The Implications of The Michelson-Morley's Experiment on the behavior of Light.

Like I promised in my last post, that I shall be discussing more on the Michelson-Morley's experiment on light behavior and some other interesting parts of Einstein’s theories. So, let's start by getting to know what the experiment is all about.

^{Luminiferous Aether
Source: Wikimedia, Cronholm144; CC BY-SA 3.0}

The Michelson-Morley Experiment

It appeared evident in the late 19th century that, if light were to be a wave, then there must be a method to conveying it. Scientists had the notion that, since light traversed through the vacuum of space, a vacuum should exhibit at least some of the characteristics of a material. Just like we know that sound waves are transmitted by air, so light waves were believed to be disturbances in what was called a light producing aether filling all space and matter in the Universe. Light and all bodies were believed to travel through it.

In the beginning of 1880, an American Physicist and naval officer Albert Michelson conducted some experiments to determine the speed of the Earth using the aether. He was encountered by a lot of difficulties than he anticipated. In the course of that, he relocated to the University of Cleveland in Ohio and was joined by chemistry Professor Edward Morley.

It was concluded by the two scientists that light travels at a constant speed c in the aether. Their intention was to measure how fast the Earth is as it moved through the aether, as compared to the speed of light. If, for instance, the Earth was going through the aether in the same direction as that of the light beam of their experiment. Then they felt that the light should seem to be travelling slower than c as a result of Doppler Effect.

Let’s imagine a road and take it as the aether having a cyclist (which is assumed as the Earth) moving along it. A car (which is assumed as the light) travelling at steady speed drives up from behind the cyclist and gets very close to it. The car will get nearer and drive away from the cyclist at a speed slower than its real speed. So when the Earth moves at speed v in the same direction as a beam of light, Michelson and Morley anticipated a light speed of less than c, namely (c-v). And a light beam moving in the opposite direction should have a speed of (c+v).

^{Expected differential phase shift between light traveling the longitudinal versus the transverse arms of the Michelson–Morley apparatus.
Source: Stigmatella aurantiaca at English Wikipedia; CC BY-SA 3.0}

Since Michelson and Morley did not know the direction with which the Earth was travelling through the aether, so, they had to arrange their apparatus to calculate light speeds coming from different directions. Since it was observed that every 6 months the Earth’s direction changes by 180°, they also expected that any change of the Earth’s direction relative to this aether would also have an effect on their light-speed measurements. The apparatus they used is called an interferometer.

Basically, the two scientists measured the time it would take for light to move along a pair of equal sized arms placed perpendicular to each other. If at a particular time the Earth was stationary relative to the aether, beam 1 and beam 2 would take the same time to cover the equal distances. But if the Earth in its orbit then traveled through the aether in the direction of one of the arms, the researchers thought that normally the time taken would be different for the two light beams.

Michelson and Morley measured time in a very advanced way for more than hundred years ago in terms of the number of complete waves made by the light along each arm and detected as an interference sample at the screen. The light was monochromatic and therefore of unwavering and stable frequency and wavelength. So, when the interferometer was rotated by 90 degrees, if light took much time to move along one arm than before rotation, the number of waves would be enormous in that direction. The apparatus was so sensitive and responsive enough to detect a time gap equal to one-hundredth of the time period of a wavelength.

^{Michelson's 1881 interferometer.
Source: Wikimedia, Albert Abraham Michelson; public domain}

They were anticipating to detecting a time difference of close to four-hundredths of t, calculated from the investigated speed of the Earth in its orbit. Michelson and Morley determined the value of ΔT by swinging the whole apparatus through 90 degrees, so swapping one arm for the other. They expected this to cause the interference pattern to change by moving the fringes sideways by an amount equal to a path difference due to a time difference twice ΔT:

A simple account of the mathematics they used is summarized below:

The formula for Time difference is given as: ΔT = Lv²/c³, where L is the length of the beam in metres, v is the speed of earth and c is the speed of light. But, Path difference = c × 2ΔT Which corresponds to a shift of n fringes such that: Path difference = nλ = 2cΔT So that: n = 2cΔT/λ = 2Lv²/λc²

But after numerous experiments that were carried out, it was observed that there was no difference (no matter how minute it was) between sets of results: there was always a null result compared with the aether, the Earth occurred to be not moving- even when it swung to the other side of the Sun and was moving in the opposite direction.

This null result that was finally established in 1887 opened the way to the theory that electrical forces (i.e those associated with the electromagnetic waves of light) will reduce any object when it travels through the aether. This was the famous Lorentz - Fitzgerald contraction theory: it explained the result but still led nowhere.

^{Michelson-Morley's Experiment
Source: Wikimedia,Benjamin D. Esham; public domain}

Then in 1905, Einstein, who probably was not aware of Michelson and Morley’s research, proposed a much more fundamental theory based on two basic assumptions about the nature of physics and of light. Not only did it simplified the null result, it also forecasted the other ‘relativistic’ effects that had not then been detected.

EINSTEIN’S THEORY

Albert Einstein created the theory that unraveled the null results of the Michelson-Morley experiment. The Lorentz-FizGerald theory was seriously deficient since it was originated to describe a single effect. Einstein created a formula for contraction, which was unbelievable at first, with a straightforward presumption about the constancy of the speed of light.

Einstein’s two assumptions

Einstein put into consideration the nature of light and the fact that it was an electromagnetic effect. His theory was based on two simple assumptions otherwise ‘postulates’:
• Physical laws such as mechanical, electromagnetic and optical are the same in all uniformly moving reference frame.
• The speed of light in a vacuum is identical for all observers, in all uniformly moving reference frame.

To refreshes our memory, a frame of reference can be anything such as set of objects like desk, chairs, computer or even your pen that happen to be at rest relative to you. You and these things could well be moving with respect to other objects. Let’s assume you are performing an experiment in an aircraft or a train. Someone else that’s also performing an experiment in another train moving past you would be in a different reference frame. If the relative motions of your frames are at a steady velocity, they are called inertial frames i.e frames in which things that are in motion remain in motion at the same velocity and things that are stationary also remain at that position.

We can call Reference frames inertial frames when they are not accelerating in a straight line or rotating. In these type of frames Newtonian relationships like F = ma apply simply, whereas in rotating frames we experience imaginary forces like centrifugal and Coriolis forces.

TIME DILATION

The first and unexpected result of Einstein’s principle of relativity is time dilation. This means that an operation that takes a certain amount of time to occur in a moving system is noticed to take a longer time by someone outside that system than by someone moving with the system. For example, an observer outside the system could see a clock in a moving train move its second hand, say, 15 secs, and also see that this took 16 seconds measured by his own watch. Meanwhile, an observer in the moving system would also see that while his watch counted 16 seconds, the outsider’s watch changed by 15 seconds, Both would say that the other person’s watch counted seconds too slowly. The situation is proportional. Either could say that the other is moving but neither has the right to proclaim that they are stationary relative to the universe.

A mathematical proof of time dilation is easy and needs no more than an understanding that distance = speed x time, and a knowledge of Pythagoras’ theorem. Other proofs use even less mathematics. Though, there are two complexities: one is accepting the final consequence, the other is in creating a scheme in which time dilation is essential. In his well received explanations, Einstein used the situation of a moving train being struck by lightning, with the guard on the train and the station master some distances away arguing about exactly when the strike occurred – hardly the first thing either would worry about under the circumstances!

We shall imagine a scene such as a thought experiment that would be more common nowadays: a measurement made by astronauts in ‘deep space’. The mistake to avoid here is to think that relativity only works in the outer space, and is only of importance to astronauts. Instead, have in mind that one of the consequences of relativity and time dilation is the equivalence of mass and energy. According to the well-known formula E = mc². This relationship describes the source of the energy that powers stars – and so makes life possible on Earth.

Back to our scenario: a large, strange, deserted spacecraft is found in space and is boarded by an astronaut, Alpha, who is given the task of measuring its internal dimensions. He does this using an infrared gun, which measures distance A in terms of the time taken for an infrared pulse to go to and from an internal wall. As Alpha does this, his twin, Beta, sees him through the window of a scout vehicle from the space station where they both work. She decides to check the measurements which he has radioed in. Beta is doubtful: measuring with the same kind of infrared gun, she does not agree that the pulse travelled through space.

When Alpha and Beta return to the space station. Beta tells Alpha that, as the spacecraft was moving, the pulse actually travelled a greater distance than 2A, along two sides of a triangle. She suspects that there is something wrong with Alpha’s timing system. Alpha points out that his infrared gun is exactly the same as Beta’s. They check them by measuring the same distance inside the space station, and the results agree. Alpha also asserts that the deserted aircraft was actually at rest, and it was the scout vehicle that was doing the moving. Therefore, when Beta measured the distance the window, her infrared pulse followed the longer path so that her timing is wrong. They argue indefinitely.

^{Time dilation
Source: Wikimedia, Sacamol; CC BY-SA 4.0}

At this stage their supervisor points out that neither could claim to be at rest because there is no third fixed point to which they could refer. Either viewpoint could be true or both could in fact be moving. There is no physical process or measurement that could decide between these possibilities.

He then delivers a long lecture about the Michelson-Morley and shows that both Alpha and Beta can agree, provided that in each situation the measuring pulse travels at the same speed through space, irrespective of the motion of the transmitter or another observer. All these resulted in the effect known as time dilation. It is a consequence of the fixed and unvarying speed of light, and the result applies to any time interval Δt’ that was measured, using our clocks, for a process taking a time Δt in a body moving at a speed v relative to us. The process could be a pendulum swinging, a muon decaying or a light wave oscillating.

The quantity: (1-v²/c²)^-1/2 is called the Lorentz factor.

It is awkward to write but it keeps turning up in relativistic expressions, so it is often written as γ, so that the time dilation effect becomes Δt = γΔt’.

SOME OF THE EVIDENCE FOR TIME DILATION

• Detecting Muons
Early experiments investigating new subatomic particles of matter used the debris formed when high speed particles called cosmic rays collided with the nuclei of atoms high in the atmosphere. In these debris were to be found particles called muons. Like I wrote in one of my previous posts, Muons are unstable and decay with a half-life of very few microseconds. They were detected by balloon flight experiments at a height of about 2 km above a high mountain observatory. But 80 per cent were still detected at the observatory.

The muons are moving at a speed of 0.996c and would take 6.7 microseconds to travel 2km, which is about 3 half-lives. This means that we would expect the muon flux to have decreased by one eighth to 12%. The explanation for the ‘extra’ muons observed is time dilation, which means that the half-life is increased by the factor γ. At this speed γ = 11.2, so the muons’ half-life in the observatory’s frame of reference becomes 24 microseconds. Therefore the time of night from balloon to observatory is about one third of a half-life and only about 20% of the muons decay in this time.

• Time Dilation leads to Length Contraction
A Cosmic scientist travelling with the muons as highlighted above could measure their progress by using the same kind of calculation. His measurement of the time from balloon to observatory would be:

‘our time’ divided by γ, i.e (6.7/11.2) = 0.6 microseconds.

At a speed of 0.996c the distance travelled is:

0.6 microseconds × 0.996c = 180 metres.

^{Graphical representation using a spacetime diagram of Einstein's 1911 thought experiment on length contraction.
Source: Wikimedia, D.H; CC BY-SA 3.0}

So for the moving object the distance in our atmosphere looks much shorter than we see it to be. In another scenario, if a 2000 m long spaceship approached us at this kind of speed it would look to us to be 180 m long. We know that it is all relative. These results reinforce the fact that time and space (distance) are interdependent

More formally, in this example we can extend the relationship:

Δt’ = γΔt: Time measured by us = γ × muon time

To relate the distances involved. Within a reference frame distance travelled is proportional to time, so that we can write:

x₀/x = Δt’/Δt = γ

Here x₀ is the distance between the balloon and the observatory in our frame and x is the distance as measured by the physicist travelling with the muons. In general, a length x in one frame (e.g, the length of a moving object such as a spaceship as seen by us on Earth) measured from another frame, the length being in the same direction as the relative velocity v, is given by:

x = x₀/γ OR x = x₀(1-v²/c²)^1/2

Where x₀ is the length as measured in the object’s own frame (e.g. the length of the spaceship as the occupants would measure it). Note that when the object is moving with respect to us we see it to be shorter, so to get our observed value x we divide by γ, which is always greater than 1. This always means a Length Contraction, otherwise known as the Lorentz-FitzGerald contraction.

Till next time, I remain my humble self, @emperorhassy.

Thanks for reading.

REFERENCES

^{The results of the Michelson-Morley experiment}

^{Relativity abyss.uoregon.edu › lectures › lec06}

^{Einstein's Theory of General Relativity}

^{Michelson-Morley experiment}

^{How did Einstein come to know that the speed of light is constant in space}

^Spacetime

^{Space-Time - Special and General Relativity}

^{Space-time physics}

^{Collins Advanced Physics by Ken Dobson, David Grace and David Lovett, Chapt. 23 pg 456}

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