The Spacetime Metric
Section 6Instruments and metrology

The megahertz-to-gigahertz gravitational-wave receiver

University, on existing hardware. · 2 min read

What it proposes

Listen for gravitational waves far above the band the big interferometers cover. Nothing in the known astrophysical catalogue is small and dense enough to ring at megahertz to gigahertz, so anything found there is new physics — and, for this site specifically, that band is exactly where the laboratory emitter proposals of section 3 would radiate. Building the receiver is therefore both an astronomy programme and the detector half of the gaser experiment.

Who it is forMicrowave and cryogenic engineers · Signal-processing specialists · Data analysts

Why the library suggests it

Start with the size of the job. The living review counts the distance the best proposals in this band still fall short by, and the distance their predecessors already closed — one order of magnitude to a rung, so the two can be compared by eye.

The gaser, measured against the instruments

Stephenson's wafer is specific enough to be measured, so measure it. Here is the megahertz-to-gigahertz band with the published detectors laid across it, and 24.048 gigahertz — the frequency the gaser is designed to emit at — drawn as a line through them. Then the distance the author names himself: roughly twenty orders of magnitude of coupling still to find. A zoomable scale would hide that, because above about a million readers stop reading a logarithmic axis logarithmically. So the orders are counted instead, one rung at a time, next to two distances of known size.

What to look at
The published detectors of the megahertz-to-gigahertz band, with the gaser's emission frequency drawn through them, and the shortfall its author states counted in rungsTwo views of one subject. The band view runs frequency from one megahertz to one hundred gigahertz on a logarithmic axis, one decade per step, with a horizontal bar for each published instrument at the strain figure its paper states, and a vertical line at 24.048 gigahertz where the gaser is designed to emit. The gap view is a ladder of counted rungs, one rung per order of magnitude: the gaser's published ideal case above the noise floor of its own reciprocal detector, the twenty orders of coupling its author says are still missing, where that leaves the device today, the six orders by which the whole band still falls short of the physics it is hunting, and the sixteen orders that separated a century-ago technology from the bands LIGO and LISA now cover.
  • Strain noise per root hertz
  • An upper limit already set on a background
  • The gaser
The gaser's ledger is kept in power, in the paper's own units, because the paper's own signal-to-noise is a power ratio against the same junctions used as a detector. Converting it into a strain would mean inventing a number the paper does not publish, and this figure publishes nothing it cannot cite.Two different rulers, on purpose. Frequency is a place, so it runs as a dial: one decade per step, left to right. The orders of magnitude are a size, and sizes above about a million stop being read logarithmically — so every order is drawn as its own counted rung and numbered, and the distance a reader sees is the distance there is.Three quantities, kept apart. Most of these figures are strain noise per root hertz, the number a running instrument quotes. ARCADE 2's is an upper limit on a stochastic background already excluded by radio data, not an instrument noise floor. The Li–Baker figure is a dimensionless monochromatic strain amplitude its authors state the design could resolve. Drawing all three as one curve is the ordinary way to get this picture wrong, so each is marked and named.
The distances, counted
The gaser's emission frequency:
24.0 GHz
The published ideal case:
1.2E-1 W / 6E-10 W
The shortfall the author states:
20
Where that leaves the device today:
-11.7

Reading: How far the whole band still is. 6.0 — One rung is one order of magnitude.

Six rungs. Twenty-five authors of the megahertz-to-gigahertz living review conclude that none of the proposals they catalogue yet reaches the sensitivity the new physics would need, the best being at least six orders of magnitude short. Every instrument on the band view is inside that verdict. This is what the frontier of a field looks like from the inside.

The published ideal case assumes nearly perfect conversion, and the author is explicit that the conversion is the open problem. Subtract the shortfall he states and the ledger closes where the drawing shows it.

This is what taking a proposal seriously looks like. A programme that names no frequency and no output cannot appear on these axes at all; the gaser can, because it names a wafer, a bias voltage, an emitter count, a predicted power, a detector and its own missing number. The distance is real, and so is the fact that it is stated rather than discovered by a critic.

Three things would move the line. The frequency scaling Stephenson gives on the same broadcast: strain rises with the square of the frequency and radiated power with the fourth, so the whole ledger moves with the band a future wafer is designed for. The coherence law the array exists for: radiated power grows with the square of the number of emitters kept in step, so 81 pads on a 150 mm wafer is the smallest version of the device, not the largest. And the conversion efficiency itself — the doping sweep across d-wave and s-wave regimes that the paper recommends as the first experiment is the measurement that would put a real number where twenty orders of magnitude currently stand.

Read the source sheets. The 100-megahertz recycling interferometerA microwave cavity on ADMX parametersARCADE 2, recastThe Li–Baker detectorThe gaser

Twenty-five authors catalogue the hardware routes — levitated nanoparticles, quartz acoustic resonators, microwave cavities, superconducting rings, ferromagnetic crystals whose spin waves a passing wave can excite, and above all magnetic conversion, in which a gravitational wave crossing a strong magnetic field turns into a photon — and are frank that the best proposals fall about six orders of magnitude short, noting that a century ago the gap was sixteen (Challenges and opportunities of gravitational-wave searches at MHz to GHz frequencies, 2021). The most immediately actionable route needs no new hardware at all: a ripple crossing a strong static magnetic field inside a metal cavity drives a current and rings the cavity, and cavities already built and running to hunt axion dark matter are already sensitive to gigahertz gravitational waves at strains near ten to the minus twenty-two — they need only reanalyse data they have already taken, and reading several modes at once could give the wave's direction (Detecting high-frequency gravitational waves with microwave cavities, 2022). The optimisation of those haloscopes specifically for gravitational-wave searches is worked out in Symmetries and selection rules: optimising axion haloscopes for Gravitational Wave searches (2024), and a complementary large-aperture route is Potential of Radio Telescopes as High-Frequency Gravitational Wave Detectors (2021).

The experiment or build

Stage one is a reanalysis: take archived axion haloscope data and run the gravitational-wave selection rules over it. Stage two is a purpose-built cavity placed beside the section 3 emitter, so that the two experiments share a clock and a shield. The settling measurement is a strain sensitivity in the gigahertz band, published as a curve, against which any laboratory emitter's predicted output can be plotted directly. Once that curve and the gaser's predicted output are on the same axes, the gap between them stops being rhetorical and becomes a number of orders of magnitude with a year on it.

Research context

The cavities exist and are taking data, the analysis that would turn them into gravitational-wave detectors is published, and the dedicated instrument is not yet built.

Take it up

The measurement that settles it
The settling measurement is a strain sensitivity in the gigahertz band, published as a curve, against which any laboratory emitter's predicted output can be plotted directly.
What it costs to start
University, on existing hardware.
The engineer it grows
It is the receiver every emitter proposal in this programme is waiting for.

What it rests on

Where it sits in the curriculum

Gravity Control and Superconductors · Longitudinal Electrodynamics and Scalar Waves