Cosmic Adventure 2.09 Lorentz Contraction

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RESURRECTION OF THE MMX –LENGTH CONTRACTION


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.


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.


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.


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.


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


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


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 = 𝑙𝑜 1 − 𝑣2/𝑐2

𝑙𝑜 is the length at absolute rest

𝑙 is the shrunken length on the move

𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑚𝑜𝑡𝑖𝑜𝑛 𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝐿𝑖𝑔ℎ𝑡


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. . .


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



99.99% the speed of light


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 BBeam A

Light Source

Beam B

Beam A

Light Source


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


Beam

B

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


The Data from Michelson

𝐵𝑒𝑎𝑚 𝐴 𝑃𝑟𝑒𝑠𝑒𝑡 𝑃𝑎𝑡ℎ 𝑙𝑒𝑛𝑔𝑡ℎ

2𝑙𝑜

𝐵𝑒𝑎𝑚 𝐴 𝑇𝑖𝑚𝑖𝑛𝑔

=2𝑙𝑜

𝑐 1 − 𝑣2/𝑐2

* 1 − 𝑣2/𝑐2

𝐵𝑒𝑎𝑚 𝐵 𝑃𝑟𝑒𝑠𝑒𝑡 𝑃𝑎𝑡ℎ 𝐿𝑒𝑛𝑔𝑡ℎ

2𝑙𝑜

𝐵𝑒𝑎𝑚 𝐵 𝑇𝑖𝑚𝑖𝑛𝑔

=2𝑙𝑜

𝑐 1 − 𝑣2/𝑐2

** 1 − 𝑣2/𝑐2


Transformation

Applying the equation to Beam A:


=2𝑙𝑜

𝑐 1 − 𝑣2/𝑐2× 1 − 𝑣2/𝑐2

=2𝑙𝑜

𝑐 1 − 𝑣2/𝑐2


=2𝑙𝑜

𝑐 1 − 𝑣2/𝑐2

Then the two timings are the same


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:

=2𝑙𝑜

𝑐 1 − 𝑣2/𝑐2× 1 − 𝑣2/𝑐2

Shrinkage applied to length:

=2𝑙𝑜 × 1 − 𝑣2/𝑐2

𝑐 1 − 𝑣2/𝑐2


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.

Beam

B

Beam A

Viewer

Diagram showing over emphasized contraction

Shorter path thus less time


Application to MMX

By doing the length contraction, the two timings in MMX matched perfectly.


=2𝑙𝑜 × 1 − 𝑣2/𝑐2

𝑐 1 − 𝑣2/𝑐2

=2𝑙𝑜

𝑐 1 − 𝑣2/𝑐2


=2𝑙𝑜

𝑐 1 − 𝑣2/𝑐2


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


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.

?*

*


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.


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.


𝜸 =𝟏

𝟏−𝒗𝟐

𝒄𝟐

WAS BORN

But in such a way


THE REBIRTH OF 𝜸 IN RELATIVITY

To be continued in Episode 3.01

Cosmic Adventure 2.09 Lorentz Contraction

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Transcript of Cosmic Adventure 2.09 Lorentz Contraction