| spin (physics) | |
|---|---|
| Name | Spin |
| Caption | Schematic of spin up and spin down states |
| Unit | ħ (reduced Planck constant) |
| Dimension | Angular momentum |
| Introduced | Early 20th century |
| Related | Pauli exclusion principle, Magnetic moment, Angular momentum (physics) |
spin (physics) Spin in physics is an intrinsic form of angular momentum carried by elementary particles, composite particles, and quasiparticles that has no classical analogue. It is a central concept in Quantum mechanics and Quantum field theory, determining particle statistics, magnetic moments, selection rules, and many technologies from magnetic resonance imaging to quantum computing.
In quantum theory, spin denotes an intrinsic angular momentum described by a vector operator whose components satisfy the so(3) commutation relations. Unlike orbital angular momentum, spin does not arise from spatial motion but is a fundamental degree of freedom of particles such as the electron, proton, neutron, and photon. Spin determines important physical properties: half-integer spins (fermions) obey the Pauli exclusion principle and Fermi–Dirac statistics, while integer spins (bosons) follow Bose–Einstein statistics. Spin couples to external fields through the magnetic moment, producing observable effects in phenomena like Stern–Gerlach deflection and electron spin resonance.
Spin is formalized using representations of the rotation group SO(3) and its double cover SU(2). For a particle of spin quantum number s, the total spin operator S has eigenvalues S^2 = s(s+1)ħ^2, with 2s+1 magnetic sublevels labeled by m_s = −s,...,s. Spinors provide the representation space for half-integer s and transform under spinor representations of SU(2), central to the Dirac equation for relativistic fermions. For field-theoretic treatments, spin is encoded in the Lorentz group representations used in Quantum field theory for fields such as the Dirac spinor, Majorana fermion, and vector boson fields. The connection between spin and statistics is formalized in the spin–statistics theorem proven in axiomatic quantum field theory.
Electrons (spin-1/2) provide the archetypal example: their spin gives rise to the electronic magnetic moment and underlies atomic fine structure. Nuclear spins (e.g., in protons and neutrons) produce nuclear magnetic resonance signals used in NMR spectroscopy and magnetic resonance imaging. Photons carry spin-1 associated with circular polarization and helicity states rather than rest-frame angular momentum; massless particles require careful treatment via helicity (physics). Composite particles inherit spin from constituents via angular momentum addition: e.g., the deuteron (bound proton–neutron) has spin-1, while many mesons are integer-spin bosons. In solid-state physics, effective quasiparticles such as magnons and excitons carry spin-like quantum numbers relevant to condensed matter physics and spintronics.
Spin measurements correspond to projective measurements of spin operators S_x, S_y, S_z with discrete eigenvalues ħ m_s. The canonical measurement apparatus historically is the Stern–Gerlach experiment, performed first by Otto Stern and Walther Gerlach, which spatially separates spin components of neutral silver atoms. In quantum mechanics, spin observables are described by Pauli matrices for spin-1/2 and by higher-dimensional angular momentum operator matrices for larger s. Eigenstates form basis vectors (e.g., |↑⟩ and |↓⟩) used in Bloch sphere representations and in describing coherence and entanglement in quantum information science. Measurement back-action and noncommuting components exemplify fundamental quantum features such as uncertainty relations.
Atomic and nuclear structure depend crucially on coupling schemes for orbital and spin angular momenta. The LS coupling (Russell–Saunders coupling) combines individual electron orbital (L) and spin (S) angular momenta into total J = L + S, effective in light atoms; the jj coupling scheme couples single-particle j = l + s values first and is important in heavy atoms with strong spin–orbit coupling. Addition of angular momenta follows the Clebsch–Gordan coefficient rules and Wigner 3-j symbols, with selection rules governed by parity (physics) and total angular momentum conservation. In nuclear physics, shell model configurations use spin–orbit splitting to explain magic numbers, while in particle physics angular momentum algebra classifies states in multiplets of Poincaré group representations.
Techniques exploiting spin underlie many experimental methods and technologies. Nuclear magnetic resonance and electron spin resonance detect nuclear and electronic spins via resonant transitions; these techniques are central to chemical analysis (NMR spectroscopy) and medical imaging (magnetic resonance imaging). Spintronics leverages electron spin and spin currents in materials and devices investigated at institutions like IBM and Hitachi; effects such as giant magnetoresistance enabled advances in data storage (e.g., hard disk drive read heads). In quantum computing, spin qubits realized in quantum dots, NV centers in diamond, and donor spins in silicon form leading platforms studied by groups at University of New South Wales, University of California, Santa Barbara, and companies like Microsoft (Station Q). Precision measurements of spin-related quantities constrain fundamental physics via experiments at facilities such as CERN and Brookhaven National Laboratory (e.g., muon g−2), while spin transport and manipulation underpin emerging quantum sensors and spin-based logic.