spin (physics)

spin (physics). In quantum mechanics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, and atomic nuclei. Unlike orbital angular momentum, it does not correspond to physical rotation but is a fundamental quantum property. The concept was first proposed in the Stern–Gerlach experiment and later incorporated into the Dirac equation, which describes relativistic quantum mechanics.

Introduction

The discovery of spin resolved critical anomalies in atomic spectra, such as the fine structure observed in the hydrogen atom. Early models of the atom, like the Bohr model, could not explain these details. The concept was formally introduced by George Uhlenbeck and Samuel Goudsmit to account for the Zeeman effect. This property is quantized, meaning particles have discrete spin states, a fact confirmed by experiments like the Frank–Hertz experiment.

Quantum mechanical description

In the formalism of quantum mechanics, spin is described by operators that obey the same commutation relations as angular momentum. The spin quantum number *s* is fixed for each type of particle; for example, electrons have *s* = ½, making them fermions that obey the Pauli exclusion principle. The spin operator components do not commute, leading to the uncertainty principle. The mathematical framework uses Pauli matrices for spin-½ systems and the more general Clebsch–Gordan coefficients for coupling spins.

Experimental evidence and measurement

The first direct evidence came from the Stern–Gerlach experiment, where a beam of silver atoms split in a magnetic field, revealing quantized angular momentum. Later, techniques like electron paramagnetic resonance and nuclear magnetic resonance (NMR), pioneered by Felix Bloch and Edward Mills Purcell, became essential tools. Modern experiments at facilities like CERN and the Fermi National Accelerator Laboratory continue to measure spin properties of particles like the Higgs boson and top quark.

Relativistic quantum mechanics and spin

The full incorporation of spin arose from relativistic quantum mechanics. Paul Dirac formulated the Dirac equation, which naturally predicted the spin of the electron and led to the prediction of the positron. In quantum field theory, spin is a consequence of particles transforming under specific representations of the Poincaré group, as described in the Wigner classification. The Standard Model classifies all fundamental particles by their spin, with bosons having integer and fermions half-integer values.

Applications and phenomena

Spin underpins vast areas of modern technology and physics. Spintronics exploits electron spin in devices like hard disk drive read heads and magnetic random-access memory. Medical magnetic resonance imaging (MRI) relies on the spin magnetic moment of nuclei like hydrogen. In condensed matter physics, collective spin behavior leads to phenomena like ferromagnetism in iron and superconductivity in materials studied at the Max Planck Institute. The Einstein–de Haas effect demonstrates the connection between spin and macroscopic rotation.