Physics › Turning points › The Michelson-Morley experiment
The Michelson-Morley experiment
If light is a wave, Victorian physics reasoned, something must be waving, and the Earth must be ploughing through it. The most sensitive instrument of the century was built to catch that motion, and its magnificent failure handed Einstein his starting point.
Builds on The nature of light and Interference and Young's double slit.
IN THIS TOPIC
- Describe the principle of the interferometer and the experiment as a hunt for absolute motion.
- Explain the significance of the null result: the speed of light is invariant.
- State what an inertial frame is, and the two postulates of special relativity.
WHAT YOU PROBABLY THINK
Light must travel through something; empty space cannot carry a wave.
The ether, and how to catch it
Every wave the nineteenth century knew needed a medium: sound needs air, ripples need water. So light, freshly confirmed as a wave, was assigned one, the ether, an invisible substance filling all space. The Earth orbits the Sun at 30 km s−1, so it must rush through this ether, and an ether wind must blow across every laboratory. Light travelling with, against or across that wind should show slightly different speeds. Measure the difference and you have measured the Earth's absolute motion through space itself.
WORKED EXAMPLE
The rower's problem
A boat travels at 5.0 m s−1 in still water, on a river flowing at 3.0 m s−1. Compare the round-trip times for 60 m straight across and back, and 60 m downstream and back.
Across: the boat must angle upstream, leaving √(5.02 − 3.02) = 4.0 m s−1 of cross-river speed, so t = 120/4.0 = 30 s.
Along: t = 60/(5.0 − 3.0) + 60/(5.0 + 3.0) = 30 + 7.5 = 37.5 s.
Same boat, same distances, different times: motion of the medium separates the two round trips. Swap boat for light and river for ether wind, and this asymmetry is the entire design of the experiment.
The interferometer
Albert Michelson's instrument raced light against itself. A half-silvered mirror splits one beam into two, sent down two equal arms at right angles to mirrors that return them. Recombined, the beams interfere, and the fringe pattern records any difference in their travel times to within a fraction of a wavelength: the most sensitive stopwatch ever built, with no clock in it.
The rower's asymmetry says the arm lying along the ether wind should lose the race, and by a calculable margin. The masterstroke is that no absolute lengths matter: rotate the whole apparatus by 90°, so the arms swap roles, and the fringe pattern should visibly slide as the time difference reverses. Michelson and Morley floated the instrument on liquid mercury and turned it, watching for a shift they calculated at several tenths of a fringe, well within its sensitivity.
YOUR TURN
The size of the expected effect
For an effective arm of 11 m, an ether wind of 3.0 × 104 m s−1 and c = 3.0 × 108 m s−1, the expected time difference is roughly Δt ≈ (L/c)(v2/c2). Evaluate it, and the path difference it represents, before opening the working.
Show the working
Δt ≈ (11 / 3.0 × 108) × (10−4)2... careful: v/c = 10−4, so v2/c2 = 10−8, giving Δt ≈ 3.7 × 10−16 s.
Path difference cΔt ≈ 1.1 × 10−7 m: about a fifth of a wavelength of visible light, an easily visible fringe shift for the instrument. The experiment was sensitive enough; that is what makes the result mean something.
The null result, and Einstein's answer
The fringes did not move. Not that day, not six months later with the Earth travelling the opposite way round the Sun, not at any orientation: the most careful measurement of the age returned nothing. The significance took years to digest. No experiment could detect the ether wind, so no experiment can detect absolute motion; and the racing beams tied even when they plainly should not have, so the speed of light comes out the same however the apparatus moves: c is invariant. The ether, having no detectable property at all, was quietly retired, and with it the idea that a wave must have something to wave in: an electromagnetic wave is self-propagating fields, and needs no medium.
In 1905 Einstein rebuilt mechanics on that result. First, a definition: an inertial frame of reference is one moving at constant velocity, in which Newton's first law holds, no accelerations, no rotations. Then two postulates:
1. Physical laws have the same form in all inertial frames. No experiment done inside a smoothly moving laboratory can reveal its motion; there is no privileged frame at rest.
2. The speed of light in free space is invariant. Every inertial observer measures the same c, whatever the motion of the source or the observer.
TRY IT UNSEEN
Taking the postulate seriously
A spacecraft travelling at 0.5c directly toward you switches on a headlamp. Using the second postulate, state the speed at which the light reaches you, and contrast it with a ball thrown forward at 10 m s−1 from a train moving at 30 m s−1.
Show the working
The light arrives at exactly c, not 1.5c. The source's motion is irrelevant: that is what invariance means.
The ball arrives at 40 m s−1, because everyday velocities add. Light refuses the addition, and forcing the two facts to coexist is what makes time and space themselves give way, the business of the next lesson.
THE EXAM BIT
- The interferometer's principle in one line: split one beam along two equal perpendicular arms, recombine, and read differences in travel time as fringe positions.
- The experiment hunts absolute motion: the ether wind should make the along-wind round trip slower than the across-wind one, so rotating the apparatus should shift the fringes.
- The result is a null result, and the word carries marks: no fringe shift at any orientation or season, despite sensitivity comfortably better than the predicted effect.
- Significance is two statements: absolute motion cannot be detected, and the speed of light is invariant. Both, not either.
- Define an inertial frame before quoting the postulates, and give the postulates word-perfect: same physical laws in all inertial frames; c in free space invariant.
CHECK YOURSELF
State the two postulates of special relativity, and explain which one the Michelson-Morley result supports and how.
Show a hint
The fringes that refused to move are a statement about one particular speed.
Show the answer
One: physical laws have the same form in all inertial frames. Two: the speed of light in free space is invariant, the same for every inertial observer.
The null result supports the second. The two beams' round trips tied exactly, whatever the Earth's motion through space and however the arms were oriented.
So the measured speed of light does not depend on the motion of the apparatus carrying the source and detector, which is precisely the invariance the second postulate asserts.
The most sensitive race ever staged ended in a dead heat, every single time.
No detectable absolute motion, an invariant c, and two postulates to rebuild physics on.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
CHECK YOUR PROGRESS
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- Describe the principle of the interferometer and the experiment as a hunt for absolute motion.
- Explain the significance of the null result: the speed of light is invariant.
- State what an inertial frame is, and the two postulates of special relativity.
Open the full revision checklist to track your progress across the whole unit.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.