The Spacetime Metric
Section 3Metric and propulsion engineering

Condition the field, not the power

University. · 3 min read

What it proposes

Ordinary electromagnetism couples to gravitation far too feebly to be useful. The conditioning programme says the weakness is not about how much energy you put in but about the form the field takes — give an electromagnetic field a structure closer to the one underlying gravitation and the coupling gets much louder. The hardware for imposing that structure already exists in accelerator laboratories: an undulator or a helix that forces electrons onto a sinusoidal path so the beam carries a coherent vector potential. And the physics licence is settled: the vector potential shifts a particle's phase in a region where no force acts, with no energy exchanged.

Who it is forAccelerator and beam-line engineers · Electromagnetics designers · Precision magnetometry engineers

Why the library suggests it

The licence the whole programme rests on, as an instrument. Dial the flux sealed inside the toroid and the fringes slide sideways by exactly one fringe per flux quantum, while both electron paths stay inside a corridor where the magnetic field is zero.

The interferometer with the field switched off

Split an electron beam, send the two halves either side of a magnetic flux that is completely confined and completely shielded, and bring them back together. On the paths themselves the magnetic field is exactly zero — the shaded corridor below is field-free the whole way. The vector potential there is not zero, and the fringes move. Dial the enclosed flux and watch the pattern slide sideways by exactly one fringe for every flux quantum. Then try the second control. It changes the gauge — the potential itself, at every point on both paths, as the arrows show — and the fringes do not move at all. Both controls are live; only one of them changes anything a detector can see.

Two controls: one moves the fringes, one cannot
Two electron paths around a shielded flux, and the fringe pattern they produceAn electron beam splits, passes either side of a small shielded magnet, and recombines at a detector. The corridor carrying both paths is shaded as a field-free region: the magnetic field on the electron paths is zero for every setting. The confined flux inside the shield is not zero, and the interference pattern drawn beneath the paths slides sideways as that enclosed flux changes, returning to its starting position after each whole flux quantum. Short arrows along the two paths show the vector potential there; they swing and change length whenever the gauge control is moved, while the fringe pattern beneath them stays exactly where it was.
  • Upper path
  • Lower path
  • Confined flux
  • Vector potential on the paths
The detector axis is drawn in fringe widths and the intensity is normalised, so the pattern is a shape, not an absolute brightness. The flux is given in units of the single-electron flux quantum h/e, which is about 4.14 × 10⁻¹⁵ webers.Nothing here moves on its own. The pattern is redrawn only when you change the enclosed flux; the gauge control redraws the arrows and leaves the pattern exactly where it was.

What is happening: The enclosed flux is near a whole number of quanta, so the pattern is near its starting position. Adding one whole quantum repeats the pattern.

Magnetic field on the electron paths
zero, at every setting
Vector potential on the upper path, in this gauge
0.00 nWb/m
Vector potential on the lower path, in this gauge
0.00 nWb/m
Phase the gauge adds to each half
0.00 radians — the same for both halves, so it cancels
Phase difference between the two halves
0.00 radians
Fringe shift
0.00 fringe widths
What no choice of gauge can change
the field on the paths, the phase difference, the fringe shift

The enclosed flux controls phase difference. Changing gauge changes the potential assigned to each point, not the observable phase difference or fringe pattern. This instrument calculates phase and interference, not stored energy or power output.

Nothing happening is the result here, not a broken control. The potential is not unique: for any smooth function χ you may replace A by A + ∇χ, which changes the potential at every point and changes the magnetic field nowhere, because the curl of a gradient is zero. This instrument performs that substitution for real and then integrates the full potential, gauge term included, around the closed loop the two halves of the beam make between them. Each half does pick up a phase from the gauge term — exactly 2λ radians in this family — and both halves pick up the same one, so it cancels out of their difference. What survives is the loop integral, which is the enclosed flux, and that is the observable.

Tonomura's 1986 experiment answered the obvious objection by construction: the flux sat inside a toroidal magnet wrapped in a superconducting shield, so stray field was not merely small on the electron wave but excluded from it. The shift was still there, and it was still one fringe per flux quantum.

An ideal two-path diagram comparing steady flux settings, not an exact reconstruction of the apparatus or a simulation of changing flux over time. A real changing magnetic flux can induce an electric field. Beam energy, path length, magnet size and absolute intensity are not modelled. Φ₀ = h/e ≈ 4.136e-15 Wb.

The source sheet: Tonomura et al. 1986, Evidence for Aharonov–Bohm effect with magnetic field completely shielded from electron wave

David Froning and Terence Barrett set out the programme in a NASA Breakthrough Propulsion Physics context: several ways of conditioning ordinary radiation into a form with a richer gauge structure, and several ways such fields might interact with gravity or with the vacuum's zero-point state (Space coupling by specially conditioned electromagnetic fields, 1998). The later paper in the series states the tuning condition the conditioned field would have to satisfy — the vacuum's electric and magnetic response behaving as a vector whose direction turns with the craft's speed while its magnitude stays at the vacuum value (Unlabored system motion by specially conditioned electromagnetic fields in higher dimensional realms, 2010). The strong, defensible form of the claim is phase control, and that is settled physics: the potential has measurable physical effect where the fields vanish (Significance of EM potentials in quantum theory, 1959, confirmed in Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave, 1986). Moe Arman and Charles Chase patented hardware that uses exactly that: a chip-scale mesh of electron diodes in about a hundred gauss, whose streams fall into step within nanoseconds and merge into a coherent matter beam, at room temperature, with no cryogenics (Systems and methods for generating coherent matterwave beams, 2011). Write the claim as phase control rather than as energy stored in the potential — the first survives scrutiny and the second does not need to be made.

And the shape rung two actually asks for: the same single poloidal winding, laid on a former that is deliberately not a doughnut.

A toroid wound with one continuous wire, its core shaped as a teardrop — a round bulb at one end and two straight limbs meeting in a point at the other — with closed curves drawn in the space outside it, each one threading the ring.
The turns stay evenly spaced all the way around the point, and the curves outside link the ring exactly as they do on a round toroid — the linkage is the same, the pattern is not.

The experiment or build

There are two rungs and the first is deliberately unambitious. Rung one: build the coherent matter-wave source from the patent and measure the coherence — beam brightness against the number of contributing diodes, looking for the square-law that coherence implies. Rung two, which the corpus records as having been attempted and reported successful but never independently repeated: a wound toroid built deliberately out of round, a teardrop rather than a doughnut, driven with alternating current so that the electric and magnetic fields stay inside while a non-zero vector potential remains outside — and then a measurement of whether the local zero-point field density outside it has changed, using the direct field-sampling instrument of section 6. The settling measurement is the sampled vacuum electric-field variance just outside the toroid, with the drive on and off, and with a round toroid of identical winding as the control. A machinable asymmetry with a measurable field-sampling readout is a rare and cheap thing in this subject.

Research context

The conditioning proposals are peer-reviewed, the matter-wave device is patented, the toroid measurement has been reported on air from a book rather than from a journal, and no independent group has repeated any of it.

Take it up

The measurement that settles it
The settling measurement is the sampled vacuum electric-field variance just outside the toroid, with the drive on and off, and with a round toroid of identical winding as the control.
What it costs to start
University.
The engineer it grows
This card is where the site's oldest thread — Whittaker's scalar potential functions, through Aharonov-Bohm, to the undulator — becomes a machine.

What it rests on

Where it sits in the curriculum

Longitudinal Electrodynamics and Scalar Waves · The Metric Tensor, Warp Drives, and Wormholes · Inertial Mass Reduction, the Navy Patents, and Transmedium Craft