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Faraday attempts to detect the magnetism of gravity (illustration reproduced with permission of A. de Rújula).
Source publication
In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a magnetic-like force must be present whenever two or more bodies are in motion. The exact expression for this gravitomagnet...
Context in source publication
Context 1
... to measure some kind of gravitational magnetism can be dated back to the pioneer experiments of Faraday [1], performed about 1840. In these experiments, Faraday was wondering if gravity would produce some effect analogous to the electromagnetic induction that himself discovered before (see figure 1). If Faraday had been successful, the existence of gravitational magnetic fields would have been established from the very beginning but, unfortunately, he did not find any positive result. ...
Citations
... His original paper [59] is one of the first to formulate a proven link between relativistic quantum mechanics and weak gravitational fields. This was successfully demonstrated by modern research, and the 'gravitomagnetic potential' was deduced from special relativity alone [80]. In most cases, the approaches formulated in the mathematical "language" of the general theory(s) of gravity do not seem to yield useful results. ...
What is the main message of the book:
"...The idea presented here is unconventional, different from our current view of the world. I think it can be said in a sentence or two: it is possible that quantum mechanics can be extended to solar system-like systems. According to the analogy given, the World is nothing more than "a few litres of gas-like swirling matter", i.e. "10^24 subsystems". The relativistic quantum mechanics model seems to support this idea. One of the great challenges of the 21st century, or in other words of the third millennium, or in other words of the physics of today's scientific world, would be to 'unite' the theory(s) of gravity and relativistic quantum mechanics. Several attempts have been made. The physical model published here is very simple - attractive in its simplicity. If the theory is correct, it will fundamentally change the way we have always seen the world. TIME plays, as always, a key role in our understanding of the world...."
... His original article [8] is one of the first to formulate a proven link between relativistic quantum mechanics and weak gravitational fields. All this has been successfully demonstrated by modern research, using only special relativity to derive the "gravitomagnetic potential" [51]. ...
This paper attempts to describe the large-scale (solar system-like, astronomical-scale) systems of the known world using the physical models and mathematical tools of relativistic quantum mechanics. The value of Hx can be introduced and approximated as an analogue of the constant ℏ. Based on the quantum mechanical approach, the proper time scale of the solar system can be determined.
... In summary, the fields (30) are defined, one can write the field equations [11,19,28,32,63,67,68,76,[78][79][80][81][82][83][84][85][86][87][88][89][90][91]: ...
... From this point of view, if we want to be very close to the effective critical T c , it could be easier to consider a low-T c sample, the temperature transition range being very narrow for the latter. However, this in turns results in a reduced alteration of the local field, since, close to T c , the Ginzburg-Landau coherence length ξ(T) diverges, see Equation (84). In light of the above discussion, an optimized experimental settings should involve a large high-T c superconducting sample at a temperature very close to T c . ...
We review and discuss some recent developments on the unconventional interaction between superconducting systems and the local gravitational field. While it is known that gravitational perturbations (such as gravitational waves) can affect supercondensates and supercurrents dynamics, we want to focus here on the more subtle superfluid back-reaction acting on the surrounding gravitational field, analysing some specific favourable situations. To this end, we will consider suitable quantum macrosystems in a coherent state, immersed in the static weak Earth’s gravitational field, investigating possible slight local alterations of the latter not explained in terms of classical physics.
... and ¶ ¶t F 2 go to zero faster than r 1 2 as ¥ r then F 1 and F 2 are uniquely given by (11). ...
... Here the gravitational permittivity constant of vacuum is defined as˜( [9], McDonald [10] and recently, Vieira and Brentan [11] have discussed this gravitational theory, whose equations have also been obtained using an alternative approach [12]. ...
An extension of the Helmholtz theorem is proved, which states that two retarded vector fields and satisfying appropriate initial and boundary conditions are uniquely determined by specifying their divergences and and their coupled curls and , where c is the propagation speed of the fields. When a corollary of this theorem is applied to Maxwell's equations, the retarded electric and magnetic fields are directly obtained. The proof of the theorem relies on a novel demonstration of the uniqueness of the solutions of the vector wave equation.
... In current efforts being made on both the theoretical (e.g., Adler et al., 2012;Exirifard, 2013;Mashhoon, 2008;Nordtvedt, 1988;Vieira and Brentan, 2018), and, observational front (e.g., Chicone and Mashhoon, 2011;Iorio, 2011;Iorio et al., 2011;Mashhoon et al., 2001;Soffel et al., 2008); gravitatomagnetism is predominately understood in the context of Einstein (1915bEinstein ( ,c, 1916a's linearised first order approximation of the General Theory of Relativity (GTR). Our approach is different to this predominant approach. ...
This paper demonstrates that gravitomagnetism can be given a geometric justification on spacetime.
... By an entirely similar procedure, we can show the remaining wave equations given in (16). Considering (11), (14) and (16), we can now prove that F 1 and F 2 satisfy (8) and (9). We take § In physical applications, the vector C 2 usually represents a localised quantity. ...
... Theorem. If the divergences D 1 and D 2 and the coupled curls C 1 and C 2 of two retarded vector functions F 1 and F 2 are specified, and if F 1 , F 2 , ∂F 1 /∂t and ∂F 2 /∂t vanish at t = 0, and if ∇F 1 , ∇F 2 , ∂F 1 /∂t and ∂F 2 /∂t go to zero faster than 1/r 2 as r → ∞, and if F 1 and F 2 themselves go to zero as r → ∞, then F 1 and F 2 are uniquely given by (11). This theorem has the following corollary: The fields F 1 and F 2 can be expressed as ...
... It follows that˜ 0μ0 = 1/c 2 , where c is the speed of light in vacuum. Jefimenko [9], McDonald [10] and recently, Vieira and Brentan [11] have discussed this gravitational theory, whose equations have also been obtained using an alternative approach [12]. ...
An extension of the Helmholtz theorem is proved, which states that two retarded vector fields and satisfying appropriate initial and boundary conditions are uniquely determined by specifying their divergences and and their coupled curls and , where c is the propagation speed of the fields. When a corollary of this theorem is applied to Maxwell's equations, the retarded electric and magnetic fields are directly obtained. The proof of the theorem relies on a novel demonstration of the uniqueness of the solutions of the vector wave equation.
We estimate the conjectured interaction between the Earth’s gravitational field and a superconductor immersed in external, static electric and magnetic field. The latter is close to the sample upper critical field and generates the presence of a vortex lattice. The proposed interaction could lead to multiple, measurable effects. First of all, a local affection of the gravitational field inside the superconductor could take place. Second, a new component of a generalized electric field parallel to the superconductor surface is generated inside the sample.
The analysis is performed by using the time-dependent Ginzburg–Landau theory combined with the gravito-Maxwell formalism. This approach leads us to analytic solutions of the problem, also providing the average values of the generated fields and corrections inside the sample. We will also study which are the physical parameters to optimize and, in turn, the most suitable materials to maximize the effect.
We here-in demonstrate that the proposed hitherto unknown gravitomagnetic dark-force that hypothetically explains the Flat Rotation Curves of Spiral Galaxies — this same force, explains very well, the logarithmic and as-well, the barred spiral shapes of spiral galaxies. That is, much in line with Edward Arthur Milne (1896-1950)’s 1946 ideas — albeit , on a radically and asymptotically different philosophical train of thought, the galactic disk is here assumed to be in a state of free-fall around the central bulge with the hypothetical gravitomagnetic dark-force being the dominant force determining all gravity-related dynamics of the disk, thus leading to logarithmic and barred spiral orbits, hence the shape of spiral galaxies.
This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter field. Equations of motion, continuity equation, energy conservation, field tensor, energy-momentum tensor, constraints, and Lagrangian formulation are presented as a simple and unified formulation that can be useful for future research.
