Historical research guide · 1020 · 2009
Do Mirrors for Gravitational Waves Exist?
Stephen J. Minter · Kirk Wegter-McNelly · Raymond Y. Chiao
In one minute
Stephen Minter, Kirk Wegter-McNelly and Raymond Chiao press a question almost nobody had pressed: can anything reflect a gravitational wave? Their answer is yes, and the mirror is unglamorous — a superconducting film thinner than the depth a magnetic field reaches into it, a few tens of nanometres of lead. The argument is a tug-of-war between two principles. The equivalence principle says a particle in free fall simply rides along with space, so it can take no energy out of a passing wave. But the Cooper pairs carrying a supercurrent are not localised: the uncertainty principle smears them across the whole film, and the superconductor’s energy gap protects that smearing from being destroyed. The pairs therefore cannot ride along, while the positive ions of the lattice do. Charge separates, an enormous Coulomb force answers, and the film stiffens against the wave by the ratio of the electric to the gravitational force between two electrons — 4.2 times ten to the forty-second. That factor is what makes a thin film a mirror.
Connection
Chapter 11 asks whether coherent quantum matter can grip gravity hard enough to be useful, and this is the paper that says yes and shows the arithmetic — 42 orders of magnitude of enhancement from an effect the authors name and derive. It reaches chapter 4 because a mirror is the first piece of hardware in any gravitational-wave optics, and chapter 2 because the same apparatus would test whether the gravitational field has a Casimir force, and therefore whether gravity is quantised.
From the source
The uncertainty principle limits the applicability of the equivalence principle. Because a Cooper pair sits in a zero-momentum eigenstate relative to the centre of mass of the system, its position inside the superconductor is completely uncertain and its trajectory completely delocalised, so it cannot free-fall along a geodesic with the ions; the ions, localised by decoherence, do. The relative motion between the two electrically polarises the superconductor in the presence of a gravitational wave.Section 2, and Section 1 paragraphs 3 and 4
Linearised general relativity yields Maxwell-like equations, and with them a gravitational characteristic impedance of free space of 2.8 times ten to the minus eighteenth in SI units — a property of spacetime itself, independent of any material. An object cannot reflect an appreciable part of an incident gravitational wave unless its own impedance is far below that number, which is why ordinary dissipative matter is a hopeless reflector and a superconductor near absolute zero is not.Section 5, and Section 1 paragraph on Section 5
Treat the Cooper pairs as if they were electrically neutral and the conventional answer follows: a gravitational plasma skin depth of order ten to the thirteenth metres and a kinetic inductance length scale of order ten to the thirty-sixth metres, which would put the gravitational roll-off frequency at effectively zero and rule out any laboratory-scale mirror. Restoring the pairs’ electric charge, and with it the Coulomb back-action of the charge separation, collapses that length scale by the full 42 orders of magnitude to its electromagnetic value and lifts the gravitational roll-off frequency to the electromagnetic one.Sections 6 and 7, equation 1 and the closing paragraphs of Section 7
Transduction does not spoil the mirror. Writing the loss into an outgoing electromagnetic wave as a real part of the gravitational conductivity gives a loss ratio of 1.3 times ten to the minus eleventh at 6 gigahertz, and a gravitational reflectivity of one over one plus 3.8 times ten to the minus eleventh. A superconducting film near absolute zero is therefore a highly reflective mirror for gravitational microwaves and a highly inefficient converter of them into electromagnetic microwaves — and, by the same algebra, the mirror-image statement holds for an incident electromagnetic wave, consistent with the Glover and Tinkham measurements.Section 8, equations 127 to 129
The first proposed test needs no gravitational wave at all. Two superconducting bodies several centimetres apart, allowed to fall freely, converge by of order microns over the free-fall distances already available in aircraft zero-gravity flights — readily measurable by laser interferometry. Join them with a thin slack superconducting wire so that they become one coherent system and the authors predict the convergence should vanish: the Cooper pairs drag the lattice into co-motion and the bodies keep a constant separation, departing from geodesic motion. Null convergence corresponds to the maximal Heisenberg-Coulomb effect.Section 10, paragraphs 2 to 6
What to watch: three further experiments the paper names. A gravitational Casimir-like force between two type I superconducting plates, appearing as they are cooled through their transition, would be evidence that gravitational fields are quantised. A pair of levitated superconducting bodies charged to the point where electrostatic repulsion cancels gravitational attraction becomes a quantum transducer with 50 percent efficiency in both directions between gravitational and electromagnetic radiation. Two such transducers in tandem would be a gravitational Hertz experiment, and would open gravitational-wave communication and wireless power transfer, since all ordinary matter is transparent to gravitational radiation.Section 10, paragraphs 7 to 12
The way in
https://arxiv.org/abs/0903.0661How to cite it
Stephen J. Minter, Kirk Wegter-McNelly, Raymond Y. Chiao (2009) Do Mirrors for Gravitational Waves Exist? doi:10.1016/j.physe.2009.06.056