Interaction of gravitational waves with superconductors
N. A. Inan · J. J. Thompson · R. Y. Chiao
Abstract and summary · read the original at the source
In one page
A gravitational wave stretches and squeezes everything it passes through, including a superconductor. Nader Inan, Jay Thompson and Raymond Chiao work out what a superconductor does back. They rewrite weak-field general relativity so that the wave has an electric-like and a magnetic-like part, exactly as an electromagnetic wave does, and find that the magnetic-like part is pushed out of the superconductor the way an ordinary magnetic field is — a gravitational version of the Meissner effect. Then they treat the two things inside the metal separately. The lattice of ions, modelled as quantum oscillators, responds strongly; the Cooper pairs, locked into one coherent quantum state, barely respond at all — about ten thousand times less. Because the ions are positive and the pairs negative, the wave pulls them apart and leaves a charge separation behind. Their other result is the interesting one for this site: the wave modulates the zero-point energy of the lattice phonons, which is a dynamical Casimir effect made of sound.
Why it matters hereChapter 11 asks whether coherent quantum matter can couple to gravity strongly enough to use, and this paper gives that question a full theoretical machine — London equations, Meissner effect, penetration depth and shear modulus, all written for gravity instead of electromagnetism. It also feeds chapter 3, because the quantity doing the work here is the zero-point energy of the lattice, modulated by a passing ripple in the metric.
What it claims
01Applying the Helmholtz decomposition to linearised general relativity gives a gauge-invariant formulation in which the transverse-traceless part of the metric perturbation describes gravitational waves inside matter, not only plane waves in vacuum as the transverse-traceless gauge alone allows.Section 1, Introduction
Published and peer-reviewed02A gravitational wave incident on a superconductor obeys a London-like constituent equation set by a gravitational shear modulus, which yields a gravitational plasma frequency and a gravitational penetration depth in the same form as their electromagnetic counterparts.Sections 2 and 3, Equation 6
Published and peer-reviewed03In the DC limit the magnetic-like gravitational tensor field is expelled from the superconductor in a gravitational Meissner-like effect, and the expulsion holds for all frequencies down to DC, with the upper frequency bound set by the BCS energy gap, above which the Cooper pairs break and superconductivity is destroyed.Section 4, Equation 16
Published and peer-reviewed04The zero-point energy of the ionic lattice phonons is modulated by the gravitational wave, which is a dynamical Casimir effect of the acoustic kind — the authors name it a dynamical gravito-phonon Casimir effect — and it predicts a rise in the occupation number of the lattice phonon modes, the quantum analogue of a Weber-bar effect in which incoming gravitational wave energy is converted into sound energy in the lattice.Section 6, following Equation 34
Designed, not yet built05For niobium, the zero-point energy density term dominates the gravitational shear modulus of the lattice, giving about 2.8 times ten to the eighth joules per cubic metre against a sum-of-modes term near 9 times ten to the minus twelfth, so the lattice ions are on the order of 10⁴ times more responsive to a gravitational wave than the Cooper pair density.Section 6, Equations 37 and 38
Published and peer-reviewed06Because the lattice and the Cooper pairs move differently, the relative strain between them is about one percent of the gravitational wave strain, and since lattice ions are positively charged and Cooper pairs negatively charged, a gravitational wave induces a macroscopic charge separation with no classical analogue — confined to the London penetration depth, since the wave itself decays exponentially deeper in.Section 7, Conclusion, Equations 39 and 40
Designed, not yet built
Read it · abstract
Abstract
Applying the Helmholtz Decomposition theorem to linearized General Relativity leads to a gauge‐invariant formulation where the transverse‐traceless part of the metric perturbation describes gravitational waves in matter. Gravitational waves incident on a superconductor can be described by a linear London‐like constituent equation characterized by a “gravitational shear modulus” and a corresponding plasma frequency and penetration depth. Electric‐like and magnetic‐like gravitational tensor fields are defined in terms of the strain field of a gravitational wave. It is shown that in the DC limit, the magnetic‐like tensor field is expelled from the superconductor in a gravitational Meissner‐like effect. The Cooper pair density is described by the Ginzburg‐Landau theory embedded in curved space‐time. The ionic lattice is modeled by quantum harmonic oscillators coupled to gravitational waves and characterized by quasi‐energy eigenvalues for the phonon modes. The formulation predicts the possibility of a dynamical Casimir effect since the zero‐point energy of the ionic lattice phonons is found to be modulated by the gravitational wave, in a quantum analog of a “Weber‐bar effect.” Applying periodic thermodynamics and the Debye model in the low‐temperature limit leads to a free energy density for the ionic lattice. Lastly, we relate the gravitational strain of space to the strain of matter to show that the response to a gravitational wave is far less for the Cooper pair density than for the ionic lattice. This predicts a charge separation effect in the superconductor as a result of the gravitational wave.
The way in
https://doi.org/10.1002/prop.201600066Published in Fortschritte der Physik (Progress of Physics) in 2016 by Nader Inan and Jay Thompson of UC Merced with Raymond Chiao. The manuscript is free to read on arXiv as 2207.08062, but that posting carries arXiv’s non-exclusive distribution licence rather than a Creative Commons licence, and Wiley’s page carries its standard terms, so this page holds the summary, the claims and the authors’ own abstract and sends the reader to the source. The paper builds on the Minter, Wegter-McNelly and Chiao proposal that superconductors could act as mirrors for gravitational waves.
How to cite it
N. A. Inan, J. J. Thompson, R. Y. Chiao (2016) Interaction of gravitational waves with superconductors. doi:10.1002/prop.201600066
Where it sits in the curriculum
Gravity control and superconductorsInertia and gravity from the vacuumThe metric, warp drives and wormholes