The Spacetime Metric
Section 7New theories to test

If a cavity changes electron-phonon coupling, then it changes the screening energy

University. · 2 min read

What it proposes

Two settled facts have never been put in the same room. First: an unpowered resonator placed near a superconductor changes its transition temperature, and first-principles calculations trace the effect to the vacuum field reshuffling how electrons trade energy with lattice vibrations. Second: the rate at which two nuclei fuse inside a metal depends on the screening energy of the electrons around them, a quantity that varies by more than a factor of twenty between hosts and is directly measurable on an accelerator. If a cavity can reshuffle the electron-phonon interaction in a solid, then a cavity around a hydrogen-loaded lattice should move the screening energy — and therefore the fusion rate — in that lattice. If the electromagnetic vacuum around a loaded metal is reshaped, then the screening energy measured in that metal changes. That is the vacuum-catalysed fusion hypothesis reduced to an experiment with two known instruments, and it is, as far as this library shows, unstated anywhere.

Who it is forNuclear physicists · Terahertz photonics engineers

Why the library suggests it

Here is the first of the two settled facts, as an instrument: the shift along one continuous flake, largest under the antenna's field maximum and zero on the part of the flake outside the resonator, with the sign reversing when the antenna is detuned below resonance.

The dark cavity, and what it does to a superconductor

Two measurements, two samples: a two-layer NbSe₂ flake mapped along its length, and a ten-layer sample compared at different resonator frequencies. Neither resonator was externally illuminated. Choose a dataset to explore its reported shifts.

Measurement dataset
The dark cavity, and what it does to a superconductor
Separate position and frequency measurements in NbSe₂Left: the bilayer at a fixed resonator frequency of 0.92 terahertz, with shifts of 0.39, 0.27 and approximately zero kelvin at three positions. Right: a different, ten-layer sample, with shifts of minus 0.12, plus 0.10 and approximately zero kelvin at 0.69, 0.92 and 2.00 terahertz. Slider positions between these anchors follow illustrative straight lines, not additional measurements.
  • Measured points
  • Drawn between them
The six filled points summarize reported values: three positions in the bilayer and three frequencies in the ten-layer sample. Straight lines only connect these values. The paper also reports a peak near 0.96 THz; no numerical peak height is assigned here, so this drawing is not a fit to the full frequency response.The position axis is schematic, not a distance in micrometres. Each panel is independent: moving along the bilayer does not rescale the ten-layer frequency results.Choose a dataset to enable its slider. The other panel retains its own measurements; nothing moves automatically.
Shift in the transition:
0.39 K
Transition temperature:
3.41 K
Baseline, with no resonator:
3.02 K

Selected dataset: A positive shift means superconductivity persisted to a higher transition temperature in this comparison. Between the marked anchors, the displayed number is an illustration, not a measured value.

The ten-layer measurements change sign between 0.69 and 0.92 THz. The interpolated zero is not a measured resonance or a proof of mechanism. The paper also reports metal-structure and temperature-sweep controls addressing thermalization.

The cavity experiments this library carries

The authors interpret these changes as cavity-mediated tuning of superconductivity. They discuss several possible microscopic mechanisms; the measurements do not establish one complete microscopic explanation. No external illumination does not mean the cryogenic transport apparatus consumes no energy.

Read the measurement this instrument draws

The cavity effect is measured by three independent groups, with the shift tracking the simulated field map along a single flake, going to zero outside the resonator, and reversing sign when the antenna is detuned below resonance (Cavity-enhanced superconductivity in the two-dimensional limit of NbSe2, 2026; Evidence for vacuum-enhanced superconductivity in NbSe2, 2026; Cavity-enhanced superconducting response in an underdoped cuprate, 2026). The screening energy is measured on an accelerator, host by host: about 27 electronvolts in titanium, about 310 in palladium, about 600 in palladium oxide, with a hundredfold rate difference at 2.5 kiloelectronvolts of bombarding energy (Screening energy for low energy nuclear reactions in condensed matter, 2020). The mechanism linking conduction-electron density to reaction rate, with the reaction-rate gain calculated at up to twenty orders of magnitude below 10 keV, is Electron Screened and Enhanced Nuclear Reactions (2022), and the reactions themselves are on the record with a NASA byline (Novel nuclear reactions in bremsstrahlung-irradiated deuterated metals, 2020).

And here is the second, host by host: the bare Coulomb law, which nothing on the instrument can move, and the same law offset downward by the host's measured screening energy — with the sliver between them read off as orders of magnitude in rate.

Electron screening, and what it really changes

Two deuterons approaching each other push apart by the bare Coulomb law, and they fuse only by tunnelling through that repulsion. Pack the deuterium into a metal and the metal's own conduction electrons crowd around each nucleus, cancelling part of its charge over the screening length. The pair then behaves exactly as a bare pair would if it had arrived with a little more energy — a few hundred electronvolts more, measured host by host. Because tunnelling is exponential, that small shift multiplies the rate by orders of magnitude. Choose a host, move the collision energy, and read what moves and what does not.

Collision energy and host material

Beam experiments quote a bombarding energy; for two deuterons the collision energy is half of it.

The bare Coulomb barrier and the effective barrier, drawn against separationA logarithmic plot of the repulsion between two deuterons against how far apart they are. The bare Coulomb curve is drawn as one solid line and never moves. The effective barrier inside the metal is the same curve offset downward by the measured screening energy, so it falls away at large separations. A horizontal line marks the collision energy, and the two curves meet it at two different separations: the pair inside the metal has to tunnel through the shaded sliver between them, and the sliver is narrower.
  • Bare Coulomb barrier
  • Effective barrier inside the host
  • The barrier still to be tunnelled
Energy (electronvolts). Both axes are logarithmic, because the quantities here span decades. The solid curve is the bare Coulomb law, one over the separation, and it is identical for every host on the list. The dashed curve is that same law offset downward by the host's measured screening energy — the effective barrier the pair faces, and the only thing on this drawing that a metal changes.Nothing here moves on its own. The drawing changes only when you move a control.

What the screening does at this energy: The pair inside the host tunnels as though it had arrived with the screening energy added to its own. The bare Coulomb law, Planck's constant and the fine-structure constant are unchanged; the rate is not.

Tunnelling rate, screened divided by bare:
19
Orders of magnitude gained:
1.3
Turning point moves inward from
1,152 to 921 femtometres
The measured ladder, host by hostEach bar is the orders of magnitude that host's measured screening energy buys at the collision energy you have selected. The screening energies are measurements with error bars, not fitted parameters, and the Huke values are stated by their authors as lower limits: surface contamination can only shrink an inferred screening energy.
Orders of magnitude gained at the selected energyEach bar is the orders of magnitude that host's measured screening energy buys at the collision energy you have selected. The screening energies are measurements with error bars, not fitted parameters, and the Huke values are stated by their authors as lower limits: surface contamination can only shrink an inferred screening energy.
  • Deuterium gas (reference): 0.1
  • Titanium: 0.1
  • Aluminium: 0.8
  • Zirconium: 1.2
  • Palladium: 1.3
  • Tantalum: 1.3
  • Palladium oxide: 2.2

The tunnelling factor. Barrier penetration follows the Gamow factor, the exponential of minus the square root of the Gamow energy divided by the collision energy. For two deuterons the Gamow energy is about 986 kiloelectronvolts, fixed by the charges and the reduced mass. A screened pair at one energy is arithmetically a bare pair at a slightly higher one, which is why a few hundred electronvolts is worth so much.

The precision point: this is an increased tunnelling rate, not a lowered bare Coulomb barrier. Douglas Miller, who coined the phrase vacuum-catalysed fusion, states the same limit himself — the idea does not require or establish any change in Planck's constant, the fine-structure constant or the bare Coulomb law.

Scope: this instrument draws the barrier-penetration factor and its ratio. The nuclear physics inside the barrier is held fixed, so every number here is a ratio of tunnelling rates — not a cross-section, not a heat measurement and not a power output. The energy balance of a lattice reactor is a separate measurement that has not been made.

The measured screening energies come from these source sheets

The experiment or build

Take Kasagi's accelerator screening measurement exactly as published and add one component: a terahertz split-ring or antenna resonator around the target, unpowered, tuned to the target's own phonon band. Measure the screening energy with the resonator on resonance, detuned, and absent, in one session, on the same target. The settling measurement is the screening energy in electronvolts, measured the standard way, as a function of cavity detuning — with the shift going to zero off resonance and outside the mode volume, exactly as the superconducting version does. No new physics has to be assumed for this experiment to be worth doing; if the shift is zero the result bounds the coupling, and if it is not, it is the most important measurement in this programme.

Research context

Both halves are published and peer-reviewed, and the combination has never been attempted.

Take it up

The measurement that settles it
The settling measurement is the screening energy in electronvolts, measured the standard way, as a function of cavity detuning — with the shift going to zero off resonance and outside the mode volume, exactly as the superconducting version does.
What it costs to start
University.
The engineer it grows
Nuclear physicists and terahertz photonics engineers in the same room — that combination barely exists yet, which is exactly why the test has not been run.

What it rests on

Where it sits in the curriculum

Casimir Physics and Vacuum-Force Engineering · Gravity Control and Superconductors · Lattice Confinement Fusion: The Energy Substrate