﻿ The Michelson Interferometer

7: THE  MICHELSON  INTERFEROMETER

Michelson's goal was to detect the phase shift shown on the left.

However, there is no phase shift because the interferometer contracts.

A GREAT IDEA

 In 1887, Albert A. Michelson tried to detect the speed of the Earth through the aether by means of an interferometer. But his apparatus revealed nothing. It was a "failure". Actually, this experiment led to a fantastic scientific discovery: the Lorentz transformations and the theory of Relativity. A race between two planes. Michelson explained to his children that his interferometer reproduces a race on a river between two swimmers. In 1887 planes did not exist. Otherwise, he would certainly have spoken about a plane race while a strong wind is blowing. Let us consider two identical airplanes whose constant speed is 100 mph and suppose that the wind is blowing at 50 mph. Then the beta normalized speed is given by v / c = 50 / 100 = .5. According to the rules, both pilots must perform a round trip between two points 100 miles apart. The first pilot prefers to fly in the direction of the wind. But the second one chooses the transverse route and surprisingly, he easily wins the race. The point is that those planes behave exactly like the light waves. It is all about the Doppler effect. Their speed may be compared to the speed of light, and one may consider that there is an aether wind because the emitter is moving.

The Michelson interferometer works like a race between two planes.

 Let's make it simple. The relative speed on a go and return trip is given by Lorentz's contraction factor g, which is the reciprocal of the gamma factor. In this example, beta = .5 and g = .866: Then the relative speed on a round trip is:  Along the wind :  g2 c          g2 = .75 c          75 mph Across the wind :  g c          g = .866 c          86.6 mph Across the wind, planes (or waves) will be tilted to 30° according to the theta angle: theta = arc sin (beta) In the absence of wind, the round trip would last 2 hours whatever the direction. However, in the presence of wind, the duration increases more severely in the direction of the wind according to g squared instead of g in the transverse direction. 1 - The round-trip duration along the wind:  2 hours / g2 = 2.6667 hours. 2 - The round-trip duration across the wind :  2 hours / g = 2.3094 hours. So the plane flying across the wind will be: .357 hour = 21 minutes faster and the plane flying along the wind will be defeated. However, George F. FitzGerald and Hendrick Lorentz noted after Michelson's experiment that a shorter circuit on the displacement axis would cancel the difference. On condition that there is no transverse contraction, the interferometer must contract in accordance with  Lorentz's contraction factor. This is only one of the Lorentz transformations because there is also a time effect: The Lorentz transformations. This equation set was simplified by Henri Poincaré thanks to beta and g. Please note that x stands for distance to origin in the contracted moving frame of reference. So it is smaller than x'. This was almost never pointed out.      The Michelson transformations. Prior to the Lorentz transformations, Michelson discovered a mechanical property of waves when they are observed in a moving frame of reference. This could be called the Michelson transformations but it is more simply the regular Doppler effect. A wavelength contraction according to g occurs on both transverse y and z axes, but a more severe one according to g squared can be observed along the motion x axis. x'  =  (x – beta * t)  / g 2 y'  =  y / g        z'  =  z / g t'  =  t + beta * x According to our example, planes flying inside such an x, y and z contracted space would always perform the round trip in two hours whatever the speed of the wind or its direction. This explains why no abnormal time effect occurs. So the main difference here is the time effect because both points of view lead to a null result. Galileo's transformation. Galileo's transformation is more simply a uniform translation motion. There is no transverse contraction and the time is the same everywhere. x'  =  x – beta * t y'  =  y        z'  =  z t' = t Here too, x is the coordinate in the moving frame of reference. Thus:  x = x' + beta * t. This was Galileo's point of view. However, according to Descartes, the x position should definitely refer to the Cartesian frame of reference, which is postulated to be at rest. After a given t time, because the rightward motion is a well admitted convention, this procedure creates an artificial secondary moving frame of reference. As a matter of fact, according to Descartes, the light propagates by means of the aether, which is postulated to be at rest. So the aether is not only a preferred frame of reference, it is the only admissible Cartesian frame of reference. This should lead to this inversion:  x' = x + beta * t. But let us be honest: inside the moving frame of reference, the light traveling forward clearly propagates slower and the Doppler effect should be considered. The equation works for moving objects to a first approximation, but what if matter is made of waves?  One should bear in mind that Galileo's transformation is wrong because matter actually transforms according to the Lorentz transformations. Matter especially cannot reach the speed of light for this reason. A race between two waves. Michelson noticed that the relative speed of light on a go and return trip is slower in the direction of motion. He realized that two orthogonal light beams could not produce the same interference fringes after a 90° rotation. He deduced from this that an interferometer could detect the speed of the aether wind. Here is a diagram showing Michelson's apparatus:

The Michelson interferometer.

 Only one half of the light beam emitted by the source is reflected by means of a beam splitter containing a 45° partially reflecting mirror. Then the beams are reflected on a flat mirror back to the beam splitter, which then reunifies them.   Finally, both beams could be compared in a special scope. Michelson was expecting a phase shift. Waves would add themselves constructively or destructively, showing a characteristic interference pattern. The goal was to measure the fringes displacement after a 90° rotation. Such a rotation could be performed easily without any stress because the instrument was mounted on a large stone floating on a mercury pond. The temperature was also severely controlled. The Michelson interferometer animated diagrams. The animations below show what is going on inside the interferometer branches. I had to use a very high speed in order to obtain a clearly visible phase shift: one third of the speed of light. Then beta = .3333  and g = .9428. Such a speed produces a 2 : 1 wavelength ratio R along the displacement axis, according to:  R  =  (1 + beta) / (1 – beta) This ratio indicates that on-axis planes crossing the starting point each minute, one at a time, would be two times nearer while flying against the wind. So one can imagine that each small red or green line shown below represents a plane. The aether wind blows from the right.  The diagram on the left displays exactly the same length for both branches. This distance was calculated to obtain a full lambda / 2 phase shift. The wave fronts (or planes) along the motion axis are pictured in red and they are green crosswise. Michelson was expecting the phase shift shown on the left:

The contraction cancels the relative speed difference.

The Doppler effect.

STANDING  WAVE  CONTRACTION

beta = 0      g = 1      Standard standing waves. No contraction.

Mr. Yuri Ivanov's "Lively standing waves" showing nodes and antinodes motion and contraction.

beta = .5      g = .866      Same frequency, contraction to 75%  according to g 2.

Here, the observer is at rest with respect to the wave medium.

beta = .5      g = .866      Same frequency, contraction to 75%  according to g 2.

Here, the observer is moving with the system's frame of reference.

beta = .707      g = .707      Same frequency, contraction to 50% according to g 2.

 The Michelson interferometer undergoes a length contraction in the direction of motion according to Lorentz's contraction factor.

THE LIGHT BEAM LENGTH

 The animated diagrams shown above indicate that for one third of the speed of light, the interferometer arm length must be about 4 wavelengths in order to obtain the phase opposition. This length must be greater for smaller speeds. So Michelson had to build a very large interferometer. Michelson's calculus was rather complex because he considered the relative speed of light. One can more easily obtain the same length using the standing wave compression method. Theoretically, the calculus must take the slower frequency into account. So, in the absence of contraction, the formula for obtaining two beams in phase opposition using the computer should be: According to the absolute wavelength at rest:   L  =  lambda / 4 g (1 – g) However, Michelson was unaware of the Lorentz transformations, hence the slower frequency. But surprisingly, his measurements for the yellow light wavelength would remain unchanged at any speed. Because the frequency does change, the formula above simplifies to: L  = lambda / 4 ( 1 – g ) Example. Let us suppose a g = .9 contraction. Then  beta = .4359 and 1 – g = .1. The formula yields 2.5 wavelengths, or 5 half-wavelengths. The plane mirror produces standing waves and the distance between two nodes is one half of a wavelength. The goal is to make a node coincide with the nearest antinode. One may add that, from Michelson's point of view, moving the mirror only a quarter of a wavelength produces a full phase opposition because of the go and return trip.  So only a quarter of a wavelength difference is needed: If g = .9, the first phase opposition occurs for 5 half-wavelengths.     The worst of scenarios. The speed of the sun through galaxies all around us has been estimated to be about 300 km/sec. It could be its absolute speed through the aether, but it could also be much faster. If beta is 300 / 300 000 = .001 the Lorentz contraction factor is .9999995 and the formula yields 500,000 wavelengths. So 500,000 times .0006 (yellow light) is 300 mm or 30 cm (about one foot). This suggests that a one foot tall interferometer should be enough in most cases. However, Michelson preferred to play safe. The sun being perfectly at rest, which is highly improbable, the speed of the Earth would still be 29 km/sec (about 18 miles per second). So he preferred a rather large interferometer according to the following values: beta = .0000966667 g = .9999999953 lambda = .0006 mm yellow light. The formula indicates 1 / 4 (1 – g) = 53,419,000 times the wavelength. So the arm length should be 32,000 mm or 32 meters (105 feet) in order to detect the Earth's minimum 29 km/s speed through aether. Michelson added many mirrors in order to elongate the total light trip.  The arm length for the 1887 experiment was 11 meters (36 feet). This should have been enough because one does not really need a full half-wavelength phase shift. Edward W. Morley tried again in 1902 with a longer 32 meters (105 feet) interferometer and the null result was confirmed.

THE  KENNEDY-THORNDYKE  EXPERIMENT  WAS A  MESS

 Believe it or not, the second arm is useless. It can be omitted like this:

A simpler interferometer.

 Planes can be identified, but waves must be compared because they are all identical. The comparison does not produce an immediate result and Michelson had to rotate the apparatus in order to observe the difference in the interference fringes. So the length for the shorter arm is optional because it is used only as a reference.  This is not what Kennedy and Thorndyke thought. They claimed that different lengths would reveal the aether wind in spite of the contraction. So, because the Kennedy-Thorndyke experiment still ended with a null result, scientists deduced from it that aether does not exist. This is weird: believe it or not, nobody could correctly calculate this in accordance with the Lorentz transformations! It should be pointed out that the Lorentz transformations do not solely involve a contraction. The time equation also predicts that any periodic phenomenon should be slowed down in accordance with Lorentz's contraction factor. This means that the basic wavelength becomes longer. Then, whatever the shorter arm length, the correct length formula for the longer one remains: L  =  lambda / 4 (1 – g) Quite simply, because it is made of standing waves, matter must contract exactly the way its standing waves do. The consequence is that any length yields a null result. Today, scientists still think that the Kennedy-Thorndyke experiment ruled out matter contraction. Once again, this is totally false. Clearly, Kennedy and Thorndyke were wrong.

LORENTZ'S  ANGULAR  ABERRATION

 Some authors noticed that the 45° angle for the beam splitter cannot be constant because of the Lorentz transformations. Any contraction would cause it to be tilted in accordance with: arc tan (1 / g). Then, because of the well known opticians' equal angle law, the beam could not be reflected along the orthogonal axis according to a 90° angle any more. The truth is that this equal angle law is false inside a moving frame of reference. Lorentz himself discovered that a special "angular aberration" should occur. So he wrote to Michelson, who agreed and changed his calculus. Lorentz probably applied Huygens' Principle, which postulates that any wave can be seen as billions of "wavelets". Huygens' Principle. This web site does explain light by such wavelets, but this detail is not relevant here. However, one must admit that those wavelets should be spherical. Obviously, their center of curvature should remain at rest inside the aether. Lorentz noticed that any abnormal deviation could invalidate Michelson's calculus. Some authors are misleading because they speak about Bradley's stellar aberration. This phenomenon occurs when the emitter and the receptor speed is not the same. The aberration is different here because the light source moves at the same speed. One should observe carefully how those wavelets behave in the animation below. According to the Huygens Principle, they reinforce themselves along their common envelope, and this produces a wave front. The absolute speed is half of the speed of light:  beta = 0.5 and g = .866. The mirror angle is increased to: arc tan (1 / g) = 49.1066° because of Lorentz's contraction, but surprisingly the wave front is still deviated according to a 90° angle. The Doppler effect accounts for Lorentz's 30° theta angle. This means that waves traveling crosswise are tilted according to this angle, the same way the planes studied above are.

The 49° mirror angle still produces a 90° deviation.

 Additionally, one can now experiment such phenomena in Philippe Delmotte's amazing Virtual Aether. Using my Ether19 program, I made several mpeg-4 videos showing how the light waves behave in the vicinity of the beam splitter: Those experiences are much better then Michelson's because one can truly see what is going on inside the interferometer. The Virtual Aether shows that Lorentz was right: the angle can no longer be 45° at high speed. But surprisingly an angular aberration occurs which maintains the light beam reflected to a 90° angle. It is absolutely amazing!

On the right, the unchanged 45° mirror angle produces an incorrect reflection angle.

On the left, the contraction according to Lorentz works perfectly.

Note that upward transverse waves are tilted according to the theta angle like the planes shown above.

Moreover, the transverse light beam also contracts according to Lorentz.

Clearly, Lorentz was right!

 The Lorentz transformations are decidedly a fantastic phenomenon. They always prove to be correct. A dramatic argument. So the 45° aberration is no longer an objection. It is rather a spectacular confirmation. On the one hand, the apparatus undergoes a contraction which cancels the waves' speed difference. On the other hand, the beam splitter angle is increased in order to deviate the light beam in the correct direction. Finally, waves arrive in the scope without any phase difference. This explains the null result. Many authors, even sometimes highly respectable and well known scientists, still think that Michelson's experience ruled out aether. Such people are "Panurge's sheep". They studied physics but just memorized and repeated what their professor said. They did not verify. They forgot Descartes' maxim: doubt is the origin of wisdom. "Dubium sapientiae initium"

LORENTZ  WAS  RIGHT

 The interferometer really undergoes a contraction in the direction of motion. Lorentz's explanation was the right one, but nobody believed him. All scientists preferred Poincare's version and Einstein's special theory of Relativity, which predict the same effects but negate the absolute point of view. This was an enormous mistake. There is a mechanical explanation for all phenomena. This includes gravity, light, magnetic and electrostatic fields, nuclear forces, etc. The absolute point of view is important because the goal is to explain what is really going on.

 One must firstly postulate that aether exists and that matter really transforms according to its absolute speed the way Lorentz showed. Then the goal is to establish carefully how a moving observer sees phenomena from his own frame of reference. The result is Lorentz's Relativity.

 Relativity is not complicated. It is not a mysterious theory any more. It is a law of nature. The next pages show that it can be deduced from elementary calculus, especially the Lorentz transformations and the Doppler effect. The main difference from Einstein's concept is that any moving observer is wrong about his situation, while one at rest sees phenomena the way they really occur. The moving observer also thinks that he is at rest because he sees the observer at rest undergoing the Lorentz transformations. Finally, nobody can tell for sure who is really moving. So the main difference is that the one at rest only is right. Einstein postulates that they are both right. His Special Relativity cannot explain the difference between appearances and reality. So it is false. Lorentz's Relativity can predict the same phenomena and it can also explain them. This is an important improvement. Starting from now, scientists can mechanically explain matter and all physical phenomena. The aether thus should be rehabilitated. It was banished wrongfully, and it proves to be essential. Matter transforms the way Lorentz explained. This web site explains matter and all physical phenomena from a mechanical point of view. Our world is made of waves. It is no longer a theory which will be confirmed some day, it is a verifiable fact. In any event, there is at the present time only one logical explanation: The Michelson interferometer really undergoes a contraction. This occurs because matter is made out of standing waves. The aether is essential in order to explain them and also forces such as light, gravity, magnetism, etc. This explains Relativity.

 Gabriel LaFreniere, On the Internet since September 2002. Last update December 3, 2009.