completely
impossible to detect such a
short time delay. However,
this is where Michelson’s
expertise laid. His trick was
to use the interference
properties of the light
waves. If there was a path
difference, there would be
interference fringes.
Fringe pattern caused by source shift in the
Michelson-Morley interferometer.

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RESULTS

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Nil Result
But to the astonishment of the
scientific community, when the first
experiment was carried out in 1881,
Michelson was unable to find any
interference fringes.
It implied that both the returning
beams have arrived at the half
silvered mirror at the same time
contrary to their expectation that the
‘perpendicular beam’ would take
longer for the return trip than the
‘parallel beam’.

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Improved Setup
Later in 1887, he teamed up with
Edward Morley (1838-1923), a very
experienced experimenter, and set
up a much more accurate version of
the experiment.
Michelson had the interference
effect greatly magnified and using
multiple reflections. The effective
length was increased to 1,100 cm so
that an interference difference
caused by an apparatus velocity of 3
km/sec would be easily detected.
To their disappointment, no
difference was observed at all.

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More and Better Tests
In 1905 and in the subsequently
years more tests were carried out
with even greater precision and
better technique.
One of the most accurate
experiments was done in 1960 by
Charles H. Townes (1915-2015)
using masers. The set-up was so
sensitive that even if the earth
moved at only one-thousandth of
its actual speed, the ether wind so
generated can still be detected.
The results were all the same. Not
even the slightest trace of ether
wind was detected.
Charles H. Townes (1915-2015) and his masers

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The most Famous Failed experiment
To the scientists, the null result implied three possibilities:
1) Either there wasn’t anything called Ether
2) or the Earth must be dragging a ‘blob’ of Ether around it so there
wouldn’t be any Ether wind to detect.
3) There is the mysterious effect of time dilation.
However, evidence from other observations has disproved the possibility
of Ether drag; time dilation was also later found not acceptable. So the
scientific community was left with the first possibility and interpreted the
null result in MM experiment as a firm disproof of the existence of the
Ether medium.
The experiment became what has been called the most famous failed
experiment in history.[

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Epitaph to the Experiment
Michelson wrote about the "decidedly negative result" in a letter to Lord
Rayleigh in August 1887:
The Experiments on the relative motion of the earth and ether have been
completed and the result decidedly negative. The expected deviation of
the interference fringes from the zero should have been 0.40 of a fringe –
the maximum displacement was 0.02 and the average much less than 0.01
– and then not in the right place. As displacement is proportional to
squares of the relative velocities it follows that if the ether does slip past
the relative velocity is less than one sixth of the earth’s velocity.
— Albert Abraham Michelson, 1887

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Where did it go
wrong?
You must be wondering
that this is a dead issue,
coffined and nailed. But
this is not. The water is just
starting to boil. It is the
Pandora’s box of modern
time being widely open
now.
The key question is, where
did the experiment go
wrong?

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Sword in the Stone
The scientist of the nineteenth
century had come up with many
valuable solutions like aether drag,
Lorentz contraction, and many other
fanciful ideas.
But to us, none of them can explain
the null result convincingly.
We had fun with the problem as
well. We called it the sword in the
stone. Whoever pulls it out will be
able to cut all the misconceptions
engendered by the experiment.

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THE SECRET OF THE MM EXPERIMENT
To be continued on: Episode 2.07