STM-D-1020Paper2009Published and peer-reviewed

Do Mirrors for Gravitational Waves Exist?

Stephen J. Minter · Kirk Wegter-McNelly · Raymond Y. Chiao

Abstract and summary · read the original at the source · arXiv non-exclusive distribution licence

In one page

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.

Why it matters hereChapter 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.

What it claims

01The 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
Published and peer-reviewed
02Linearised 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
Published and peer-reviewed
03Treat 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
Published and peer-reviewed
04Transduction 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
Published and peer-reviewed
05The 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
Designed, not yet built
06What 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
What to watch

Read it · abstract

Abstract

Thin superconducting films are predicted to be highly reflective mirrors for gravitational waves at microwave frequencies. The quantum mechanical non-localizability of the negatively charged Cooper pairs, which is protected from the localizing effect of decoherence by an energy gap, causes the pairs to undergo non-picturable, non-geodesic motion in the presence of a gravitational wave. This non-geodesic motion, which is accelerated motion through space, leads to the existence of mass and charge supercurrents inside the superconducting film. On the other hand, the decoherence-induced localizability of the positively charged ions in the lattice causes them to undergo picturable, geodesic motion as they are carried along with space in the presence of the same gravitational wave. The resulting separation of charges leads to a virtual plasma excitation within the film that enormously enhances its interaction with the wave, relative to that of a neutral superfluid or any normal matter. The existence of strong mass supercurrents within a superconducting film in the presence of a gravitational wave, dubbed the “Heisenberg-Coulomb effect,” implies the specular reflection of a gravitational microwave from a film whose thickness is much less than the London penetration depth of the material, in close analogy with the electromagnetic case. The argument is developed by allowing classical gravitational fields, which obey Maxwell-like equations, to interact with quantum matter, which is described using the BCS and Ginzburg-Landau theories of superconductivity, as well as a collisionless plasma model. Several possible experimental tests of these ideas, including mesoscopic ones, are presented alongside comments on the broader theoretical implications of the central hypothesis.

Stephen J. Minter and Raymond Y. Chiao, University of California, Merced, and Kirk Wegter-McNelly, Boston University School of Theology, Do Mirrors for Gravitational Waves Exist?, arXiv:0903.0661, version 10 dated 30 June 2009, 59 pages; published as Physica E: Low-dimensional Systems and Nanostructures 42, issue 3, pages 234 to 255, January 2010. The manuscript is at arxiv.org/abs/0903.0661 and the published article at doi.org/10.1016/j.physe.2009.06.056.

(Abstract only — see the rights note above. On this site, the authors’ own four-page condensation of this argument is at /library/stm-9f833c131a, the transducer programme it leads to is at /library/stm-f6a447f155, the later full theoretical machine for gravitational waves inside superconductors is at /library/stm-1bb9e8dfb4, the reference review of the whole gravity-and-superconductors literature is at /library/stm-c909553daa, and the high-frequency gravitational-wave applications case is at /library/stm-590495077c and /library/stm-be42f591d1.)

The way in

https://arxiv.org/abs/0903.0661SOURCE REACHED AND READ IN FULL. The 59-page manuscript, version 10 dated 30 June 2009, was fetched from arXiv as 0903.0661 and read end to end; every claim below carries its section number from that text. The version of record is Physica E, Low-dimensional Systems and Nanostructures, volume 42, issue 3, pages 234 to 255, January 2010, doi 10.1016/j.physe.2009.06.056, and Elsevier holds it under its standard terms. The arXiv posting carries arXiv’s non-exclusive distribution licence, which is not a Creative Commons licence and does not permit republication, and no Creative Commons statement appears in the manuscript or on the arXiv page. So this page holds the summary, the claims and the authors’ own abstract, and sends the reader to the source. Stephen Minter and Raymond Chiao were at the University of California, Merced; Kirk Wegter-McNelly at the Boston University School of Theology.

How 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

Where it sits in the curriculum

Gravity control and superconductors The metric, warp drives and wormholes Inertial mass reduction and transmedium craft What the vacuum is