A Constant Worth Measuring
From lanterns on hills to a constant fixed by definition.
Lesson at a glanceShow the key points
- Light has the same speed in every frame: the key fact behind special relativity.
- Since 1983 c = 299,792,458 m/s exactly; the metre is defined from it, so timing light now measures distance.
- Galileo's two lanterns: human reaction time (~0.1 s) is far longer than light's round trip between hills (~10⁻⁴ s for 15 km).
- Rømer (1676) from the timing of Jupiter's moon eclipses: about 2.1 × 10⁸ m/s. Bradley (1728) from stellar aberration: close to the true value.
Light is so fast that for most of history it seemed to arrive instantly. Measuring its speed took clever astronomy, then spinning wheels and mirrors, and finally led us to fix it by definition.
A very special speed
The speed of light in vacuum is a fundamental constant with a remarkable property: anything moving at this speed in one frame of reference moves at the same speed in every other frame. This forced a complete rethink of space and time, the basis of the special theory of relativity.
Fixed by definition
Since 1983 the speed of light has been defined to be exactly , and the metre is defined as the distance light travels in 1/299,792,458 of a second. So today, timing light over a path measures the length of the path, not c. Before 1983 the metre was defined separately, and c was a quantity to be measured.
Galileo’s lanterns
Galileo proposed an experiment with two people on distant hills, each with a covered lantern. A uncovers his lantern; B uncovers hers the moment she sees A’s light; A covers his the moment he sees B’s. The time between A uncovering and covering, together with the distance, would give the speed.
Bars on a logarithmic scale (1 µs to about 3 s). Ratio ≈ 3,997 to 1.
It couldn’t work: for hills 15 km apart, light takes only about 10⁻⁴ s for the round trip, thousands of times shorter than human reaction times.
Astronomy gets there first
- Rømer (1676) noticed that eclipses of Jupiter’s moon Io came progressively later as the Earth moved away from Jupiter: light needed extra time to cross the extra distance. His result was about 2.1 × 10⁸ m/s, too low but the right size.
- Bradley (1728) found that stars appear slightly shifted in the direction of the Earth’s motion (aberration of starlight), which gave a value quite close to the correct one.
The first measurements on Earth came in the 1800s with Fizeau, Foucault and Michelson: the next two lessons.
If each lantern operator takes 1/100 s to work the shutter, how far apart must they be for that delay to be only a tenth of light’s one-way travel time?
- 1c is the same in every frame: the basis of special relativity.
- 2Since 1983 c = 299,792,458 m/s exactly; the metre is defined from it.
- 3Galileo's lantern method failed: reaction times dwarf light's travel time.
- 4Rømer (Io's eclipses, ≈ 2.1 × 10⁸ m/s) and Bradley (stellar aberration) made the first estimates.
Check yourself
Keep exploring
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