Michelson-Morley Experiment: Unveiling the Invariance of Light Revision Notes | A Level AQA Physics

1. The Problem That Shook Physics

By the late 19th century, physicists had a problem they could not ignore. Maxwell had shown that light is an electromagnetic wave — but every wave they knew of needed a medium to travel through. Sound needs air. Water waves need water. So what does light travel through in the vacuum of space?

The answer physicists proposed was the aether: an invisible, massless medium filling all of space. If the aether existed, then Earth — moving through it on its orbit around the Sun — should experience an 'aether wind', much like a cyclist feels wind even on a calm day. That wind, they reasoned, should affect the measured speed of light in different directions.

This was not idle speculation. It was a testable prediction. In 1887, Albert Michelson and Edward Morley built an extraordinarily precise instrument to detect exactly that effect. What they found — or rather, what they failed to find — changed physics permanently.

2. The Principle of the Michelson-Morley Interferometer

Picture a beam of light hitting a half-silvered mirror — a beam-splitter — set at 45° to the incoming light. Half the light passes straight through; the other half reflects at 90°. You now have two beams travelling along perpendicular arms of equal length. Each beam hits a fully reflecting mirror at the end of its arm, bounces back, and the two beams recombine at the beam-splitter.

When the two beams recombine, they interfere. If they arrive perfectly in phase, you see a bright fringe; if they arrive out of phase, you see a dark fringe. The key insight is this: any difference in the time taken to travel along the two arms will shift the interference pattern. Even a tiny time difference — far smaller than a human could measure directly — produces a visible fringe shift.

To maximise sensitivity, Michelson and Morley mounted the entire apparatus on a massive stone slab floating in a pool of mercury, so it could be rotated smoothly without vibration. They used multiple reflections to extend the effective arm length to about 11 metres. The apparatus was sensitive enough to detect a fringe shift of just 0.01 of a fringe — yet the predicted shift from Earth's orbital velocity was around 0.4 of a fringe. The instrument was more than capable of detecting the effect, if it existed.

3. Detecting Absolute Motion: The Experimental Design

Here is the logic of the experiment. If the aether exists and Earth moves through it at velocity $v$ (approximately $3.0 \times 10^4$ m/s due to Earth's orbital speed), then light travelling along the direction of Earth's motion should be partially 'fighting' the aether wind on the way out and 'aided' by it on the way back — or vice versa. Light travelling perpendicular to Earth's motion would be affected differently.

Using classical wave mechanics, the predicted round-trip time for light along the arm parallel to the aether wind is slightly longer than for the perpendicular arm. The difference is tiny — proportional to $(v/c)^2$ — but the interferometer was sensitive enough to detect it. Rotating the apparatus by 90° should swap which arm is parallel and which is perpendicular, causing the fringe pattern to shift by a predictable amount.

Worked example: Estimating the Expected Fringe Shift

Using the Michelson-Morley apparatus with effective arm length $L = 11$ m, light of wavelength $\lambda = 590 \times 10^{-9}$ m, and Earth's orbital speed $v = 3.0 \times 10^4$ m/s, estimate the expected fringe shift $\Delta n$.

1. $\Delta n \approx \dfrac{2L}{\lambda} \left(\dfrac{v}{c}\right)^2$ — This is the classical prediction for the fringe shift when the interferometer is rotated 90°.
2. $\dfrac{v}{c} = \dfrac{3.0 \times 10^4}{3.0 \times 10^8} = 1.0 \times 10^{-4}$, so $\left(\dfrac{v}{c}\right)^2 = (1.0 \times 10^{-4}) \times (1.0 \times 10^{-4}) = 1.0 \times 10^{-8}$ — Earth's orbital speed is about ten-thousandth of the speed of light. Squaring makes the ratio very small — this is why the effect is so hard to detect.
3. $\dfrac{2L}{\lambda} = \dfrac{2 \times 11}{590 \times 10^{-9}} = \dfrac{22}{590 \times 10^{-9}} \approx 3.73 \times 10^{7}$ — This large prefactor amplifies the tiny $(v/c)^2$ ratio enough to produce a detectable fringe shift.
4. $\Delta n \approx 3.73 \times 10^{7} \times 1.0 \times 10^{-8} \approx 0.37$ — The predicted shift is roughly 0.37 of a fringe — well above the instrument's detection threshold of 0.01 fringes. The experiment should have seen this shift clearly.
5. Observed fringe shift $\approx 0.01$ fringes (consistent with zero within experimental uncertainty) — The observed shift was at least 40 times smaller than predicted. This null result was not a measurement failure — it was a profound physical discovery.

Answer: Predicted fringe shift $\approx 0.37$ fringes; observed shift $\approx 0.01$ fringes. The experiment found no evidence of the aether wind.

4. The Null Result and Its Significance

When Michelson and Morley rotated their apparatus, the fringe pattern did not shift by the predicted amount. It barely shifted at all. They repeated the experiment at different times of day and different times of year — in case Earth's velocity relative to the aether happened to be zero at one particular moment — and still found nothing. The aether wind was undetectable.

This was not a minor anomaly to be quietly filed away. The entire framework of 19th-century wave physics rested on the aether. If light is a wave and there is no medium, what is waving? The null result forced physicists to confront a deeply uncomfortable conclusion: there is no preferred reference frame for the propagation of light. The concept of absolute motion — motion measured against the fixed aether — had no experimental support.

Several attempts were made to rescue the aether hypothesis. Fitzgerald and Lorentz independently proposed that objects moving through the aether physically contract along the direction of motion by exactly the right amount to cancel the expected fringe shift — the Lorentz-Fitzgerald contraction. This was mathematically consistent but felt deeply ad hoc: a hypothesis invented purely to explain away an inconvenient result, with no independent evidence.

The deeper implication took time to crystallise. If no experiment can detect absolute motion through the aether, perhaps absolute motion is not a physically meaningful concept at all. This is the idea that Einstein formalised in 1905 with his special theory of relativity — but the Michelson-Morley experiment was the experimental foundation that made the old framework untenable.

5. The Invariance of the Speed of Light

The Michelson-Morley result pointed towards a radical conclusion: the speed of light is the same in all directions, regardless of Earth's motion. Einstein elevated this from an experimental observation to a fundamental postulate. The speed of light in a vacuum, $c = 3.0 \times 10^8$ m/s, is invariant — it is the same for all inertial observers, regardless of their velocity or the velocity of the light source.

To appreciate why this is so startling, consider how velocities add in everyday life. If you throw a ball at 10 m/s from a train moving at 30 m/s, someone on the platform measures the ball's speed as 40 m/s. Classical physics — Galilean relativity — says velocities add. Apply the same logic to light: if Earth moves at $v$ towards a distant star, you might expect to measure the star's light arriving at $c + v$. The Michelson-Morley experiment showed this does not happen. The measured speed of light is $c$, always.

This invariance has profound consequences. If $c$ is fixed for all observers but distance and time can vary, then time and space themselves must be flexible — leading directly to time dilation and length contraction. The Michelson-Morley experiment did not just disprove the aether; it was the first experimental signal that Newtonian mechanics needed to be replaced at high velocities.

6. Comparing Classical and Relativistic Expectations

It is worth being precise about what classical physics predicted versus what was observed, because examiners frequently ask you to compare these two positions directly.

The table makes the contrast stark. Every classical prediction was falsified. The experiment was not ambiguous — the sensitivity was sufficient, the methodology was sound, and the result was replicated. The aether model was not merely unsupported; it was contradicted.

7. Exam Technique and Mark-Winning Guidance

Questions on the Michelson-Morley experiment tend to fall into a small number of patterns. Recognising them early lets you structure your answer efficiently and collect every available mark.

When asked to describe the principle of the interferometer, you need three elements: the beam-splitter divides light into two perpendicular beams; each beam reflects from a mirror and returns; the beams recombine to form an interference pattern. A fringe shift indicates a path difference, which would indicate different travel times, which would indicate different speeds of light in different directions. Examiners want this chain of reasoning, not a vague statement about 'interference'.

When asked to explain the significance of the null result, the key phrase to use is 'no evidence for absolute motion' or 'no evidence for the aether'. Do not say the experiment 'proved the aether does not exist' — absence of evidence is not proof of absence, and examiners at A-level will penalise overclaiming. The correct framing is that the result is inconsistent with the aether hypothesis and supports the invariance of the speed of light.

The Michelson-Morley experiment stands as one of the most important null results in the history of science. A null result — finding nothing where something was expected — can be just as informative as a positive detection, provided the experiment was sensitive enough to have found the effect if it existed. Here, the sensitivity was unambiguous. The absence of a fringe shift was not silence; it was a clear message that the aether model was wrong and that something more fundamental governed the behaviour of light.

That something more fundamental is the invariance of the speed of light: the single experimental pillar on which Einstein's special relativity rests. Every consequence of special relativity — time dilation, length contraction, mass-energy equivalence — follows from taking seriously what Michelson and Morley measured in 1887. The experiment did not merely close a chapter on the aether; it opened the entire field of modern physics.