Physics › Turning points › The Michelson-Morley experiment
The Michelson-Morley experiment
If light needs a medium, the Earth's motion through it should make light take longer along one interferometer arm than the other and shift the fringes. Michelson and Morley found no shift at any orientation or time of year. The null result means absolute motion is undetectable and the speed of light is invariant.
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Builds on Electromagnetic waves and the speed of light and Interference and Young's double slit.
IN THIS TOPIC
- Describe the principle of the interferometer and the experiment as a search 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.
COMMON MISCONCEPTION
Light must travel through something; empty space cannot carry a wave.
Light needs no medium: the interferometer could have detected the supposed ether wind but found no significant shift in any orientation or season, undermining the ether picture and supporting the postulate that light's speed is the same in every inertial frame.
The ether, and how to catch it
Every wave the nineteenth century knew needed a medium. Sound needs air, and 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.
Going 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.
Going along, t = 60/(5.0 − 3.0) + 60/(5.0 + 3.0) = 30 + 7.5 = 37.5 s.
Same boat and same distances, yet different times, because the medium is moving. Swap boat for light and river for ether wind, and the whole experiment is designed around this asymmetry.
The interferometer
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, with no clock involved anywhere.
By the rower's asymmetry, the round trip along the ether wind should take longer than the one across it, by a calculable margin. No absolute lengths need to be known. Instead, rotate the apparatus bodily by 90° so the arms swap roles, and the fringe pattern should then visibly slide as the time difference reverses. Michelson and Morley floated the instrument on liquid mercury and turned it, watching for a shift they had calculated at several tenths of a fringe, well within what it could see.
GUIDED PRACTICE
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.
Show the working
With v/c = 10−4, the factor v2/c2 is 10−8, giving Δt ≈ (11/(3.0 × 108)) × 10−8 ≈ 3.7 × 10−16 s.
Path difference cΔt ≈ 1.1 × 10−7 m, about a fifth of a wavelength of visible light. Rotating through 90° reverses the difference, so the fringes should move by roughly two fifths of a fringe, which the instrument could see easily. The experiment was comfortably sensitive enough, and that is what makes the result mean anything at all.
The null result, and Einstein's answer
No shift of the predicted size appeared, within the instrument's sensitivity. 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 a null result.
Its significance took years to digest, and it comes in two parts. The experiment found no ether wind at its sensitivity, later experiments only sharpened the null, and the working conclusion became that absolute motion is undetectable. And no travel-time difference appeared where the stationary-ether picture required one, which is what an invariant light speed predicts: the speed of light comes out the same however the apparatus moves.
The first response was not Einstein's. Lorentz and FitzGerald proposed that lengths contract along the direction of motion, saving the ether by adjustment. The ether, left with 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 consists of self-propagating fields and needs no medium.
In 1905 Einstein rebuilt mechanics on the null result. A definition comes first. An inertial frame of reference is one moving at constant velocity, in which Newton's first law holds, with no accelerations and 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.
INDEPENDENT PRACTICE
Taking the postulate seriously
A spacecraft travelling at 0.5c directly towards 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 makes no difference at all, and that is what invariance means.
The ball arrives at 40 m s−1, because everyday velocities add. Light does not follow that addition rule, and reconciling the two is what the relativistic treatment of time and length does.
ASSESSMENT FOCUS
- The interferometer's principle fits in one line. Split one beam along two equal perpendicular arms, recombine them, and read differences in travel time as fringe positions.
- Say what the experiment was hunting. An 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 that word belongs in the answer. No significant fringe shift at any orientation or season, within a sensitivity comfortably better than the predicted effect.
- Significance is two statements, and both are needed. Absolute motion cannot be detected, and the speed of light is invariant. Define an inertial frame before quoting the postulates, then give them word-perfect. Same physical laws in all inertial frames, and c in free space the same for every inertial observer.
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
Postulate one, physical laws have the same form in all inertial frames. Postulate 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 to within the instrument's sensitivity, 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 the detector, and that is precisely the invariance the second postulate asserts.
No fringe shift of the predicted size was observed, at any orientation or time of year, within the instrument's sensitivity: absolute motion is undetectable and c is invariant for every observer.
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.
Or read them with their mark schemes on the Michelson-Morley experiment questions page.
CHECK YOUR PROGRESS
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- Describe the principle of the interferometer and the experiment as a search 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.
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