cosmic adventure episode 2.06 mm experiment

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THE MICHELSON-MORLEY EXPERIMENT

Cosmic Adventure Episode 2.06


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


Beam 1 Forward Trip

Upwind Speed:

𝑐 − 𝑣

Upwind Time :

𝑡1𝑎 =𝑙𝑜

𝑐 − 𝑣

Beam 1

Beam 2


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 =𝑙𝑜

𝑐 + 𝑣

Beam 1𝑣𝑡


Timing for Beam 1

The total time taken by Beam 1 is:

𝑡𝐵𝑒𝑎𝑚 1 𝐹𝑜𝑟𝑤𝑎𝑟𝑑 + 𝑡𝐵𝑒𝑎𝑚 1 𝑟𝑒𝑡𝑢𝑟𝑛

=𝑙𝑜

𝑐 − 𝑣+

𝑙𝑜𝑐 + 𝑣

=2𝑙𝑜

𝑐 𝑐2 − 𝑣2

As if it has not suffered any deviation.

Beam 1


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


So now the beam shoots at a slanting angle to its original path 𝑙𝑜.

By the Pythagoras theorem:

𝑙𝑜2 = 𝑐2𝑡2

2 − 𝑣2𝑡22

= 𝑡22 𝑐2 − 𝑣2

𝑡22 =

𝑙𝑜2

𝑐2 − 𝑣2

𝑡2 =𝑙𝑜

𝑐 1 − 𝑣2/𝑐2

𝑣𝑡

𝑐𝑡𝑙𝑜

𝑙𝑜

𝑣𝑡

𝑐𝑡


Complete Trip Time

Doubling the trip:

𝑇𝑖𝑚𝑒 = 2𝑡2

=2𝑙𝑜

𝑐 1 − 𝑣2/𝑐2

𝑐𝑡𝑙𝑜

𝑣𝑡


Comparison

𝑇𝑖𝑚𝑒 𝑓𝑜𝑟 𝐵𝑒𝑎𝑚 1

=2𝑙𝑜

𝑐 𝑐2 − 𝑣2

𝑇𝑖𝑚𝑒 𝑓𝑜𝑟 𝐵𝑒𝑎𝑚 2

=2𝑙𝑜

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.


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


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.


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 interferenceproperties 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.


RESULTS


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’.


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.


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


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.[


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


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?


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.


THE SECRET OF THE MM EXPERIMENT

To be continued on: Episode 2.07

cosmic adventure episode 2.06 mm experiment

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