Illustrated Physics
physics, drawn
Concept

Synchronisation — where it appears

The procedure that assigns a common time to clocks at different places, which requires a rule about how long a signal took to travel. The rule is a convention rather than a measurement, and for a rotating observer no convention is globally consistent — only over a patch whose size is computable.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

Where to put the far clock's zero. Two clocks three light-seconds apart, synchronised by radar: a pulse leaves the near clock at 0, bounces off the far one, and returns at 6 seconds. The far clock must be set to some time between those, and every choice is drawn. Einstein's convention puts it at 3 — halfway — and gives the same speed of light in both directions. Any other value is equally consistent with every measurement that can be made, because everything measurable involves a round trip and the round trip takes 6 seconds under every one of them: computed here across the five conventions, the round-trip times differ by 0e+0 seconds. The lines are the resulting surfaces of simultaneity, which fan out from the halfway choice. What each choice fixes is the one-way speed of light — ε = 0.25 makes it 2.00c outward and 0.67c back, ε = 0.4 makes it 1.25c outward and 0.83c back, ε = 0.5 makes it 1.00c outward and 1.00c back, ε = 0.6 makes it 0.83c outward and 1.25c back, ε = 0.75 makes it 0.67c outward and 2.00c back — and no experiment distinguishes them, because measuring a one-way speed requires two synchronised clocks and synchronising them requires the answer.

The speed that cannot be measured one way

Every measurement of the speed of light ever made has sent it out and brought it back. Measuring it one way needs two clocks that agree, and making two distant clocks agree needs a rule about when the far one should read what — which is a choice, not a discovery. The constancy of c is a fact about round trips; its isotropy is a convention, chosen because it makes the equations simple.

relativity · Simultaneity How large now is, on this planet. By how much a synchronisation carried around a region of the rotating Earth fails to come back to itself, against the size of that region — from a metre to the whole planet, both axes logarithmic. The three horizontal lines are what three kinds of clock can resolve, and where each crosses the curve is where that clock can detect that 'now' is not a global notion: a good wristwatch at 785 thousand km, a quartz oscillator at 25 thousand km, a caesium clock at 785 km. Carried the whole way round the equator the defect is 207 nanoseconds, which is sixty metres of light travel and is the correction every satellite-navigation system applies. The effect is not small and not exotic; it is a routine engineering term, and the reason it was not an engineering term before 1955 is that nothing could measure it. A wristwatch's now is global out past the Moon; a caesium clock's reaches about the width of a large country.

How big now is

Three earlier arguments have established that a global now is a choice, that part of the choice is convention, and that for a rotating observer no consistent global choice exists at all. What survives is a size. Every observer has a local now, and how local is computable: on the rotating Earth it is 785 kilometres to the nanosecond, and a freely falling frame is inertial over the tolerance times the distance to the centre, divided by two.

relativity · Simultaneity A clock that takes the drive's frequency over a whole range. The frequency a self-sustained oscillator actually runs at, relative to the frequency of a weak drive, against how far its own natural frequency is from the drive's, both in units of the locking strength K. Without the drive it would lie on the dashed diagonal, keeping its own frequency. With it, every natural frequency within ±K of the drive's is pulled all the way in: the oscillator runs at exactly the drive's frequency, a flat plateau where it has abandoned its own. Outside the plateau it runs free again but not at its own frequency; it is pulled towards the drive, its offset shrinking from the detuning to the square root of (detuning squared minus K squared) — 0.66 K instead of 1.2 K just outside, 2.83 K instead of 3 K further out.

The clock that is pulled into step

In 1665, ill in bed, Christiaan Huygens noticed that two of his pendulum clocks hanging from the same beam were swinging in exact opposition, and that however he disturbed them they returned to it within half an hour. A clock is not a passive resonator waiting to be pushed; it keeps its own time, by its own mechanism. What a weak push can do to it is not change how strongly it swings but pull its phase — and within a range of frequencies set by the push's strength, pull it all the way into step. The same arithmetic locks lasers, pacemaker cells, power stations and the body's daily clock.

waves · Resonance Too little noise, the right amount, too much. The particle's position over 8 cycles of the push (thin grey line, scaled to the wells), with noise of intensity 0.03, 0.085, 0.3 (top to bottom), the barrier being 0.25. With little noise it stays almost always in its starting well and only trembles: 0 hops in eight cycles. With noise 0.085 it hops 30 times, almost always once per half-cycle and almost always while the push is helping — a clean square wave following a push too weak to cause a single hop. With noise 0.3 it hops 285 times, at random, and the push is lost again. There is a best amount of noise, and it is not zero.

The noise that helps a weak signal through

A system that can sit in either of two states, nudged back and forth by a periodic push too weak to switch it, does nothing at all — until noise is added. Then it begins to switch, and with the right amount of noise it switches in step with the push, once each half-cycle, as though the push had been strong enough all along. Too little noise and it never switches; too much and it switches at random. The response peaks at a nonzero noise, which is why the effect is called a resonance, and why crayfish, paddlefish and human fingertips appear to use it.

waves · Resonance

Named alongside it

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

Reference frameSimultaneityBeatsBistabilityCircadian rhythmClock synchronisationClock transportConventionalismCoordinate timeEquivalence principleInjection lockingInvariance

All concepts