Gravitomagnetic London moment and the graviton mass inside a superconductor
C.J. de Matos · M. Tajmar
Abstract and summary · read the original at the source
In one page
Spin a superconductor and it makes a magnetic field. That is the London moment, and it is textbook physics. Clovis de Matos at the European Space Agency and Martin Tajmar at ARC Seibersdorf ask where it comes from and what its gravitational twin would look like. Their route is the Proca equations — Maxwell’s equations rewritten for a photon that has acquired mass, which is what happens to light inside a superconductor when gauge symmetry breaks. Take the curl of the fourth Proca equation and both the Meissner effect and the London moment fall straight out of that photon mass. Then they run the identical argument for gravity, where the weak-field form of Einstein’s equations looks like electromagnetism, and ask what graviton mass inside the metal would produce a gravitational London moment big enough to close a real gap: Jackie Tate’s precision measurement of the Cooper-pair mass in niobium, which came out heavier than theory says it should.
Why it matters hereThis is the theoretical spine of chapter 11’s hardest experiment — it says exactly which quantity, a mass for the graviton inside the metal, would have to be non-classical for a spinning superconductor to drag spacetime measurably, and it says what would change that quantity. For chapter 3 it is the same argument in reverse: if the properties of the vacuum inside a material set the reach of the gravitational field, then gravity is a medium effect and the medium is engineerable.
What it claims
01Inside a superconductor gauge symmetry is broken and the photon acquires mass, so Maxwell’s equations become the Proca equations. Taking the curl of the fourth Proca equation and setting the photon wavelength equal to the London penetration depth returns both the Meissner–Ochsenfeld expulsion of an applied field and the London moment, minus two times the Cooper-pair mass over its charge times the angular velocity — so the London moment is a direct consequence of the photon’s mass in the metal.Section ‘The London Moment Derived from Proca Equations’, Eqs. 3 to 6
Published and peer-reviewed02Tate, Cabrera, Felch and Anderson measured the Cooper-pair mass in niobium from the London field and got a ratio to twice the electron mass of 1.000084 plus or minus 0.000021, against a theoretical prediction of 0.999992. The authors take that gap as real and unresolved, and the paper is written to explain it rather than to explain it away.Introduction, final paragraph; references 5 and 6
Published and peer-reviewed03Conserving the full canonical momentum adds a gravitomagnetic term to the London moment, and the field needed to account for Tate’s number is minus two times the angular velocity times the fractional mass excess. Compared against the gravitomagnetic field a classically rotating ring of Tate’s own geometry would produce, that conjectured field is 31 orders of magnitude larger.Section ‘The Gravitomagnetic London Moment and the Graviton Mass’, Eqs. 7 and 8 and the paragraph following
Published and peer-reviewed04Running the same Proca treatment on the gravitomagnetic equations gives a gravitational London moment proportional to minus twice the angular velocity, exactly the form the anomaly requires. Inverting it against Tate’s measurement fixes a complex graviton mass inside niobium of i times 4.61 times 10 to the minus 55 kilograms, with a wavelength of i times 7.63 times 10 to the 11 metres. The authors note the precedent: the photon’s mass inside a superconductor is about 10 to the minus 35 kilograms, some 34 orders above its free-space upper limit.Section ‘The Gravitomagnetic London Moment and the Graviton Mass’, Eqs. 9 to 13
Published and peer-reviewed05The gravitomagnetic London penetration depth comes out imaginary rather than real, which the authors read as meaning the field would fill the whole superconducting bulk with an oscillating signature instead of hugging a thin surface layer. A complex graviton mass also matches Novello and Neves, who argue it must be complex in a de Sitter background, and Modanese’s calculation of the cosmological constant inside a lead superconductor points the same way.Eqs. 10 and 11 and the paragraph between them; Discussion, first paragraph
Published and peer-reviewed06The named handle is composition. Verheijen and colleagues measured the London-moment slope for barium-lead-bismuth-oxide 25 per cent below its predicted value while lead and YBCO agreed to within 10 per cent, and in the Proca picture that slope can only move if the photon wavelength differs from the London penetration depth — which would trade photon mass against graviton mass. The authors call for the theoretical and experimental work that would settle it, and say the payoff would be gravitational effects large enough to detect on a laboratory bench.Discussion, paragraphs 3 to 5; Conclusion, final paragraph
What to watch
The way in
https://doi.org/10.1016/j.physc.2005.08.004Published in Physica C: Superconductivity by Clovis de Matos, then General Studies Officer at ESA headquarters in Paris, with Martin Tajmar, then Head of Space Propulsion at ARC Seibersdorf research in Austria. The manuscript is free to read on arXiv as cond-mat/0602591, but that posting carries arXiv’s assumed licence for legacy submissions and the version of record carries the Elsevier 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. This is the theory paper behind the same group’s laboratory programme: the 2006 first announcement has its own sheet at /library/stm-21102decd7 and the 2007 curl-configuration progress report is at /library/stm-1cb16dd1bc. Read this one for where the conjectured field comes from, and those two for what the accelerometers and laser gyroscopes actually registered.
How to cite it
C.J. de Matos, M. Tajmar (2005) Gravitomagnetic London moment and the graviton mass inside a superconductor. doi:10.1016/j.physc.2005.08.004
Where it sits in the curriculum
Gravity control and superconductorsInertia and gravity from the vacuum