Abstract
Recently reported [Eur. Phys. J. C., 77, 549 (2017). https://doi.org/10.1140/epjc/s10052-017-5116-y] gravitoelectromagnetic equations of Ummarino and Gallerati (UG) in their linearized version of general relativity (GR) are shown to match with (a) our previously reported special relativistic Maxwellian Gravity equations in the non-relativistic limit and with (b) the non-relativistic equations derived here, when the speed of gravity c_g (an undetermined parameter of the theory here) is set equal to c (the speed of light in vacuum). Seen in the light of our new results, the UG equations satisfy the Correspondence Principle (cp), while many other versions of linearized GR equations that are being (or may be) used to interpret the experimental data defy the cp. Such new findings assume significance and relevance in the contexts of recent detection of gravitational waves and the gravitomagnetic field of the spinning earth and their interpretations. Being well-founded and self-consistent, the equations may be of interest and useful to researchers exploring the phenomenology of gravitomagnetism, gravitational waves and the novel interplay of gravity with different states of matter in flat space-time like UG’s interesting work on superconductors in weak gravitational fields.
Highlights
In a recent interesting theoretical study on the interplay of superconductivity and weak static gravitational field, Ummarino and Gallerati [1] concluded that the reduction of the gravitational field in a superconductor, if it exists, is a transient phenomenon and depends strongly on the parameters that characterize the superconductor
Following Schwinger’s non-relativistic formalism of classical electrodynamics, here we derived the fundamental equations of Non-Relativistic Maxwellian Gravity (NRMG), which matches with Heaviside’s Gravity of 1893 and offers a plausible mechanism for resolving the problem of action-ata-distance in Newtonian gravity, within Galileo-Newtonian domain of physics by demanding the existence of gravitational waves propagating in vacuum at a non-zero finite speed cg, whose value has to be determined from experiments on measurable quantities involving cg or from some more advanced theory
Most importantly the equality mg = m0 emerges as a consequence of the Lorentzinvariance of physical laws and the Law of Universality of Free Fall emerges as a consequence of mg = m0, not an initial assumption in Special relativistic Maxwellian gravity (SRMG)
Summary
In a recent interesting theoretical study on the interplay of superconductivity and weak static gravitational field, Ummarino and Gallerati [1] concluded that the reduction of the gravitational field in a superconductor, if it exists, is a transient phenomenon and depends strongly on the parameters that characterize the superconductor. They happen to coincide in the context of Galileo-Newtonian physics where m0 = m = mg but may diverge in the context of special relativity where m = m0 and Einstein’s wrong inference of m0 = m = mg from a non-relativistic Eq (65), which is exactly the Eq (13) of NRMG, where m = m0 and mg = m0 is a condition for Galileo’s law of Universality of Free Fall to be true To explore this possibility, to get new insights for making Newtonian gravity compatible with the SR, to regard old problems from a new angle, we re-examined [3] an often cited [29,30] Salisbury-Menzel’s [31]10 thought experiment (SMTE) from a new perspective as discussed in the following subsection. The gravitational charge (or rest mass) invariance may be interpreted as a consequence of the Lorentzinvariance of the physical laws These findings are in conformity with Poincare’s [34] remark that if equilibrium is to be a frame-independent condition, it is necessary for all forces of non-electromagnetic origin to have precisely the same. It is to be noted that the Lorrain’s (See Lorrain in footnote 10 of this paper) exact special relativistic derivation of gravitational analogue of the magnetic force from SMTE matches with our SRMG results
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