Identical particles

related topics
{math, energy, light}
{math, number, function}
{rate, high, increase}
{line, north, south}
{specie, animal, plant}

Identical particles, or indistinguishable particles, are particles that cannot be distinguished from one another, even in principle. Species of identical particles include elementary particles such as electrons, as well as composite particles such as atoms and molecules which are in precisely the same quantum state.

There are two main categories of identical particles: bosons, which can share quantum states, and fermions, which do not share quantum states due to the Pauli exclusion principle. Examples of bosons are photons, gluons, phonons, and helium-4 atoms. Examples of fermions are electrons, neutrinos, quarks, protons and neutrons, and helium-3 atoms.

The fact that particles can be identical has important consequences in statistical mechanics. Calculations in statistical mechanics rely on probabilistic arguments, which are sensitive to whether or not the objects being studied are identical. As a result, identical particles exhibit markedly different statistical behavior from distinguishable particles. For example, the indistinguishability of particles has been proposed as a solution to Gibbs' mixing paradox.

Contents

Distinguishing between particles

There are two ways in which one might distinguish between particles. The first method relies on differences in the particles' intrinsic physical properties, such as mass, electric charge, and spin. If differences exist, we can distinguish between the particles by measuring the relevant properties. However, it is an empirical fact that microscopic particles of the same species have completely equivalent physical properties. For instance, every electron in the universe has exactly the same electric charge; this is why we can speak of such a thing as "the charge of the electron".

Full article ▸

related documents
Bell's theorem
Polar coordinate system
Quantum superposition
Atomic orbital
Standard Model
Lorentz force
Kinematics
Mathematical formulation of quantum mechanics
Casimir effect
Magnetohydrodynamics
Modified Newtonian dynamics
Electromagnetic radiation
Fluid dynamics
Lagrangian point
Bose–Einstein condensate
Navier–Stokes equations
Lens (optics)
Black body
Gravitational lens
Angular momentum
Frame of reference
Magnet
Sundial
Bohm interpretation
Mercury (planet)
Superconductivity
Cosmic ray
Roche limit
Ohm's law
Parallax