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Frames of reference and the aether
Inertial frames of reference and Galilean relativity, the problem Maxwell's constant c created, the aether and the Michelson–Morley experiment, Einstein's two postulates of special relativity and the evidence for them, and the relativity of simultaneity.
Sitting on a smooth plane at 900 km/h, you can pour a drink, toss a coin and catch it, or bounce a ball, and everything behaves exactly as it does at home. With the window blinds down, no experiment with balls or drinks can tell you that you're moving. At 16, Einstein wondered whether the same is true of light: what would a light wave look like if you could ride alongside it? Ten years later, his answer rebuilt our ideas of space and time.
Frames of reference
A frame of reference is the viewpoint from which measurements of position, time and velocity are made, such as the ground, a moving train or a spacecraft. An inertial frame is one that is not accelerating: it is at rest or moving at constant velocity. In an inertial frame Newton's first law holds; objects with no net force on them keep moving in a straight line at constant speed.
A non-inertial frame accelerates. In a car braking hard, a phone on the seat slides forwards with no force pushing it. That "fictitious" motion shows that the car's frame is accelerating.
Galilean relativity
Galileo realised that the laws of mechanics are the same in every inertial frame. No mechanical experiment can show whether you are "really" at rest or moving at constant velocity. There is no absolute rest, only motion relative to something.
In Galilean (everyday) relativity, velocities simply add. If a train moves at $v$ and a ball is thrown forwards at $u$ relative to the train, an observer on the ground sees the ball move at $u + v$. Time is the same for everyone: a second on the train is a second on the ground.
A train travels east at 30 m/s. A passenger walks towards the front at 2 m/s, and a beam of light from the headlight travels forwards. Using Galilean relativity, what speeds would a person beside the track measure for the passenger and for the light?
The problem with light
Maxwell's equations (7A) predict that electromagnetic waves travel at $c = 1/\sqrt{\mu_0\varepsilon_0}$, a fixed number. But according to Galilean relativity, speeds depend on the observer. So $c$ relative to what?
Nineteenth-century physicists had a natural answer. Every known wave travels through a medium, so light must travel through an invisible medium filling all space, the luminiferous aether. $c$ would be light's speed relative to the aether, and the aether would be a special frame of absolute rest. Earth orbits the Sun at about 30 km/s, so it must move through the aether, and we should feel an "aether wind" that changes the measured speed of light depending on direction.
That would also mean Maxwell's equations were only exactly true in one special frame, unlike Newton's laws, which hold in all of them.
The Michelson–Morley experiment, 1887
Albert Michelson and Edward Morley built an interferometer sensitive enough to detect the aether wind. A beam of light is split in two by a half-silvered mirror. The two beams travel along perpendicular arms, reflect from mirrors and recombine to make interference fringes. They used multiple reflections to make each path about 11 m long, and floated the whole apparatus on a pool of mercury so it could be turned smoothly.
If Earth moved through the aether, light along the arm parallel to the motion would take a little longer for the round trip than light along the perpendicular arm. Rotating the apparatus by 90° swaps the arms, so the fringe pattern should shift. The expected shift was about 0.4 of a fringe, which they could easily have detected (they could see 0.01 of a fringe).
The result: no significant shift was seen at any orientation, at any time of day or any season. The observed shift was less than 0.02 of a fringe, and consistent with zero. This "null result" is one of the most famous experiments in physics.
For an arm length $L$, the aether theory predicts a path difference between the arms of about $L\dfrac{v^2}{c^2}$, and rotating by 90° doubles the effect. Find the predicted fringe shift for $L = 11$ m, $v = 30$ km/s and $\lambda = 590$ nm.
Physicists tried to rescue the aether. Perhaps Earth dragged the aether along with it (but that conflicted with the aberration of starlight). FitzGerald (1889) and Lorentz (1892) suggested that motion through the aether physically squashes objects along the direction of motion by exactly the right amount to hide the effect. The maths of this "Lorentz contraction" turned out to be correct, but the reason was not.
Einstein's two postulates, 1905
Einstein took a bolder approach. Instead of explaining away the null result, he made it a principle. His 1905 paper "On the Electrodynamics of Moving Bodies" starts from two postulates:
- The principle of relativity: the laws of physics, including electromagnetism, are the same in all inertial frames of reference. No experiment can detect absolute uniform motion.
- The constancy of the speed of light: the speed of light in a vacuum, $c$, is the same for all observers in inertial frames, regardless of the motion of the source or the observer.
The aether is unnecessary: there is no special frame. The price is that if everyone measures the same $c$, then space and time can no longer be the same for everyone. Distances and time intervals must depend on the observer's frame (7K).
Evidence for the postulates
- Michelson–Morley (1887) and many repeats with lasers since, now sensitive to $10^{-17}$ of $c$: no direction-dependence of $c$.
- Moving sources. In 1964 at CERN, Alväger and colleagues measured gamma rays emitted by pions travelling at 0.99975$c$. The gamma rays travelled at $c$, not nearly $2c$, agreeing to within 0.01%. Light from a fast source is not faster.
- Binary stars. If light from an approaching star travelled faster than light from a receding one, the images of binary stars would appear scrambled. They don't (de Sitter, 1913).
- Everything that follows. Time dilation, length contraction and $E = mc^2$, which follow from the postulates, are confirmed daily in particle accelerators and GPS (7K, 7L).
Relativity of simultaneity
One surprising consequence is that two events that are simultaneous in one frame need not be simultaneous in another.
Imagine a long train carriage moving at high speed. A lamp in the exact middle flashes. For a passenger, light travels at $c$ in both directions and the carriage is at rest, so the flash reaches the front and back doors at the same moment. Now consider an observer on the platform. They also see light travel at $c$ in both directions (postulate 2). But while the light is travelling, the back of the carriage moves forwards to meet its light, and the front moves away from its light. So the platform observer sees the light reach the back door first.
Both are right. Simultaneity is not absolute; it depends on the frame. The effect is only noticeable when relative speeds are a large fraction of $c$, which is why we never notice it. It has to be built into the clock-synchronisation of GPS satellites.
- With the defaults (11 m arms, 30 km/s, 590 nm light), read the predicted shift on a 90° turn: 0.37 fringe. Check it with the worked example.
- Turn on Keep rotating and watch the fringes. How many times per full turn do they go back and forth?
- Reduce the arm length to 1 m. Why did Michelson and Morley use mirrors to fold their light path?
- Double Earth's speed to 60 km/s. By what factor does the predicted shift change? Why?
- Switch to What Michelson and Morley saw. What can you conclude about the aether wind, and about the speed of light along the two arms?
Test yourself
Which of these is an inertial frame of reference?
Only constant velocity (constant speed AND direction) is inertial.
The Michelson–Morley experiment was designed to
It looked for a change in light's speed with direction; relativity came 18 years later.
A spacecraft travels at 0.5$c$ towards a star and shines a laser forwards. According to special relativity, an observer at the star measures the laser light's speed as
Postulate 2: $c$ is independent of the source's motion.
Two lightning strikes hit the ends of a moving train simultaneously according to an observer on the platform. An observer at the centre of the train sees
The train observer moves towards the light from the front, so it reaches them first; in their frame the strikes were not simultaneous.
Label the interferometer
Sort these frames of reference.
Put these in time order.
A frame moving at constant velocity is called . The medium once thought to carry light was the . Michelson and Morley expected the to shift as they rotated the apparatus, but obtained a result. Einstein's second postulate states that the speed of light is the same for all .
Evaluate the evidence that the speed of light in a vacuum is the same for all observers. In your answer, describe the Michelson–Morley experiment and at least one other piece of evidence.
In the 19th century light was thought to travel through an aether at speed $c$, so an observer moving through the aether should measure different speeds of light in different directions. Michelson and Morley (1887) split a beam into two perpendicular paths about 11 m long and recombined them to form interference fringes. If Earth moved through the aether at 30 km/s, rotating the apparatus should have shifted the fringes by about 0.4 of a fringe. They observed less than 0.02, at all orientations and times of year. This null result showed no detectable aether wind: light travelled at the same speed in both directions.
A second line of evidence concerns moving sources. In 1964 gamma rays emitted by pions travelling at 0.99975$c$ were measured at CERN to travel at $c$ to within 0.01%, not at nearly $2c$ as Galilean addition predicts. Observations of binary stars, whose light would otherwise arrive scrambled, agree.
The evidence is strong: these experiments have been repeated with much greater precision, using lasers, with the same null result. The consequences of a constant $c$, such as time dilation of fast muons and the clock corrections needed for GPS, are also confirmed. Together these support Einstein's postulate that $c$ is the same for all inertial observers.