Unified Field Theory

In the Einstein field equations, the geometry or the curvature of space-time defined as depended on the distribution of mass and energy principally resides on the left-hand side is set identical to a non-geometrical tensorial representation of matter on the right-hand side. In one or another form, general relativity accords a direct geometrical significance only to the gravitational field while the other physical fields are not of space time. They reside only in space time. Less well known, though of comparable importance is Einstein’s dissatisfaction with the fundamental asymmetry between gravitational and non-gravitational fields and his contributions to develop a completely relativistic geometrical field theory of all fundamental interactions, a unified field theory. Of special note in this context and equally significant is Einstein’s demand to replace the symmetrical tensor field by a non-symmetrical one and to drop the condition gik = gki for the field components. Historically, many other attempts were made too, to extend the general theory of relativity’s geometrization of gravitation to non-gravitational interactions, in particular, to electromagnetism. Still, progress has been very slow. It is the purpose of this publication to provide a unified field theory in which the gravitational field, the electromagnetic field and other fields are only different components or manifestations of the same unified field by mathematizing the relationship between cause and effect under conditions of general theory of relativity.

A NON-DUALISTIC UNIFIED FIELD THEORY OF GRAVITATION,ELECTROMAGNETISM AND SPIN

The wisdom of classicalunified field theories in the conceptual framework of Weyl, Eddington, Einstein and Schrodinger has often been doubted and in particular there does not appear to be any empirical reason why the Einstein-Maxwell (E-MJ theory needs to be geometrized. The crux of the matter is, however not whether the E-M theory is aesthetically satisfactory but whether it answers all the modern questions within the classical context. In particular, the E-M theory does not provide a classical platform from which the Dirac equation can be derived in the way Schrodinger's equation is derived from classical mechanics via the energy equation and the Correspondence Principle. The present paper presents a non-dualistic unified field theory (UFT) in the said conceptual framework as propounded by M. A. Tonnelat. By allowing the metric form ds2=g,dx dx and the non-degenerate two-form F=(1/2t)rdx dx to enter symmetrically into the theory we obtain a UFT which contains Einstein's General Relativity and the Born-Infeld electrodynamics as special cases. Above all, it is shown that the Dirac equation describing the electron in an 'external' gravito-electromagnetic field can be derived from the non-dualistic Einstein equation by a simple factorization if the Correspondence Principle is assumed.

Cosmic Ether, Possessing Electric-Tension and Magnetic-Resistance, Is the Unified Field for Physics

The paper presents the case that physics is already and effectively unified by the energetic tension field, ether. We identify this integrating power of ether first, by re-defining the action generating parameters of this energetic tension field as the electric-tension, , and the magnetic-resistance, μ0, while re-deriving the Maxwell’s wave equation in analogy with the mechanically stretched string, where the . Then, replacing by and m0 by , one can find that almost all working physics theories are being energized byand μ0. To complete the unification, we can now postulate that the particles are also freely propagating EM waves, but they are spatially localized as in-phase, close-looped (IP-CL) vortex-like propagation modes of ether. Because of their IP-CL mode structure, they have space-finite spatial structures and remain spatially stationary in the absence of any spatially influencing potential gradients (forces) in their vicinity. Particles’ harmonic phase driven interactions between quantum particles give birth to the appearance of wave-particle duality. There is no need for the confusing and unnecessary de Broglie’s Pilot Wave. The inertia to spatial motion of IP-CL modes automatically accommodates Newton’s laws of motion. The cosmic universality of Maxwellian wave velocity, and particles as IP-CL modes, jointly accommodate the two key postulates of special relativity without the need for unphysical four-dimensionality. The observable universe is represented only by its diverse oscillatory excited states. The stable and stationary Cosmic Ether keeps holding 100% of its energy all the time. We have proposed a one-way light pulse propagation experiment to directly validate the existence of ether, rather than approaching Michelson’s way of measuring the ether drag. We have identified a good number of examples of working theoretical expressions in terms of and μ0 and presented our critical views in physics thinking, belonging to Classical, Relativity, Quantum and Cosmology Physics.

The Geometrization of the Electromagnetic Field

Einstein used the term “unified field theory” in a title of a publication for the first time in 1925. Somewhat paradoxically, an adequate historical, physical and philosophical understanding of the dimension of Einstein’s unification program cannot be understood without fully acknowledging one of Einstein’s philosophical principles. Despite many disappointments, without finding a solution besides of the many different approaches along the unified field theory program and in ever increasing scientific isolation, Einstein insisted on the unity of objective reality as the foundation of the unity of science. Einstein’s engagement along his unification program was burdened with a number of difficulties and lastly in vain. Nevertheless, a successful geometrization of the gravitational and the electromagnetic fields within the framework of the general theory of relativity is possible. Thus far, it is a purpose of the present contribution to geometrize the electromagnetic field within the framework of the general theory of relativity.

Thermo-hydro-mechanical-air coupling finite element method and its application to multi-phase problems

In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.

Vacuum Fluctuations, Isolated Systems and Hierarchical Cosmology

Einstein's general theory of relativity rests on the convention of constant units for time and length, specified by standards at a fired world point P. It is valid to flatten space-time by choice of unit fields, obtained by applying time dilation and length contraction to standards in accordance with an aether velocity field vg(r,t). Two equally valid descriptions for gravitation result. Cosmology in flat space-time is first developed. Zero-point radiation is renormalized to finite energy Kpoc2 density by inclusion of gravitational self-potential energy density provided that Kpoc2 closes the uni- verse at radius R. It is shown that such a universe satisfies the black hole condition, and hence behaves as an isolated system. A single constant defines a finite universe with respect to any mass, due to self-adjustment of boundary surface. The equivalent Einstein model is found by a units transformation to be de Sitter space-time. Einstein's equations must contain only the cosmological term as source term. The Hubble redshift is shown to emerge in both Doppler-gravitational and frequency-decay guises. By postulating an infinite Cosmos containing universes on a hierarchy of scales specified by a geometric series of constants, it is possible for gravitation and electromagnetism to acquire equal complementary status. Unified field equations are proposed, and the relationship between an electron and a universe is explored. A theoretical value of the Hubble constant emerges, H= 108 km s-1Mpc-1.

Anti Aristotle—The Division of Zero by Zero

Today, the division of zero by zero (0/0) is a concept in philosophy, mathematics and physics without a definite solution. On this view, we are left with an inadequate and unsatisfactory situation that we are not allowed to divide zero by zero while the need to divide zero by zero (i.e. divide a tensor component which is equal to zero by another tensor component which is equal to zero) is great. A solution of the philosophically, logically, mathematically and physically far reaching problem of the division of zero by zero (0/0) is still not in sight. The aim of this contribution is to solve the problem of the division of zero by zero (0/0) while relying on Einstein’s theory of special relativity. In last consequence, Einstein’s theory of special relativity demands the division of zero by zero. Due to Einstein’s theory of special relativity, it is (0/0) = 1. As we will see, either we must accept the division of zero by zero as possible and defined, or we must abandon Einstein’s theory of special relativity as refuted.

Anti Chsh—Refutation of the Chsh Inequality

Today, quantum-mechanical concepts i.e. such as non-locality refer to some mathematical foundations, especially to Bell’s inequality and the Chsh inequality. Experimental data, analyzed while using Bell’s inequality or the Chsh inequality, favor a quantum mechanical description of nature over local hidden variable theories (often referred to as local realism). In general, the use of mathematically inconsistent methods can imply a waste of money, time and effort on this account. Under some certain conditions (the assumption of independence) Bell’s theorem and the Chsh inequality are already refuted. The purpose of this publication is to explore the terra incognita, the interior logic that may lie beyond Bell’s original theorem and the Chsh inequality and to refute both Bell’s original theorem and the Chsh inequality under any circumstances by the proof that we can derive a logical contradiction out of Bell’s inequalities. Thus far, if you accept Bell’s theorem or the Chsh inequality as correct, then you must accept too that +0 = +1, which is a logical contradiction. Bell’s theorem and the Chsh inequality are refuted in general. In this insight, it appears to be necessary to revisit the very foundations of quantum theory and of physics as such.

Anti Heisenberg—The End of Heisenberg’s Uncertainty Principle

In contrast to many other physical theories, quantum mechanics is generally regarded as above any theory we have ever had and perhaps the best candidate for a universal and fundamental description of objective realty as such. Heisenberg’s uncertainty principle is not the only aspect of the conceptual difference between quantum and classical physics but is certainly one of the most important and famous aspects of quantum mechanics. As we will see, quantum mechanics as a theory and especially Heisenberg’s uncertainty principle challenges not only our imagination but violates some fundamental principles of classical logic as such. Heisenberg’s uncertainty principle is refuted.

The Physical Meaning of the Wave Function

Under some well-defined conditions, the mathematical formalism of quantum mechanics enables physicists, chemists and others to calculate and predict the outcome of a vast number of experiments. In fact, especially the Schr?dinger equation which involves an imaginary quantity describes how a quantum state of a physical system changes with time and is one of the main pillars of modern quantum mechanics. The wave function itself is a determining part of the Schr&oumldinger equation, but the physical meaning of the wave function is still not clear. Altogether, does the wave function represent a new kind of reality? This publication will solve the problem of the physical meaning of the wave function by investigating the relationship between the wave function and the theory of special relativity. It is shown that the wave function is determined by notion co-ordinate time of the special theory of relativity. Moreover, the result of this investigation suggests a new understanding of the wave function, according to which the wave function and co-ordinate time of the theory of special relativity are equivalent.

The Electromagnetic Nature of Gravitation and Matter-Antimatter Antigravity. Surmise on Quantum Vacuum Gravitation and Cosmology

We show that the electromagnetic quantum vacuum derives directly from Maxwell’s theory and plays a primary role in quantum electrodynamics, particle physics, gravitation and cosmology. It corresponds to the electromagnetic field ground state at zero frequency, a zero-energy cosmic field permeating all of space and it is composed of real states, called kenons (κενο = vacuum). Photons are local oscillations of kenons guided by a non-local vector potential wave function with quantized amplitude. They propagate at the speed imposed by the vacuum electric permittivity ε0 and magnetic permeability μ0, which are intrinsic properties of the electromagnetic quantum vacuum. The electron-positron elementary charge derives naturally from the electromagnetic quantum vacuum and is related to the photon vector potential. We establish the masse-charge equivalence relation showing that the masses of all particles (leptons, mesons, baryons) and antiparticles are states of the elementary charges and their magnetic moments. The equivalence between Newton’s gravitational law and Coulomb’s electrostatic law results naturally. In addition, we show that the gravitational constant G is expressed explicitly through the electromagnetic quantum vacuum constants putting in evidence the electromagnetic nature of gravity. We draw that G is the same for matter and antimatter but gravitational forces should be repulsive between particles and antiparticles because their masses bear naturally opposite signs. The electromagnetic quantum vacuum appears to be the natural link between quantum electrodynamics, particle physics, gravitation and cosmology and constitutes a basic step towards a unified field theory. Dark Energy and Dark Matter might originate from the electromagnetic quantum vacuum fluctuations. The calculated electromagnetic vacuum energy density, related to the cosmological constant considered responsible for the cosmic acceleration, is in good agreement with the astrophysical observations. The cosmic acceleration may be due to both “quantum vacuum fluctuations” and “matter-antimatter gravitational repelling”. All the above results are established without stating any assumptions or postulates. Next, we advance two hypotheses with cosmological impact. The first is based on the possibility that gravitation is due to the electromagnetic quantum vacuum density of states fluctuations giving rise to a photon pressure at the characteristic collective oscillation frequencies of the charge densities composing the bodies (Electromagnetic Push Gravity). The second advances that energy, matter and antimatter in the universe emerge spontaneously from the quantum vacuum fluctuations as residues that remain stable in space and we present the main principles upon which a new cosmological model may be developed overcoming the well-known Big Bang issues.

Newton’s Gravitational Constant Big G Is Not a Constant

Newton’s gravitational constant Big OG, appearing in both Newton’s law of gravity and Einstein’s general relativity, is essential for our today’s understanding of gravity. Thus far, despite of the very long history of measurements of Newton’s gravitational constant Big OG, a definite value is still not in sight. Surprisingly, the results of different experiments have varied by much more than would be expected due to systematic or random errors. Why do measurements of Newton’s gravitational constant Big OG vary so much? The purpose of this publication is to provide a logically and mathematically self-consistent theoretical proof that Newton’s gravitational constant Big OG is not a constant.

A new unified theory of electromagnetic and gravitational interactions

In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the five-dimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is obtained: del F-a(ab) - xi R-b (a)A(a) = -4 pi J(b) with xi = -2, where F-ab is the antisymmetric electromagnetic field tensor defined by the potential vector A(a), R-ab is the Ricci curvature tensor of the hypersurface, and J(a) is the electric current density vector. The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term xi R-b (a)A(a), whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge, as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. 48, 28 (2016)]. Hence, the new unified theory is physically different from Kaluza-Klein theory and its variants in which the Einstein-Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under certain conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe.