Historical research guide · 0892 · 2020
Interaction between superconductors and weak gravitational field
Antonio Gallerati
In one minute
Antonio Gallerati, of the Politecnico di Torino and Italy’s National Institute for Nuclear Physics, asks what happens to Earth’s gravity right beside a superconductor that is flickering into its superconducting state. His method has two halves. First he writes Einstein’s equations for a weak field in the same shape as Maxwell’s, so gravity acquires its own electric-like and magnetic-like fields with their own vacuum permittivity and permeability. Then he merges those with the ordinary electromagnetic fields into one generalised field and feeds it into time-dependent Ginzburg-Landau theory, the standard description of a superconductor near its critical temperature, where thermal fluctuations briefly create pockets of accelerated superfluid electrons. The result is a short pulse in the local gravitational field: above a niobium disc the field first dips below normal, then peaks about 1.8 times ten to the minus seven metres per second squared above it, 7.45 nanoseconds after the switch, then relaxes. A high-temperature superconductor gives an effect roughly a thousand times larger.
Connection
Chapter 11 turns on whether a superconductor can move the local gravitational field at all, and this is the calculation that says how much, in what material, and for how long — a number, a sample and a stopwatch rather than an anecdote. It also carries chapter 3’s claim in concrete form: gravity is written here as a field with a vacuum permittivity and permeability, exactly the language a polarizable-vacuum account of gravity needs.
From the source
For a nearly flat spacetime the Einstein equations in the harmonic De Donder gauge take, to first order, the same structure as Maxwell’s equations: a gravitoelectric field and a gravitomagnetic field built from the metric perturbation, sourced by a mass density and a mass current density in place of charge and current.Section 2.1, equations 5 and 6
Combining the electromagnetic and gravitational fields into single generalized fields, weighted by the ratio of the electron mass to its charge, gives generalized Maxwell equations in which the vacuum acquires a gravitational permittivity equal to the electron charge squared divided by four pi times Newton’s constant times the electron mass squared, and a matching gravitational permeability.Section 2.2, equations 7 to 10
Near the critical temperature a superconductor’s order parameter fluctuates thermodynamically, creating superfluid regions of accelerated electrons; treated with the time-dependent Ginzburg-Landau equations, the resulting fluctuation supercurrent produces a generalized electric field that carries both the Earth-surface gravitational field and a geometrical factor set by the shape of the sample.Section 3, equations 11 to 17
For a niobium disc of radius 15 centimetres and thickness 2 centimetres, held one thousandth of a kelvin above its 9.25 kelvin critical temperature and allowed to enter the superconducting state at time zero, the gravitational field measured 0.25 centimetres above the base first falls below its unperturbed value, then rises to a maximum excess of 1.82 times ten to the minus seven metres per second squared at 7.45 nanoseconds, and then relaxes to the external value.Section 4, figures 1 and 2
The same calculation for a mercury-barium-calcium-copper-oxide sample, a high-temperature superconductor with a 230 nanometre coherence length and a 126 kelvin critical temperature, gives a maximum variation of 1.14 times ten to the minus four metres per second squared at 7.5 picoseconds; the peak scales inversely with the coherence length, so short-coherence high-temperature materials give a larger effect, and the duration scales inversely with the temperature difference from the critical point, so working closer to it lengthens the window.Section 4, figures 3 and 4
Gallerati’s own verdict on measurability is the experiment to watch: the field variation is in principle perceptible, especially in high-temperature superconductors, but the very short intervals complicate direct measurement, so the recipe is a large sample of dirty material, a high-temperature superconductor for the short coherence length, and a temperature very close to the critical one.Section 5, conclusions and future developments
The way in
https://doi.org/10.1088/1742-6596/1690/1/012141How to cite it
Antonio Gallerati (2020) Interaction between superconductors and weak gravitational field doi:10.1088/1742-6596/1690/1/012141