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All of us spend a considerable fraction of our time eating. But most of us have not spent any appreciable amount of time on a scientific study of how to specify what we eat or how to determine the optimum nutrition.

Belief in the Trinity is a categorical imperative for most Christian faiths. The Holor Trinity relates God to the Father, the Son and the Holy Spirit as the mathematical entity, Gⁱ = G¹, G², G³. Linguistically this relationship may be expressed less precisely as God is the Father, the Son and the Holy Spirit as one. This lecture will show how the "Theory of Holors" can enhance one's Christian ecumenical faith.

Classical Physics can be represented with vectors in a 3-dimensional space. Chemistry, on the other hand, is described in terms of holors with 116 merates. Chemical reactions are represented by the addition of suitable holors in this 116 dimensional space.

Since the time of Newton and even before there have been scientists who discussed and possibly utilized a family of chemical reactions in which two or more chemicals could combine to form a different element from any of the original chemicals. Such a chemical reaction is called a transmutation. The holor representation of transmutations is also suggested.

The objective of this paper is to determine which postulates on the velocity of light and the force between moving charges are necessary to explain unipolar induction. A major experiment which can not be explained by Maxwell's equations is the unipolar generator which is a metal disc rotating in the fields produced by a permanent magnet or a current carrying conductor. A voltage is induced between the center and the edge of the rotating metal disc which is proportional to the angular velocity. This paper will compare the predictions of the New Gaussian and the Classical equations for the force between moving charges with experimental measurements. Only the New Gaussian equation correctly predicts the emf that was first observed by Faraday in 1831.

In order to mathematically describe the astonishing phenomenon of entanglement it is necessary to introduce a new type of holor. If a beam of light is incident on a barium borate crystal the incident light breaks into a pair of twin beams which make equal but opposite angles with the normal direction to the surface of the crystal. In order to represent this extraordinary behavior it is necessary to introduce a trivalent holor , which we have called a twinor.

Hitherto most of the discussions of the Natural Philosophy Alliance have been devoted to the study of classical physics. We have studied the postulates on the velocity of light. Is the velocity of light a constant as was postulated by Einstein? Or can we conclude that the universal time postulate, that the velocity of light is a constant relative to the source at any instant, is the only postulate that is consistent with all of the experiments hitherto analyzed? Is Newton?s law of gravity universally valid, or must it be modified to take into account the seasonal variation that was discovered by the Monti? Can we believe that Maxwell?s equations, as postulated by Einstein, are universally valid, or must they be replaced with the New Gaussian Electromagnetic Theory?

The forces on a rigid body can always be expressed as the sum of a sliding vector and a rotation. This paper shows how the sum of any set of forces acting on a rigid body can be described by a bivalent alternating holor, and can be decomposed into a single sliding vector plus a single rotation. This problem was first studied by Study (Geometrie der Dynamen, Leipzig, 1901). The holor representation of rigid body motion was developed after tensor calculus had been developed by this author [?Geometric Figures in Affine Space?, J. Math. Phys. 23, 1 (1944) and ?The Tensor Interpretation of the Figures of Study's ?Geometrie der Dynamen?, J. Math Phys 23, 103 (1944)], and is now included in the recent text Theory of Holors by Moon and Spencer (Cambridge University Press, 1986, paperback 2005).

The paper develops and analyses the stability conditions for a spinning charged ring according to the Maxwellian Electromagnetic Theory and according to the New Gaussian Electromagnetic Theory. Conclusions are drawn as to whether a charge cluster can be modeled by a spinning charged ring according to either electromagnetic theory for particles with any ratio of mass to electric charge.

The paper studies the modifications of Newton?s law of gravity proposed by Andre Assis and Jaroslav Klyushin in order to determine whether either of these can predict the seasonal Monti effect. Both of these equations add terms which are functions of velocity and acceleration to the original function of position proposed by Newton.

The study of any branch of Natural Philosophy should be based on:

1. A clear statement of the physical postulates on which the branch of natural philosophy to be studied is based
2. A careful study of the optimum mathematical representation of each physical concept to be employed.

What type of holor most perfectly describes each physical concept employed? Is each concept best represented by: a scalar, a complex number, a vector, a matrix, a tensor, or a new type of holor?

The simplest model of a charge cluster is a spinning charged ring. The gravitational and electromagnetic forces must add to zero if charge clusters are to be in dynamic equilibrium. The paper investigates whether spinning rings of charge can be in dynamic equilibrium according to classical electromagnetic theory and according to the New Gaussian electromagnetic theory.

Galileo was the first person to attempt to measure the velocity of light. Einstein was remarkable in 1905 in recognizing that a postulate on the velocity of light was necessary. But only two years later in 1907 he found it necessary to revise his original postulate. The very next year in 1908 Ritz proposed a radically different postulate. It was nearly half a century later that the universal time postulate was first proposed by Moon and Spencer in 1956. It was not until 1990 that the general formulation of the universal time postulate was developed by Moon, Spencer and Moon. Today we know that electromagnetic signals from moving sources can be synchronized. The paper reviews the experimental evidence for accepting the universal time postulate.

The remarkable Monti experiments show that some chemical reactions occur in spring and fall but not in summer or winter. In this paper it is proposed that Newton?s law of gravity be modified by the addition of a force term that varies with the seasons. Investigation of the equations of planetary motion shows that certain functions of the derivative of the radius with respect to angle have such a seasonal variation. The proposed modification of Newton?s law of gravity is compared with the modifications previously proposed by Assis and by Kluyshin.

The gravitational and electromagnetic forces on the spinning charged ring are analyzed in the following two ways:

1. the Classical Electromagnetic Theory and Newton?s Gravitational Equation
2. the New Gaussian Electromagnetic Theory and the newly modified gravitational equation proposed in the previous paper

Conclusions are drawn on the possible existence of a spinning charged ring, from the point of view of classical physics, and from the point of view of the most recent formulation of gravitational and electromagnetic theory.

The paper gives a comparative derivation of the fundamental equations of electromagnetic theory in the two formulations that have been investigated most extensively:  the Classical Electromagnetic Theory and the New Gaussian Electromagnetic Theory.  The principal differences are that the Classical Theory is based on Einstein's postulate on the velocity of light and on the absolute velocity of moving charges while the New Gaussian Theory is based on the universal time postulate on the velocity of light and on the relative velocity of moving charges.  The paper outlines the derivation of the expressions for the force between moving charges and the divergence and curl of the electromagnetic field vectors in both systems.  Since we now have five experimental proofs of the validity of the New Gaussian Electrodynamics and the failure of Classical Electrodynamics, it is time to seriously study the beautiful system that explains our actual phsyical experiments.

The paper presents a mathematical derivation of the Doppler shift based on two postulates on the velocity of light:  Postulate I* proposed by Einstein in 1907, and Postulate III* proposed by Moon, Spencer and Moon in 1990.

The paper considers the special case of a charged particle moving in a uniform electric field. Three formulations of the problem are compared, utilizing the Weber equation. and the new Gaussian equation. The critical difference is whether the force is defined in terms of absolute velocity (classical) or relative velocity (Weber and new Gaussian). The actual trajectory of the charged particle can be explained in two ways: if the force is a function of absolute velocity it is necessary to introduce a variable mass. However. if the force is a function of relative velocity the correct trajectory is predicted with a constant mass. Consequently. both the Weber Equation and the new Gaussian equation explain the experimental trajectories of charged particles in a uniform electric field with a mass which does not vary.

The problem of the trajectory of a charged particle in both electric and magnetic fields is formulated in three ways: utilizing the Weber equation for the force between moving charges. the classical equation and the new Gaussian equation: In the analysis. in terms of the classic equation, it is necessary to assume that mass varies with velocity. Since both the Weber equation and the new Gaussian equation are expressed in terms of relative velocity, it is possible to retain the simpler concept of constant mass. Applications will be made to the key high velocity configurations. It is not possible to discriminate between the three theories studies on the basis of this set of applications. since the classical theory can be made to conform with real measurements by introducing variation of mass with velocity.

Previous papers have shown that the only postulate on the velocity of light that is consistent with all of the experiments hitherto analyzed is the universal time postulate on the velocity of light which was proposed by Moon and Spencer in 1956. This paper will concentrate on the interpretation of the universal time postulate. Light travels outward from its source in a spherical wave whose radius always increases at velocity c. as suggested by Huygens. The center of this sphere is always at the source. If the source travels at a constant velocity. this reduces to the corpuscular hypothesis of Newton. But if the source is accelerated. the result is slightly different than was suggested by either Huygens or Newton. It is this small difference which permits the synchronization of all moving clocks and makes possible the existence of clocks which tell universal time. Such clocks are now commercially available, controlled by the satellite system.

On the hundredth anniversary of the birth of Professor Parry Moon. February 14, 1898. the paper summarizes his work on the study of the foundations of relativity. The beginning was his first project when he came to M.I.T. in 1924, as assistant to Vannevar Bush. an attempt to disprove relativity experimentally-and its nearly fatal end. Rather than questioning the details of Einstein's theory of relativity, Professor Moon chose to question the postulates on which the theory of relativity rests: the postulate that the velocity of light is always constant and the general validity of the Maxwell equations. First came many years of study of the Ritz and Einstein postulates on the velocity of light, finally the proposal of the universal time postulate in 1956 and eventually the experimental proof of its validity. Half a century was devoted to the search for the keystone of electromagnetic theory, the equation for the force between moving charges, which culminated in the development of the new Gaussian equation for the force between moving charges and the realization that the Maxwell equations themselves must be slightly modified.

The field of a static charge distribution will be examined from three viewpoints: the Weber equation, the classical equation on which special relativity is based and the new Gaussian equation. It will be shown that with the Weber equation the force is a function of both velocity and acceleration and with the new Gaussian equation the force in a uniform electric field depends on the velocity of the test charge. But with the classical equation the force is independent of the velocity of the test charge. Experimental trajectories require mass to vary with velocity if the classical equation is postulated as in special relativity. But these trajectories may be consistent with a constant mass in both the Weber and the new Gaussian formulations. The field of a stationary current element is also examined from the three viewpoints. Extra terms occur with the Weber and the New Gaussian equations that will be significant in the analysis of high-speed charges moving in magnetic fields. Finally the force between stationary current elements is analyzed. According to classical theory the force is always perpendicular to the current element on which it acts. Tangential forces such as have been observed in many experiments can occur with both the Weber and the New Gaussian Equations.

Aka "The Uniform Electric Field from Three Viewpoints"

An elementary geometric construction enables one to clearly visualize and fully comprehend the differences between three postulates on the velocity of light -- those of Einstein (1905, 1907), Ritz (1908), and Moon and Spencer (1956, 1989). The universal time postulate of Moon and Spencer is the only one of these three in full agreement with a11 experiments hitherto analyzed. It displays an essential simplicity, and involves a simple method of synchronizing the clocks of two moving observers that is not possible in general for the Ritz and Einstein postulates.

The force on a charge moving in a uniform electric field is calculated in three ways: from the Weber equation proposed in 1846: from the classtcal equation generally taught today; and from the new Gaussian equation recently proposed and published by Moon, Spencer, Mirchandaney, Shama and Mann (Proceedings of the International Conference on Problems of Space, Time, Gravitation (Sept. 1996. St. Petersburg, Russia: pp. 188-195)). The classical field 150 a constant, but the Weber and new Gaussian fields are different functions of velocity.

The Hering furnace and overhead welding have previously been analyzed from the po1ot of view of the currently taught classical equation and the new Gaussian equation of Moon, Spencer, et al for the force between moving charges. This paper extends this analysis to the Weber equation of 1846. Conclusions are drawn on the validity of each of these three electrodynamic equations.

The general formulation of the electroaagnetlc induction problem is applied to three special cases for which experimental results are available; (I) Only the copper disc rotates; (II) Both copper disk and magnetic field rotate at same angular velocity; and (III) Only the magnetic field rotate. Each will be analyzed in terms of the same three viewpoints used in the previous papers: Weber's 1846 equation: the currently taught classical equation; and the new Gaussian equation of Moon, Spencer, et al. Significant conclusions 101111 be drawn on the validity of these three electrodynamic equations.

The general electromagnetic induction problem is formulated in three ways: from the Weber equation proposed in 1846; from the classical equation generally taught today: and from the new Gaussian equation recently proposed by Moon, Spencer, Mirchandaney, Shama, and Mann. The angular velocity of the copper conductor (Omega) and the angular velocity of the magnetic field Q are arbitrary.

The paper proves the mathematical necessity for a new postulate on the velocity of light, if universal time is a reality. This is the universal time postulate on the velocity of light proposed by Moon and Spencer in 1956. Moon, Spencer and Moon developed the general form of this postulate in 1989. The paper then summarizes the recent proofs of the validity of the universal time postulate: stellar aberration based on the astronomical observations of Bradley in 1728 and the current establishment of universal time by the GPS satellite system. Both prove that Einstein's postulate on the velocity of light must be abandoned.

The text of our entire meeting could be taken from Psalm 1, Verse 2, "... in his law doth he meditate day and night". In our meditation we are inspired by the ideas of Einstein: by his use of clearly stated postulates, his use of tensor calculus, his introduction of the Einstein summation convention, his venture into dimensional space, and the idea that the fundamental equations of physics should be expressed in tensor form. Yet we must not follow Einstein slavishly. Experiments which have already been studied impel us to modify Einstein's postulate on the velocity of light and to modify MaxweU's equations. We visualize a formulation of the fundamental equations of physics which is valid in all coordinate system and is expressed in terms of holors rather than tensors.

Weber's equation for the force between moving charges was published in 1846. In 1848 Weber published a second paper in which he claimed to have derived his equation for the force between moving charges from the gradient of a scalar potential which was a function of position and relative velocity. I n this paper we prove that Weber's mathematical derivation does not employ the correct tensor definition of the gradient. Weber's formulation for the derivation of his force equation from his scalar potential is flawed from the point of view of modern holor theory. However, this does not invalidate Weber's force equation. It may be useful even though it cannot be derived from the gradient of Weber's scalar potential.

The paper presents an experimental verification of the validity of the new Gaussian equation for the force between moving charges. Equations for the force between current elements which are derived from the Weber equation, the classical equation and the new Gaussian equation are presented. These equations are applied to the Hering furnace. The operation of the Hering furnace is consistent with the new Gaussian equation for the force between moving charges. There are difficulties with the Weber equation and the classical equation predicts that a furnace which has been used In industry for nearly a century cannot possibly operate.

The paper presents a second experimental verification of the validity of the new Gaussian equation for the force between moving charges. Three equations for the force between moving charges are applied to the problem of overhead welding: the Weber equation, the classical equation and the new Gaussian equation. From the new Gaussian equation, it is found that large electromagnetic forces are present which hold the weld bead in place. According to the classical equation, these forces do not exist and overhead welding is impossible. According to the Weber equation, the weld bead is repelled by a large electromagnetic force!

How do you set your watch? If observers A and B are not in relative motion, there is no problem. But if A and B are moving relative to each other, they must communicate by light signals. The paper shows how the universal time postulate on the velocity of light, first suggested by Moon and Spencer in 1956, was derived by considering the process of synchronization of clocks. In this paper, the motion of A and B is confirmed to a straight line. The 3-dimensional generalization was obtained by Moon, Spencer and Moon in 1989.

It is generally believed that the fundamental equations of physics can be expressed in terms of tensors. The paper considers the electromagnetic field vectors and shows that they must be represented by holors rather than tensors except in very special cases.

This paper presents a simple proof of the validity of the universal time postulate on the velocity of light based on the experimental data on stellar aberration observed by Bradley in 1728. It is demonstrated that Einstein's postulate on the velocity of light predicts stellar aberration correctly in coordinate systems in which the star is stationary but fails to predict the phenomenon at all in the earthbound coordinate system in which it is observed.

It is generally considered that one of the most crucial experiments in support of the special theory of relativity is the Hafele-Keating experiment. Four atomic clocks were flown around the world and then compared with the master clock in Washington, D.C. However, the original paper did not publish the raw data. Dr. Keating has been kind enough to permit us to analyze the raw data. We have found that an entirely different interpretation of the experimental data, which supports the universal time postulate on the velocity of light, is perfectly consistent with the experimental data obtained by Hafele and Keating. Thus, one of the essential experimental supports of the relativistic theory of time dilation is shown to be invalid. Instead, the original data provide additional strongsupport of the reality of the universal time postulate on the velocity of light.

This article aka "Analysis of the Hafele-Keating Experiment"

I.E.S. Trans. 23 (1994), 12

Amp?re proposed an equation for the force between current elements in 1823. Gauss and Weber suggested equations for the force between moving charges which are derived from scalar potentials and are consistent with the Amp?re equation. Grassmann derived an alternative equation for the force between current elements in 1845, which is often called the Lorentz force. This paper derives a time-variant generalization of this equation. It also proposes a new equation for the force between current elements that satisfies the basic criteria suggested by Gauss and Hertz.

This paper is based on the fundamental criteria for the electrodynamic equation suggested by Gauss. It considers the definitions of the electric field proposed by Neumann and by Hertz. The classical formulation utilizing Neumann's definition and Einstein's postulate on the velocity of light does not satisfy the criteria suggested by Gauss. A new electrodynamic equation is proposed, utilizing the Hertzian definition of the electric field and the universal time postulate on the velocity of light, which does satisfy the Gaussian criteria.

In Eves? Circles, the Mathematical Assoc. of Am. Notes 34 (1994)

Presented at The Fall
Meeting of the Northeastern Section was held on November 18-19, 1994 at the University of Hartford in West Hartford, Connecticut.

Presented at The Fall Meeting of the Northeastern Section was held on November 18-19, 1994 at the University of Hartford in West Hartford, Connecticut.

Presented at The
Fall Meeting of the Northeastern Section was held on November 18-19,
1994 at the University of Hartford in West Hartford, Connecticut.

This paper presents the transformation equations for point coordinates, velocity, and acceleration in accelerated coordinate systems. It is shown that in general these three quantities transform not as tensors but as holors. In some special cases the holor transformation equations reduce to tensor transformations.

Presented at the 1993 Fall Meeting of the New England Section of the American Physical Society, 15-16 October 1993, Amherst, Massachusetts.

Presented at the
1993 Fall Meeting of the New England Section of the American Physical
Society, 15-16 October 1993, Amherst, Massachusetts.

Presented at the
1993 Fall Meeting of the New England Section of the American Physical
Society, 15-16 October 1993, Amherst, Massachusetts.

Presented at The Fall Meeting of the Northeastern Section was held on November 20-21, 1992 at Trinity College in Hartford, Connecticut.

Presented at The
Fall Meeting of the Northeastern Section was held on November 20-21,
1992 at Trinity College in Hartford, Connecticut.

Maxwell?s theory was based on the idea of a stationary aether. When the concept of the aether became untenable, two obvious procedures suggested themselves:

1. Keep Maxwell?s equations but replace the Galilean transformation by the Lorentz transformation,
2. Keep Galilean relativity but replace Maxwell?s equations by an extension of the Amp?re-Gauss formulation.

The first of these procedures was chosen by Einstein in his celebrated paper of 1905. But there is no necessity for such a deinfication of Maxwell?s equations. The experimental results seem to be satisfied equally well by the second alternative (the ?new electrodynamics?) which eliminates the concept of a magnetic field, replaces the four equations of Maxwell by a singe force equation, and retains Galilean relativity.

The present paper consists of an examination of the experimental results and how they fit into the new electrodynamics. Simultaneity, astronomical aberration, the de Sitter effect, the Sagnac experiment, and the Kaufmann effect are considered. The attempt is made to show that the triumphs of Einstein?s restricted relativity are explicable also on the basis of Galilean relativity.