# Spin (physics)

Spin is a quantum phenomenon constituting an intrinsic form of angular momentum found in the elementary particles of the Standard Model, composite particles (baryons or mesons), and atomic nuclei. It is distinct from orbital angular momentum (which is more akin to the concept of quantized angular momentum as proposed in the Bohr model of the atom).

## Quotes

* The spin S = 3/2 nucleus and the S = 1/2 valence electron spin combine to gives states with a total spin of either S = 2 or S = 1.
** James F. Annett: Superconductivity, superfluids, and condensates. Oxford: Oxford Univ. Press. 2004. p. 11.
* Protons behave like quantum spinning tops with spin ½ in units of Planck's constant $\hbar$. This spin is responsible for many fundamental properties of nature including the proton's magnetic moment, the different phases of matter in low temperature physics, the properties of neutron stars and the stability of the known Universe. One of the main questions in particle and nuclear physics the last 20 years has been: How is the proton's spin built up from its quark and gluon constituents?
** Steven D. Bass: The Spin Structure of the Proton. World Scientific. 2008. p. 1. ISBN 978-981-270-946-2.
* In dealing with problems about electrons according to quantum mechanics, one finds one does not get agreement with experiment if one assumes the electrons to be simply point charges repelling one another according to the Coulomb law of forces. It is necessary to make the assumption that each electron is spinning and so has an internal angular momentum, and also that it has a magnetic moment. To make the theory agree with experiment we must assume that the eigenvalues of the Cartesian component of the spin angular momentum in any direction are ½$\hbar$ and –½$\hbar$, and that the magnetic moment of the electron (with its sign reversed) always lies in the same direction as the spin angular momentum ...
** P. A. M. Dirac: The Principles of Quantum Mechanics. Clarendon Press. 1930. p. 136.
* ... when one has to deal with very many electrons ... one then requires a ... simpler and rougher method. Such a method is provided by Thomas' atomic model, in which the electrons are regarded as forming a perfect gas satisfying the Fermi statistics and occupying the region of phase space of lowest energy. This region of phase space is assumed to be saturated, with two electrons with opposite spins in each volume (2πh)$^3$, and the remainder is assumed to be empty. Although this model hitherto has not been justified theoretically, it seems to be a plausible approximation for the interior of a heavy atom and one may expect it to give with some accuracy the distribution of electric charge there.
** P. A. M. Dirac: (July 1930)"Note on Exchange Phenomena in the Thomas Atom". Mathematical Proceedings of the Cambridge Philosophical Society 26 (3): 376-385. DOI:10.1017/S0305004100016108.
* For a spin-one particle only—because it requires three amplitudes—the correspondence with a vector is very close. In each case, there are three numbers that must transform with coordinate changes in a certain definite way. In fact, there is a set of base states which transform just like the three components of a vector.
** Richard Feynman: (1965). 5–7. Transforming to a different base in Chapter 5. Spin One, The Feynman Lectures on Physics, Volume III, Quantum Mechanics
* The investigations of Dirac (1936) on relativistic wave equations for particles with arbitrary spin have recently been followed up by one of us (Fierz, 1939, ... ) It was there found possible to set up a scheme of second quantization in the absence of an external field, and to derive expressions for the current vector and the energy-momentum tensor. These considerations will be extended in the present paper to the case when there is an external electromagnetic field, but we shall in the first instance disregard the second quantization and confine ourselves to a c-number theory. The difficulty of this problem is illustrated by the fact that the most immediate method of taking into account the effect of the electromagnetic field, proposed by Dirac (1936), leads to inconsistent equations as soon as the spin is greater than 1.
** Markus Fierz and Wolfgang Pauli, (1939). "On relativistic wave equations for particles of arbitrary spin in an electromagnetic field". Proc. Roy. Soc. Lond. A 173 (953): 211–232. DOI:10.1098/rspa.1939.0140.
* ... Before the year 1928, every physicist knew what we meant by an elementary particle. The electron and the proton were the obvious examples, and at that time we would have liked simply to take them as point charges, infinitely small, defined simply by their charge and their mass. We had to agree reluctantly that they must have a radius, since their electromagnetic energy had to be finite. We did not like the idea that such objects should have properties like a radius, but still we were happy that at least they seemed to be completely symmetrical, like a sphere. But then the discovery of electron spin changed this picture considerably. The electron was not symmetrical. It had an axis, and this result emphasized that perhaps such particles have more than one property, and that they are not simple, not so elementary as we had thought before.
** Werner Heisenberg: Encounters with Einstein: And Other Essays on People, Places, and Particles. Princeton University Press. 1989. p. 31. ISBN 0-691-02433-2. translated from Heisenber, W. (1977). Tradition in der Wissenschaft. Münich: R. Piper.
* With the exception of experts on the classification of spectral terms, the physicists found it difficult to understand the exclusion principle, since no meaning in terms of a model was given to the fourth degree of freedom of the electron. The gap was filled by Uhlenbeck and Goudsmit’s idea of electron spin ..., which made it possible to understand the anomalous Zeeman effect simply by assuming that the spin quantum number of one electron is equal to 1/2 and that the quotient of the magnetic moment to the mechanical angular moment has for the spin a value twice as large as for the ordinary orbit of the electron. Since that time, the exclusion principle has been closely connected with the idea of spin.
** Wolfgang Pauli: Exclusion Principle and Quantum Mechanics, Nobel Prize Lecture 29–30. nobelprize.org (December 13, 1946).