Let's do the reverse Fourier transform since that's a bit clearer. In fact, it is made up of quarks, which are electrically charged particles.We can do this with a bit of a trick. This fact was an early indication that the neutron is not an elementary particle. In particular, the neutron possesses a non-zero magnetic moment despite being electrically neutral. Ĭomposite particles also possess magnetic moments associated with their spin. The value of 2 arises from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties, and the deviation from −2 arises from the electron's interaction with the surrounding electromagnetic field, including its own field. What is measured is the off-diagonal matrix element of the dipole operator between the states with. One of the triumphs of the theory of quantum electrodynamics is its accurate prediction of the electron g-factor, which has been experimentally determined to have the value −2.002 319 304 362 56(35), with the digits in parentheses denoting measurement uncertainty in the last two digits at one standard deviation. So the ammonia dimer in fact has no permanent dipole moment. The electron, being a charged elementary particle, possesses a nonzero magnetic moment. For exclusively orbital rotations it would be 1 (assuming that the mass and the charge occupy spheres of equal radius). Where the dimensionless quantity g s is called the spin g-factor. However, spin implies that the phase of the particle depends on the angle as e i S θ Since elementary particles are point-like, self-rotation is not well-defined for them. Quantization fundamentally alters the character of both spin and orbital angular momentum. : 131 While the names based on mechanical models have survived, the physical explanation has not. Historically orbital angular momentum related to particle orbits. Relation to orbital angular momentum Īs the name suggests, spin was originally conceived as the rotation of a particle around some axis. Spin represents polarization for other vector bosons as well. Thus, light of a defined circular polarization consists of photons with the same spin, either all +1 or all −1. Photon spin is the quantum-mechanical description of light polarization, where spin +1 and spin −1 represent two opposite directions of circular polarization. This same concept of spin can be applied to gravity waves in water: "spin is generated by subwavelength circular motion of water particles". The classical analog for quantum spin is a circulation of energy or momentum-density in the particle wave field: "spin is essentially a wave property". Any model for spin based on mass rotation would need to be consistent with that model. In the Standard Model, the fundamental particles are all considered "point-like": they have their effects through the field that surrounds them. The very earliest models for electron spin imagined a rotating charged mass, but this model fails when examined in detail: the required space distribution does not match limits on the electron radius: the required rotation speed exceeds the speed of light. Often, the "spin quantum number" is simply called "spin". In practice, spin is usually given as a dimensionless spin quantum number by dividing the spin angular momentum by the reduced Planck constant ħ, which has the same dimensions as angular momentum. The SI unit of spin is the same as classical angular momentum (i.e., N These are indicated by assigning the particle a spin quantum number. All elementary particles of a given kind have the same magnitude of spin angular momentum, though its direction may change. Spinors and bispinors behave similarly to vectors: they have definite magnitudes and change under rotations however, they use an unconventional "direction". Spin is described mathematically as a vector for some particles such as photons, and as spinors and bispinors for other particles such as electrons. The existence of the electron spin can also be inferred theoretically from the spin–statistics theorem and from the Pauli exclusion principle-and vice versa, given the particular spin of the electron, one may derive the Pauli exclusion principle. The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. : 183–184 Spin should not be understood as in the "rotating internal mass" sense: spin is a quantized wave property. Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. For the concept in classical mechanics, see Rotation. This article is about the concept in quantum mechanics.
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