Historical research guide · 1038 · 2009
Laboratory-Scale Superconducting Mirrors for Gravitational Microwaves
Raymond Y. Chiao · Stephen J. Minter · Kirk Wegter-McNelly
In one minute
This is the four-page version of the long argument, written by Raymond Chiao, Stephen Minter and Kirk Wegter-McNelly to be checked quickly. Take Einstein’s equations in the weak-field limit and they read like Maxwell’s, which means empty space has a gravitational impedance the way it has an electrical one — a fantastically small number, 2.8 times ten to the minus eighteenth. To reflect a gravitational wave a material has to be quieter still, and only a superconductor near absolute zero is. Then comes the turn. Treat the Cooper pairs in the film as though they were electrically neutral and the numbers are hopeless: the length scale that governs reflection runs out to ten to the thirty-sixth metres. But they are not neutral. When the wave pulls the delocalised pairs one way and the lattice ions the other, charge separates and the Coulomb force answers, and that one correction shrinks the length scale by forty-two orders of magnitude. The conclusion is stated flatly: laboratory-scale mirrors for gravitational microwaves exist.
Connection
Chapter 11 wants the shortest checkable statement of the gravity-and-superconductor claim, and this is it — five pages of algebra ending in a number a laboratory can chase. It belongs to chapter 4 as well, because a mirror is the first optical component anyone would need before gravitational waves become something you steer rather than something you wait for.
From the source
In the weak-field, non-relativistic limit Einstein’s equations become Maxwell-like, with a gravitational analogue of the permittivity of free space equal to one over four pi G, or 1.2 times ten to the ninth in SI units, a gravitational analogue of the permeability equal to four pi G over c squared, or 9.3 times ten to the minus twenty-seventh, and therefore a gravitational characteristic impedance of free space of 2.8 times ten to the minus eighteenth. That impedance is a property of spacetime itself and not of any material, and an object must be far below it before it can reflect any appreciable part of an incident gravitational wave.Equations 8a to 9
For an electromagnetic wave on a superconducting film near absolute zero, specular reflection depends only on the ratio of the speed of light to the kinetic inductance length scale of the film’s Cooper pairs. For the lead films used in the Glover and Tinkham measurements that length scale is about 30 micrometres and the roll-off frequency, where reflectivity falls to one half, is about 2 pi times 840 gigahertz.Equations 6 and 7
Treating the Cooper pairs as if they were neutral particles, so that only their mass matters, gives a gravitational kinetic inductance length scale of order ten to the thirty-sixth metres and appears to preclude any laboratory-scale reflection of a gravitational microwave. The authors state plainly that this analysis is flawed, because it ignores the enormous Coulomb forces inside the film that arise from the electric charge of its delocalised Cooper pairs.Equations 12 and 13, and the paragraph immediately following
Applying DeWitt’s minimal coupling rule, in which the momentum operator picks up both the electromagnetic vector potential and a gravitational vector potential, the quantum velocity field induced in the condensate is minus the charge-to-mass ratio times the electromagnetic vector potential, minus the gravitational one. The total force on a Cooper pair is therefore the electric force plus the gravito-electric force, the plasma frequency acquires a factor that differs from unity by exactly the reciprocal of 4.2 times ten to the forty-second, and the corrected gravitational kinetic inductance length scale collapses to the microscopic film thickness times the square of the ratio of the plasma skin depth to that thickness.Equations 15 to 25
The Heisenberg-Coulomb effect reduces the gravitational kinetic inductance length scale by 42 orders of magnitude, down to the level of its electromagnetic counterpart, and raises the gravitational roll-off frequency by the same factor to the level of the electromagnetic roll-off frequency. The authors conclude that laboratory-scale superconducting mirrors for gravitational microwaves exist.Final paragraph, following equation 25
What to watch: this letter is deliberately written as the short, testable form of the claim. What would settle it is the experimental programme set out in the companion paper — a free-fall test of whether two coherently connected superconducting bodies stop converging, a search for a gravitational Casimir force between superconducting plates, and a charged pair of superconductors operated as a gravitational-to-electromagnetic transducer.Opening paragraph, read against Section 10 of the companion 59-page paper
The way in
https://arxiv.org/abs/0903.3280How to cite it
Raymond Y. Chiao, Stephen J. Minter, Kirk Wegter-McNelly (2009) Laboratory-Scale Superconducting Mirrors for Gravitational Microwaves arXiv:0903.3280