Illustrated Physics
physics, drawn
Concept

Probability — where it appears

The measure a theory assigns to each possible outcome, which for a quantum measurement is all that can be predicted about a single event. The state's evolution is deterministic and the outcome is not, and no further information about the system has ever been found that would restore it.

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

A quarter of the time, an object is found without being touched. The outcomes of sending one photon into a balanced interferometer, with and without an opaque object in one arm, computed from the same amplitudes. With the arm clear, every photon leaves by the bright port and the dark port receives nothing. With the object in place, 50 per cent of photons are absorbed by it, 25 per cent reach the bright port and say nothing, and 25 per cent reach the dark port — which is impossible unless something is in the arm, and which happens with the object still sitting there unabsorbed and unlit. The photon that produced that click did not go through the blocked arm, because a photon that goes through a blocked arm is absorbed. So an object has been located by light that never met it. The price is that 50 per cent of attempts destroy the thing being looked for: an efficiency of 33 per cent, which the Zeno version of the apparatus takes as close to one as one likes.

The measurement that never touched it

A balanced interferometer sends every photon to one output and none at all to the other. Put an object in one arm and the empty port starts clicking — and a click there is caused by a photon that cannot have gone near the object, because a photon that goes near it is absorbed. The object has been found by light that never met it.

quantum · Measurement Four predictions no list of answers can keep. The four measurements a three-particle GHZ state predicts with certainty, and what the best possible list of pre-agreed answers does with them. Each row is a choice of which quantity to measure on each of the three particles; the quantum value is not an average but a certainty, so a single run of any row has a determined outcome. Every list of answers assigns a value to X and to Y at each particle, which is sixty-four lists in all, and the enumeration finds that 32 of them get three of the four right and 32 get one. None gets four, and none can: multiplying the four left-hand sides together gives every X and every Y twice, so the product is +1 for any list whatever, while the product of the four quantum values is −1. The column on the right is one such list, which agrees with the first three rows and is then forced into the opposite of the fourth. That is the whole argument, and it needs no inequality, no average and no repetition: measure the first three rows on three copies, and the fourth is predicted with certainty and comes out the other way.

The disagreement that one run settles

Bell's argument is a statistical one — a correlation of 2.828 where a pre-agreed list of answers is stuck at 2, dug out of hundreds of coincidences. Add a third particle and the argument stops being about how often. Three measurements predict a fourth with certainty, every list of answers that gets the three right gets the fourth exactly backwards, and one run of the experiment is enough.

quantum · Entanglement Every toss already decided. The outcome of a coin toss as a map of how it was launched: the upward speed in metres per second across, the spin in radians per second up, with the region where the coin shows the face it started with shaded and the region where it shows the other face left clear. A coin spinning about a diameter and caught at the height it left is in the air for 2v/g and turns 2vω/g radians, so the boundaries are the hyperbolae vω = nπg/2, one for every half-turn. Near the origin the bands are wide: a slow toss with little spin is easy to control, and a conjuror's "honest" toss lives there. Nothing in the map is random. Every point is a definite outcome, and the bands are smooth curves — there is no fractal boundary, no region where a tiny change has an unpredictable effect. What makes a toss a fair bet is only how narrow the bands become further out.

The toss that is random without chaos

A coin toss is the textbook random event and the textbook deterministic one at the same time. Its flight is a few lines of Newtonian mechanics with no chaos anywhere: two tosses that start almost alike stay almost alike, drifting apart only in proportion to time. Its outcome is fixed the moment it leaves the thumb, by a map of launch speed and spin carved into bands of heads and tails. It is a fair bet because the bands, at a real toss, are only a few per cent wide and no hand repeats itself that well — and it is not quite fair, because a coin wobbles as it flips, and the wobble keeps its starting face up a little more than half the time: 50.8 per cent, predicted in 2007 and counted in 2023 over 350,757 tosses.

mechanics · Chaos

Named alongside it

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

DeterminismMeasurementSuperpositionAmplitudeAngular momentumBell inequalityChaosCoherenceComplementarityCorrelationEntanglementHidden variables

All concepts