In previous papers, the quantum behavior of matter has been shown to emerge as a result of its permanent interaction with the random zero-point radiation field. Fundamental results, such as the Schrödinger and the Heisenberg formalism, have been derived within this framework. Further, the theory has been shown to provide the basic QED formulas for the radiative corrections, as well as an explanation for entanglement in bipartite systems. This paper addresses the problem of spin from the same perspective. The zero-point field is shown to produce a helicoidal motion of the electron, through the torque exerted by the electric field modes of a given circular polarization, which results in an intrinsic angular momentum, of value ℏ /2. Associated with it, a magnetic moment with a ( g -factor of 2 is obtained. This allows us to identify the spin of the electron as a further emergent property, generated by the action of the random zero-point field.
In previous papers, the quantum behavior of matter has been shown to emerge as a result of its permanent interaction with the random zero-point radiation field. Fundamental results, such as the Schrödinger and the Heisenberg formalism, have been derived within this framework. Further, the theory has been shown to provide the basic QED formulas for the radiative corrections, as well as an explanation for entanglement in bipartite systems. This paper addresses the problem of spin from the same perspective. The zero-point field is shown to produce a helicoidal motion of the electron, through the torque exerted by the electric field modes of a given circular polarization, which results in an intrinsic angular momentum, of value ℏ /2. Associated with it, a magnetic moment with a ( g -factor of 2 is obtained. This allows us to identify the spin of the electron as a further emergent property, generated by the action of the random zero-point field.
A new way of arriving at the quantum formalism is presented, based on the recognition of the reality of the random zero-point radiation field (ZPF). The quantization of both matter and radiation field is shown to emerge as a result of the permanent interaction of matter with the ZPF. Quantum mechanics (QM) is obtained both in its Schrödinger and its Heisenberg version, under certain well-defined conditions and approximations. The theory provides for an explanation of the origin of entanglement. Further, the same physical elements and hypotheses allow us to cross the doorway and go beyond QM, to the realm of (nonrelativistic) quantum electrodynamics (QED).
Quantization is derived as an emergent phenomenon, resulting from the permanent interaction between matter and radiation field. The starting point for the derivation is the existence of the (continuous) random zero-point electromagnetic radiation field (zpf) of mean energy ℏω/2 per normal mode. A thermodynamic and statistical analysis leads unequivocally (and without quantum assumptions) to the Planck distribution law for the complete field in equilibrium. The problem of the quantization of matter is then approached from the same perspective: A detailed study of the dynamics of a particle embedded in the zpf shows that when the entire system eventually reaches a situation of energy balance thanks to the combined effect of diffusion and dissipation, the particle has acquired its characteristic quantum properties. To obtain the quantum-mechanical description it has been necessary to do a partial averaging and take the radiationless approximation. Consideration of the neglected radiative terms allows to establish contact with nonrelativistic quantum electrodynamics and derive the correct formulas for the first-order radiative corrections. Quantum mechanics emerges therefore as a partial, approximate and time-asymptotic description of a phenomenon that in its original (pre-quantum) description is entirely local and causal.
Are we to accept quantization as a fundamental property of nature, the origin of which does not require or admit further investigation? To get an insight into this question we consider atomic systems as open systems, since they are by necessity in contact with the electromagnetic radiation field. This includes not only photonic radiation, but, more importantly for our purposes, the random zero-point or nonthermal radiation that pervades the Universe. The Heisenberg inequalities, atomic stability and the existence of discrete solutions are explained as a result of the permanent action of this field upon matter and the balance between mean absorbed and emitted powers in the equilibrium regime. A detailed study carried out along the years has led to the usual quantum-mechanical formalism as a powerful and revealing statistical description of the behavior of matter in the radiationless approximation, as well as to the radiative corrections of nonrelativistic QED. The theory presented gives thus a response to the question posed above, within a local, realist and objective framework: quantization appears as an emergent phenomenon due to the matter-field interaction.
A rigorous derivation of the Schrödinger theory from the Pauli (or Dirac) theory implies that the Schrödinger equation describes an electron in an eigenstate of spin. Furthermore, the ground-state kinetic energy is completely determined by the electron spin density. This can be explained by interpreting the spin as an orbital angular momentum, which is necessarily accompanied by a kinetic energy. Thus, the spin is a zero-point angular momentum associated with the zero-point energy of the electron. Since the dispersion in electron momentum is determined by the zero-point energy, the Heisenberg uncertainty relations for an electron can be interpreted as a property of the electronspin motion. The kinetic interpretation of spin and the statistical interpretation of quantum mechanics can be jointly sustained by regarding the electron as a point particle. It follows that stationary electron states are sources of fluctuating electric fields. There is reason to believe that these fluctuating fields are responsible for the Van der Waals force and can be identified with electromagnetic vacuum field fluctuations. The kinetic interpretation of spin then implies that the Van der Waals forces are spin dependent. These ideas are not only consistent with the conventional mathematical formalism of quantum mechanics, they provide a more complete and coherent interpretation of many details in the formalism than does the alternative Copenhagen interpretation. They present some difficulties, however, which, if the kinetic interpretation of spin is correct, probably require some modification of quantum electrodynamics to be resolved.
Spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, and atomic nuclei. It is wildly believed that spin is a purely quantum mechanical concept and has no classical analogue. In fact, elementary particles are conceived as point objects which have no axis to “spin” around. Therefore, there is no explaining how spin arises at the fundamental level, why particles have the values they do, and what underpins the Pauli Exclusion principle and Bose-Einstein behavior. However, spin is like a vector quantity; it has a definite magnitude, and it has a “direction”, in order to spin should be composite. In this paper we propose a physical explanation for spin of the electron at the sub-particle level, relying on the vortex model of the electron. The electron is described as a superfluid frictionless vortex which has a mass, angular momentum and spin to provide a complete explanation of all properties of the electron: it composite, spinning around its own axis, produces a tiny magnetic fields independent of those from its orbital motions. The classical hydrodynamic laws are used to describe the quantum properties of the electron, such as spin, angular momentum, magnetic momentum and a magnetic dipole. The circulation in the vortex is constant, and the angular momentum of the vortex is conserved and has the same value of Planck constant. The direction of the angular momentum of a spinning electron vortex is along the axis of rotation and determined by the direction of spin. The spin quantum number 1/2 has a fixed value which represents the gap between the circulation rate of the core of the vortex and the boundaries of the vortex. The changeable values +1/2 “spin-up” or -1/2 “spin-down” indicate the direction of the magnetic dipole of the vortex. The relation between spin and Planck constant is discussed and the origin h/4pi angular momentum units are revealed.
First, the experimental foundations for the existence of a new dynamical variable, the spin of particles, are presented. The Pauli equation is then derived in detail, two applications are given and the energy levels of a particle with spin in a constant magnetic field are studied. This is the analysis of Landau levels, which can be performed by using the known results on the spectrum of harmonic oscillators. In this chapter we also study in detail the addition of orbital angular momentum and spin, as well as the spin–orbit interaction with the resulting Thomas precession. Stern-Gerlach experiment and electron spin The hypothesis that the electron has an intrinsic magnetic moment and an angular momentum, in short a spin , was first suggested in Uhlenbeck and Goudsmit (1926). They noticed, even before the discovery of quantum mechanics, that a complete description of spectra was not possible unless a magnetic moment and a mechanical moment were ascribed to the electron, and hence the concept of an electron as a point charge was insufficient. First, let us therefore try to understand how a magnetic moment can be associated to an atomic system. For this purpose, consider for simplicity the Bohr model of an hydrogen atom, where the electron moves along a circular orbit and rotates with orbital angular momentum L .