Particle number refers to the count of elementary particles (such as electrons, photons, or quarks) in a given system. In classical physics, this number is usually fixed, but in relativistic quantum theories—especially quantum field theory—particle number is not conserved. Particles can be created and destroyed through interactions, and even the vacuum can fluctuate with virtual particle-antiparticle pairs.
History
The non-conservation of particle number emerged in the 1930s with the development of quantum electrodynamics, particularly through the work of Paul Dirac and later the renormalization program of the 1940s. The full implications were clarified with the advent of quantum field theory.
How it works
In quantum field theory, particles are excitations of underlying fields. The number operator, which counts particles, does not commute with the Hamiltonian in interacting theories, meaning that the number of particles can change over time. For example, an electron and a positron can annihilate to produce two photons, and a high-energy photon can pair-produce an electron and a positron. The concept of particle number becomes particularly subtle in curved spacetime, where an accelerating observer perceives a different particle content than an inertial one (the Unruh effect).
In practice
Particle number non-conservation is essential in particle accelerators, where collisions create new particles, and in cosmology, where the early universe's particle creation explains the matter-antimatter asymmetry.
Fun fact
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