Gravitomagnetic field of a rotating superconductor and of a rotating superfluid
Martin Tajmar · Clovis J. de Matos
Abstract and summary · read the original at the source
In one page
Spin any material and its elementary magnets line up, making a magnetic field — the Barnett effect. Martin Tajmar of ARC Seibersdorf and Clovis de Matos of the European Space Agency had already shown that general relativity, written in its weak-field Maxwell-like form, predicts a gravitational twin of that effect. In ordinary matter it is hopelessly small. Here they ask whether quantum materials break the rule. Their handle is the quantisation condition that governs superconductors and superfluids: the momentum of the flowing carriers, counted around a closed loop, comes in whole numbers of Planck’s constant. Add a gravitomagnetic term to that momentum and the London moment of a spinning superconductor picks up a gravitational correction — and, crucially, the tiny constant that suppresses gravity in the classical calculation never enters the quantisation condition. They then use existing measurements, including Tate’s Cooper-pair mass anomaly in niobium, to bound how large the effect could be, and name the experiment that would settle it.
Why it matters hereChapter 11 is the superconductor thread, and this paper is where the programme starts: it identifies the one place — a quantisation condition rather than a field equation — where gravity’s weakness might not apply, and it converts existing precision measurements into an upper bound on the effect. For chapter 3 it is the same proposition in general form, that the vacuum properties inside a coherent quantum material set how far the gravitational field reaches.
What it claims
01In the weak-field approximation of general relativity the field equations can be written in a form similar to Maxwell’s, with a gravitoelectric field in metres per second squared playing the role of the electric field and a gravitomagnetic field in radians per second playing the role of the magnetic field. The gravitomagnetic permeability is four pi times Newton’s constant divided by the speed of light squared, about 9.31 times ten to the minus 27 in metres per kilogram — so small that the gravitomagnetic Barnett field outside an ordinary spinning substance cannot be detected.Introduction, Eqs. 1 and 2
Settled physics02London’s quantisation of the canonical momentum of the superelectrons around a closed path, with the loop taken deep inside a thick superconducting ring where the current vanishes, gives the London moment: a rotating superconductor produces a magnetic field equal to minus twice the Cooper-pair mass over its charge times the angular velocity. That field has been verified by several experiments to within a few per cent, including for high-temperature and heavy-fermion superconductors.Rotating Superconductors, Eqs. 3 to 5
Settled physics03In the most accurate measurement of its kind, Tate and colleagues used a niobium ring and a SQUID to obtain a Cooper-pair mass of 1.000084 times twice the free electron mass, with systematic errors estimated at 21 parts per million, against a theoretical prediction of 0.999992 that already accounts for the kinetic energy of electrons near the Fermi surface. The authors note that this disagreement is discussed in the literature without any apparent solution.Rotating Superconductors, Eq. 6 and the paragraph following
Published and peer-reviewed04Extending the quantisation condition to include a gravitomagnetic vector potential alongside the magnetic one modifies the London moment by a term equal to the carrier mass over its charge times the gravitomagnetic field. Because permeabilities do not enter a quantisation condition, the classical suppression factor that makes gravitomagnetic effects negligible may not apply here — which is the paper’s central proposition.Rotating Superconductors, Eqs. 7 to 9
Published and peer-reviewed05The authors convert existing data into bounds. For a thick ring, the few-per-cent margin within which Hildebrandt’s experiment matches the classical London moment would admit a gravitomagnetic field as large as about 7000 radians per second — a figure they call unrealistically high and say must be tested and reduced by later experiments. For a thin ring in Tate’s geometry, a gravitomagnetic flux contribution from the superconductor’s neutral lattice of about 1.065 times ten to the minus 8 radians per second would close the Cooper-pair mass gap exactly, which is far above anything classical coupling allows.Rotating Superconductors, Eqs. 10 to 12
What to watch06For a neutral superfluid there is no gravitomagnetic Meissner effect, so London’s argument that the loop integral vanishes does not hold and a superfluid should behave like a very thin superconductor. Folding the gravitomagnetic term into the weak-link current of Simmonds and colleagues’ helium-3 double-path interferometer changes the predicted phase by a factor of about 1.00007 relative to their measurement — orders of magnitude below their few-per-cent accuracy, so any such effect would still be hidden in the noise. The named next experiment is to measure the torque on a spinning gyroscope placed near a rotating superconductor or superfluid, which the authors state has not been done.Rotating Superfluids, Eqs. 13 to 15; Conclusion
What to watch
Read it · abstract
Abstract
The quantization of the extended canonical momentum in quantum materials including the effects of gravitational drag is applied successively to the case of a multiply connected rotating superconductor and superfluid. Experiments carried out on rotating superconductors, based on the quantization of the magnetic flux in rotating superconductors, lead to a disagreement with the theoretical predictions derived from the quantization of a canonical momentum without any gravitomagnetic term. To what extent can these discrepancies be attributed to the additional gravitomagnetic term of the extended canonical momentum? This is an open and important question. For the case of multiply connected rotating neutral superfluids, gravitational drag effects derived from rotating superconductor data appear to be hidden in the noise of present experiments according to a first rough analysis.
The way in
https://doi.org/10.1016/S0921-4534(02)02305-5Published in Physica C: Superconductivity by Martin Tajmar, then a research scientist in space propulsion at ARC Seibersdorf research in Austria, with Clovis J. de Matos, then scientific advisor in the Directorate of Scientific Programmes at ESA-ESTEC. The manuscript is free to read on arXiv as gr-qc/0203033, but that posting carries arXiv’s assumed licence for submissions from 1991 to 2003 and the version of record carries Elsevier’s text-and-data-mining user licence — neither is a Creative Commons licence — so this page holds the summary, the claims and the authors’ own abstract and sends the reader to the source. The publisher’s metadata record carries no abstract; the one below is transcribed from the manuscript itself. This is the earliest of the group’s sheets in the library: the 2005 Proca-equation theory paper is at /library/stm-7a8e18ad7b, the 2006 first experimental announcement at /library/stm-21102decd7, and the 2007 curl-configuration progress report at /library/stm-1cb16dd1bc.
How to cite it
Martin Tajmar, Clovis J. de Matos (2003) Gravitomagnetic field of a rotating superconductor and of a rotating superfluid. doi:10.1016/S0921-4534(02)02305-5
Where it sits in the curriculum
Gravity control and superconductorsInertia and gravity from the vacuumThe evidence ladder