Superconductor Meissner Effects for Gravito-Electromagnetic Fields in Harmonic Coordinates Due to Non-Relativistic Gravitational Sources

Abstract

There is much discrepancy in the literature concerning the possibility of a superconductor expelling gravito-electromagnetic fields just as it expels electromagnetic fields in the Meissner effect. Contradicting results are found in at least 18 papers written collectively by more than 20 authors and published over the course of more than 55 years (from 1966 to the present year of 2022). The primary purpose of this paper is to carefully explain the reason for the discrepancies, and provide a single conclusive treatment which may bring coherence to the subject. The analysis begins with a covariant Lagrangian for spinless charged particles (Cooper pairs) in the presence of electromagnetic fields in curved space-time. It is known that such a Lagrangian can lead to a vanishing Hamiltonian. Alternatively, it is shown that using a “space + time” Lagrangian leads to an associated Hamiltonian with a canonical momentum and minimal coupling rule. Discrepancies between Hamiltonians obtained by various authors are resolved. The canonical momentum leads to a modified form of the London equations and London gauge that includes the effects of gravity. A key result is that the gravito-magnetic field is expelled from a superconductor with a penetration depth on the order of the London penetration depth only when an appropriate magnetic field is also present. The gravitational flux quantum (fluxoid) in the body of a superconductor, and the quantized supercurrent in a superconducting ring, are also derived. Lastly, the case of a superconducting ring in the presence of a charged rotating mass cylinder is used as an example of applying the formalism developed.

Measurement of Anomalous Forces From a Cooper-Pair Current in High-Tc Superconductors With Nano-Newton Precision

“…We decided to test both BSCCO and YBCO superconductors with and without the addition of a strong permanent magnetic field in the direction of the current flow as Podkletnov did use a similar configuration but Poher did not. Moreover, some recent theoretical work by Inan suggests that a magnetic field may be necessary for superconductors as a pre-condition for gravitational experiments [22]. Our maximum current always stayed below the critical current listed for both superconductors also in the presence of the magnetic field.…”

Graviton mass due to dark energy as a superconducting medium-theoretical and phenomenological aspects

“…In fact, there exist many other approaches for describing the coupling of gravity to the Ginzburg-Landau scalar field model [85][86][87][88][89][90]. A variety of other possibilities is also discussed in [91].…”