Illustrated Physics
physics, drawn
Concept

Speed of light — where it appears

The speed at which light and every other massless signal travels in empty space, 299,792,458 metres per second, the same for every observer and every source. Binary X-ray stars show that light carries at most two parts in a thousand million of its source's speed.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The same loop, spanned two ways. A 100 cm² capacitor with a 2 mm gap, charged at 1.0 million volts per second. A loop drawn round the wire can be spanned by a flat surface, which the current of 44.271 µA passes through, or by a bag-shaped surface that passes between the plates, which no charge crosses at all. Ampère's law as it stood gave two different answers for one circulation. The rate of change of electric flux between the plates, multiplied by ε₀, is 44.271 µA — the same number to every figure, because C = ε₀A/d is the same ε₀A/d either way. That is the term, and it is not an approximation or a correction: it is what makes the law consistent at all.

The term that made light

Ampère's law contradicts itself the moment a current stops being steady, and the contradiction is visible in one picture: two surfaces on the same loop, with a current through one of them and nothing through the other. The term that repairs it turns four equations into a wave, whose speed is two constants measured in a room with the lamps off.

electromagnetism · Maxwell equations The orbit an observer would reconstruct. The star's velocity along the line of sight, measured from the Doppler shift of its spectrum, as a fraction of its true orbital speed, plotted against the time the light arrives, in orbital periods, if light left the star at c plus the star's velocity. With light at c (dotted) the curve is the sine wave of a circular orbit. At 0.6 times the critical distance (solid) the same circular orbit arrives as a lopsided curve — a slow rise and a steep fall — that an astronomer would fit with a highly eccentric orbit that is not there. At twice the critical distance (dashed) the curve doubles back on itself: at some moments the spectrum would show two or three velocities at once, as if the star were in several places. Willem de Sitter pointed out in 1913 that spectroscopic binaries show nothing of the kind.

The binary star that would be seen twice

If light thrown forward by a moving source travelled faster, the way a ball thrown from a moving train does, then light from a star swinging towards the Earth in a binary orbit would catch up with light it had sent out earlier. From far enough away the two would arrive together, and the star would be seen in two places at once. Willem de Sitter pointed out in 1913 that nothing of the kind is seen, and that this settles whether the speed of light depends on its source. The argument had a loophole that took half a century to notice — interstellar gas re-emits light at its own speed — and closing it needed X-ray stars.

relativity · Velocity addition

Named alongside it

The objects these essays reach for when they reach for this one.

Amperes lawBinary starDisplacement currentElectric fluxElectromagnetic waveEmission theoryExtinction theoremMaxwells equationsNull experimentPermeabilityPermittivityRelativity principle

All concepts