The Michelson-Morley Experiment (1887)

 The Michelson-Morley Experiment (1887) 

The Michelson-Morley Experiment of 1887 is one of the most famous and important experiments in the history of science. It was carried out by Albert A. Michelson and Edward W. Morley in an attempt to detect the existence of something called the "luminiferous aether." The aether was believed to be a substance that filled all of space, and it was thought to be the medium through which light waves travel, similar to how sound waves travel through air.

Background and Hypothesis

Before the Michelson-Morley experiment, scientists believed that light, being a wave, must travel through a medium, just as sound waves travel through air or water. This hypothetical medium was called the luminiferous aether. The idea was that the Earth moves through this aether as it orbits the sun, and this motion should cause changes in the speed of light, depending on the direction of the Earth's motion relative to the aether.

In simple terms, imagine running in the wind. If you run in the same direction as the wind, you feel less resistance, and if you run against the wind, you feel more resistance. Scientists thought that light should behave in a similar way when the Earth moves through the aether. If the Earth were moving in the direction of the aether, the speed of light should be faster. If the Earth were moving against it, the speed of light should be slower.

This experiment was designed to test whether the speed of light changes depending on the Earth's motion through the aether.

The Experiment Setup

Michelson and Morley used an interferometer, a device designed to split a beam of light into two separate beams, reflect them off mirrors, and then recombine them. If the aether existed, the motion of the Earth through it would cause one of the light beams to travel faster than the other, resulting in a change in the time it takes the beams to recombine, and creating an interference pattern—a visible change in the waves' alignment.

Steps in the experiment:

1. Light Split: A beam of light was split into two perpendicular beams by a beam splitter.
2. Beams Travel: Each beam traveled in different directions: one in the direction of Earth's motion (through the supposed aether) and one perpendicular to it.
3. Beams Recombine: The two beams were reflected back to the point where they originally split, recombining them.
4. Interference Pattern: If the speed of light differed between the two directions (due to the Earth's motion through the aether), the recombined beams would create an interference pattern, which would be visible as a shift in the light waves.

The Null Result

To their surprise, Michelson and Morley observed no difference in the speed of light in any direction, regardless of how the apparatus was rotated. This result was a null result, meaning that the experiment failed to detect the aether. The speed of light was the same in all directions.

This was a groundbreaking discovery because it suggested that there was no aether at all! The idea that light needed a medium (like aether) to travel through space was wrong. The speed of light is constant, no matter what direction you're moving in.

Mathematical Explanation

The Michelson-Morley experiment can be described using the principles of wave interference and the expected time difference between light beams traveling different paths.

Let’s take a simplified example:

• c = speed of light
• v = velocity of the Earth relative to the supposed aether

For the light beam moving in the direction of the Earth's motion, the time taken (t₁) can be approximated as:

$$t₁ = \frac{L}{c - v} + \frac{L}{c + v}$$

where L is the distance traveled by the light beam in each direction. This formula represents the time it takes for the light to travel in the direction of the Earth's motion (with the aether), and then back in the opposite direction (against the aether).

For the perpendicular beam, the time (t₂) is:

$$t₂ = \frac{2L}{\sqrt{c^2 - v^2}}$$

This is because the light is moving perpendicular to the Earth's motion, and Pythagoras' theorem applies to the beam's motion.

According to this hypothesis, if the Earth is moving through the aether, there should be a time difference between t₁ and t₂, which should result in an interference pattern. However, Michelson and Morley found no time difference—the light beams recombined without showing any interference pattern.

The Importance of the Null Result

This experiment was revolutionary because it showed that the speed of light is constant in all directions, regardless of the observer's motion. This result shook the foundations of physics because it contradicted the aether theory, which had been widely accepted for many years.

Later, Albert Einstein used this result as one of the key pieces of evidence for his theory of special relativity (1905). Einstein's theory showed that the speed of light is the same for all observers, regardless of their motion, and that time and space are not absolute but relative.

Fun Facts and Curiosities

• Michelson was the first American scientist to win a Nobel Prize in 1907 for his work on the measurement of light.
• The experiment was so precise that its failure to detect the aether surprised even Michelson and Morley. They repeated the experiment multiple times, each time improving the accuracy, but still found no difference in the speed of light.
• The Michelson-Morley experiment is considered a major stepping stone to modern physics and the development of quantum mechanics and general relativity.
• The interferometer Michelson and Morley used is still an essential tool in modern physics. For example, a similar device was used in the LIGO experiment to detect gravitational waves in 2015.

Hypotheses and Theories After the Experiment

Many scientists attempted to explain the null result before Einstein's theory of relativity. Some of these hypotheses include:

1. Lorentz-FitzGerald Contraction Hypothesis: Hendrik Lorentz and George FitzGerald suggested that objects contract in the direction of motion through the aether, which could explain why no interference pattern was seen. This contraction would compensate for the expected change in the speed of light.

2. Stokes-Drag Hypothesis: Another theory proposed that the aether might be "dragged" along with the Earth, meaning the Earth and the aether move together, preventing any relative motion between them.

However, these explanations were eventually replaced by Einstein's special theory of relativity, which explained that the speed of light is always constant, and there is no need for the concept of aether.

Conclusion

The Michelson-Morley experiment was a crucial experiment in the history of physics that led to the downfall of the aether theory and paved the way for modern physics, including Einstein’s theory of special relativity. The experiment demonstrated that the speed of light is constant and independent of the motion of the observer, which changed our understanding of space and time forever.

References:

• Michelson, A.A., & Morley, E.W. (1887). On the Relative Motion of the Earth and the Luminiferous Ether. American Journal of Science.
• Einstein, A. (1905). On the Electrodynamics of Moving Bodies. Annalen der Physik.
• Lorentz, H.A. (1899). Electromagnetic Phenomena in a System Moving with Any Velocity Less Than That of Light.