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Journal of Physics Conference Series

Emergent Spin and New Physics

I. B. Pestov

Published Dec 1, 2017• 1 citation
Publisher

Abstract

In quantum mechanics and particle physics, spin is considered as an intrinsic form of orbital angular momentum. Our goal here is to demonstrate that the well known fundamental idea of Kronig, Uhlenbek and Goudsmit can be presented as an intrinsic form of symmetric top rotation motion. It will be shown that internal symmetry of intrinsic top can be realized on a set of the simplest geometrical quantities, which themselves do not exhibit this property. That is why an intrinsic form of top angular momentum will be called emergent spin. The concept of emergent spin is more general than the concept of spin and, hence, it can be interesting in terms of discussion of the possible ways to look for a physics beyond the Standard Model.

DOI
10.1088/1742-6596/938/1/012034

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•Jan 1, 2019•0 citations
In quantum mechanics and particle physics, spin is considered as an intrinsic form of orbital angular momentum. Our goal here is to demonstrate that the well known fundamental idea of Kronig, Uhlenbek and Goudsmit can be presented as an intrinsic form of symmetric top rotation motion. It will be shown that internal symmetry of intrinsic top can be realized on a set of the simplest geometrical quantities, which themselves do not exhibit this property. That is why an intrinsic form of top angular momentum will be called emergent spin. The concept of emergent spin is more general than the concept of spin and, hence, it can be interesting in terms of discussion of the possible ways to look for a physics beyond the Standard Model.
In quantum mechanics and particle physics, Spin is considered as an intrinsic form of the quantum orbital angular momentum. The goal of this paper is to demonstrate that in accordance with the creative original idea of Kronig, Uhlenbeck and Goudsmit, Spin can be represented as an intrinsic form of quantum Spherical Top angular momentum. It will be shown that this internal symmetry can be realized on a set of the simplest geometrical quantities, which themselves do not exhibit this emergent property. That is why this phenomenon will be called Emergent Spin. The concept of Spin as an emergent property is more general than the habitual concept of Spin and, hence, it can be interesting in terms of discussion of possible ways to look for a physics beyond the Standard Model. Now, there is no doubt that new physics really exists and we need clear guidance on the best place to look.
Spin-s systems Angular momentum is one of the fundamental quantities of Newtonian physics, and in quantum physics its importance is at least as great. In quantum mechanics we often distinguish between two types of angular momentum: orbital angular momentum , which a system of particles possesses due to particle motion through space; and spin angular momentum , which is an intrinsic property of a particle. The distinction will be important later, but for now we will ignore it. We will here refer to angular momentum of any sort as “spin” and develop general-purpose mathematical tools for its description. We have already dealt with spin systems, particularly the example of a spin-½ particle. Our approach began with the empirical observation that a measurement of any spin component of a spin-½ particle could yield only the results +ħ/2 or −ħ/2. We introduced the basis states | z ±〉 for the two-dimensional Hilbert space ℋ. We also gave other basis states such as {| x ±〉} and {| y ±〉} in terms of the | z ±〉 states. From basis states and measurement values we constructed operators for the spin components S x , S y , and S z . With the operators in hand, we could then examine the algebraic relations between them (such as the commutation relation in Exercise 3.56). Our job here is to generalize our analysis to systems of arbitrary spin. To do this, we will reverse our chain of logic.
One of the most important applications of the quantum mechanical formalism developed in the previous chapter is to angular momentum. This is because many microsystems are spherically symmetric, or approximately so, and angular momentum is therefore conserved. This chapter discusses that a careful study of quantized angular momentum leads to a completely new physical phenomenon – intrinsic spin. The fact that the angular momentum vector of a quantum particle must point in certain restricted directions is a bizarre quantum property. In some respects the abstract idea of an internal angular momentum is reminiscent of the classical concept of a spinning body. In classical mechanics angular momentum is added vectorially but in the quantum case the issue is more subtle. The procedure will be illustrated by the example of the addition of two spins. As in classical mechanics a charged quantum system with angular momentum possesses a magnetic moment μ.
In the introductory remarks to Chapter 5 mention was made of the 1925 proposal of Uhlenbeck and Goudsmit that to an electron there should be assigned an intrinsic angular momentum or spin S = (S x , S y , S z )—this in addition to its quantum angular momentum (or orbital angular momentum) M = (M x , M y , M z ) defined in (5.4.4). This is not to be taken to mean that an electron actually spins about an axis in some physical way. Experiments (in particular the noted Stern-Gerlach experiment) have provided adequate justification for the proposed concept of spin, a proposal also made by R. Bichowsky and H. Urey. Dirac has shown that the notion of spin is necessary if quantum mechanics and Einstein relativity are to be consistent theories. Chemical properties of atoms, and their ability to combine and form molecules, the splitting of spectral lines by a magnetic field applied to an atom (i.e., the Zeeman effect, which we discuss later), all depend on this important notion.
In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the latter cannot. The difference leads to a radical deviation in the formulation of their corresponding dynamics in which an orbital angular momentum can be described by using a coordinate system but a spin angular momentum cannot. In this work, we show that it is possible to treat spin angular momentum in the same manner as orbital angular momentum by formulating spin dynamics using Schrödinger equation in an intrinsic coordinate system. As an illustration, we apply the formulation to the dynamics of a hydrogen atom and show that the intrinsic spin angular momentum of the electron can take half-integral values and, in particular, the intrinsic mass of the electron can take negative values. We also consider a further extension by generalising the formulation so that it can be used to describe other intrinsic dynamics that may associate with a quantum particle, for example, when a hydrogen atom radiates a photon, the photon associated with the electron may also possess an intrinsic dynamics that can be described by an intrinsic wave equation that has a similar form to that for the electron.
In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the later cannot. The difference leads to a radical deviation in the formulation of their corresponding dynamics in which an orbital angular momentum can be described by using a coordinate system but a spin angular momentum cannot. In this work we show that it is possible to treat spin angular momentum in the same manner as orbital angular momentum by formulating spin dynamics using Schrodinger equation in an intrinsic coordinate system. As an illustration, we apply the formulation to the dynamics of a hydrogen atom and show that the intrinsic spin angular momentum of the electron can take half-integral values and, in particular, the intrinsic mass of the electron can take negative values. We also consider a further extension by generalising the formulation so that it can be used to describe other intrinsic dynamics that may associate with a quantum particle, for example, when a hydrogen atom radiates a photon, the photon associated with the electron may also possess an intrinsic dynamics that can be described by an intrinsic wave equation that has a similar form to that for the electron.