Questions on the Michelson-Morley experiment

Question 1

Describe the principle of the Michelson interferometer.

Accepted Answer

A half-silvered mirror splits one light beam along two equal arms at right angles to mirrors that return them (1); the recombined beams interfere, and the fringe pattern registers any difference in the two round-trip times (1).

Question 2

State the two postulates of Einstein's theory of special relativity.

Accepted Answer

One: physical laws have the same form in all inertial frames (1). Two: the speed of light in free space is invariant, the same for every inertial observer (1).

Question 3

State what is meant by an inertial frame of reference.

Accepted Answer

A frame of reference moving at constant velocity, without acceleration or rotation (1), in which Newton's first law holds: objects with no resultant force stay at rest or move uniformly (1).

Question 4

Explain why nineteenth-century physicists expected light to require a medium, the ether.

Accepted Answer

Every known wave travelled through a medium: sound through air, ripples through water (1). Light, established as a wave, was therefore assumed to need a medium of its own filling all space, which was named the ether (1).

Question 5

State what the Michelson-Morley experiment was designed to detect.

Accepted Answer

The Earth's absolute motion through the ether, appearing as an ether wind blowing across the apparatus (1).

Question 6

A boat travels at 4.0 m s⁻¹ in still water on a river flowing at 2.4 m s⁻¹. Calculate the round-trip times for 48 m straight across and back, and 48 m downstream and back, and state the relevance to the Michelson-Morley experiment.

Accepted Answer

Across: cross-stream speed √(4.0² − 2.4²) = 3.2 m s⁻¹ (1)
t = 96/3.2 = 30 s (1)
Along: 48/1.6 + 48/6.4 = 37.5 s (1)
A medium's motion separates the two round trips, which is exactly what the interferometer's two arms were built to detect for light in the ether (1)

Question 7

For an effective arm length of 11 m and an ether wind equal to the Earth's orbital speed of 3.0 × 10⁴ m s⁻¹, the expected time difference is roughly Δt ≈ (L/c)(v²/c²). Evaluate Δt and the corresponding path difference.

Accepted Answer

v/c = 10⁻⁴, so Δt ≈ (11/(3.0 × 10⁸)) × 10⁻⁸ (1)
Δt = 3.7 × 10⁻¹⁶ s (1)
Path difference cΔt = 1.1 × 10⁻⁷ m, about a fifth of a wavelength of visible light, well within the instrument's sensitivity (1)

Question 8

Explain why the apparatus was rotated through 90° during the experiment.

Accepted Answer

Rotation swaps which arm lies along the supposed ether wind (1), reversing the predicted time difference between the arms (1). The fringes should therefore shift visibly as the apparatus turns, without needing the two arms to be perfectly equal in length (1).

Question 9

The experiment was repeated at different times of year. Explain why this mattered.

Accepted Answer

Six months apart, the Earth moves in opposite directions around the Sun (1), so its velocity through any ether must differ by twice the orbital speed (1). A null result at every season rules out the lucky case of the laboratory happening to be momentarily at rest in the ether (1).

Question 10

The interferometer was mounted on a massive stone block floated on liquid mercury. Suggest why.

Accepted Answer

So the whole apparatus could be rotated smoothly and continuously while the fringes were watched (1); vibration or distortion of the arms during rotation would itself shift the fringes and mask the effect being looked for (1).

Question 11

State and explain whether each of the following is an inertial frame of reference: (a) a train travelling at a steady 55 m s⁻¹ on a straight track; (b) a car rounding a bend at constant speed; (c) a rocket accelerating uniformly upwards.

Accepted Answer

(a) Inertial: constant velocity, so Newton's first law holds on board (1). (b) Not inertial: the direction of motion is changing, so the car is accelerating even though its speed is constant (1). (c) Not inertial: its velocity is changing, an accelerating frame (1).

Question 12

State and explain the two conclusions drawn from the failure of the Michelson-Morley experiment to detect any fringe shift.

Accepted Answer

Absolute motion cannot be detected (1): no measurement revealed the Earth's motion through any ether, so there is no privileged frame at rest (1). And the speed of light is invariant (1): the two beams' round trips tied exactly whatever the apparatus's motion or orientation, so the measured speed of light does not depend on the motion of source or observer (1).

Question 13

A spacecraft approaching Earth at 0.40c switches on a landing light. Using the second postulate, state the speed at which the light arrives at Earth, and explain why the everyday rule for adding velocities fails here.

Accepted Answer

It arrives at exactly c, not 1.40c (1). The invariance of c means the speed of light is independent of the source's motion (1); the everyday addition of velocities is only a low-speed approximation and cannot be applied to light (1).

Question 14

Explain why the Michelson-Morley result, though "null", is counted among the most important measurements in physics.

Accepted Answer

It was sensitive enough to see the predicted effect and cleanly saw nothing, so the absence is itself a measurement (1): it retired the ether, established the invariance of c, and supplied the experimental foundation on which special relativity was built (1).

Question 15

Michelson's first interferometer of 1881 had an effective arm length of only 1.2 m and could just detect a path-difference change of 0.05 wavelengths of the light used (λ = 5.5 × 10⁻⁷ m). The expected time difference from an ether wind of v = 3.0 × 10⁴ m s⁻¹ is Δt ≈ (L/c)(v²/c²), with c = 3.0 × 10⁸ m s⁻¹. Deduce whether this first instrument could have detected the ether wind, and hence suggest why the 1887 apparatus used repeated reflections to give an 11 m effective arm.

Accepted Answer

Δt ≈ (1.2/(3.0 × 10⁸)) × 10⁻⁸ = 4.0 × 10⁻¹⁷ s (1). Path difference cΔt = 1.2 × 10⁻⁸ m (1), which is 1.2 × 10⁻⁸/(5.5 × 10⁻⁷) ≈ 0.02 of a wavelength (1). This is below the 0.05-wavelength detection limit, so the 1881 instrument could not reliably have seen the effect (1). The expected shift scales with arm length: at 11 m it becomes about 0.2 of a wavelength, comfortably detectable, hence the repeated reflections (1).

Question 16

Every other wave known in 1887 travelled through a material medium. Explain how an electromagnetic wave is able to travel through empty space.

Accepted Answer

It is self-propagating: the oscillating electric field generates an oscillating magnetic field, which in turn regenerates the electric field (1). Nothing material has to oscillate, so no medium is required (1).

Question 17

Describe the Michelson-Morley experiment and explain the significance of its result. Your answer should include the principle of the interferometer, the reason the apparatus was rotated, and the conclusions drawn.

Accepted Answer

A half-silvered mirror splits a single beam along two equal arms at right angles; mirrors return the beams, which recombine and interfere, so the fringe pattern records any difference in the two round-trip times (1). If an ether wind blew through the laboratory, the arm lying along it should have the longer round-trip time (1). Rotating the whole apparatus through 90° swaps the arms' roles and reverses the difference, so the fringes should shift as it turns (1). No fringe shift was seen, at any orientation or time of year, despite sensitivity well beyond the predicted effect (1). Conclusions: absolute motion, through any ether, cannot be detected (1); and the speed of light is invariant, the same whatever the motion of the apparatus, the experimental foundation of special relativity (1).

Question 18

Before 1905, Lorentz and FitzGerald proposed that objects contract along their direction of motion through the ether, by exactly the amount needed to hide the expected fringe shift. Explain how Einstein's treatment of the null result differed from this proposal.

Accepted Answer

The contraction hypothesis was an adjustment made to save the ether: it explained away the null result while keeping the idea of absolute motion (1). Einstein replaced the patch with a principle, that the speed of light in free space is invariant, the same for every inertial observer, and rebuilt mechanics on it (1). The ether, left with no detectable property at all, was abandoned: an electromagnetic wave is self-propagating fields and needs no medium (1).