The omnium vortex

The record

What was measured

Two records meet in this paper. The first is the frame drag of the Earth. Gravity Probe B carried four gyroscopes through it in a polar orbit of semi-major axis 7027.4 km. On the axis to its guide star, general relativity predicts −39.2 mas/yr and the experiment measured −37.2 ± 7.2 mas/yr, in the experiment’s sign convention. The node drag of the LAGEOS satellites returned 99 ± 5 % of the general-relativistic value, LARES with LAGEOS returned 0.9910 ± 0.02, and LARES-2, with LAGEOS and the GRACE gravity field, reaches a relative uncertainty at the one-part-in-a-thousand level.

The second is the magnetic record of fifty-one bodies, every row sourced: Mercury, the Earth, Ganymede and the four giant planets, all with active fields, with the Sun and the T Tauri star BP Tau; Venus, Mars and the Moon, which carry no global dipole; ten magnetic O and B stars; two magnetic white dwarfs; twenty magnetars; five young radio pulsars; and two millisecond pulsars. One number compares each body’s measured dipole moment μ with its angular momentum J, the Blackett number:

Bk = 2μ / (√(4πε₀G) J)

Bk = 1 is the field a body would carry if its magnetism were its present swirl, the body’s rotation read through I‑1. That is the snapshot law, the hypothesis of Schuster and Wilson, which Blackett took up in 1947 and tested in 1952, and it predicts one value for every body. The record gives this:

Measured span: 10.4 decades, from 2.4 × 10⁻⁸ (B1937+21) to 5.6 × 10² (SGR 1806−20); 15.1 decades with the lower limit on the white dwarf Grw+70°8247
Same spin: the Earth turns in 23.9 h and carries Bk = 0.32; Mars turns in 24.6 h and carries Bk < 2.4 × 10⁻⁵, more than four decades lower
Two magnetars: SGR 0418+5729 and SGR 1806−20 turn in 9.1 s and 7.5 s, and carry Bk = 2.0 and 560, a factor of 270
Sign and axis: the Earth and Ganymede carry their dipoles against their spins, Jupiter and Saturn with theirs; Uranus holds its at 58.6°, Neptune at 46.9°; the Sun reverses every 11 years
Neutron stars: across 27, log Bk rises with log P at slope 2.4, and log P alone carries 91 % of the variance

Fifty-one bodies against one prediction. Each dot is a body’s Blackett number on a logarithmic axis. Open circles with arrows are limits: upper limits for Venus, Mars and the Moon, lower limits for NGC 1624-2 and Grw+70°8247. The snapshot law puts every body on the dashed line. Choose a same-spin pair, hover or tap any body, or switch to the neutron stars, where Bk sorts with the spin and its spin-down history together. Every value is computed from the paper’s sourced table.

Proposition 9, R1

The FDT reading

0.1c The flow reading, P-⁠5 Magnetism is geometry

One substance is read through two windows. In the gravitational window the omnium around a body flows, and that flow carries the frame drag. In the medium window a body’s own medium keeps a vortex, and that vortex is the field the body carries. The record decides which window each measurement belongs to.

The gravitational window

Read in the time its patterns keep, the exterior of a static source is a flow. Patterns falling from rest far away move inward at v = c√α_ext, the flow is an Euler flow with zero Bernoulli constant, and the field equation on its flat slices is the second invariant of its strain rate:

⅔Θ² − Σ:Σ = 0 outside a source⅔Θ² − Σ:Σ = 16πGρ inside

Outside a source the omnium’s convergence and its shear balance exactly; inside, the excess is the density. A rotating source adds a swirl,

ω_sw(r_f) = 2GJ / (c²r_f³)

with the form of the Stokes rotlet, the creeping flow around a turning sphere. Among all swirls with its value at the skin it is the one of least shear, and half its curl is the precession a gyroscope reads: 39.05 mas/yr for Gravity Probe B on its guide-star axis. At the skin the swirl entrains the omnium by the fraction k_Iα_ext of the body’s spin, with k_I = I/(𝓜R²) its moment-of-inertia factor: 4.6 × 10⁻¹⁰ at the Earth’s surface, where α_ext = 1.39 × 10⁻⁹, and 0.123 at the skin of a 1.4 M_⊙, 12 km neutron star, where α_ext = 0.345.

The inflow lines wind with the swirl. In the azimuth of the flow form the winding is finite on the whole exterior branch,

Δφ = (a_⋆/3) α_ext^3/2, a_⋆ = cJ/(G𝓜²)

and it tends to a_⋆/3 toward the fold. In the static azimuth of the distant bookkeeper the same line wraps without bound, because that bookkeeper’s static time runs without bound toward the fold. The azimuths are bookkeepings of one geometry, and they agree on the gyroscope’s precession.

The whirlpool. Inflow lines around a rotating source, in units of R_s, at first order in its spin. Raise the spin a_⋆ and switch azimuths: the flow form winds by a finite angle, a_⋆/3 at the fold, while the static azimuth wraps without bound. The dotted circle is the seam, α_ext = ½; the dark disc is the fold, approached and never crossed.

Propositions 1–3

The swirl’s own clock

The swirl is stationary, and it keeps its own time. At the skin it turns once in

τ_s = P / (k_Iα_ext)

10 ms above the millisecond pulsar B1937+21, 51 s at the magnetar SGR 1806−20 and 5.9 million years at the Earth. Set against a time of watching, the ratio is a Deborah number, and across these bodies it spans twenty-four decades. Each turn repeats the last, so a record of any length reads the swirl as a rate, at every Deborah number: Gravity Probe B and LARES-2 at the Earth’s 5.9 × 10⁴, the precessing inner flows of X-ray binaries and the polar caps of pulsars far below one.

The swirl’s own clock. For each body the open circle is the spin period and the dot one turn of the swirl at the skin; the gap between them on the logarithmic axis is the factor 1/(k_Iα_ext). Move the time of watching: dots to its left turn within the watch. Values from the paper’s ladder; the Galaxy’s row is an estimate outside the evaluation domain.

Proposition 4

The medium window

The patterns that fall freely through the gravitational flow are irrotational, so the field a body carries belongs to a second window: the medium’s own. A medium’s patterns have a flow 1-form ϖ, built from their four-velocity and their enthalpy per count, and their vorticity is its exterior derivative dϖ. Maxwell’s source-free pair is then an identity, because d(dϖ) = 0: the vorticity of a flow is the derivative of something. The medium’s free fall is the frozen-in law with a baroclinic source. Kelvin keeps the circulation of every carried loop, and vorticity is born where the temperature gradient crosses the entropy gradient.

P‑5 states that mechanical vorticity and magnetic moments are two grade projections of one density-gradient topography. Each kind of pattern carries one 2-form with a mechanical grade and a magnetic grade, and Kelvin keeps the circulation of the whole. A condensate cancels the two grades: a spinning superconductor carries B = (2m_e/e)Ω parallel to its spin, the London moment through which Gravity Probe B read its rotors.

Read this way, the record is the record of a kept vortex. It is born where the medium’s flow is helical, kept by Kelvin when the drive stops, carried with its flux through every change of support, and it answers to the body’s later spin only through slow exchange. The magnetars carry fluxes of 4 × 10²⁵ to 1.3 × 10²⁸ G cm², the magnetic O and B stars 1 × 10²⁶ to 3 × 10²⁸ G cm²: the same range. A 4 kG field at 2.5 solar radii and 8.4 × 10¹³ G at 12 km are one flux. Kept angular momentum links the spins of the two populations in neither direction, and their fluxes are linked.

What remains to derive

D-⁠01 to D-⁠07 Targets, never results

The paper claims no divergence from general relativity or from the measured record, and every reading of the record above is in-sample. The observables that separate the omnium reading from the standard one are seven derivations, each a target:

D-⁠01
The grade split of an active vortex. The fraction of the medium’s vorticity a charge probe reads, from the helical flow of the interior, reproducing the active band Bk = 0.015 to 6.9 against the radius-scaling null of Cain et al.
D-⁠02
Inheritance and generation. The share of a kept vortex carried from the configuration a dense seed was inherited with, and the share an active flow generates, with its saturation. The kinematics bind to O‑14 and O‑15.
D-⁠03
Departures from perfect form. Viscous stress, heat flux and resistive terms, which set the decay clock of a kept vortex, its exchange with the spin, and the relaxation of the swirl to its least-shear minimum (O‑12).
D-⁠04
The London kernel. The condensate’s inertia per pair at the 21 ppm accuracy of Tate et al., against the measured excess of 92 ppm in niobium, through the confinement operator (O‑9).
D-⁠05
The polar-cap slip. The Goldreich–Julian density as the charge reading of the slip Ω − ω_sw, and the accelerating potential from k_Iα_ext, reducing to Muslimov and Tsygan and to Philippov et al.
D-⁠06
The galactic vortex. The mass shadow that holds the enclosed-mass ratio constant across a disk (O‑14), and the growth of the disk’s field in the medium window.
D-⁠07
The rotating exterior beyond first order. The band R_H < r_f < R_s outside a rotating source’s horizon, exterior and read through the multipole remainder of O‑5.

Readings declined

Use 6 Data yes, interpretation not necessarily

Standard reading

Spacetime flow and frame drag are strong-field effects of compact objects.

FDT reading

They are the flow of the geometry at every size, the frame drag the local rotation of the bookkeeper’s flow, half the curl of its swirl. Gravity Probe B and LARES-2 read it at the Earth, where α_ext = 1.39 × 10⁻⁹ (0.1c).

The magnetic field is an independent entity.

It is a helical density gradient of the omnium, the magnetic grade of a medium’s vorticity 2-form, with the measured fields accepted in full (P‑5).

A plasma is a fluid pushed by pressure forces across a fixed spacetime background.

Its patterns fall freely on clocks and rulers rescaled together by their enthalpy per count, and the pressure force is the bookkeeper’s reading (0.1c, I‑7).

Fluid flows that reproduce a metric are analogue models of gravity.

The identity is direct, because the flow is the omnium’s own (0.1c).

Neutron stars form by the collapse of massive stellar cores.

Compact objects are inherited dense seeds unwinding by decompressive fission, their kept vortices carried by Kelvin. The record of fluxes and spins is accepted as measured (0.8, I‑1a).

Convergence

Use 2 Same source, same data

For the same source and data FDT returns the measured record, and it reads that record as one substance seen through two windows.

In the gravitational window the flow form is the Schwarzschild exterior, and the swirl is Hartle’s slow-rotation frame drag, Kerr’s at the fold at first order in J. The gyroscope’s reading is the Lense–Thirring precession: 39 mas/yr for Gravity Probe B, against −39.2 mas/yr predicted and −37.2 ± 7.2 mas/yr measured. The node drag of LAGEOS, LARES and LARES-2 is returned with it, and so is the iron-line modulation over the quasi-periodic cycle of the black-hole binary H1743−322.

In the medium window Maxwell’s source-free pair is an identity, and flux freezing, magnetic helicity, the Biermann battery, the London moment, flux quantisation and the neutron vortex follow from the vorticity 2-form. Every measured field, moment, spin and period of the record is accepted as measured. The Schuster–Wilson–Blackett hypothesis is refuted by the record, as the mine measurements and Blackett’s negative experiment found, and the kept-vortex reading recovers the same record as the dynamo and fossil-field accounts.

No divergence is claimed from α, a chart or a branch tag. What separates the readings is D-⁠01 to D-⁠07.