The spin-statistics theorem is generalized to include quantum entanglement. Specifically, within ... more The spin-statistics theorem is generalized to include quantum entanglement. Specifically, within the context of spin entanglement, we prove that isotropically spin-correlated (ISC) states must occur in pairs. This pairing process can be composed of parallel or anti-parallel states. Consequently, the article proposes using ISC states as a unifying principle to explain better Bose-Einstein condensates, the theory of superconductivity, and molecular and atomic orbitals, all of which involve a pairing process. The theoretical framework is established in sections 1 and 2. The other qualitative sections focus primarily on the experimental evidence to support the theory.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Algebraic structures such as Rings, Fields, Boolean Algebras (Set Theory) and σ−Fields are well k... more Algebraic structures such as Rings, Fields, Boolean Algebras (Set Theory) and σ−Fields are well known and much has been written about them. In this paper we explore some properties of rings related to the distribution law. Specifically, we shall show that for rings there exists only one distribution law. Moreover, for the ring (Z p(p−1)n +, •), where (p, n) = 1 there exist isomorphic groups (G, +), (H, •), G, H ⊆ Z p(p−1)n of the order (p − 1). Finally, we note that every ring (Zpn, +, •) contains subfields mod(pn).
The EPR paradox dates back to 1935 when Einstein et al., through the use of non commuting operato... more The EPR paradox dates back to 1935 when Einstein et al., through the use of non commuting operators, proposed that quantum mechanics was not complete[1] in that it suggested a "spooky action at a distance." Later in 1964 John Bell was able to express the dilemma in a simple inequality[2] involving spin singlet states. If the inequality were satisfied then Einstein was correct and if it were violated then it favored the quantum mechanics point of view. In what follows, we present two approaches to Bell's inequality, and then offer an interpretation from the viewpoint of quantum mechanics based on the principle that the whole is more than the sum of its parts. This is then combined with the properties of the SU (2) group to give a more intuitive understanding of non-locality and spin entanglement from the perspective of the relativistic characteristics of rotations.
Bell's inequality has been traditionally used to explore the relationship between hidden variable... more Bell's inequality has been traditionally used to explore the relationship between hidden variables and the Copenhagen interpretation of quantum mechanics. In this paper, another use is found. Bell's inequality is used to derive a coupling principle for elementary particles and to give a deeper understanding of baryonic structure. We also give a derivation of the Pauli exclusion principle from the coupling principle.
In this article, we begin with a review of Pauli's version of the spinstatistics theorem and then... more In this article, we begin with a review of Pauli's version of the spinstatistics theorem and then show, by redefining the parameter associated with the Lie-Algebra structure of angular momentum, that another interpretation of the theorem may be given. It will be found that the vanishing commutator and anticommutator relationships can be associated with independent and dependent probability events respectively, and not spin value. Consequently, it gives a more intuitive understanding of quantum field theory and it also suggests that the distinction between timelike and spacelike events might be better described in terms of local and non-local events.
In the history of quantum mechanics, much has been written about the double-slit experiment, and ... more In the history of quantum mechanics, much has been written about the double-slit experiment, and much debate as to its interpretation has ensued. Indeed, to explain the interference patterns for subatomic particles, explanations have been given not only in terms of the principle of complementarity and wave-particle duality but also in terms of quantum consciousness and parallel universes. In this paper, the topic will be discussed from the perspective of spin-coupling in the hope of further clarification. We will also suggest that this explanation allows for a realist interpretation of the Afshar Experiment.
We construct a model of Brownian motion in Minkowski space. There are two aspects of the problem.... more We construct a model of Brownian motion in Minkowski space. There are two aspects of the problem. The first is to define a sequence of stopping times associated with the Brownian "kicks" or impulses. The second is to define the dynamics of the particle along geodesics in between the Brownian kicks. When these two aspects are taken together, the Central Limit Theorem (CLT) leads to temperature dependent four dimensional distributions defined on Minkowski space, for distances and 4-velocities. In particular, our processes are characterized by two independent time variables defined with respect to the laboratory frame: a discrete one corresponding to the stopping times when the impulses take place and a continuous one corresponding to the geodesic motion in-between impulses. The subsequent distributions are solutions of a (covariant) pseudo-diffusion equation which involves derivatives with respect to both time variables, rather than solutions of the telegraph equation which has a single time variable. This approach simplifies some of the known problems in this context.
In the normal presentation of the EPR problem a comparison is made between the (weak) Copenhagen ... more In the normal presentation of the EPR problem a comparison is made between the (weak) Copenhagen interpretation of quantum mechanics which seems to suggest that at times action at a distance may take place, and the hidden parameter interpretation which must satisfy Bell's inequality, in contradiction to the predictions of quantum mechanics. In this paper, we consider a relativistic approach to the paradox. However, the frame of reference under consideration is not the usual Lorenz frame but rather the spin frame of reference which is invariant with respect to the SU(2) group.
In this paper a one to one correspondence is established between spacetime metrics of general rel... more In this paper a one to one correspondence is established between spacetime metrics of general relativity and the wave equations of quantum mechanics. This is done by first taking the square root of the metric associated with a space and from there, passing directly to a corresponding expression in the dual space. It is shown that in the case of a massless particle, Maxwell's equation for a photon follows while in the case of a particle with mass, Dirac's equation results as a first approximation. Moreover, this one to one correspondence suggests a natural explanation of wave-particle duality. As a consequence, the distinction between quantum mechanics and classical relativistic mechanics is more clearly understood and the key role of initial conditions is emphasized.
In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general re... more In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general relativity and shown to be a generalized Dirac equation for quantum mechanics. This lends itself to a natural definition of wave-particle duality in quantum mechanics. This theory is now further developed to show that a free spinless quantum particle moving with velocity v obeys the standard wave equation of electro-magnetism. We also discuss the implications for the zitterbewegung problem and its relationship to isotropy. Moreover, it is also shown that for the theory to be consistent, the momentum defined by the Hamilton-.!acobi function presupposes the existence of a universal parameter internal to the system. In the case of particles with mass this invariant can be defined by dX = dt/m(t) where t has the units of time and m = m(t) has the units of mass.
In a previous article a relationship was established between the linearized metrics of General Re... more In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves is investigated. In the case of scalar fields, a relationship between mass and temperature is also worked out.
In this article we generalize the spin statistics theorem and show that a state obeys Fermi-Dirac... more In this article we generalize the spin statistics theorem and show that a state obeys Fermi-Dirac statistics if and only if the state is invariant under the action of SL(n, C). We also briefly discuss the experimental evidence and how the theorem relates to spin entanglement.
In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first writte... more In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles. In this essay, we take a different starting point. We begin with the metrics of general relativity and show how they can be used to construct by inspection constants of motion, which can then be used to write down the equations of the trajectories. This will be achieved by deriving a Hamiltonian-Jacobi function from the metric and showing that its existence requires all of the above mentioned properties. The article concludes with four applications, which includes a derivation of Kepler's First Law of Motion for planets, and a formula for describing the trajectories of galaxies moving in a space defined by the Robertson-Walker metric.
In this article, the rotational invariance of entangled quantum states is investigated as a possi... more In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This will be referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of this coupling while the Bose-Einstein follows by breaking it. Finally, the experimental evidence to justify the above classification will be discussed.
In this article, the rotational invariance of entangled quantum states is investigated as a possi... more In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This is referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of this coupling while the Bose-Einstein follows by breaking it. In section 5, the above approach is related to Pauli's original spin-statistics theorem and finally in the last two sections, a theoretical justification, based on Clebsch-Gordan coefficients and the experimental evidence respectively, is presented.
The spin-statistics theorem is generalized to include quantum entanglement. Specifically, within ... more The spin-statistics theorem is generalized to include quantum entanglement. Specifically, within the context of spin entanglement, we prove that isotropically spin-correlated (ISC) states must occur in pairs. This pairing process can be composed of parallel or anti-parallel states. Consequently, the article proposes using ISC states as a unifying principle to explain better Bose-Einstein condensates, the theory of superconductivity, and molecular and atomic orbitals, all of which involve a pairing process. The theoretical framework is established in sections 1 and 2. The other qualitative sections focus primarily on the experimental evidence to support the theory.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Algebraic structures such as Rings, Fields, Boolean Algebras (Set Theory) and σ−Fields are well k... more Algebraic structures such as Rings, Fields, Boolean Algebras (Set Theory) and σ−Fields are well known and much has been written about them. In this paper we explore some properties of rings related to the distribution law. Specifically, we shall show that for rings there exists only one distribution law. Moreover, for the ring (Z p(p−1)n +, •), where (p, n) = 1 there exist isomorphic groups (G, +), (H, •), G, H ⊆ Z p(p−1)n of the order (p − 1). Finally, we note that every ring (Zpn, +, •) contains subfields mod(pn).
The EPR paradox dates back to 1935 when Einstein et al., through the use of non commuting operato... more The EPR paradox dates back to 1935 when Einstein et al., through the use of non commuting operators, proposed that quantum mechanics was not complete[1] in that it suggested a "spooky action at a distance." Later in 1964 John Bell was able to express the dilemma in a simple inequality[2] involving spin singlet states. If the inequality were satisfied then Einstein was correct and if it were violated then it favored the quantum mechanics point of view. In what follows, we present two approaches to Bell's inequality, and then offer an interpretation from the viewpoint of quantum mechanics based on the principle that the whole is more than the sum of its parts. This is then combined with the properties of the SU (2) group to give a more intuitive understanding of non-locality and spin entanglement from the perspective of the relativistic characteristics of rotations.
Bell's inequality has been traditionally used to explore the relationship between hidden variable... more Bell's inequality has been traditionally used to explore the relationship between hidden variables and the Copenhagen interpretation of quantum mechanics. In this paper, another use is found. Bell's inequality is used to derive a coupling principle for elementary particles and to give a deeper understanding of baryonic structure. We also give a derivation of the Pauli exclusion principle from the coupling principle.
In this article, we begin with a review of Pauli's version of the spinstatistics theorem and then... more In this article, we begin with a review of Pauli's version of the spinstatistics theorem and then show, by redefining the parameter associated with the Lie-Algebra structure of angular momentum, that another interpretation of the theorem may be given. It will be found that the vanishing commutator and anticommutator relationships can be associated with independent and dependent probability events respectively, and not spin value. Consequently, it gives a more intuitive understanding of quantum field theory and it also suggests that the distinction between timelike and spacelike events might be better described in terms of local and non-local events.
In the history of quantum mechanics, much has been written about the double-slit experiment, and ... more In the history of quantum mechanics, much has been written about the double-slit experiment, and much debate as to its interpretation has ensued. Indeed, to explain the interference patterns for subatomic particles, explanations have been given not only in terms of the principle of complementarity and wave-particle duality but also in terms of quantum consciousness and parallel universes. In this paper, the topic will be discussed from the perspective of spin-coupling in the hope of further clarification. We will also suggest that this explanation allows for a realist interpretation of the Afshar Experiment.
We construct a model of Brownian motion in Minkowski space. There are two aspects of the problem.... more We construct a model of Brownian motion in Minkowski space. There are two aspects of the problem. The first is to define a sequence of stopping times associated with the Brownian "kicks" or impulses. The second is to define the dynamics of the particle along geodesics in between the Brownian kicks. When these two aspects are taken together, the Central Limit Theorem (CLT) leads to temperature dependent four dimensional distributions defined on Minkowski space, for distances and 4-velocities. In particular, our processes are characterized by two independent time variables defined with respect to the laboratory frame: a discrete one corresponding to the stopping times when the impulses take place and a continuous one corresponding to the geodesic motion in-between impulses. The subsequent distributions are solutions of a (covariant) pseudo-diffusion equation which involves derivatives with respect to both time variables, rather than solutions of the telegraph equation which has a single time variable. This approach simplifies some of the known problems in this context.
In the normal presentation of the EPR problem a comparison is made between the (weak) Copenhagen ... more In the normal presentation of the EPR problem a comparison is made between the (weak) Copenhagen interpretation of quantum mechanics which seems to suggest that at times action at a distance may take place, and the hidden parameter interpretation which must satisfy Bell's inequality, in contradiction to the predictions of quantum mechanics. In this paper, we consider a relativistic approach to the paradox. However, the frame of reference under consideration is not the usual Lorenz frame but rather the spin frame of reference which is invariant with respect to the SU(2) group.
In this paper a one to one correspondence is established between spacetime metrics of general rel... more In this paper a one to one correspondence is established between spacetime metrics of general relativity and the wave equations of quantum mechanics. This is done by first taking the square root of the metric associated with a space and from there, passing directly to a corresponding expression in the dual space. It is shown that in the case of a massless particle, Maxwell's equation for a photon follows while in the case of a particle with mass, Dirac's equation results as a first approximation. Moreover, this one to one correspondence suggests a natural explanation of wave-particle duality. As a consequence, the distinction between quantum mechanics and classical relativistic mechanics is more clearly understood and the key role of initial conditions is emphasized.
In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general re... more In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general relativity and shown to be a generalized Dirac equation for quantum mechanics. This lends itself to a natural definition of wave-particle duality in quantum mechanics. This theory is now further developed to show that a free spinless quantum particle moving with velocity v obeys the standard wave equation of electro-magnetism. We also discuss the implications for the zitterbewegung problem and its relationship to isotropy. Moreover, it is also shown that for the theory to be consistent, the momentum defined by the Hamilton-.!acobi function presupposes the existence of a universal parameter internal to the system. In the case of particles with mass this invariant can be defined by dX = dt/m(t) where t has the units of time and m = m(t) has the units of mass.
In a previous article a relationship was established between the linearized metrics of General Re... more In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves is investigated. In the case of scalar fields, a relationship between mass and temperature is also worked out.
In this article we generalize the spin statistics theorem and show that a state obeys Fermi-Dirac... more In this article we generalize the spin statistics theorem and show that a state obeys Fermi-Dirac statistics if and only if the state is invariant under the action of SL(n, C). We also briefly discuss the experimental evidence and how the theorem relates to spin entanglement.
In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first writte... more In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles. In this essay, we take a different starting point. We begin with the metrics of general relativity and show how they can be used to construct by inspection constants of motion, which can then be used to write down the equations of the trajectories. This will be achieved by deriving a Hamiltonian-Jacobi function from the metric and showing that its existence requires all of the above mentioned properties. The article concludes with four applications, which includes a derivation of Kepler's First Law of Motion for planets, and a formula for describing the trajectories of galaxies moving in a space defined by the Robertson-Walker metric.
In this article, the rotational invariance of entangled quantum states is investigated as a possi... more In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This will be referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of this coupling while the Bose-Einstein follows by breaking it. Finally, the experimental evidence to justify the above classification will be discussed.
In this article, the rotational invariance of entangled quantum states is investigated as a possi... more In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This is referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of this coupling while the Bose-Einstein follows by breaking it. In section 5, the above approach is related to Pauli's original spin-statistics theorem and finally in the last two sections, a theoretical justification, based on Clebsch-Gordan coefficients and the experimental evidence respectively, is presented.
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