Gravitational 4-Vector Potential

Gravitational 4-Vector Potential

(With much thanks to Dr. John Cramer, which a lot of this material was borrowed from)

My favoured theory regarding Dark Matter/Dark Energy is that it does not exist.

My favoured theories regarding Dark Matter/Dark Energy are those which basically say they don't exist, or at least not in the quantities predicted by Relativity. That is not to say that I don't believe in axions, sterile neutrinos or WIMPs, whatever, but that they might not be necessary.

There are a few gaps not explained well by Relativity. Dark matter is a way to avoid having to replace or refine Relativity. There is a natural hesitancy to try to falsify Relativity's description of gravity, because there are not great alternatives.

Many people act as if there is a general consensus about gravitation, but the clever minds out there in the galaxy have managed many alternative theories, some of which are actually useful.

The Jordan–Brans–Dicke theory suggests gravitational interaction is mediated by a scalar field as well as a tensor field. It suggests that the gravitational constant which can vary from place to place with time. As strange as this sounds, there is physical evidence, such as a naturally occurring fission reaction going on in Oklo, Gabon.

Andrei Sakharov’s Emergent Quantum Field Theory ofGeneral Relativity has many applications.

f(R) theory is an entire family of theories. A wide range of phenomena can be produced from this family theory by adopting different functions; however, many functional forms can now be ruled out on observational grounds, or because of pathological theoretical problems.

Horndeski Gravitation is the most general theory of gravity in four dimensions whose Lagrangian is constructed out of the metric tensor and a scalar field and leads to second order equations of motion. It has found numerous applications, particularly in the construction of cosmological models of Inflation and dark energy. Horndeski's theory contains many theories of gravity, including General Relativity, Jordan–Brans–Dicke theory, Quintessence, Dilaton, Chameleon and covariant Galileon as special cases.

Supergravity Theory combines principles of Supersymmetry and General Relativity; this is in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model. Supergravity is the gauge theory of local supersymmetry. WOW, that sounds like techno-gibberish Since the supersymmetry generators form together with the Poincaré algebra a superalgebra, called the super-Poincaré algebra, supersymmetry as a gauge theory makes gravity arise in a natural way. You guessed it, lots and lots of math. These two theories simultaneously may explain all, however, scientists were finding a theory that may explain both quantum theory and theory of gravitation together - a theory of everything. The theory of supergravity revolves around this intention, to establish a theory that is applicable everywhere.

Self-Creation Cosmology Theory of gravity in which the Brans-Dicke theory is modified to allow mass creation. Seriously.

Loop Quantum Gravity (LQG) is the leading contender for quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It makes a lot more sense than string theory. Loop quantum gravity is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a force. In LQG theory space and time are quantized analogously to the way quantities like energy and momentum are quantized in quantum mechanics. The theory gives a physical picture of spacetime where space and time are granular and discrete directly because of quantization just like photons in the quantum theory of electromagnetism and the discrete energy levels of atoms. An implication of a quantized space is that a minimum distance exists. LQG postulates that the structure of space is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale on the order of a Planck length, approximately 10−35 metres, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure.

Nonsymmetric Gravitational Theory (NGT) is a classical theory of gravitation that tries to explain the observation of the flat rotation curves of galaxies, which is what started the whole mess with dark matter.

In General Relativity, the gravitational field is characterized by a symmetric rank-2 tensor, the metric tensor. A general (nonsymmetric) tensor can always be decomposed into a symmetric and an antisymmetric part. As the electromagnetic field is characterized by an antisymmetric rank-2 tensor, there is an obvious possibility for a unified theory: a nonsymmetric tensor composed of a symmetric part representing gravity, and an antisymmetric part that represents electromagnetism. Research in this direction ultimately proved fruitless; the desired classical unified field theory was not found. The antisymmetric part of the generalized metric tensor need not necessarily represent electromagnetism; it may represent a new, hypothetical force. The field corresponding with the antisymmetric part need not be massless, like the electromagnetic (or gravitational) fields.

Gravity as an entropic force, gravity arising as an emergent phenomenon from the thermodynamic concept of entropy.

Tensor–vector–scalar gravity (TeVeS), a relativistic modification of MOND by Jacob Bekenstein

Superfluid Vacuum Theory the gravity and curved space-time arise as a collective excitation mode of non-relativistic background superfluid.

Flux Theorem for Gravity, is a law of physics that is equivalent to Newton's law of universal gravitation. Flux Theorem for gravity is often more convenient to work from than is Newton's law. The form of Flux Theorem for gravity is mathematically similar to Gauss's law for electrostatics, one of Maxwell's equations. Flux Theorem for gravity has the same mathematical relation to Newton's law that Gauss's law for electrostatics bears to Coulomb's law. This is because both Newton's law and Coulomb's law describe inverse-square interaction in a 3-dimensional space.

Massive gravity, a theory where gravitons and gravitational waves have a non-zero mass

Chameleon Gravitational Theory, Pressuron Gravitational Theory, Conformal Gravity, the list goes on an on.

The General Theory of Relativity describes gravitational forces as arising from the mass-induced curvature of space instead of some force mitigating field or particle like other forces, but that was not his first theory about gravity.

Prof. Carver Mead is the Gordon and Betty Moore Professor Emeritus of Engineering and Applied Science at Caltech. He is the person who named Moore's Law and demonstrated mathematically and experimentally that transistors and other integrated circuit elements actually work better and faster when they are made smaller, blazing the trail that has led to the modern era microelectronics revolution.

Mead developed a simpler approach to gravitation (G4v) that employs a gravitational 4-vector potential. G4v makes much the same predictions as GR (General Relativity), but it predicts behavior for gravitational waves that is qualitatively different from that of GR.

The NSF's Advanced LIGO gravitational wave detector system, 4-km long L-shaped interferometers located at sites in Hanford, Washington and Livingston, Louisiana, was built to detect gravitational waves from merging neutron stars or black holes. Such detection is a make-or-break test that could falsify G4v, and possibly GENERAL RELATIVITY (or both).

Mead's book, Collective Electrodynamics, is unusual in that it starts with superconductors involving electrons acting collectively, instead of the usual approach that starts with individual electric charges acting in isolation. Mead formulated this alternative approach to electrodynamics, and brought in quantum mechanics of collective systems (like superconductors) in a very natural way. It is simple and straightforward (but disorienting) approach and represents essentially an alternative to conventional quantum electrodynamics, the prevailing standard model of electromagnetic phenomena at the quantum scale.

In E&M Theory there are two ways of looking at interactions and forces between charges:

(1) as resulting from the electric E and magnetic B fields that exert forces on at-rest and moving charged particles,

and

(2) as resulting from the electric scalar potential and the magnetic vector potential that directly modify the momentum of charged particles.

Mead ignores the electric E and magnetic B fields and their forces and combines the scalar and vector potentials into a 4-vector potential, with the magnetic vector potential as the space-like parts and the electric scalar potential as the time-like part. Mead uses this 4-potential approach to get many familiar results in an interestingly unfamiliar and simple way.

Mead presents an important calculation about a fundamental problem with the Standard Theory of Quantum Mechanics, in that it uses the mechanism of "wave-function collapse", an abrupt change in a quantum wave function whenever a measurement is made or a quantum event occurs. The standard quantum formalism does not provide mathematics describing such a collapse. Mead fills this gap using his 4-potential formalism along with standard quantum mechanics to describe a "quantum jump", a quantum event in which an atom in its excited state delivers a photon to an identical atom in its ground state.

This process was the center of a controversy between Neils Bohr and Erwin Schroedinger, in which Schroedinger refused to believe that quantum jump could be "instantaneous", as Bohr insisted they must be. Mead resolves this difficulty. He employs the exchange of advanced and retarded waves from John Cramer’s Transactional Interpretation of Quantum Mechanics. Mead assumes that the initial positive-energy retarded wave from an excited atom-A, interacting with some ground-state atom-B, perturbs atom-B into a mixed state that adds a very small component of excited-state wave function to its ground-state wave function. Similarly, a negative-energy advanced wave from atom-B, interacting with atom-A, perturbs it into a mixed state that adds a very small component of ground-state wave function to its excited-state wave function. Because of these added components, both atoms develop small time-dependent dipole moments, tiny antennas that oscillate with the same beat frequency because of the mixed-energy states and act as coupled dipole resonators. The phasing of their resulting waves is such that energy is transferred from A to B at a rate that initially rises exponentially.

"The energy transferred from one atom to another causes an increase in the minority state of the superposition, thus increasing the dipole moment of both states and increasing the coupling and, hence, the rate of energy transfer. This self-reinforcing behavior gives the transition its initial exponential character.''

Mead showed mathematically that the perturbations induced by the initial advanced/retarded exchange triggers the formation of a full-blown quantum jump in which a photon-worth of energy is transferred from one atom to the other. This is the long-sought mathematical description of quantum wave function collapse.

Mead extended his 4-vector potential formalism to gravitation as well as electromagnetism, producing G4v. This is a theory that is still being developed, but it promises to provide the key to the long-sought problem of unifying gravitation and quantum mechanics. This approach to gravity theory was nearly realized by Einstein in a 1912 paper published in an obscure medical journal and largely ignored. Einstein turned in a different direction in his 1915 formulation of General Relativity.

Mead's four-vector gravitation gives predictions that are mostly indistinguishable from those of General Relativity for most of the well known General Relativity. These include the gravitational deflection of light, the perihelion shift of the orbit of Mercury, the gravitational red shift, the frame-dragging effects of Gravity Probe B, and the rate of gravitational-wave energy loss from neutron-star binary pulsars.

When attention is turned to the production and detection of gravitational waves, there is an important difference. In considering a binary star system with two masses rotating in circular or elliptical orbits, both theories predict radiation at twice the rotation frequency of the binary source, but the G4v theory and General Relativity predict qualitatively different angular dependence of gravitational wave emission and different behavior of gravitational wave "antennas" like LIGO in detecting such waves. In particular, if the binary star system rotates in a certain plane, General Relativity predicts that the emission of gravitational waves has a maximum along the axis perpendicular to that plane, while G4v predicts that the emission is maximum in directions that see the plane of rotation edgewise.

Why this difference? The gravitational waves predicted by General Relativity have squeeze-stretch tensor polarization, with the two polarization modes denoted by "+" and "-" indicating that the squeeze-stretch of space is aligned either with the vertical/horizontal axes or with the diagonal/anti-diagonal axes perpendicular to the direction of motion of the wave. On the other hand, the gravitational waves predicted by G4v have more normal vector polarization, with the two polarization modes denoted by "i" and "x" indicating vectors in the i or inclination direction or in the x direction perpendicular to inclination, both perpendicular to the direction of motion of the wave. The General Relativity waves have roughly equal intensities in the two polarizations modes, while for the G4v waves the "x" polarization is dominant.

General Relativity gravitational waves are traveling distortions of space, and for a binary star system they add to a maximum pointing perpendicular to the orbit plane. The G4v waves from the two members of the binary system are vectors that tend to cancel when they travel the same distance because the source stars are moving in opposite directions, so their maximum intensity comes when there is a large phase difference between them due to the distance difference from the two source-stars to the observer. This occurs when the orbit plane is edgewise to the observer.

There is also a significant difference in the way an interferometric gravitational wave detector like Advanced LIGO should respond to the gravitational waves predicted by the two theories. The stretch-squeeze tensor gravitational waves of GENERAL RELATIVITY should modify the distances between interferometer mirrors in the LIGO arms, producing a characteristic signature template that the LIGO data-analysis software is designed to extract from the incoming data. In contrast, the perpendicular component of the gravitational waves of G4v should directly modify the momentum of the interferometer mirrors, causing them to move and to shift the interference pattern. This produces a qualitatively different signature template that the LIGO data-analysis software must be designed to extract from the incoming data. Thus, the response of Advanced LIGO to the gravitational waves predicted by the two theories will be quite different, and the data analysis software must be on the lookout for waves of either type. Fortunately, the scientists operating Advanced LIGO are aware of this dichotomy, and they are prepared to detect either type of gravitational waves.

Thus a critical make-or break test of General Relativity vs. G4v is waiting for the arrival of the first detectable gravitational waves in the improved Advanced LIGO detector system. The data run with the new system in the Fall of 2015, detected its first gravitational waves. The results were not such that the polarity aspect was verifiable, it will have to wait for the orbital version of the LIGO, eLISA.

What would be the consequences if Advanced LIGO should definitively detect gravitational waves of the type that is predicted by G4v? It would herald nothing less than a major revolution in theoretical physics. Einstein's general theory of Relativity, with its treatment of gravitational forces as arising from space curvature, would be falsified. Black holes would become simply ultra-degenerate compact stars, with no singularity, naked or otherwise, lying in wait at the bottom of the gravity well. There would be no dark energy, because G4v explains the dimming of distant receding Type IIa supernovas as partially due to relativistic beaming, without the need for a non-zero cosmological constant.

Further, the approach of quantum field theory, with its churning vacuum full of virtual particle, would be called into question by the G4v approach to fundamental interactions. This would resolve a problem created by quantum field theory, which predicts an energy density of the quantum vacuum that is 10120 times larger than its actual value. Moreover, the work on developing a unified theory that unites quantum mechanics and gravity would be set on a much smoother path that should lead to a solution to that vexing problem.

There is some other work by everyone’s favorite Ukrainian Physicist, Oleg Jefimenko, who derived all of the equations of relativistic electrodynamics just by using retardation (“retardation” is the technical term for explicitly taking into account the light speed limitation of electromagnetic interactions). That is to say, Special Relativity is a short cut—albeit a valid short cut in most (but not all) cases. Retardation is more fundamental than Special Relativity, requiring no postulates and simply the experimental fact of c-speed EM interactions.

“…we obtained correct relativistic transformation equations on the basis of the retarded length and volume of moving charge distributions, taking into account that Lorentz contraction requires not one but two observers (two points of observation) for its exact manifestation, and taking into account that electromagnetic fields and light propagate with the same speed, we have hardly any choice but to conclude that the relativistically correct visual shape of a moving body is its retarded shape. We then also have a clear answer to why the retarded field theory, without using Lorentz contraction for determining the effective shape of a moving charge, yields relativistically correct fields of the charge. The answer is very simple: as a physical phenomenon the relativistic (kinematic) Lorentz contraction does not exist. And the fact that the several revisions of this concept had no ill effect on relativistic electrodynamics or on any other branch of physics is an excellent indication that the concept does not represent a physical phenomenon in the conventional sense.”

Jefimenko is by no means an “anti-relativist,” he is not at all arguing that Relativity is wrong—he is arguing that the correct application of the relativistic transformation equations to the problem of moving line charges (and moving rods) does not support the idea of real shrinkage.

This might seem obscure, but it means that applying electrodynamics and simply updating Newton’s Gravity to include gravity working at the speed of light, most of Special Relativity can be derived. Jefimenko is a widely respected physicist, you can look up Jefimenko’s Equations if you like. The big deal to me, is that Jefimenko’s work shows, like Carver Mead’s, that gravity might actually be a field and not merely the curvature of space; a major controversy.

Until that controversy is resolved, there will not be the much needed resolution between Gravity and quantum mechanics. The Gravititational Wave Observatories are the first step towards that.

References:

Carver Mead, G4v: An Engineering approach to Gravitation (video): https://www.youtube.com/watch?v=XdiG6ZPib3c

Carver Mead, Collective Electrodynamics, The MIT Press, (2000), ISBN 0-262-13378-4.

Carver Mead, "Gravitatational Waves in G4v", ArXiV preprint 1503.04866 [gr-qc] (2015).

Maximiliano Isi, Alan J. Weinstein, Carver Mead, and Matthew Pitkin, "Detecting Beyond-Einstein Polarizations of Continuous Gravitational Waves", Phys. Rev. D 91, 082002 (2015); ArXiV preprint 1502.00333 [gr-qc].