Michelson and Morley's Experiment

Purpose

The purpose of the Michelson and Morley's experiment is to detect if the speed of light is a function of the speed v of the Earth. The outcome is negative i.e. the speed of light is the same in all directions. The implications are that the length of the Earth is contracted in its direction of motion i.e. its speed v.
This document offers a possible other solution: Time dilation i.e. the effect that clock rate is influenced as a function of its speed v.

Description.

For a detailed description of this experiment see:
1. "Einsteins Theory of Relativity" By Max Born the pages 214 to 218
2. "Six not-so-easy Pieces" By Richard P. Feynman the pages 54 to 57
The Michelson and Morley's Experiment consist of two mirrors and a light source S or beam splitter.

 ``` ---------- mirror 1 /\ / \ / \ mirror 2 / \ | / \ | S---------X---------| v | -----> | ```

At the light source S or beam splitter the light is divided into two parts:
• one part moves in the vertical direction, reflects against mirror one and moves backwards.
• one part moves in the horizontal direction, reflects against mirror two and moves backwards.
• the two light rays meet each other at point X, where you will see an interference pattern.

The two important parameters of this experiment are:

• The reflection time t1 against mirror 1.
t1 = 2 * d / c * 1 / SQR (1 - v²/c²)
t1 approximate = 2 * d / c * ( 1 + 0.5*v²/c²)
• The reflection time t2 against mirror 2.
t2 = d /(c+v) + d /(c-v) = 2 * d / c * 1 / (1 - v²/c²)
t2 approximate = 2 * d / c * ( 1 + v²/c²)
• The difference between t2 and t1
t2 approximate - t1 approximate = dt = d / c * ( v²/c²) = d / c * Beta². Beta = v/c

The idea behind the experiment is to rotate the whole setup over an angle of 90 degrees and than to observe the change in interference patern. This is very difficult to perform in practice.
A more practical way is to keep the whole setup fixed, to perform the whole experiment over a 24 hour period and to monitor the interference pattern.

In reference 2 above, page 57, we read:

In carrying out the experiment, M and M oriented the apparatus so that the line BE was nearly parallel to the earth's motion in its orbit (at certain times of the day and night). This orbital speed is about 18 miles per second, and any "ether drift" etc.etc. The result of the experiment was null.

There are two explanations for this phenomena:

1. Length contraction in the direction of motion.
2. Time Dilation in the direction of motion.
3. Length contraction is the name for the phenomena that the horizontal length d is changed by a factor: SQR(1-Beta²)
As such the time t2 becomes:
t21 = 2 * d / c * 1 /(1-Beta²) * SQR(1-Beta²)
t21 = 2 * d / c * 1 / SQR(1-Beta²)
The reflection time t21, using length contraction, is equal to t1, which explains the null result of the Michelson and Morley's experiment.
4. Time dilation is the name for the phenomena that the horizonta time duration of t2 is corrected by a factor: 1/SQR(1-Beta)²
As such the time t2 becomes:
t21 = 2 * d / c * 1 / SQR (1 - v²/c²) /( 1 / SQR(1-Beta²))
t21 = 2 * d / c * 1 / SQR (1-Beta²)
The reflection time t21, using time dilation, is equal to t1, which explains the null result of the Michelson and Morley's experiment.
The result of both effects is the same: the Michelson and Morley's experiment is not a function of the speed v of the Earth.

The speed of the surface of the Earth is a function of:

1. The rotation speed of the Earth around its axis. This speed is roughly 0.5 km/sec at the equator.
2. The speed of the Earth around the Sun. This speed is roughly 30 km/sec.
3. The speed of the Sun around our Galaxy. This speed is roughly 250 km/sec.
4. The speed of our Galaxy. This speed is roughly 40 km/sec.
The first parameter requires a comment. IMO if you perform the MM experiment solely on a rotating object "at the equator" you will not detect any change in the interference pattern because the x direction of the experiment will always coincide with the direction of the rotating movement. This is true whereever you are at the equator. Length contraction of a rotating object as such is a difficult concept. See also Length Contraction part 1

IMO if you want to do the MMX experiment than you should use the ecliptic as your baseline and not the equator i.e. you should place the setup where the latitude (measured from the ecliptic plane) is zero.

On the other hand because the final outcome of the experiment is that the setup is independent of v (which is not known) it is not possible which of the arms is actual contracting (or expanding). Over a 24 hour period the answer is that the length of both arms has changed, but you can not specify how much and when.

Simulation Program of this experiment

Your author has written a program in QBASIC to simulate the Michelson and Morley's Experiment.
1. For a copy of the program select: MMX.BAS.
2. For a listing of the program select: MMX.HTM.
3. To execute the program select: MMX.ZIP.
4. For an explanation of the program See: progrm16.htm
Your author has also written the same program in Visual Basic to simulate the Michelson and Morley's Experiment.
1. To execute the program select: VB MMX.ZIP.
2. For an explanation of the program See: VB MMX program.htm

Reflection

Above I have written that the explanation for the null effect of the Michelson and Morley's Experiment is Length Contraction and Time Dilation. The problem is: it can not be both, it can only be one or the other.

My best guess is that it is Length Contraction. Time Dilation is a function of behavior of clocks and is caused by Length Contraction. See also Time and Clocks

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Created: 17 December 2000