Illustrated Physics
physics, drawn
Concept

Calibration — where it appears

Fixing the relation between an instrument's reading and the quantity it is meant to report, by measuring something already known. A null instrument needs almost none, because it reads a difference rather than a value — which is why the most precise measurements in physics are comparisons.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

A force that points across the beam, not along it. The intensity of a beam focused to a waist of 0.5 µm, and the force it exerts on a 60 nm polystyrene sphere in water, across the beam. The force is not a pressure and does not point along the light: it is the pull on an induced dipole sitting in a non-uniform field, proportional to the gradient of the intensity rather than to the intensity, and it points up the gradient — towards the bright axis from either side. It vanishes exactly on the axis, which is what makes the axis a trap rather than a place. The well is 47 times kT deep at 100 milliwatts, which is why the particle stays: thermal motion explores it and does not escape it. The stiffness near the bottom is 3.070 piconewtons per micrometre, and a particle in a spring that stiff wanders 36 nanometres from centre.

The light that pulls rather than pushes

Radiation pressure is momentum arriving, and it points along the beam. A gradient of intensity does something else entirely — it polarises a particle and then pulls the induced dipole up the gradient — so a focused beam holds a particle at its waist against the push, and the force that does it is not a pressure at all.

astrophysics · Radiation pressure The height a clock can see. The fractional difference in rate between two clocks against how far apart in height they are, on logarithmic axes — a straight line of slope one, since the shift is gh/c² and comes to 1.09e-16 per metre near the ground. a caesium fountain, good to 1e-16, resolves 91.6 cm; an optical lattice clock, good to 1e-18, resolves 0.9 cm; the best clocks built, good to 8e-19, resolves 0.7 cm. The caesium fountains that define the second reach about a metre. The optical clocks that will replace them reach a centimetre, and the best of them a few millimetres. That is the whole of why this has stopped being a test of relativity and become a way of measuring the ground. A shift once so small that it took a Mössbauer experiment in a tower to see at all is now large enough to be a nuisance: two clocks in the same building disagree, and the disagreement has to be corrected for before either can be used to keep time.

The clock that measures a height

A clock a metre higher runs faster by a part in ten thousand million million million. That was once so small it took a tower and a Mössbauer source to see; the best clocks now resolve a centimetre of height, at any distance, without a line of sight. What began as a test of general relativity has become a surveying instrument that measures the quantity surveying actually wants.

astrophysics · Gravitational redshift The oldest age a trace of modern carbon allows. The age a radiocarbon measurement would report against the sample's true age, when a fraction of the carbon in it is modern contamination — from groundwater, roots, handling or the chemistry of preparation — of 5, 1 and 0.1 per cent; dashed, no contamination. Young samples are barely affected. Old ones are ruled by the contamination, because their own carbon-14 has dwindled to less than it: with 1 per cent, a sample of any age beyond about 60,000 years reads 38.1 thousand years, and 5 per cent caps it at 24.8 thousand. Even 0.1 per cent, a microgram of modern carbon in a milligram sample, caps it at 57 thousand. The limit of radiocarbon dating, usually quoted as about fifty thousand years, is a limit on cleanliness, not on the half-life.

The clock read by counting atoms

Radiocarbon dating reads a clock that ticks slowly: a gram of living carbon holds sixty thousand million carbon-14 atoms, and only thirteen and a half of them decay each minute. Counting those decays to date a milligram of bone would take years. Counting the atoms themselves, one by one in an accelerator, takes an hour, because in any measurement shorter than the clock's mean life almost every atom is still there, undecayed and countable. And the method's famous limit of about fifty thousand years turns out not to be set by the half-life at all. It is set by how much modern carbon a sample has picked up, because a trace of contamination outweighs whatever carbon-14 a very old sample has left.

quantum · Decay

Named alongside it

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

Accelerator mass spectrometryBrownian motionClockContaminationCosmogenic isotopeCounting statisticsDipoleEquipartitionEquivalence principleFrequencyGeodesyGradient force

All concepts