General Relativity

What it claims: Proposed by Einstein in 1915, general relativity (GR) describes gravity not as a force but as the geometry of spacetime itself — mass and energy curve spacetime, and free objects follow the straightest available path (a geodesic) through that curvature. There is no separate “gravitational force” pulling or pushing anything; a falling object is simply following a geodesic, and an object standing still on the ground is the one being pushed off its natural path, by the ground beneath it. See What’s Actually Holding Us Down? for the full, worked version of this on this site.

Catalog status: Proven Systems. GR is among the most rigorously tested theories in physics, confirmed across an enormous range of independent methods and scales:

• Mercury’s perihelion precession — GR exactly accounts for the ~43 arcseconds/century excess Newtonian gravity couldn’t explain, known since the 19th century.
• Light bending — confirmed during the 1919 solar eclipse (Dyson, Eddington & Davidson, 1920), matching GR’s prediction of $\theta\approx1.75’’$ for light grazing the Sun; modern very-long-baseline radio interferometry confirms this to well under 1% precision.
• Gravitational time dilation — measured directly, from the 22.5-meter Pound-Rebka tower experiment (1959) down to a 1-millimeter height difference (Bothwell et al., Nature, 2022); GPS satellites apply this correction continuously or they’d drift kilometers per day.
• Gravitational waves — directly detected by LIGO in 2015 (Abbott et al., Phys. Rev. Lett. 116, 061102), a real ripple in spacetime itself, exactly as GR predicts for merging black holes.
• Black hole imaging — the Event Horizon Telescope produced the first direct image of a black hole’s shadow (M87, 2019), matching GR’s predicted size and shape.

Gravitational-wave polarization: the measurement, and why it matters here

(Added 2026-08-06. This site had no coverage of the polarization test, which is the single most discriminating gravitational-wave measurement for any theory proposing a mechanical alternative to spacetime curvature — including this one.)

What GR predicts. A gravitational wave has exactly two tensor (spin-2) polarization modes, conventionally $+$ and $\times$. A ring of free test masses is stretched along one axis while being compressed along the perpendicular one, and the pattern rotates between the two modes. A general metric theory of gravity permits up to six polarizations — two tensor, two vector, two scalar — so the number and type actually present is a real discriminator, not a formality.

Why it took until 2017 to test. LIGO’s two detectors, at Hanford and Livingston, are very nearly co-aligned, so they record almost the same combination of polarizations and cannot separate them. Adding Virgo, at a different orientation in Italy, broke that degeneracy. GW170814 was the first three-detector observation, and the first event on which the question could be asked at all.

The result. The LIGO–Virgo Collaboration reported Bayes factors of more than 200 in favour of purely tensor polarization over purely vector, and more than 1000 over purely scalar. A 2021 reanalysis using waveforms consistent with modified theories of gravity found $\ln B = 2.775$ and $3.636$ respectively — consistent with the original conclusion, though it noted the inferred binary parameters are significantly biased when non-tensorial templates are used.

A distinction worth keeping straight, because it is easy to blur. Quadrupole radiation and tensor polarization are not the same claim. Leading-order quadrupole emission follows from conservation laws alone — monopole radiation is forbidden by mass conservation, dipole by momentum conservation — and would hold in any theory respecting them, including a scalar one. Polarization is the independent question: it is about how test masses actually move as the wave passes, and that is what the measurement above constrains.

Where this touches PBT, stated directly. A medium without shear rigidity carries longitudinal modes only — which is precisely the inference seismology makes when S-waves fail to cross Earth’s liquid outer core. Transverse tensor polarization requires shear rigidity, which is why the nineteenth-century luminiferous aether had to be an elastic solid to carry light at all. Paper 18 leaves the medium’s polarization deliberately undetermined for exactly this reason, treating it as a property to be read off rather than assumed, and it cites GW170814 in doing so.

And a gap this makes visible, recorded rather than glossed: across all of this project’s papers, gravitational waves appear only as constraints — GW170814 for polarization, GW170817 for propagation speed — and never as something PBT explains. Paper 18’s W8 states the wave sector does not produce gravity, while the shadowing sector is a flux of particles rather than a wave. A directly measured phenomenon therefore has no home in either component. See Gaps in Science, item 11.

Real, acknowledged limits: GR doesn’t unify with quantum mechanics — it predicts its own breakdown (singularities) inside black holes and at the Big Bang, and no confirmed theory of quantum gravity exists yet. See Unknowns and Gaps in Science.

Where PBT touches this: Paper 1 and Paper 2 reproduce GR’s weak-field light-bending prediction ($\theta\approx4GM/(c^2b)$) via aether refraction rather than spacetime curvature — a deliberate consistency check with GR’s own confirmed number, not an independent test of anything. Paper 4’s black-hole-collapse simulation claims to avoid GR’s singularity via pressure stabilization; that specific claim was found in the 2026-07-21 audit not to follow from the paper’s own equations (see the revision note on Paper 1). See Tensor Calculus and the Einstein Field Equation for the actual mathematical formalism GR is built on — the object PBT proposes a mechanical alternative to.

References

1. Einstein, A. (1915). “Die Feldgleichungen der Gravitation.” Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften.
2. Dyson, F.W., Eddington, A.S., Davidson, C. (1920). “A Determination of the Deflection of Light by the Sun’s Gravitational Field.” Phil. Trans. R. Soc. A 220, 291–333.
3. Pound, R.V., Rebka, G.A. (1960). “Apparent Weight of Photons.” Phys. Rev. Lett. 4, 337.
4. Bothwell, T. et al. (2022). “Resolving the gravitational redshift across a millimetre-scale atomic sample.” Nature 602, 420–424.
5. Abbott, B.P. et al. (LIGO). (2016). “Observation of Gravitational Waves from a Binary Black Hole Merger.” Phys. Rev. Lett. 116, 061102.
6. Event Horizon Telescope Collaboration. (2019). “First M87 Event Horizon Telescope Results.” Astrophys. J. Lett. 875, L1.
7. Abbott, B.P. et al. (LIGO/Virgo). (2017). “GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence.” Phys. Rev. Lett. 119, 141101.
8. Takeda, H. et al. (2021). “Pure polarization test of GW170814 and GW170817 using waveforms consistent with modified theories of gravity.” Phys. Rev. D 103, 064037 (arXiv:2010.14538).