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By the 1870s, the wave theory of light was experimentally established (lesson 2) and Maxwell had identified light as an oscillation of electromagnetic fields propagating at c = 1/√(ε₀μ₀) (lesson 3). One question, however, refused to go away. Every mechanical wave students had ever met — sound, water waves, waves on a string — propagated through a medium. If light is a wave, what is waving? The 19th-century answer was the luminiferous aether: a tenuous, all-pervading medium that filled the space between bodies (and apparently penetrated everything, since light reached us from distant stars through what we now call vacuum). If such a medium existed, the Earth in its orbital motion around the Sun should be moving through it, and the resulting "aether wind" should produce a detectable difference between the speed of light measured parallel to the Earth's motion and the speed measured perpendicular to it. Albert Michelson and Edward Morley, working at Case School of Applied Science in Cleveland, Ohio, built an interferometer designed to detect exactly this difference. Their 1887 experiment — repeated several times over subsequent years and decades, with increasing precision — found nothing. No aether wind. The result was so unexpected and so well-confirmed that within twenty years it had forced a complete rethink of space, time, and motion at the foundation of physics. This lesson covers the conceptual problem the aether was invented to solve, the interferometer apparatus, the expected versus observed result, the failed rescue attempts (Lorentz contraction, FitzGerald), and the road to special relativity (lesson 7).
Spec mapping: This lesson covers AQA 7408 section 3.12.3 — the 19th-century luminiferous aether hypothesis, the Michelson-Morley interferometer experiment, the null result, alternative interpretations (Lorentz-FitzGerald contraction), and the way the result paved the road to special relativity. (Refer to the official AQA specification document for exact wording.)
Synoptic links:
- Section 3.3 (waves) and section 3.12.2 (Maxwell): the aether hypothesis was the 19th century's answer to "what is waving in an EM wave?" It is the question the Michelson-Morley result eventually killed.
- Section 3.12.3 (special relativity, lesson 7): the null result is one of two pieces of experimental evidence that fed into Einstein's 1905 postulates — specifically, the postulate that c is the same in all inertial frames.
- Section 3.3 (interference): the Michelson interferometer is a beautiful application of two-beam interference and is still in use today (LIGO is a 4-km Michelson interferometer in everything but scale).
In the 1860s, the dominant view was that light is a transverse wave in a substance, the luminiferous aether, that fills all of space. The properties this medium needed to have were strange:
These properties were uncomfortable but not obviously self-contradictory. The crucial pedagogical and experimental implication of a stationary aether was that the Earth, in its 30 km s⁻¹ orbital motion around the Sun, must be moving through the aether — and an observer on Earth should therefore measure a slightly different speed for light moving with the aether wind versus across it, just as a swimmer measures different effective speeds swimming up-river versus across a river.
Consider a swimmer in a river of width L flowing at speed u, swimming at speed c relative to the water.
Round trip across the river (perpendicular to flow): the swimmer must aim slightly upstream to counter the drift. Effective forward speed across the river is √(c² − u²). Round-trip time:
t_perp = 2L/√(c² − u²) = (2L/c) × 1/√(1 − u²/c²)
Round trip parallel to the flow (downstream then back upstream, distance L each way): downstream effective speed is c + u, upstream effective speed is c − u. Round-trip time:
t_par = L/(c + u) + L/(c − u) = 2Lc/(c² − u²) = (2L/c) × 1/(1 − u²/c²)
The two times are different. For u ≪ c (which applies for the Earth's orbital speed: u/c ≈ 10⁻⁴):
t_par − t_perp ≈ (L u²) / c³
For an arm length L = 11 m (Michelson-Morley's effective arm length after multiple reflections to fold a longer path) and Earth's orbital speed u ≈ 3 × 10⁴ m s⁻¹:
Δt ≈ (11 × (3 × 10⁴)²) / (3 × 10⁸)³ = (11 × 9 × 10⁸) / (2.7 × 10²⁵) = 9.9 × 10⁹ / 2.7 × 10²⁵ ≈ 3.7 × 10⁻¹⁶ s
The corresponding number of light wavelengths (for λ = 589 nm, sodium D-line):
Δ(path) = c × Δt = (3 × 10⁸)(3.7 × 10⁻¹⁶) = 1.1 × 10⁻⁷ m Δ(in wavelengths) = 1.1 × 10⁻⁷ / 5.89 × 10⁻⁷ ≈ 0.19 wavelengths of one-way path difference
When the apparatus is rotated through 90° — swapping the roles of the two arms — the fringe shift doubles to about 0.4 fringes. This was the predicted observable: a shift of about four-tenths of a fringe as the interferometer was slowly rotated. Michelson and Morley's apparatus could resolve about one-hundredth of a fringe, so the predicted shift was 40 times their experimental resolution.
The 1887 experiment was performed in a basement room with the interferometer mounted on a massive sandstone slab (1.5 m square, ~30 cm thick) floating on a bath of mercury so that the entire apparatus could be slowly rotated without vibration. The optical layout was a classic two-beam Michelson interferometer:
graph TD
A["Monochromatic source<br/>(Na lamp)"] --> B["Beam splitter<br/>(half-silvered mirror)"]
B --> C["Mirror 1<br/>(arm L₁)"]
B --> D["Mirror 2<br/>(arm L₂)"]
C --> B
D --> B
B --> E["Telescope<br/>(fringe observation)"]
style B fill:#1d4ed8,color:#fff
style E fill:#27ae60,color:#fff
A monochromatic source (sodium lamp) emits light that hits the half-silvered beam splitter. Half the light is transmitted to mirror 1 (arm 1, length L₁); half is reflected to mirror 2 (arm 2, length L₂, perpendicular to arm 1). Each beam returns to the beam splitter, where the two are recombined and the result is observed in the telescope. The arms each contained an arrangement of mirrors that folded the light path back and forth several times, giving an effective optical arm length of about 11 m — much longer than the physical dimensions of the apparatus. Interference fringes are seen in the telescope; their positions depend on the difference in optical path length between the two arms.
The crucial measurement was not the absolute fringe pattern (which depends on tiny variations in arm length and is affected by temperature, vibration, and many other systematics). It was the change in fringe position as the apparatus was slowly rotated through 90°. If the Earth's motion through the aether were producing a path-length difference, the rotation would reverse the roles of "parallel" and "perpendicular" arms and the fringes would shift by ~0.4 fringes — easily detectable.
Michelson and Morley made the measurement at several times of day and at several seasons (to control for the Earth's rotation, which adds and subtracts from the orbital velocity, and for the seasonal variation in orbital direction). The observed shift was, within experimental error, zero. They reported an upper limit of about 0.01 fringes — a factor of ~40 below the predicted aether-wind shift. No aether wind was detected.
The null result was so unexpected that physicists initially tried to rescue the aether hypothesis with modifications that would conceal the wind from observation.
Perhaps the Earth carries a layer of aether with it as it orbits, so that there is no relative motion between the apparatus and the local aether. This was suggested in various forms by Stokes and others. The problem: aether drag is hard to reconcile with stellar aberration, an annual ~20 arcsecond apparent shift in the positions of stars caused by the Earth's orbital motion. Aberration shows that starlight is not dragged with the Earth — the velocity vector of incoming light is the velocity in the aether frame, and the Earth's motion through that frame produces the angle shift. Aether drag would eliminate aberration; aberration is observed; drag is therefore wrong.
Hendrik Lorentz (1892) and George FitzGerald (1889) — independently — proposed that any object moving through the aether at speed u contracts in the direction of motion by a factor √(1 − u²/c²). The contraction is exactly such that the longer round-trip in the parallel arm is shortened to match the perpendicular arm, eliminating the predicted fringe shift. This was an extremely ad hoc fix — there was no independent reason to expect such a contraction, and it required precisely the right factor to cancel the observed effect — but it worked mathematically. Lorentz later embedded the contraction in a more systematic theory of how moving charges interact with the aether.
The Lorentz approach was the best 19th-century rescue. It saved the aether at the cost of giving it an ever-more-mysterious set of properties: the aether existed, but produced no observable effects whatsoever in any conceivable experiment, because every measuring apparatus contracted exactly enough to mask its presence. By 1900 the aether had become a "thing whose existence is undetectable by any conceivable means" — and many physicists, including the young Einstein, were ready to ask whether it was needed at all.
Einstein, in his 1905 paper On the Electrodynamics of Moving Bodies, took the radical step of dispensing with the aether entirely. His two postulates (developed in detail in lesson 7) are:
The second postulate makes the Michelson-Morley null result automatic — the speed of light is the same in all directions in any frame, including the lab on Earth, regardless of the Earth's motion. The Lorentz-FitzGerald contraction reappears in Einstein's theory but as a kinematic consequence of relativity, not as a property of a material medium. The aether disappears entirely. The price is that simultaneity, time intervals, and length intervals all become frame-dependent — a price Einstein was willing to pay.
It is worth emphasising that Einstein did not base his 1905 paper directly on the Michelson-Morley experiment. He cited the experiment only briefly and may not have been deeply familiar with it. But the philosophical point — that a stationary aether had become indistinguishable from no aether at all, and that the apparent constancy of c in all directions was begging for a deeper explanation — was very much on his mind. The null result and Einstein's postulates are two faces of the same physical fact.
A Michelson interferometer has arm length L = 11 m and is illuminated by sodium light of wavelength λ = 589 nm. The Earth's orbital speed is u = 3.0 × 10⁴ m s⁻¹. Calculate the fringe shift expected when the apparatus is rotated through 90°, assuming a stationary aether.
Solution.
Expected path difference per arm (one direction): Δ = (L u²)/c² = (11)(3.0 × 10⁴)² / (3.0 × 10⁸)² = (11)(9.0 × 10⁸) / (9.0 × 10¹⁶) = 9.9 × 10⁹ / 9.0 × 10¹⁶ = 1.1 × 10⁻⁷ m
In wavelengths: Δ/λ = (1.1 × 10⁻⁷)/(5.89 × 10⁻⁷) = 0.187 wavelengths of one-way path difference.
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