Is the electron physically spinning?

No; spin is an intrinsic quantum property, not literal rotation. Modeling the electron as a spinning ball gives an inconsistent picture, so spin is best understood as a fundamental degree of freedom obeying the angular-momentum algebra with a half-integer value.

Why does a spinor need two full rotations to come back to itself?

Under a rotation a spin one-half state acquires a sign change after a single full turn and returns to its original form only after two, reflecting that spinors transform under the double cover of the rotation group rather than the rotation group itself.

Electron Spin

Electron spin is an intrinsic angular momentum carried by the electron that has no classical counterpart; it takes only two values along any axis, is described by two-component spinors and the Pauli matrices, and gives the electron a magnetic moment.

Encontrar tema com PaperMindEm breveFind papers & topics

Tools & resources

Baixar slides

Learn & explore

VídeoEm breve

Definition

Electron spin is the intrinsic angular momentum of the electron with quantum number one-half, represented by two-component spinors acted on by the Pauli spin matrices, and associated with an intrinsic magnetic moment.

Scope

The topic covers the experimental discovery of spin, the spin one-half algebra and the Pauli spin matrices, two-component spinor states and their behavior under rotation, the spin magnetic moment and the gyromagnetic ratio, spin precession in a magnetic field, and the role of spin in the Stern-Gerlach experiment and magnetic resonance.

Core questions

What experimental evidence established that the electron carries intrinsic spin?
How is a spin one-half state represented mathematically?
Why does a spin one-half state require a rotation of two full turns to return to itself?
How does spin give the electron a magnetic moment and how does it precess?

Key concepts

spin one-half
Pauli matrices
spinor
magnetic moment
Stern-Gerlach experiment
Larmor precession

Key theories

Spin one-half and the Pauli matrices: A spin one-half particle lives in a two-dimensional state space spanned by spin-up and spin-down, with the three spin components represented by the Pauli matrices; measurement along any axis yields only two outcomes, a hallmark of the smallest nontrivial quantum system.
Spin magnetic moment and precession: Spin endows the electron with a magnetic moment roughly twice the classical expectation, so in a magnetic field the spin precesses at the Larmor frequency, the basis of the Stern-Gerlach deflection and of magnetic resonance techniques.

Clinical relevance

Electron and nuclear spin underpin major measurement technologies: nuclear magnetic resonance and magnetic resonance imaging read out precessing nuclear spins, electron spin resonance probes unpaired electrons, and spintronics and spin qubits use the electron's spin to store and process information.

History

The Stern-Gerlach experiment of 1922 showed space quantization; Goudsmit and Uhlenbeck introduced electron spin in 1925 to explain spectral doublets, and Pauli built the two-component spinor formalism in 1927, later given a relativistic foundation by Dirac.

Key figures

Wolfgang Pauli
Samuel Goudsmit
George Uhlenbeck
Otto Stern

Seminal works

sakurai2017
cohentannoudji2019

Frequently asked questions

Is the electron physically spinning?: No; spin is an intrinsic quantum property, not literal rotation. Modeling the electron as a spinning ball gives an inconsistent picture, so spin is best understood as a fundamental degree of freedom obeying the angular-momentum algebra with a half-integer value.
Why does a spinor need two full rotations to come back to itself?: Under a rotation a spin one-half state acquires a sign change after a single full turn and returns to its original form only after two, reflecting that spinors transform under the double cover of the rotation group rather than the rotation group itself.