ARCHE Analogue Of Gravitoelectromagnetism And Consciousness Sam Henry Larsen New Hampshire, USA | arche-effect.com Keywords: Electrokinetic field Magnetodielectric field Electric field Magnetic field Gravitation field Cogravitation field Quantum effects Field geometry Visualization Ferrofluid nanoparticles Superparamagnetism Fluid dynamics James-Lange theory Consciousness Highlights: • Gravitoelectromagnetism summary • Diamagnetism and permanent magnets • Ferrofluid nanoparticles and ferrocell observation • Introductory fluid dynamics analogue • Golden section summary • James-Lange theory summary and analogue ABSTRACT Dr. Oleg Jefimenko’s theory of gravitoelectromagnetism consists of a set of analogous equations between electromagnetism and gravity (excluding nonlinear gravitational effects). Jefimenko stated the expression “magnetic force” is a misnomer since the magnetic field has no causal link with the force. Likewise, he stated “electromagnetic induction” is also a misnomer. Magnetic fields do no cause electric fields and electric fields do not cause magnetic fields. The electric and magnetic fields have the same causative source: a changing electric current. Jefimenko’s theory of gravitoelectromagnetism is summarized in the first chapter, however, this chapter will exclude his equations for nonlinear gravitational effects and some of the examples given for the application of his equations. Observational phenomena is assessed in the second chapter in accordance with Jefimenko’s model. The James-Lange theory is summarized in the third chapter, drawing causative comparisons between arousal and emotion to the theory of gravitoelectromagnetism. The goal is to create an analogue between the James-Lange theory and gravitoelectromagnetism. The conclusions of the summarized and compared theories indicate there are seamless analogues between many branches of science. These analogues are important to point out, since they may give predictable insight into unknown phenomenon. ANALOGUE OF GRAVITOELECTROMAGNETISM AND CONSCIOUSNESS ii TABLE OF CONTENTS 1. Theory of Gravitoelectromagnetism 1 1.1 The Lorentz Force ·········································································································· 1 1.2 Electromagnetic Induction and Electrokinetic Fields ···················································· 2 1.3 Gravitational Induction and Gravikinetic Fields ···························································· 5 1.4 Generalized Newtonian Theory for Time-Dependent Systems ····································· 5 1.5 Gravitation and Antigravitation ······················································································ 7 1.6 The Five Forces of Gravity ···························································································· 9 1.7 Gravitoelectromagnetic Equations ··············································································· 11 2. Observational Discussion 15 2.1 Diamagnetism ··············································································································· 15 2.2 Permanent Magnets ······································································································ 15 2.3 Ferrofluid and Ferrocell ································································································ 16 2.4 Fluid Dynamics Analogue ···························································································· 17 2.5 The Golden Section ······································································································ 18 3. Psychology Analogue 20 3.1 James-Lange Theory ···································································································· 20 4. Conclusions 22 4.1 The Difference Between Gravity and Electromagnetism ············································· 22 4.2 Unified Theory of Physics and Consciousness ····························································· 22 1 THEORY OF GRAVITOELECTROMAGNETISM 1.1 The Lorentz Force There are multiple orientations of the hand rule. With the thumb and first two figures oriented as 3D coordinate axes, the index finger is the direction of the The Lorentz force, commonly known as the electromagnetic force, is the magnetic field, the middle finger is the direction of electric current, and the combining measurement of electric and magnetic force on a point charge due thumb is the direction of thrust or force [Fig. 1.1-1]. The curl right-hand rule to electromagnetic fields. This electromagnetic force and its associated hand is another orientation where the fingers are curled around two axes and the rules are fundamental in the foundation for understanding electromagnetic thumb is in the direction of the third axis. As the electric current occurs along phenomena. A particle of charge q moving with a velocity v in relation to an a straight wire, the magnetic field occurs in a helix formation 90° to the electric electric field E and a magnetic field B experiences a force of F=qE+qv×B, current. Coiled wires will produce an altered state of this phenomenon. When where the electromagnetic force on a charge q is a combining measurement of the electric current occurs along a coiled helix wire, the magnetic field is 90° a force in the direction of the electric field E proportional to the magnitude of to the coil direction along the axis of the coil [Fig. 1.1-2]. the field and the quantity of charge, and a force at right angles to the magnetic field B and velocity of charge, proportional to the magnitude of the field, the charge, and the velocity. Variations of this basic expression describe the magnetic force on a current-carrying wire (sometimes called the Laplace force), the electromotive force in a wire loop moving through a magnetic field, and the force on a moving charged particle. Historians suggest that the law is implicit in a paper published by James Clerk Maxwell in 1865. Hendrik Lorentz arrived at a complete derivation in 1895, identifying the contribution of electric force a few years after Oliver Heaviside correctly identified the contribution of the magnetic force. MAGNETIC FIELD ELECTRIC CURRENT F=B×I FORCE Fig. 1.1-2 It should be noted for later understanding that the magnetic field of a timevarying propagation is actually a magnetodielectric field, whereas the magnetic field of constant current is a magnetostatic field. It should also be MAGNETIC FIELD noted for later understanding that the directional axis of the current is the electrokinetic field. For an increasing current, the electrokinetic field is opposite to the inducing current, and for a decreasing current, the electrokinetic field is in the same direction as the inducing current. For gravity, ELECTRIC CURRENT Lenz’s law is opposite to electromagnetism, where for an increasing mass current, the gravikinetic field is in the same direction as the inducing mass current, and for a decreasing mass current, the gravikinetic field is opposite to the inducing mass current. Fig. 1.1-1 In mathematics and physics, the hand rules are a common mnemonic for understanding orientation of axes in three-dimensional space. Left-hand and right-hand rules arise when dealing with coordinate axes. These hand rules can be used to find the direction of the magnetic field, rotation, spirals, electromagnetic fields, mirror images, and enantiomers. THEORY OF GRAVITOELECTROMAGNETISM 1.2 Electromagnetic Induction and Electrokinetic Fields 2 Faraday had discovered two basic effects of electromagnetic induction: the induction of electric current in a circuit due to a changing current of the Electromagnetic induction is one of the most important physical phenomenon. inducing circuit, and the induction of a current in a circuit due to a relative Its induction is commonly explained as a phenomenon in which a changing motion of this circuit with respect to a current-carrying circuit or magnet (he magnetic field produces an electric field (“Faraday induction”) and a changing also discovered “self-induction” of current in a single circuit). Although electric field produces a magnetic field (“Maxwell induction”). However, Faraday was the originator of the concept of the magnetic field (which he according to Jefimenko’s analysis of Maxwell’s equations, there is no causal described in terms of the “magnetic curves”), he never suggested that the relation between electric and magnetic fields. induced currents were a result of changing magnetic fields. On the contrary, he clearly associated the phenomenon of electromagnetic induction with The causal equations given by Jefimenko for electric and magnetic fields in a changing electric currents, even when the induction was caused by a motion vacuum are of a permanent magnet (reference to Ampère in the letter to Phillips). E= [ρ] 1 ∂J 1 1 ∂[ρ] 1 + r dv′ − dv′ 4πϵ0 ∫ { r 2 rc ∂t } u 4πϵ0c2 ∫ r [ ∂t ] (1.2-1) [J] 1 1 ∂[J] + × rudv′ 4π ∫ { r 2 rc ∂t } (1.2-2) and H= The mathematical formulation of the phenomenon of electromagnetic induction was due to Maxwell. In Chapter III entitled “On the Induction of Electric Currents” of Vol. 2 of his famous Treatise on Electricity and Magnetism he wrote: “It was perhaps for the advantage of science that Faraday, though thoroughly conscious of the fundamental forms of space, According to these equations, for time-variation systems electric and magnetic time, and force, was not a professed mathematician… He was thus left at fields are always created simultaneously since they have a common causative leisure to do his proper work, to coordinate his ideas with the facts, and to source: the changing electric current [last term of Eq. 1.2-1 and the last term express them in natural, untechnical language. It is mainly with the hope of in the integral of Eq. 1.2-2]. Once created, the two fields coexist without any making these ideas the basis of a mathematical method that I have undertaken effect upon each other. Therefore, electromagnetic induction as a phenomenon this treatise.” Maxwell then reviewed Faraday’s observations in four sections in which one of the fields creates the other is an illusion. The illusion of the entitled “Induction by Variation of the Primary Current,” “Induction by “mutual creation” arises from the facts that in time-dependent systems, the two Motion of the Secondary Circuit,” and “Induction by the Relative Motion of a fields always appear prominently together, while their causative sources Magnet and the Secondary Circuit.” Next he analyzed Faraday’s concept of remain in the background. If the two fields are created simultaneously and the electrotonic state. Finally he formulated his law of electromagnetic coexist from then on as a dual entity, then the concept of electromagnetic induction: “The number of lines of force which at any instant pass through the induction requires a thorough reexamination. circuit is mathematically equivalent to Faraday’s earlier conception of the electrotonic state of that circuit… It is only since the definitions of In 1820, Oersted discovered the fundamental electromagnetic phenomenon, electromotive force… and its measurement have been made more precise, that the fact that an electric current was accompanied by a magnetic field we can enunciate completely the true law of magneto-electric induction in the encircling that current. In the same year, Ampère discovered that current- following terms: The total electromotive force acting round a circuit at any carrying conductors attracted each other if the currents were in the same instant is measured by the rate of decrease of the number of lines of magnetic direction, and repelled each other if they were in opposite directions. He force which pass through it… Instead of speaking of the number of lines of named these forces between the current-carrying conductors as “electro- magnetic force, we may speak of the magnetic induction through the circuit, dynamic” forces. Later he identified these forces as magnetic and suggested or the surface-integral of magnetic induction extended over any surface that magnetism was really an electrical phenomenon, where magnetized bounded by the circuit.” As written by Maxwell, like Faraday, considered the bodies owed their magnetic effects to circular electric currents within the electromagnetic induction as a phenomenon in which a current (or bodies. Also in 1820, Biot and Savart provided a mathematical description of electromotive force) is induced in a circuit, but not as a phenomenon in which Oersted’s discovery, and Davy discovered that a current-carrying wire a changing magnetic field causes an electric field. Maxwell clearly said that attracted iron filings to itself. These theories inspired Faraday to start his the induced electromotive force is measured by, not caused by, the changing popular researches in electricity and magnetism. magnetic field. Just as Faraday, Maxwell made no allusion to any causal link between magnetic and electric fields. Michael Faraday was first mainly interested in finding answers for two questions: can a current induce a secondary current in neighboring bodies, and The expression “Maxwell induction” is of a relatively recent origin. The can magnetism be converted into electricity? By 1831, Faraday had the expression refers to an alleged phenomenon where a magnetic field is created answers to both questions. A detailed account of the various and numerous by a changing electric field. Its theoretical basis is presumed to be in the fourth experiments that had led Faraday to his discovery and to the study of Maxwell’s equation, specifically in the last term of this equation: the time- electromagnetic induction was communicated to the Royal Society and was variable displacement current density ∂D/∂t. The reality of this phenomenon published in Philosophical Transactions and later his famous Experimental has never been demonstrated experimentally. There is one frequently used Researches in Electricity. The experiments that he conducted in 1831 “theoretical” illustration of Maxwell induction: the computation of the comprised the first 75 pages of the first volume of Experimental Researches. magnetic field between the plates of a thin parallel-plate capacitor with 3 THEORY OF GRAVITOELECTROMAGNETISM circular plates in a circuit, with a slowly varying current. However, this move parallel to the convection current, rather than toward or away from the illustration actually demonstrates the utility of the displacement current charges forming the convection current [the total electric force is given by all concept and does not really manifest an induction phenomenon. More three terms of Eq. 1.2-1]. The electric field created by time-variable currents intriguing, it has been repeatedly shown that the same result can be obtained is very different from all other fields encountered in electromagnetic from the Biot-Savart law applied to the conduction current in the lead wires phenomena. Therefore a special name should be given to it. Taking into and in the capacitor plates, without using the displacement current at all. account that the cause of this field is a motion of electric charges (current), it Attempts have been made by some investigators to observe displacement may be called the electrokinetic field, and the force which this field exerts on current experimentally, however, according to the investigators, these attempts an electric charge the electrokinetic force. The electrokinetic field is were futile. The concept of the displacement current was introduced in the designated by the vector Ek. From Eq. 1.2-1 there is electromagnetic theory by Maxwell. In Chapter I of Vol. 1 of his Treatise, Ek = − Maxwell concluded displacement current was not a changing electric field, as we interpret it today, but a displacement of actual electric charges residing 1 ∂J 1 dv′ 4πε0c2 ∫ r [ ∂t ] (1.2-3) inside dielectric media. In this respect, it should be noted that in Maxwell’s The electrokinetic field provides a precise and clear explanation of one of the times it was believed that all space was occupied by ether, a dielectric medium. most remarkable properties of electromagnetic induction: the Lenz’s law. It is therefore completely baseless to associate Maxwell’s name with the idea Consider a straight carrying conductor parallel to another conductor. that a changing electric field can cause a magnetic field. Since this idea is According to Lenz’s law, the current induced in the second conductor is without any experimental or theoretical support, it must be completely opposite to the inducing current in the first conductor when the inducing discarded. Faraday induction, as a phenomena where an electric current is current is increasing, and is in the same direction as the inducing current when generated in a conductor by a changing electric current in another (or in the the inducing current is decreasing. In the past no convincing explanation of same) conductor, is a true physical effect. “Maxwell induction,” on the other this effect was known. But the electrokinetic field provides the definitive hand is an inappropriately named illusion. explanation of Lenz’s law: by Eq. 1.2-3, the sign (direction) of the electrokinetic field is opposite to the sign of the time derivative of the inducing It must be emphasized that there is only one phenomenon that can be called current. When the derivative is positive, the electrokinetic field is opposite to electromagnetic induction in systems at rest. Since as we have seen, electric the inducing current, when the derivative is negative, the electrokinetic field is and magnetic fields cannot cause one another, the only electromagnetic in the same direction as the inducing current. Since the induced current is induction in systems at rest is Faraday induction of an electric current in a caused by the electrokinetic field, the direction of the electrokinetic field conductor due to a changing electric current in some other (or the same) determines the direction of the induced current: opposite direction to the conductor. As far as the electromagnetic induction in conductors moving with inducing current when the inducing current increases (positive derivative), and respect to other conductors (or magnets) is concerned, this induction is the same direction as the inducing current when the inducing current decreases reducible to the induction in systems at rest, and, as an alternative can be (negative derivative). Since the direction of the inducing current varies from considered in terms of Lorentz’z fields and forces without invoking any point to point in space, the ultimate direction of the electrokinetic field and of induction effect at all. the current that it produces is determined by the combined effect of all the current elements of the inducing current in the integral of Eq. 1.2-3. The true nature of electromagnetic induction is quite simple. According to Eq. 1.2-1, a time-variable electric current creates an electric field parallel to that The electrokinetic field also gives a simple explanation of the fact (first noted current [last term of Eq. 1.2-1]. This field exerts an electric force on the by Faraday) that the strongest induced current is produced between parallel charges in nearby conductors thereby creating induced electric currents in conductors, whereas no induction takes place between conductors at right them. Thus, the term “electromagnetic induction” is actually a misnomer, angles to each other. This phenomenon is now easily understood from the fact since no magnetic effect is involved in the phenomenon, and since the induced that the electrokinetic field due to a straight conductor carrying an inducing current is caused solely by the time-variable electric current and by the electric current is always parallel to the conductor. If Eq. 1.2-3 is compared with the field produced by that current. Observe that the electric field produced by a expression for the retarded magnetic vector potential A* produced by time-variable current differs in two important respects from the ordinary a current J, electric field produced by electric charges at rest: the field is directed along the current rather than along a radius vector, and it exists only as long as the current is changing in time. Therefore, the electric force caused by this field is A∙= μ0 [J] dv′ 4π ∫ r (1.2-4) also different from the ordinary electric (electrostatic) force: it is directed it is recognized that the electrokinetic field is equal to the negative time along the current and it lasts only as long as the current is changing. Unlike the derivative of A* (observe that µ0=1/ɛ0c2): electrostatic force, which is always an attraction or repulsion between electric charges, the electric force due to a time-variable current is a dragging force: it causes electric charges to move parallel (or antiparallel) relative to the direction of the current. If the time-variable current is a convection current, then the force that this current exerts on neighboring charges causes them to Ek = − ∂A ∙ ∂t (1.2-5) 4 THEORY OF GRAVITOELECTROMAGNETISM It is interesting to note that Eq. 1.2-5 points out a possibility of a new The calculation of electrokinetic fields, calculations of electrokinetic forces, definition and interpretation of the magnetic vector potential. By integrating and calculation of currents and voltages induced by electrokinetic fields, can Eq. 1.2-5 gives be presented using examples requiring very simply calculations. The purpose A ∙ = − Ekdt + const. ∫ is to provide an unambiguous demonstration of the effects and actions of (1.2-6) electrokinetic fields, which can be best achieved with uncomplicated examples. As far as the induced voltages are concerned, the purpose of the The time integral of Ek will be called the electrokinetic impulse. It is true then calculations will be merely to demonstrate that conventional result can be that the magnetic vector potential created by a current at a point in space is obtained solely by using electrokinetic fields, without invoking any causal equal to the negative of the electrokinetic impulse produced by this current at linkage between electric and magnetic fields. For simplicity, the calculations that point when the current is switched on. Since the electrokinetic impulse is will be limited to relatively small systems and relatively slow variations of a measurable quantity, we therefore have an operational definition and a electric quantities. In such systems, retardation effects are negligible so that physical interpretation of the magnetic vector potential. It is useful to note, Eq. 1.2-3 can be written without brackets as although Eq. 1.2-5 and 1.2-6 correlate the electrokinetic field with the Ek = − magnetic vector potential, there is no causal link between the two: the correlation merely reflects the fact that both the electrokinetic field and the μ0 1 ∂J dv′ 4π ∫ r ∂t (1.2-7) magnetic vector potential are simultaneously caused by the same electric where 1/c2 is replaced by µ0ɛ0 and have cancelled ɛ0. If the current is confined current. Important as it is, the electrokinetic field has not been studied or even to a filament (wire), Eq. 1.2-7 can be given as recognized as a special force field until Jefimenko’s theory, although the fact Ek = − that the time derivative of the retarded vector potential is associated with an electric field has been known for a long time. ∂I μ0 d l′ ∂t 4π ∫ r (1.2-8) where I is the current of the filament and dl’ is a length element of the filament Like any electric field, the electrokinetic field of a moving charge exerts forces in the direction of the current. Finally, if the retardation is neglected, the on electric charges located in this field. However, a moving electric current can electrokinetic field of a current J can be found according to 1.2-5 from create not only an electrokinetic field, but also an “ordinary” electric field Ek = − given by the first integral of Eq. 1.2-1. This is because a current-carrying conductor moving in the direction of the current or in the direction opposite to ∂A ∂t (1.2-9) the current appears to acquire additional electric charges in consequences of where A is the ordinary (not retarded) magnetic vector potential associated its motion. This is erroneously considered to be a relativistic effect. Actually, with J. When an electrokinetic force acts on a charge distribution ρ, it changes however, this effect is a consequence of retardation and is explainable on the the mechanical momentum P of the charge distribution in accordance with basis of Eq. 1.2-1. “Electromagnetic induction” by a moving current, just as ΔP = Fdt = ρE dv′dt ∫ ∫∫ k the induction by a stationary current, is a result of the creation of an (1.2-10) electrokinetic field (with the creation of an additional “ordinary” electric field) by this current. However, also in this case the induction has no causal link with If Ek is a function of time only, the momentum change is any magnetic field. Its cause is not a changing magnetic field, rather the ΔP = q Ekdt = − qΔA ∫ electric field (or fields) produced by the moving electric current. As far as it is presently known, all magnetic fields are created by electric currents. (1.2-11) Therefore, a moving magnet may be represented by moving microscopic where q is the total charge of the distribution, and ΔA is the change in the electric currents forming elementary magnetic dipoles. vector potential during the time interval under consideration. If a circular electrokinetic force acts on a charge distribution restricted to a circular motion, As discussed early in this chapter, a moving charge generates not only an the angular momentum of the charge distribution changes. For a charge electrokinetic field, but also an “ordinary” electric field. The “ordinary” field distribution and electrokinetic field of circular symmetry, the change in the generated by a current constituting a moving magnetic dipole is an electric angular momentum ΔL is dipole field. The electrokinetic field itself also creates an “ordinary” electric field. This additional electric field has closed loops analogous to the magnetic field of a propagation and is called the magnetodielectric field by Eric Dollard. ΔL = ∫∫ r × Ekdqdt = − r × Adq ∫ (1.2-12) The expression “force exerted by a moving magnet” is actually a misnomer, As already mentioned, these are ordinary vector potentials for simplicity. For since this force has no causal link with the magnetic field of the magnet. The exact calculations the retarded vector potential must be used in Eqs. 1.2-9, phenomenon of “induced electric force” or “induced current” by a moving 1.2-10, 1.2-11, and 1.2-12. It should be pointed out that an association between magnet is simply the effect of the electric field caused by the collective the momentum change of a charged body and the change of the magnetic translational motion of microscopic currents participating in the motion of the vector potential at the location of the body has been noted before, however, magnet. up until the present this association was erroneously interpreted as an electromagnetic effect rather than as a consequence of the fact that both an 5 THEORY OF GRAVITOELECTROMAGNETISM electrokinetic force and a time-variable magnetic field (and its time-variable 1.4 Generalized Newtonian Theory for Time-Dependent Systems vector potential) are simultaneously created by a time-variable current. It was generally not recognized that the actual phenomenon involved the retarded Dr. Oleg Jefimenko generalized Newton’s theory of universal gravitation to vector potential rather than the ordinary one. As it is known, a magnetic vector time-dependent systems. Jefimenko thought there to be no reason to abandon potential may contain an arbitrary additive function of zero curl (“gauge Newton’s theory since it had not been completed. Newton’s theory of calibration”). However, only the vector potential given by Eq. 1.2-4 and by its gravitation is based on his gravitational law unretarded version can be used for the calculation of the electrokinetic field. F/m = − G An explanatory note is required concerning calculations of forces and torques M r2 ru (1.4-1) exerted on charge distributions by electrokinetic fields and concerning calculations of induced currents and voltages. The force experienced by a where F is the force exerted on the point mass m by the point mass M, G is the charge distribution is determined by the total electric field given by Eq. 1.2-1, constant of gravitation, r is the distance between the two masses, and ru is the not just by the electrokinetic field, Eqs. 1.2-3, 1.2-7, or 1.2-8. Therefore, a unit vector directed from M to m. This law is limited to time-independent force calculated from the electrokinetic field alone may not be the true force systems. To begin this generalization, we will first reconcile Newton’s law of experienced by the charge distribution under consideration. In contrast, only gravitation with the law of conservation of momentum. The base of the the electrokinetic force has an effect on the torque experienced by ringers of derivations will not be Eq. 1.4-1 directly, but on the two equations that charge and by similar objects. This is because the torque in such systems is formulate Newton’s theory as a force-field theory in terms of the gravitational determined by a closed line integral of the electric field, and only the field vector g. These equations are electrokinetic field gives a non-vanishing contribution to such integrals [the ∇×g=0 (1.4-2) ∇ ⋅ g = − 4πGρ (1.4-3) first term of Eq. 1.2-1, being a function of r in the direction of r, has zero curl and therefore cannot contribute to closed line integrals]. Closed line integrals of electric fields are also involved in the calculations of induced voltages. and Therefore induced voltages are also determined by electrokinetic fields alone. The gravitational field vector g is defined as 1.3 Gravitational Induction and Gravikinetic Fields g = F/m Gravitational induction and the gravikinetic field exist analogously to electromagnetic induction and the electrokinetic field. By replacing the symbols of the equations in the previous section on electromagnetic induction and electrokinetic fields with their counterpart symbols provided in the next where F is the force exerted by the gravitational field on a test mass m, which is at rest relative to an inertial reference frame (“laboratory”). In Eq. 1.4-3, ρ is the mass density defined as section, the calculation of gravitational induction and gravikinetic fields can ρ = dm /dv be observed. Basic examples are given as followed, where Ek = − 1 ∂J 1 dv′ 4πε0c2 ∫ r [ ∂t ] (1.3-1) 1 ∂J gk = 2 dv′ c ∫ r [ ∂t ] where dm is a mass element contained in the volume element dv. Let us consider two mass distributions ρ1 and ρ2 producing gravitational fields force exerted by ρ1 upon ρ2 is ∫ ρ2g1dv. If applied to the fields g1 and g2 vector (1.3-2) identity is the corresponding gravikinetic expression. These two expressions are ∫ analogous to each other by their calculations, their only differences being the constants and symbols. The induction and electrokinetic calculations discussed in the previous section may now be now converted into gravitational expressions using the corresponding gravitational constants and symbols from Table 1.7-1 (Section 1.7). It can be now understood that a changing mass current induces a secondary mass current in the neighboring bodies. The effect is similar to electromagnetic induction, except that in contrast, the direction of the induced current is the same as the original current if the original current increases, and is direction of the induced current is opposite to the original current if the original current decreases. Hence the sign of the “gravitational Lenz’s law” is opposite to the electromagnetic Lenz’s law. (1.4-5) respectively g1 and g2. The force exerted by ρ2 upon ρ1 is then ∫ ρ1g2dv, and the is the electrokinetic expression and G (1.4-4) ∮ (A ⋅ B)dS − ∮ B(A ⋅ dS) − ∮ A(B ⋅ dS) = (1.4-V) [A × ( ∇ × B) + B × ( ∇ × A) − A( ∇ ⋅ B) − B( ∇ ⋅ A)]dv obtains ∫ ρ1g2dv = − ρ2g1dv ∫ (1.4-6) Therefore, according to Newton’s theory of gravitation, the forces of action and reaction are always equal. But, the law of action and reaction cannot possibly hold for time-dependent gravitational interactions (unless gravitation propagates instantaneously, which cannot be accepted). As a result, the derivation of Eq. 1.4-6 shows that at least one of the two basic field laws of Newton’s theory of gravitation, Eqs. 1.4-2 and 1.4-3, is incompatible with the 6 THEORY OF GRAVITOELECTROMAGNETISM law of conservation of momentum. There are only three possibilities for The similarity of Eqs. 1.4-7 and 1.4-3 with Maxwell’s third and first equations modifying the Newtonian theory so that it does not conflict with the law of suggests that electromagnetic phenomena should have its gravitational conservation of momentum: (1) to make ∇×g ≠ 0, (2) to modify ∇⋅g, or (3) to counterparts. In particular, it appears gravitational waves exist analogously to modify both ∇×g and ∇⋅g. The theory can be made compatible with the law of electromagnetic waves. To confirm this analogous wave phenomena, let us conservation of momentum by making ∇×g ≠ 0. Taking into account that ∇×g take the curl of Eq. 1.4-7. We have must reduce to ∇×g = 0 for time-independent systems, it will be assumed that ∂K ∇×g=− ∂t (1.4-7) ∇×K=− repeat the derivation used for obtaining Eq. 1.4-6 and use Eq. 1-4.7 instead of 4πG ∂K1 ∂K2 1 1 g × dv = − ρ2g1dv + g × dv (1.4-8) ∫ 4πG ∫ 2 ∂t 4πG ∫ 1 ∂t J+ c2 Eq. 1-4.2, the derivation yields ∫ (1.4-12) This equation can be transformed into a wave equation by assuming that where K is some function of space and time (later to be discussed). If we ρ1g2dv − ∂ ∇×K ∂t ∇×∇×g=− 1 ∂g c2 ∂t (1.4-13) where J is some function of space and time (later to be discussed). We then obtain 2 ∇×∇×g+ where K1 is associated with the field g1, and K2 with the field g2. The two integrals containing the time derivatives can be interpreted as the rates of 1 ∂g c ∂t 2 2 = 4πG ∂J c2 ∂t (1.4-14) change of the field momentum, and Eq. 1.4-8 can be interpreted as the which is an equation for a g wave propagating in space with velocity c. As can statement of the conservation of momentum for gravitational interactions. be seen from Eqs. 1.4-13 and 1.4-7, the field vector K satisfies a similar According to this interpretation, the gravitational field is a repository of equation momentum given by 2 1 G= K × gdv 4πG ∫ ∇×∇×K+ (1.4-9) 1 ∂K c2 ∂t 2 =− 4πG c2 ∇×J (1.4-15) which is an equation for a K wave propagating in space with velocity c. and the field can exchange momentum with the bodies located in it (although there is not yet enough information to determine whether the sign in front of The significance of function J must be assessed. If we determine the the integral of Eq. 1.4-9 should be + or −, it will be presently be seen that Eq. divergence of Eq. 1.4-13, taking into account that the divergence of a curl is 1.4-9 is correct as written). Therefore, if we amend Newton’s theory by zero, we obtain accepting Eq. 1-4.7 as a basic law, the theory becomes fully compatible with 0=− the law of conservation of momentum. The function K that was previously introduced constitutes a vector field. As 4πG c2 ∇⋅J+ 1 ∂( ∇ ⋅ g) ∂t (1.4-16) c2 which, with Eq. 1.4-3, becomes can be seen by comparing Eq. 1.4-7 with the third Maxwell’s equation, K is ∇⋅J=− associated with the gravitational field g just like the magnetic field B is associated with the electric field E. Let us call K the cogravitional field. ∂ρ ∂t (1.4-17) By analogue with electromagnetism, it could then be assumed that the Equation 1.4-17 is a “continuity” equation stating that J is a mass current (and cogravitational field represents a force field acting on moving masses. If therefore also an energy current) coming out of a mass accumulation Newton’s gravitational force, Eq. 1.4-1, obeys the force transformation whenever this accumulation diminishes with time; that is, Eq. 1.4-17 is a equations of special relativity, then the existence of the cogravitational field is statement of the conservation of mass for time-dependent gravitational demanded by these equations. The force exerted by K on a mass moving with systems. By analogue with the electric convection current, the mass current velocity u is then created by a beam of mass particles of density ρ moving with a velocity v is F = m(u × K) J = ρv (1.4-10) (1.4-18) This equation can be considered to be the definition of K [the order of vectors We are now ready to complete the generalization of Newton’s theory of in the cross product reflects the fact that the gravitational force given by Eq. gravitation to time-dependent systems. The solution of Eq. 1.4-14 is 1.4-1 is always attractive]. As it is known from Helmholtz’s theorem of vector analysis, a vector field requires for its complete specification, a definition of its divergence and its curl. It will be assumed that g=− 1 [ 4π ∫ ∇′( ∇′ ⋅ g) − r 4πG ∂J c 2 ∂t ] dv′ (1.4-19) Square brackets are used as the retardation symbol to indicate that the ∇⋅K=0 (1.4-11) quantities between the brackets are to be evaluated for t’ = t − r/c, where t is the time for which g is evaluated, r is the distance between the field point 7 THEORY OF GRAVITOELECTROMAGNETISM (point for which g is evaluated) and the source point (volume element dv’), c brackets denote retarded values. For a point mass moving without acceleration, is the propagation velocity of gravitation, and ∇’ is the operator del operating Eq. 1.4-24 can be expressed in terms of the present position vector r0 as on the source-point coordinates. Substituting ∇⋅g from Eq. 1.4-3, we can write 2 g=−G Eq. 1.4-19 as g=G ∫ [ ∇′ρ + 1 ∂J c 2 ∂t ] r (1.4-20) dv′ K=− [ ∇′ × J] dv′ r G c2 ∫ (1.4-21) 2 r0 [1 − (v /c sin θ ]3/ 2 2 2 r0 (1.4-27) where θ is the angle between v and r0, and Eq. 1.4-26 can be expressed as K= The solution of Eq. 1.4-15 is, similarly, 2 m(1 − v /c ) 3 v×g c2 (1.4-28) This essentially completes the generalization of Newton’s theory of universal gravitation to time-dependent systems. where we have taken into account that, according to Eq. 1.4-11, ∇⋅K = 0. These two equations can be transformed into equations not containing spatial derivatives. We then obtain 1.5 Gravitation and Antigravitation 1 ∂[ρ] G 1 ∂J g=−G + r dv′ + 2 dv′ ∫ { r2 rc ∂t } u c ∫ r [ ∂t ] [ρ] (1.4-22) According to Einstein’s mass-energy relation, any energy has a certain mass. But mass is the source of gravitation. Therefore any energy, including and gravitational energy, should be a source of gravitation. Dr. Oleg Jefimenko 1 ∂[J] K=− 2 + × rudv′ rc ∂t } c ∫ { r2 G [J] (1.4-23) Equations 1.4-22 and 1.4-23 are the fundamental causal equations of the Newton’s gravitational theory generalized to time-dependent systems. Although we have derived them with the help of several assumptions and definitions, they should preferably be considered as postulates, and their validity should be judged not by the method by which they have been obtained, but by the agreement (or disagreement) with experimental data and with other laws and theories of proven validity. It is important to emphasize that if Eqs. 1.4-22 and 1.4-23 are regarded as postulates, then Eqs. 1.4-2, 1.4-3, 1.4-7, 1.4-11, 1.4-13, 1.4-14, 1.4-15, and 1.4-17 can be derived directly from them. outlines gravitational energy as a source of gravitation, examples of nonlinear gravitational fields, and properties of gravitational fields in free space. His conclusions state there are both attractive gravitational fields and also repulsive antigravitational fields. The field outside a uniform spherical mass distribution depends not only on the magnitude of this distribution but also on its internal field, so that such a mass distribution cannot be replaced by an equal point mass at its center, as it can be done in the conventional Newtonian theory. The most interesting aspect of the effect of the gravitational energy on gravitational fields is the possibility of the existence of mass distributions creating antigravitational fields in free space. Naturally, if such mass distributions are to be stable under gravitational forces alone, the internal gravitational field of the mass distributions must be attractive anywhere within the distributions. There can be no spherically symmetric antigravitational field Equations 1.4-22 and 1.4-23 make it possible to calculate gravitational and cogravitational fields produced by continuous mass distributions. The can be transformed, however, into equations for fields of moving point masses. For a point mass m moving with velocity v and acceleration a, the resulting equations are outside a mass distribution if the field within the distribution is everywhere attractive. Consequently, a spherical antigravitational body must be held together by some nongravitational forces in addition to the gravitational ones. There is a widespread belief that the general relativity theory is the definitive theory of gravitation. However, the generalized Newton’s theory of gravitation g=−G m s3 2 v 1 R 1 − 2 + 2 [r] × (R × [a]) [ c ] c (1.4-24) outlined by Dr. Oleg Jefimenko points out a path for an unquestionably viable new inquiry into the nature and properties of gravitational fields and interactions. The generalized Newton’s theory is based to a large extent on the and idea that the gravitational-cogravitational field is a seat of momentum and K=−G m c2 s3 2 v 1 [r] × (R × [a]) [v] 1 − 2 − [ c ] c[r] × [r] (1.4-25) energy. One of the consequences of this idea is the assumption that gravitation is caused not only by a true mass but also by the equivalent mass of the gravitational field energy. This assumption is contrary to the general relativity with theory. Even the existence of gravitational field energy is contrary to the K= [r] × g c[r] (1.4-26) where [r] is the retarded position vector of the moving point mass given by t’= t − [r]/c and directed from the mass to the point of observation; R = [r − rv/c] is the “projected” present position vector of the point mass (also directed toward the point of observation); s = [r − r⋅v/c]; and where the square general relativity theory. It is important to therefore clarify the reasons why the general relativity theory denies the existence of gravitational field energy and it is important to examine the validity of theses reasons. 8 THEORY OF GRAVITOELECTROMAGNETISM The basic gravitational equation of the general relativity theory is the an accelerated reference frame does not prove the nonexistence of Einstein’s gravitational field equation nonlocalizability of gravitational field energy, and hence the equivalence Rik − 1 8π Rg = − G 4 Tik 2 ik c principle does not forbid its appearance as a source term in Einstein’s (1.5-1) gravitational field equation. Therefore, the exclusion of the gravitational energy as a source of gravitation in the general relativity theory is merely a The sources of gravitation appear in this equation in the form of energy- matter of practical necessity (since no tensor has been found for it). Hence, momentum tensor Tik. This tensor includes all types of mass densities and all stated by Dr. Oleg Jefimenko, all presently known results of the general types of energy densities (electric, magnetic, thermal, etc.) except for the relativity theory based on Einstein’s field equation cannot be considered as energy density of the gravitational field itself. The determining reason for this reliable when these results involve gravitational fields whose gravitational- is quite simple: in spite of many effects, no energy-momentum tensor has been energy mass is comparable with the true mass of the system. The fact that the found for the gravitational energy (only a “pseudotensor” has been obtained). results obtained by Jefimenko are in conflict with the general relativity theory Various plausibility arguments have therefore been suggested to justify the does in no way indicate that these results are wrong. The conflict cannot be absence of the gravitational energy as a source of gravitation in Einstein’s field resolved by plausibility arguments. Only reliable observational data can truly equation. Since it would be difficult (if not impossible) to accept the existence resolve it. of gravitational field energy without accepting this energy as a source of gravitation, these arguments are also the arguments against the presence of The theory of nonlinear gravitational fields by Dr. Oleg Jefimenko indicate: gravitational energy in the gravitational field. The two strongest plausibility arguments for excluding gravitational energy as (1) The gravitational force acting on a body in a gravitational field is a source of gravitation are: determined not only by the mass of the field-producing body, but also by the gravitational field energy of the field-producing body. (1) Predications of the general relativity theory obtained with the aid of Einstein’s field equation without gravitational energy as a source of gravitation (2) Antigravitational bodies can exist in the universe. have been found to agree with observations. (3) The mass of the universe, of a galaxy, or of a stellar object can be much (2) Einstein’s “equivalence principle” forbids gravitational energy to be a larger than the present astrophysical measurements indicate, since there can source of gravitation. exist objects of negative or of zero apparent mass. The latter objects would constitute “hidden” masses, as they do not produce or experience gravitational However, a careful examination of these two arguments shows that neither of effects. them is truly convince or compelling according to Jefimenko. The first argument is easily refuted by the fact that all presently verifiable predictions (4) “Black holes” cannot exist, and “gravitational collapse” is impossible. of the general relativity theory are in the domain of weak fields, where the Indeed, according to the general relativity theory, a sphere creates an effects of the gravitational energy are hardly noticeable, as stated by “unescapable” gravitational field and becomes a “black hole” after its radius Jefimenko in his article Gravitation and Antigravitation. becomes smaller than the “gravitational radius” The second argument appears to be much stronger than the first. What it means rg = G 2m c2 (1.5-2 ) is that since, according to Einstein, a gravitational field is equivalent to a certain accelerated frame of reference, and since there apparently is no special But the radius of the central mass of the mass distribution shown in Fig. 1.5-1 energy in the space defined by the accelerated frame of reference, no energy is smaller than the gravitational radius, yet the field at this radius is zero rather should be present in the space containing the gravitational field (this is known than immensely strong, as is required for black holes. as the “nonlocalizability” of gravitational energy). An analysis of this argument shows, however, that it is based on an unprovable premiss and that (5) Since “gravitational collapse” is impossible, and since antigravitational it can be refuted by reversing it. Let us suppose that a gravitational field is a mass formations are possible, the normal state of the universe appears to be an seat of gravitational energy. The equivalence principle demands then that a alternating expansion and contraction. certain energy density would appear in the space defined by the equivalent reference frame. But how will this energy manifest itself? The only presently (6) Since a “hidden” mass is an object whose overall rest mass is an object known way in which it could be detected is by its gravitational effects. whose overall rest mass is zero, such a mass could conceivably move with a However, since the equivalent reference frame is flat and boundless, the velocity equal to (or even larger than) the velocity of light. “equivalent” energy density, as seen in this frame, must be uniform and must occupy all space. But, as it is well known, a uniformly distributed mass It should be noted that the generalized Newton’s theory makes it possible to (energy) occupying all space produces no gravitational effects. Hence the obtain transformation equations for gravitational and cogravitational fields “equivalent” energy is not detectable, or, as an observer in the equivalent which make the linear theory of gravitation compatible with special relativity reference frame would say, is “absent.” Thus, the absence of space energy in theory (see O. D. Jefimenko, Electromagnetic Retardation and Theory of THEORY OF GRAVITOELECTROMAGNETISM 9 Relativity) However, the nonlinear gravitational equations discussed in First let us consider Eq. 1.6-1. The field represented by the first integral in this Jefimenko’s article Gravitation and Antigravitation are not compatible with equation is the ordinary Newton’s gravitational field created by the mass the special relativity theory. Jefimenko states, although there is a widespread distribution ρ corrected for finite speed of the propagation of the field (this is opinion that all correct physical theories and equations must be compatible indicated by the square brackets—the retardation symbol—in the numerator). with the special relativity theory, the incompatibility of the nonlinear The field represented by the second integral in Eq. 1.6-1 is created by a mass gravitational equations with this theory does not mean they are wrong. In this whose density varies with time. Like the ordinary Newton’s gravitational field, connection it may be noted that there are other examples of perfectly viable these two fields are directed toward the masses which create them. The field equations which are incompatible with the special relativity theory. Maxwell’s represented by the last integral in Eq. 1.6-1 is created by a mass current whose electromagnetic equations in their vector form present the most prominent magnitude and/or direction varies with time. The direction of this field is example of such incompatibility. Furthermore, in the real world, the special parallel to the direction along which the mass current increases. All three fields relativity theory is itself only approximately correct. This is because this in Eq. 1.6-1 act on stationary masses as well as on moving masses. theory is only applicable to inertial systems, but true inertial systems do not really exist. In the end, the only reliable criterion of the correctness (or Consider now Eq. 1.6-2. The first integral in this equation represents the erroneousness) of Jefimenko’s nonlinear is the agreement (or disagreement) of cogravitational field created by the mass current. The direction of this field is these equations with the experimental data. normal to the mass current vector. The second integral in Eq. 1.6-2 represents 2 the field created by a time-variable mass current. The direction of this field is 3 ga Gm ρ 4πa 3m 2 normal to the direction along which the mass current increases. Both fields in Eq. 1.6-2 act on moving masses only. If the mass under consideration does not move and does not change with time, ρ then there is no retardation and no mass current. In this case both integrals in 1 0 Eq. 1.6-2 vanish and only the first integral remains in Eq. 1.6-1. As a g result, one simply obtains the integral representing the ordinary Newton’s gravitational field. Therefore, the ordinary Newton’s gravitational theory is a 1 2 3 4 5 6 7 r /a special case of the generalized theory, as it should be. As far as the interactions between two masses is concerned, the meaning of the five integrals discussed above can be explained with the help of Fig. 1.6-1. The 1 upper part of Fig. 1.6-1 shows the force which the mass m1 experience under the action of the mass m2 according to the ordinary Newton’s theory. The lower part of Fig. 1.6-1 shows five forces which the same mass m1 experiences Fig. 1.5-1 An example of an antigravitational field and of the corresponding mass distribution. The scale for the field is twice as large as the scale for the mass density. under the action of the mass m2 according to the generalized Newton’s theory. The time for which the positions of the two masses and the force experience 1.6 The Five Forces of Gravity by m1 are observed is indicated by the letter t. Let us note first of all that, As was explained by Jefimenko’s generalized Newton’s theory of gravitation according to the ordinary Newton’s theory, the mass m1 is subjected to one to time-dependent systems, gravitational interaction between two bodies is single force directed to the mass m2 at its presented location, that is, to its described not by one single force, as in the original Newton’s theory, but by an location at the time t. However, According to the generalized Newton’s theory, intricate juxtaposition of several different forces. Mathematically, these forces all forces acting on the mass m1 are associated not with the position of the mass result from four of Jefimenko’s equations, including Eqs. 1.4-22 and 1.4-23. m2 at the time of observation, but with the position of m2 at an earlier time When Eqs. 1.4-22 and 1.4-23 are written as five separate integrals, they t’ < t. Therefore, the magnitude of the mass m2 and its position and its state of become motion at the present time t have no effect at all on the mass m1. g=−G and G 1 ∂J [ρ] 1 ∂[ρ] r dv′ − G r dv′ + 2 dv′ ∫ r2 u ∫ rc ∂t u c ∫ r [ ∂t ] (1.6-1) The subscripts identifying the five forces shown in the lower part of Fig. 1.6-1 correspond to the five integrals in the Eqs. 1.6-1 and 1.6-2. The force F1 is associated simply with the mass m2 and differs from the ordinary Newton’s 1 ∂[J] K=− 2 × rudv′ − 2 × rudv′ c ∫ r2 c ∫ rc ∂t G [J] G (1.6-2) gravitational force only insofar as it is directed not to the mass m2 at its present position, but to the place where m2 was located at the past time t’. The force F2 Each of these integrals represents a force field. Therefore, according to the is associated with the variation of the density of the mass m2 with time; the generalized Newton’s theory, gravitational interactions between two bodies direction of this force is the same as F1. The force F3 is associated with the involve at least five different forces. Let us consider the nature of these forces. time variation of the mass current produced by m2; this force is directed along the acceleration vector a (or along the velocity vector v2) which the mass m2 THEORY OF GRAVITOELECTROMAGNETISM had at the time t’. The three forces are produced by the gravitational field g (if m2 is a point mass moving at a constant velocity, g and the resultant of the three forces are directed toward the present position of m2. The forces F4 and F5 are due to the cogravitational field K. The force F4 is associated with the mass current created by the mass m2 and with the velocity of the mass m1. Its direction is normal to the velocity vector v2 which the mass m2 had at the time t’ and normal to the velocity vector v1 which the mass m1 has at the present time t. The force F5 is associated with the velocity of the mass m1 and with the variation of the mass current of the mass m2 with time; the direction of this force is normal to the acceleration vector (or to the velocity vector) that the mass m2 had at the time t’ and normal to the velocity vector that the mass m1 has at the present time t. Although not shown in Fig. 1.6-1, additional forces associated with the rotation of m2 and m1 (angular velocities ω2 and ω1) are generally involved in the interaction between two masses due to the field K. The forces F2, F3, F4, and F5 are usually much weaker than the force F1 because of the presence of the speed of gravitation c (generally assumed to be the same as the speed of light) in denominators of the integrals representing the fields responsible for these four forces. This means that only when the translational or rotational velocity of m2 or m1 is close to c, the forces F2, F3, F4, and F5 are significant. Of course, the cumulative effect of these force in long lasting gravitational systems (such as the Solar system, for example) may be significant regardless of the velocities of the interacting masses. t m2 m1 t F a F4 F3 m1 F1 ω1 t F5 ω2 F2 t’< t v2 v1 Fig. 1.6-1 The upper part of this figure shows the force that mass m1 experiences under the action of the mass m2 according to the ordinary Newton’s theory. The lower part shows five forces which the same mass m1 experiences under the action of the mass m2 according to the generalized Newton’s theory. t m2 Fig. 1.6-2 The generalized theory of gravitation provides a clear explanation of the mechanism of energy exchange involved in gravitational interactions: the increase of the kinetic energy of a body m moving under the action of a gravitational field occurs as a consequence of the influx of gravitational field energy into the body via the gravitational Poynting vector. 10 11 THEORY OF GRAVITOELECTROMAGNETISM 1.7 Gravitoelectromagnetic Equations The gravitoelectromagnetic equations presented by Dr. Oleg Jefimenko are the analogous equations for both electromagnetic and gravitational theories. Many new gravitational equations arise that were either unknown or were ignored in the past. The electromagnetic equations and gravitational equations can be presented by two analogous sets of equations, each containing an identical three categories. These three categories are: (1) basic definition equations, (2) basic differential equations, and (3) basic causal equations. The electromagnetic equations are given by: The gravitational equations are analogously given by: 1. Basic definition of equations for electromagnetic fields 1. Basic definition of equations for gravitational fields Electric field E Gravitational field g E = F/q (1.7-1) Magnetic flux density field B (1.7-2) Electric charge density ρ F = m(u × K) (1.7-12) ρ = dm /dv (1.7-13) J = ρv (1.7-14) Mass density ρ ρ = dq/dv (1.7-3) Electric convection current density J Mass current density J J = ρv (1.7-4) 2. Basic differential equations for electromagnetic fields in a vacuum 2. Basic differential equations for gravitational fields ∇ ⋅ E = ρ/ε0 (1.7-5) ∇ ⋅ g = − 4πGρ (1.7-15) ∇⋅B=0 (1.7-6) ∇⋅K=0 (1.7-16) ∇×E=− ∇ × B = μ0 J + ∂B ∂t (1.7-7) 1 ∂E c2 ∂t (1.7-8) 3. Basic causal equations for electromagnetic fields ∇×g=− ∇×K=− 4πG c2 ∂K ∂t J+ (1.7-17) 1 ∂g c2 ∂t (1.7-18) 3. Basic casual equations for gravitational fields [ρ] 1 ∂J 1 1 ∂[ρ] 1 + r dv′ − dv′ 4πϵ0 ∫ { r 2 rc ∂t } u 4πϵ0c2 ∫ r [ ∂t ] (1.7-9) μ0 [J] 1 ∂[J] + × rudv′ 4π ∫ { r 2 rc ∂t } (1.7-10) B= (1.7-11) Cogravitational field K F = q(u × B) E= g = F/m g=−G [ρ] 1 ∂[ρ] G 1 ∂J + r dv′ + 2 dv′ ∫ { r2 rc ∂t } u c ∫ r [ ∂t ] K=− c2 ∫ { r 2 G [J] + 1 ∂[J] × rudv′ rc ∂t } (1.7-19) (1.7-20) 12 THEORY OF GRAVITOELECTROMAGNETISM If we compare the electromagnetic equations with the gravitational equations 1. Equations for calculating fields and potentials listed above, we find that to each electromagnetic equation there corresponds a gravitational equation. The corresponding equations are identical except for Basic gravitational laws in integral notation the symbols and constants occurring in them. The relations between the ∮ corresponding symbols and constants are shown in ∮ (Table. 1.7.1) ∮ Corresponding Electromagnetic and Gravitational Symbols and Constants Electrical g ⋅ dS = − 4πG ρdv ∫ ∮ Gravitational K ⋅ dS = 0 (1.7-22) ∂ K ⋅ dS ∂t ∫ (1.7-23) 1 ∂g 4πGJ − ⋅ dS ∂t ) c2 ∫ ( (1.7-24) g ⋅ dl = − K ⋅ dl = − (1.7-21) Gravitational field of a point mass q (charge) - m (mass) ρ (volume charge density) - ρ (volume mass density) σ (surface charge density) - σ (surface mass density) λ (line charge density) - λ (line mass density) φ (scalar potential) - φ (scalar potential) A (vector potential) - A (vector potential) J (convection current density) - J (mass-current density) I (electric current) - I (mass current) m (magnetic dipole moment) - d (cogravitational moment) E (electric field) - g (gravitational field) B (magnetic field) - K (cogravitational field) g=−G m r2 ru (1.7-25) Gravitational field of a mass distribution g=−G ρ r dv′ ∫ r2 u (1.7-26) Gravitational field in terms of mass inhomogeneities (constant interior mass) ε0 (permittivity of space) - −1/4πG μ0 (permeability of space) - −4πG/c2 −1/4πε0 or −μ0c2/4π - G (gravitational constant) g = − Gρ dS′ ∮ r (1.7-27) Gravitational scalar potential (with respect to ∞) It is clear that all the equations derivable from the basic electromagnetic φ =−G ρ dv′ ∫r (1.7-28) m r (1.7-29) Gravitational potential of a point mass equations listed above have their gravitational counterparts, and that gravitational equations can be obtained from the corresponding φ =−G electromagnetic equations by simply replacing the electromagnetic symbols and constants by the corresponding gravitational symbols and constants in Gravitational field in terms of scalar potential accordance with Table. 1.7-1. Symbols such as force, energy, momentum, etc., do not need to be replaced. For electromagnetic equations for fields in a g = − ∇φ (1.7-30) vacuum, replace electromagnetic symbols by the corresponding gravitational symbols in Table. 1.7-1. In all other cases, the following procedure should be Gravitational potential in terms of the field used: (1) If an electromagnetic equation is for fields in the presence of material media, reduce the equation to fields in a vacuum. (2) If the equations contain φa = The following equations are for both electromagnetism and gravitation. These g ⋅ d l + φc (1.7-31) a field vectors D or H, replace them by E or B, using the relations D = ε0E and B = μ0H. ∫ c Poisson’s equations for scalar potential 2 ∇ φ = 4πGρ (1.7-32) equations will be shown using gravitational symbols, however, the symbols can be replaced directly by their corresponding electromagnetic symbols in Gravitational field in terms of vector potential Table 1.7-1. The equations are arranged in three categories: (1) equations for calculating fields and potentials, (2) equations for calculating energy and g = − 4πG∇ × Ag (1.7-33) forces, and (3) wave equations. Cogravitational field of a moving point mass K=−G m(v × ru) c 2r 2 (1.7-34) 13 THEORY OF GRAVITOELECTROMAGNETISM Cogravitational field of a current distribution K=− J × ru G c2 ∫ r2 Maxwell’s stress integral for the gravitational field dv′ F= (1.7-35) Cogravitational field in terms of current inhomogeneities (constant mass- 1 1 2 g dS − g(g ⋅ dS) 8πG ∮ 4πG ∮ (1.7-46) Cogravitational force on a mass current current density) K=− J × dS′ r c2 ∮ G F = J × K′dv ∫ (1.7-36) (1.7-47) Cogravitational force on a mass-current dipole Cogravitational vector potential 2 A=− F=− J dv′ c2 ∫ r G (1.7-37) c (m ⋅ ∇)K′ 4πG (1.7-48) Cogravitational torque on a mass-current dipole Cogravitational field in terms of vector potential 2 T=− K=∇×A (1.7-38) c m × K′ 4πG (1.7-49) Cogravitational force in terms of vector potential (constant mass-current Poisson’s equation for cogravitational vector potential 4πG 2 ∇ A= c2 J density) Cogravitational field in terms of scalar potential K= F= (1.7-39) ∮ A′ ⋅ JdS (1.7-50) Cogravitational force in terms of scalar potential (constant mass-current density) 4πG ∇φk c2 (1.7-40) F= Cogravitational dipole moment of filamentary mass current I (S’ is righthanded relative to I) 4πG c2 ∮ φk′J × dS (1.7-51) Maxwell’s stress integral for the cogravitational field m=− 4πG c 2 2 I S′ (1.7-41) Cogravitational dipole field K= 2 c c 2 K dS − K(K ⋅ dS) 8πG ∮ 4πG ∮ F= (1.7-52) Gravitational field energy m 2πr 3 cosθ ru + m 4πr 3 sinθ θu (1.7-42) U=− 1 2 g dv 8πG ∫ (1.7-53) Gravitational energy in terms of potential 2. Equations for calculating energy and forces U= Gravitational force on a mass distribution F = ρg′dv ∫ 1 φρdv 2∫ (1.7-54) Energy of a system of point masses (1.7-43) U=− Gravitational force in terms of scalar potential (single mass of constant density) mm G ′ i k + Us ∑ r 2∑ ik i k (1.7-55) Energy of a mass distribution in an external field F=−ρ ∮ φ′dS (1.7-44) Gravitational force in terms of vector potential (single mass of constant density) F = 4πGρ ∮ Ag′ × dS (1.7-45) U′ = ρφ′dv ∫ (1.7-56) Energy of a point mass in an external field U′ = mφ′ ∫ (1.7-57) THEORY OF GRAVITOELECTROMAGNETISM Cogravitational field energy 2 U=− c 2 K dv 8πG ∫ (1.7-58) Cogravitational energy in terms of vector potential U= 1 A ⋅ Jdv 2∫ (1.7-59) Cogravitational energy of a mass current in an external field U′ = J ⋅ A′dv ∫ (1.7-60) Gravitational Poynting’s vector 2 c K×g 4πG (1.7-61) 1 K × gdv 4πG ∫ (1.7-62) P= Gravitational field momentum G= Gravitational field angular momentum L= 1 r × (K × g)dv 4πG ∫ (1.7-63) 3. Wave equations Direction of field vectors in a plane wave propagating in the z-direction K= 1 k×g c (1.7-64) Energy density in a gravitational wave 2 Uv = − 1 2 c 2 g =− K 4πG 4πG (1.7-65) Observe that gravitational wave equations are analogous to electromagnetic wave equations. There is no difference between a gravitational wave and electromagnetic wave besides the symbols of the equations. The analogue between electromagnetic and gravitational equations is not limited to the equations listed above. Any equation representing a solution of an electromagnetic problem for fields or forces not involving conducting, dielectric, or magnetic bodies, has its gravitational counterpart. However, if the propagation velocity of gravitation is not equal to the velocity of light, the c appearing in the gravitational equations should be the velocity of the propagation of gravitation rather than the velocity of light. Until recently it was believed that the analogue between electromagnetic and gravitational equations did not apply to fast moving systems, because the electric charge is not affected by velocity, but the mass of a moving body was thought to vary with velocity. It is now generally accepted that mass does not depend on velocity. 14 15 OBSERVATIONAL DISCUSSION 2.1 Diamagnetism (2.2-1a) (2.2-1b) (2.2-1c) Diamagnetism is a weak form of magnetism that is induced by a change in the orbital torsion of atomic currents due to an applied magnetic field. As stated by Jefimenko, the magnetic force is a misnomer since the force is electric and has no causal link with the magnetic field. Therefore, ferromagnetic, antiferromagnetic, paramagnetic, diamagnetic, superdiamagnetic, and other forms of magnetism are truly electrical forms. Diamagnetism is found in all materials; however, because it is so weak it can only be observed in materials that do not exhibit other forms of magnetism. Fig. 2.2-1 When an external electrical source such as a permanent magnet is applied to a diamagnetic material, a negative magnetization is produced and thus the There is no actual distinction between “magnetism” and “electricity” susceptibility is negative. This is because diamagnetic materials are composed considering the magnetic field has no causal link to the forces associated with of atoms that have no net magnetic moments where all their orbital shells are magnetism. Magnetic and electric fields cannot cause each other as concluded filled. This phenomenon of diamagnetic force is due to an atomic level Lorentz in the first chapter summarizing Jefimenko’s theory. An “electromagnetic” force, where charges moving in opposite directions repel. As the permanent propagation is shown in Fig. 2.2-2, where the magnetodielectric field is 90° to magnet is applied to a diamagnetic material, the diamagnetic material induces the direction of an electric current. The magnetodielectric field only exists an opposing electric current, repelling the magnet. during the change or motion of a magnetic dipole field and with a time-varying current. An exception to the weak nature of diamagnetism occurs when materials become superconducting. Superconductors are ideal diamagnets; when positioned in an external magnetic field, they repel the field lines from their interiors (of course this being an electrical repulsion and not magnetic). Superconducting magnets are the foremost elements of most magnetic resonance imaging (MRI) systems and are among the most important applications of diamagnetism. Bismuth displays the strongest diamagnetism in nature. Material bismuth can be melted down and molded to efficiently capture any diamagnetic properties. An induced opposing current of any system is an expansive force. Bismuth is the naturally fastest growing metal in nature. MAGNETODIELECTRIC FIELD 2.2 Permanent Magnets TIME-VARYING ELECTRIC CURRENT Fig. 2.2-2 Permanent magnets are the most common method used to generate electricity throughout the world. The magnetic field of a stationary permanent magnet is a magnetostatic field. A moving magnet or changing magnetic field is accompanied by a magnetodielectric field, the additional electric field created by the electrokinetic field that has closed loops analogous to the magnetic field. Therefore, a moving magnetic dipole field is always accompanied by an analogous secondary electric field. As shown by Eric Dollard, the phenomena of this magnetodielectric field exists without a charge carrier, always moving 90° across the current direction of a coiled wire. Using a thin piece of glass to separate two magnets, when a force is applied to the bottom magnet (Fig. 2.2-1a), the top magnet will rotate as the magnet is moving (Fig. 2.2-1b). Motion applied to the right creates a counterclockwise spin and motion applied to the left creates a clockwise spin (this also depends on the dipole orientation). This is the observation of a circulating magnetic dipole field due to an “electromagnetic” propagation (Fig. 2.2-1). It is therefore evident fields are counter-propagating during a time-varying propagation. Magnets are best understood by their quantum effects. Orbital magnetic fields are caused by the currents of intermolecular charges in half-filled atomic shells. These half-filled atomic shells define magnetic atoms of the periodic table. Although atoms such as chromium are half-filled at the atomic level, chromium solids align their magnetic fields in an alternating fashion that cancel out each other. This is the distinction between ferromagnetic and antiferromagnetic materials. As stated by Jefimenko, the expression “force exerted by a moving magnet” is a misnomer, since this fore has no causal link with the magnetic field of the magnet. The phenomenon of “induced electric force” or “induced current” by a moving magnet is simply the effect of the electric field caused by the collective translational motion of microscopic currents participating in the motion of the magnet. “Magnetic attraction” is also a misnomer, since the attractive phenomena of a magnet relates to the alignment of microscopic electric currents. According to the Lorentz force law, two charges moving in the same direction attract and two charges moving in the opposite direction 16 OBSERVATIONAL DISCUSSION repel. This is fundamental when understanding the phenomenon of “magnetic attraction,” however, instead of this force being an electrostatic force with lines of force ending in matter, this is a magnetodielectric force related to the closed loop electric field. There are no dipole ends of a magnet, rather magnetic equipotential regions separated by a domain wall or Bloch wall. The north and south regions of the magnetic dipole field are created by the aligned microscopic currents. As microscopic charges are moving in the same direction of two magnetic materials they will attract. The materials will repel if the charges are moving in opposite directions. The compression between charges moving in the same direction is noticed in neighboring wires of a coil, where the coil windings will compression as the charge is increased. The term counterspace is defined by Eric Dollard as the phenomenon of “attraction” or compression between Fig. 2.3-1 neighboring wires of a coil when the charge is increased (and currents are aligned). This means a smaller space stores a larger charge, reflecting electromagnetic waves where decreasing wavelength is increasing frequency. Similar to the iron filings, the “spiking” of ferrofluid is caused by the dipole The Casimir effect exists due to the nature of counterspace. alignment of the material. The attracting “ends” of the dipoles have aligning microscopic currents whereas the neighboring dipoles repel due to their Electrets are similar to permanent magnets. These electrets have a permanent microscopic currents opposing. This creates the “spikes” seen with iron filings electrostatic field, rather than a permanent magnetostatic field of a magnet. and in more definition seen with ferrofluid. This could also be interpreted as Since electrets exhibit an electrostatic force and magnets exhibit a wave interference, where the alignment of currents is constructive interference magnetodielectric force, it should be noted the electrostatic force is caused by and the opposition of currents is destructive interference. When using a opposing charges (terminal ends of strings) and the magnetodielectric force is ferrocell, this light geometry is created by a wave interference that is seen caused by charges moving in the same direction. The nature of counterspace similarly to the ferrofluid “spike” reaction. A stronger magnetic field displays applies to both the electrostatic and magnetodielectric forces. a more frequent and tighter wave interference, whereas a weaker magnetic field displays a less frequent and wider wave interference. This reflects the material display of the ferrofluid, where the “spikes” are more frequent and 2.3 Ferrofluid and Ferrocell tighter with a stronger magnetic field and less frequent and wider with a weaker magnetic field. It is also interesting to note as ferrofluid droplets are Ferrofluid is a superparamagnetic nanoparticle fluid used to observe the quantum effects of a permanent magnet. In accordance with Maxwell-Faraday equations, accelerating magnets due to the electrical forces of magnetism creates an temporary time-varying propagation. As the magnetic dipole field is moving or changing, it is considered a magnetodielectric field. As iron observed falling downwards towards a magnet, the droplets stretch. The frontal lobe of the droplet is accelerating faster than the occipital lobe of the droplet (Fig. 2.3-3). This is due to the magnet’s force pulling harder on the frontal lobe of the droplet since it is closer to the magnet compared to the occipital lobe that is farther away from the magnet. filings are displayed over a permanent magnet they form an electric field geometry due to the nature of accelerating magnetic fields. It is clearly seen in Fig. 2.3-1 that the iron filings are ending upon the terminal ends of the magnet, and not looping analogously with the dipole field of the magnet. As the iron filings equilibrate their local energy to the external magnetic field (really aligning electric currents), they clump together forming the illusion of electric field lines that end upon the terminal ends of the magnet. This is mistakenly considered “magnetic field lines,” however, there are no magnetic field lines displayed by the iron filings. The electric field and magnetic field can be compared in Fig 2.3-2, where the electric field has lines terminating upon the ends of a conductor and the magnetic field (including the electric field of the magnetodielectric field) has lines terminating upon themselves as closed loops surrounding a material. ELECTROSTATIC FIELD MAGNETOSTATIC FIELD Fig. 2.3-2 17 OBSERVATIONAL DISCUSSION As a magnet is placed against the surface of a thin barrier between itself and action of electromagnetic radiation.” The photon particle is merely the the ferrofluid, nanoparticles form a ring surrounding the edge of the dipole end phenomenon of a longitudinal compression and rarefaction necessitated by of the magnet. This is identical to iron filings over a large magnet, where the electric charges and currents. Therefore, there is no moving light particle, only filings will disperse in a ring formation around the edge of the dipole end of compressions and rarefactions of an ether perturbation. In accordance with the magnet. This is due to charge and current existing on the surface experiments conducted by the Large Hadron Collider (LHC) at CERN, matter surrounding materials and not in materials. As stated by Charles Proteus is nothing more than highly concentrated electromagnetic waves (light). Steinmetz, there is no electric charge or electric current inside the space of a conductor, rather surrounding the conductor’s surface. The magnet could be considered a section of a conducting wire, where the dipole axis is in the direction of the wire. During an equilibration such as iron filings adjusting to an external magnetic field of a magnet, the iron filings will equilibrate into the regions where charge and current is induced the most surrounding the magnet. The light geometry seen upon the ferrocell due to wave interference between the magnet and ferrofluid will analogously form in the same surrounding regions of the magnet as the iron filings. Fig. 2.3-4 It can therefore be concluded that the hypotrochoid geometry observed upon a ferrocell is the curvature of light due to moving charges and a result of wave interference. This geometry forms a two-dimensional torus, and from the side dipole view of a magnet displays a geometry similar to equipotential contours. This geometry is created purely by an electric phenomenon, having no magnetic contribution. The geometry could therefore be a visualization of the boundaries for equipotential domains. Fig. 2.3-3 2.4 Fluid Dynamics Analogue The ferrocell is constructed using a pair of optical flat glass planes, ferrofluid, penetrating oil, and an LED strip. Using thick dark construction paper on the back of the ferrocell lens will create a clearer image without any visual pollution. The curvature of light seen through a ferrocell is caused by microscopic moving charges of the permanent magnet, the light pattern reflecting the wave interference of the ferrofluid and permanent magnet (Fig. 2.3-4). The LED light source is highlighting and accommodating this wave interference, creating the hypotrochoid light geometry upon the ferrocell lens. This phenomenon is also analogous to the bending of light in a cathode ray tube by an external magnetic field. Following the Lorentz force, the force of a permanent magnet will direct the ray upwards or downwards depending on the orientation of the magnet. It should be noted that in J.J. Thomson’s announcement on the results of his experiments on cathode rays, he stated the rays were “corpuscles.” About 1000 corpuscles is considered 1 electron today. From the views of J.J. Thomson, the coulomb Ψ is the primary unit defining the ether. Thomson developed the ether atom ideas of Michael Faraday into his electronic corpuscle. One corpuscle terminates one farad of force, quantified as one coulomb. With Eric Dollard’s total Planck electrification considered (Q=Ψ×Φ), Q is the unit of is of the Planck constant unit joule · sec, Ψ is the unit of the coulomb, and Φ is the unit of the weber. This unit Q can be accounted for what is conventionally understood as the photon, “the quantum There are analogues between gravitoelectromagnetism and fluid dynamics, such as hydrodynamics. Water is a great analogue for describing the ether. It has been suggested that the vector potential represents some kind of fluid velocity field. Maxwell was first to suggest that the magnetic vector potential A behaves like a moving medium that mimics the velocity of a space flow around a magnetic field line. The Euler force in fluids corresponds with the Lorentz force in electromagnetism. Eddies on the surface of water correspond with the behavior of point charges. They allow energy to be expressed as a disturbance from the water’s flat equilibrium, but in a more stationary way than transient waves. Just as two moving charges in opposite directions repel, two surface eddies spinning in the same direction repel. Two surface eddies spinning in opposite directions attract, corresponding with two moving charges in the same direction. This can be seen in Fig 2.4-1, where the opposite spinning eddies have meeting currents in the same direction. In addition, if counter-rotating vortices meet they “annihilate”—the angular momentum of one neutralizing that of the other— and the energy they contained radiates away as waves, closely mimicking the dynamics of matter and antimatter. 18 OBSERVATIONAL DISCUSSION This is a Falaco soliton, modon or dipole eddy pairs (Fig. 2.4-2). These paired vortices seen in Fig 2.4-2 are extraordinarily stable compared to individual ones. They can persist for minutes at a time rather than the seconds that a vortex usually lasts. But disrupt the string that joins them, and they’ll dissipate almost instantly. While two counter-spinning eddies created individually behave like matter and antimatter, the Falaco soliton lets us see opposite “charges” interacting in a way that more closely resembles the behavior of neutrons, or of protons and electrons. Here they balance out and prevent one another from interacting as strongly with the environment. They create a “vorticity-neutral” system on the surface, the same way a neutron or a hydrogen atom is charge-neutral. 2.5 The Golden Section In Plato’s views on natural science presented in Timaeus, he considered the golden ratio as the key to the physics of the cosmos and the most biding of all mathematical relationships. This divided line is visible within the golden triangle and pentagram (Fig. 2.5-1). Fig. 2.4-1 1 While canoeing it is likely to create individual eddies on the surface of the Φ-1 water. As the paddle is pulled back and a small void is created, water ruches in 1 from the sides to fill the void and return the pond to equilibrium, where the entire surface is at the same height. When a current of this water catches its Φ tail, a persistent dimple forms. Before too long, the viscosity of the water saps away its angular momentum and the vortex dissipates. Imagine we use a plate rather than a paddle, so that the water rushes in from both sides symmetrically. Fig. 2.5-1 Done at just the right speed, this process can create a pair of counter-spinning vortices. Unlike vortices created independently, these ones won’t annihilate each other due to a special difference: they’re linked and joined by a “string” of current through the water—the eddies are two ends of a single “topological defect.” There is widespread belief that the Fibonacci spiral is the golden spiral. This also includes an altered version of the spiral that follows a golden ratio sequence instead of a Fibonacci sequence, but still is constructed as a Fibonacci spiral. The golden spiral has no direct relation to the Fibonacci spiral, however, the Fibonacci sequence is of high importance when constructing the golden spiral. The Fibonacci equation sequence is given by (Seq. 2.5-1) phi1 = 0+1⋅phi phi2 = 1+1⋅phi phi3 = 1+2⋅phi phi4 = 2+3⋅phi phi5 = 3+5⋅phi where the powers of phi are the product of the double phased Fibonacci sequence multiplied by the golden ratio. This equation sequence is used Fig. 2.4-2 to construct the scaling progression of the 108° golden spiral section (Fig. 2.5 2-3). 19 OBSERVATIONAL DISCUSSION 108º Φ-1 Φ-4 Φ-2 Φ-5 1 Φ-2 Φ-1 Φ-3 Φ-1 1 1 Φ-1 1 1 1 √5 5 Fig. 2.5-4 Fig. 2.5-2 In relation to the fluid dynamics analogue, the angle of 108° is close to the molecular bond angle of H-O-H (water). It is also understood that there is a counter-propagation of wave phenomena which could be related to the golden section, but more research must be completed. Φ-1 Φ-4 Φ-3 Φ-5 Φ-2 Fig. 2.5-3 The pentagram is the geometry of the golden ratio and defines the angular sections of the golden spiral. This golden ratio geometry is the only star polygon that can solve a square root, specifically the square root of 5. If the golden isosceles triangle of the pentagram is given a perimeter of √5, consisting of two legs each of phi-1 and a base of 1, when the perimeter of the square root of 5 is squared (√52) it extrapolates into the pentagram (Fig. 2.5-4). The pentagram consists of 5 equal 1 unit lines in this geometric calculation. Five is predominant in nature, appearing with the five forces of gravity, five lines or points of the pentagram (golden section star polygon), five fingers of a hand, and five toes of a foot. We can only see five planets with the naked eye (Mercury, Venus, Mars, Jupiter, and Saturn). We have five main components for sensing: eyes, ears, nose, mouth, and skin. The human body has five vital organs. The pentagram was also known by the Ancient Pythagoreans as good health (hygē a). 20 PSYCHOLOGY ANALOGUE 3.1 James-Lange Theory observed due to a physical interaction, its identity is described subjectively based on the empirical observations. Just like the E and B fields or g and K The James-Lange theory is a hypothesis on the origin and nature of emotions fields, subjective emotions have no effect upon charges and currents. As and is one of the earliest theories of emotion within modern psychology. It was discussed by Charles Proteus Steinmetz, the medium which surrounds matter developed independently by two 19th-century scholars, William James and is the electric charge and electric current, whereas the matter itself is an Carl Lange. The basic premise of the theory is that physiological arousal analogous form electricity in which the mass is the “charge” and the instigates the experience of emotion. Instead of feeling an emotion and acceleration of the mass is the “current.” Recently it has been observed that subsequent physiological (bodily) response, the theory proposes that the masses cannot touch due to the electrical forces between them. However, as physiological change is primary, and emotion is then experience when the concluded by Jefimenko, mass exists analogously to electric charge. This brain reacts to the informations received via the body’s electrical nervous means that a mass must have a physical interaction analogous to electric system. It proposes that each specific emotion is attached to a unique and charge. The reason why touching matter cannot be observed is because the different pattern of physiological arousal and emotional behavior in reaction observed matter is simply an emotional expression or concept caused by due to an exciting stimulus. physical charges and currents. This ultimately means the person we see in the mirror is not the true self, rather the identity of a nonphysical emotional The James-Lange theory was challenged in the 1920s by psychologists such expression caused by physical charges and currents. as Walter Cannon and Philip Bard, who developed an alternative theory of emotion known as Cannon–Bard theory, in which physiological changes There are two main components in the James-Lange theory (Fig. 3.1-1): follow emotions. A third theory of emotion is Schachter and Singer's two arousal and emotion. The arousal is the cause, which corresponds with the factor theory of emotion. This theory states that cognitions are used to charge density ρ and current density J. The emotion is the effect, which is the interpret the meaning of physiological reactions to outside events. This theory descriptions of matter and corresponds with coexisting nonphysical variables is different in that emotion is developed from not only cognition, but that (E, B, g, K). Subjective emotions have no causal link with psychological combined with a physical reaction. In 2017 Lisa Feldman Barrett reported that response. Physiological responses of the body are based on physical the James-Lange theory was created by neither William James nor Carl Lange. interactions of the electrical nervous system. The induction of electricity (and It was indeed named by the philosopher John Dewey who would have gravity) exists analogously to the induction of arousal upon the body. misrepresented Jame’s ideas on emotion. James never wrote that each Emotions are embodied as descriptive matter after a physical observation category of emotion (fear, anger, etc.) has a distinct biological state. He wrote occurs. Magnetic storage could be analogously compared to the memory of the that each instance of emotion may have a distinct biological state. Dewey’s human mind. Recent research has suggested the magnetic storage of assumed error “represents a 180-degree inversion of Jame’s meaning, as if information occurs in the human cerebral cortex. James were claiming the existences of emotion essences, when ironically he was arguing against them.” Barrett notes that “Dewey’s role in this error is forgotten.” Lisa Barrett also points out that when testing this theory with PERCEPTION OF STIMULUS PERCEPTION OF STIMULUS PERCEPTION OF STIMULUS POUNDING HEART AROUSAL POUNDING HEART AROUSAL POUNDING HEART AROUSAL and emotion category. Furthermore, Barrett says that the experience of emotion is subjective: there is no way to decipher whether a person is feeling sad, angry, or otherwise without relying on the person’s perception of emotion. CAUSE electrical stimulation, there is not a one-to-one response between a behavior Also, humans do not always exhibit emotions using the same behaviors; humans may withdraw when angry, or fight out of fear. According to Barrett’s theory of constructed emotion, a person must make meaning of the physical response based on context, prior experience, and social cues, before they know what emotion is attached to the situation. Lisa Barrett and James Gross have The analogue between consciousness and gravitoelectromagnetism can be bridged by connecting the key differences between gravitoelectromagnetism and the components of the James-Lange theory with nondualistic causality. EFFECT reviewed a variety of alternative models to the so-called James-Lange theory. Advaita Vedānta, which means non-duality, strictly follows the principle of causality. The cause is physical. The effect is illusive. The charge density ρ and current density J, analogous in both electromagnetic and gravitational equations, are the processor of the mind. The causative effects (E and B or g and K) are the emotions of the mind. This effect of emotion is the nonphysical and subjectivity of imagination. When matter is Fig. 3.1-1 PSYCHOLOGY ANALOGUE As an arousal occurs, there is an influx of energy into the body by a causative source. This influx causes thoughts and opinions directed at the source of the influx depending on the string geometry of the influx. As a car is approaching a person they receive an influx of arousal from the moving car, likewise developing a specific belief and subjective reaction to the oncoming car based upon the geometry of the influx, the person’s memory, genetics, etc. Arousals of the James-Lange theory can be considered a mental induction related to the physical interaction of charges and currents. These arousals stimulate the pure feeling of ecstasy. The ecstasy is not good nor bad, since it manifests both with fear and happiness. This is the basic reason why people can enjoy horror movies or engage in dangerous stunts. If a person is gifted a present the same type of influx in arousal, however, the overall geometry of the influx is unique from the oncoming car, hence why the reaction is different. The main key is that the arousal behind both fear and happiness is the same ecstasy. The ecstasy of an arousal is a single string, whereas the emotional subjectivity is based upon a collection of intersecting strings of specific angles and ratios. Physiological reactions do not depend on emotional opinions or subjectivity and emotions have no effect upon physical reactions since the emotions occur after the reaction, sensation, or observation. Focus on emotion can stimulate physical reactions, however, the focus and its inducing geometry is the driving factor of this phenomena and not the emotion in focus. This essentially concludes the analogues relationship between the two main components of the James-Lange theory and gravitoelectromagnetism. There is no distinction between physical interactions of physics and physiological reactions of psychology other than the applications used to describe their phenomena. 21 CONCLUSIONS 4.1 The Difference Between Gravity and Electromagnetism 22 has its own variables and unique nonlinear gravitational effects. Therefore, the basic distinction between the two are string count. The electric force is a single Dr. Oleg Jefimenko has shown gravity and electromagnetism to be analogous string between charges. The gravitational force is multiple (and intersecting) in their calculations (excluding nonlinear gravitational effects). Their only strings between masses. Thus, a body influenced by a gravitational field feels mathematical difference is the symbols and constants used in the equations, as a force due to all atomic charges of the body interconnecting with the atomic shown in the first chapter. Jefimenko has also shown that the magnetic field charges of the gravitational body. The string geometry of a mass defines the has no physical meaning, stating that both expressions “electromagnetic strength of point charges and the distribution of point charges. It is important induction” and “magnetic force of a magnet” are misnomers considering the to note that electric currents or field lines cannot cross. The crossing point of magnetic field has no causal link to the phenomena. The expressions for strings between masses is a mutual terminal null point (zero charge point), also “electricity” and “magnetism” are caused by charges and currents. Jefimenko apparent between attracting magnets when observed using a ferrocell. strongly supports evidence of “the ether,” as he’s stated “The gravitationalelectromagnetic analogy may be further extended if we allow that the ether which supports and propagates the gravitational influence can have a translational motion of its own, thus carrying about and distorting the lines of force.” Jefimenko suggested the ether was another way to expression the propagation of gravity. The ether is universal strings that interconnect all point-like phenomena. The concept of points (whether point particle or point mass) exist at the end of strings. In natural philosophy, a line is the expansion of a point and a point cannot exist without a line. Therefore, the strings and point-like phenomena always exist together as one entity. The charge and current is the phenomenon of the strings and points. It should be noted “opposing charges” are really opposite electrical polarities of a string, where + and − terminals are each “ending” point of the string. The “end” points of a string are really always the cross section of strings, since no field line of force can end in space. These strings and points are expressed in nature as geometry. Strings account for the phenomenon of volume and points account for the phenomenon of density, however, density and volume are distinct properties of a single thing, the ether. 4.2 Unified Theory of Physics and Psychology With unification given between gravity and electromagnetism, there were also analogues discussed between the James-Lange theory and physics. The consciousness is a composite of the two main components of the James-Lange theory: arousal and emotion. Arousal corresponds with charge density ρ and current density J. Emotion corresponds with symbols that have no causal link to charge and current, such as the E and B fields or the g and K fields. It is seen analogously between electromagnetism and gravity that charges and currents are physical interactions. This corresponds directly with physiological arousal of a body. What gives space or definition to this arousal is the resultant effect, the emotional subjectivity. This creates the phenomenon of imagination which has no influence upon any physical interaction, entirely nonphysical and subjective. The concept of causality analogously between components of the James-Lange theory and gravitoelectromagnetism follow the ideology of cause and effect in Advaita Vedānta. As shown by Jefimenko, there is absolutely no such thing as electromagnetic dual or any duality in nature. The notion of electromagnetic dual is just as illogical as the notion of subjective emotions manifesting as physical forces. The mechanics of the universe are constructed by a single simplex physical cause, which has at least one illusive nonphysical effect. The analogue between physics and psychology paves a new path towards a unified theory [of everything]. q4 q14 q9 q15 q5 q16 q11 q1 q7 q6 q2 q8 q13 q12 q3 q10 Fig. 4.1-1 Geometry can express the difference between electromagnetism and gravity precisely (Fig. 4.1-1). The lines of a geometry are the strings of the ether. The only difference between gravity and electromagnetism is that gravity is a massive magnitude made up of unaligned dipole domains. This is why gravity REFERENCES Jefimenko, Oleg D. 2000. Causality, Electromagnetic Induction, and Gravitation: A Different Approach to the Theory of Electromagnetic and Gravitational Fields. Second Edition. Waynesburg, PA 15370, USA. Electret Scientific. Jefimenko, Oleg D. 2004. Electromagnetic Retardation and Theory of Relativity: New Chapters in the Classical Theory of Fields. Second Edition. Waynesburg, PA 15370, USA. Electret Scientific. Jefimenko, Oleg D. 2006. Gravitation and Cogravitation. Waynesburg, PA 15370, USA. Electret Scientific. Dollard, Eric P. 1986. Representations of Electric Induction. Garberville, CA 95440-0429, USA. Borderland Research. Dollard, Eric P. 2015. A Common Language for Electrical Engineering: Lone Pine Writings. Tesla, Nikola. 1892. Experiments with Alternate Currents of High Potential and High Frequency: A Lecture Delivered Before the Institution of Electrical Engineers, London. Berkley, CA 94720, USA. The University of California. Tesla, Nikola. 1899-1900. Colorado Springs Notes. Ann Arbor, MI 48109, USA. The University of Michigan. Tesla, Nikola. 1900. The Problem of Increasing Human Energy: With Special Reference to the Harnessing of the Sun's Energy. NY, USA. Century Illustrated Magazine. Martins, Alexandre A. 2012. Fluidic Electrodynamics: On parallels between electromagnetic and fluidic inertia. Institute for Plasmas and Nuclear Fusion & Instituto Superior Técnico Av. Rovisco Pais, 1049-001 Lisboa, Portugal. Olsen, Scott A. 2002. The Indefinite Dyad and the Golden Section: Uncovering Plato’s Second Principle. Nexus Network Journal. Barrett, Lisa F. 2017. How Emotions are Made: The Secret Life of the Brain. Houghton Mifflin Harcourt. Boscovich, Roger J; Boscovich, Ruggero G; Child, Mark J; Petronijevic, Branislav. 1922. A Theory of Natural Philosophy. Ann Arbor, MI 48109, USA. The University of Michigan. 23