Illustrated Physics
physics, drawn
Concept

Boson — where it appears

A particle whose quantum state is unchanged when it is exchanged with an identical one, such as a photon or a helium-4 atom. Their amplitudes add over permutations, which makes them bunch together and makes the output of a network of identical photons a permanent to compute.

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

The hole that holds exactly one particle. How likely a second particle is to be found a distance away from a first, relative to a gas with no correlation at all, for three cases that differ in nothing but the symmetry of the state under swapping the two labels. There is no interaction anywhere in this calculation: no Coulomb term, no potential, no force. Distinguishable particles give a flat line, which is what no interaction ought to give. Identical fermions dig a hole that reaches exactly zero at zero separation and fills back in over about a wavelength. Identical bosons do the opposite and pile up to twice the density. Integrating the fermion hole gives 0.9992 particles missing from around each one — exactly one, and the sum rule holds at any density, because raising the density narrows the hole in exact proportion. That is what makes the effect worth a name of its own. It is often called an exchange force and it is not a force: nothing carries momentum between the particles, and no term in the energy is proportional to a distance. It is a statement about which states exist. What follows from it is most of chemistry — the reason two atoms with filled shells repel, the reason a metal's electrons cost so much less Coulomb energy than a random arrangement would, and the reason matter takes up room.

The force with no force in it

Two identical fermions keep apart and two identical bosons crowd together, and neither is being pushed. The Hamiltonian contains no interaction at all: what produces the hole and the pile is which many-particle states exist, and the hole it digs around each electron holds exactly one particle at any density whatever.

quantum · Exclusion Three identical photons in a three-way splitter: some outcomes are forbidden. One photon enters each input of a symmetric three-way splitter, which sends each photon to each output with equal probability. Across: the ten ways three photons can leave, written as how many leave by each output. Bars, for each outcome: photons that can be told apart, identical photons, and identical fermions. Distinguishable photons spread over all ten, as independent coins would. Identical photons never produce 210, 201, 120, 102, 021, 012 — the 6 outcomes whose output labels do not add to a multiple of three — and pile into the rest: 300 with 0.222, 111 with 0.333, 030 with 0.222, 003 with 0.222. Identical fermions leave one per output every time (probability 1.000). Each probability is a sum of amplitudes over the distinct ways to reach the outcome, and each set sums to one.

The outcomes identical photons refuse

Two identical photons meeting at a beam splitter always leave together, and that one fact carries three more. No classical light can empty the coincidence dip more than halfway, so the depth is a test of what light is; the depth measures how identical two photons are, however they differ; and with three photons in a three-way splitter whole classes of outcome become impossible — the first case of a sum over paths that no known algorithm can evaluate quickly as the photons multiply.

quantum · Photon

Named alongside it

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

AntisymmetryBeam splitterBoson samplingCoincidenceCovalent bondExchange holeExchange interactionFermionFerromagnetismIdentical particlesIndistinguishabilityPair correlation

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