Curved Spacetime

Einstein's General Relativity (1915) replaced the Newtonian picture of gravity-as-a-force with a geometric picture: mass-energy curves the four-dimensional fabric of spacetime, and matter (including light) follows the geodesics of that curved fabric. The mathematics is the Einstein field equations:

$$R_{\mu \nu }-\frac{1}{2}R{g}_{\mu \nu }+\Lambda g_{\mu \nu }=\frac{8\pi G}{c^4}{T}_{\mu \nu }$$

Beautiful, but mysterious: where does the curvature happen? On what substrate? Supreme Polarity Theory answers both: the curvature happens on the membrane of the time-string, and the substrate is real and tangible — the very same membrane on which light propagates.

The mechanism

Many nodes spinning in phase pull on the membrane and twist it locally. Each in-phase pair is a tiny tug; with billions of pairs across a planet's worth of mass, the twist is large. A photon traveling along the membrane has no straight path available — it follows the membrane's local curvature. We measure this and call it gravity.

Gravitational lensing — the smoking gun

Eddington 1919. Arthur Eddington led the famous solar-eclipse expedition and confirmed Einstein's prediction: starlight passing close to the Sun bends measurably (~1.75 arcseconds). In Supreme Polarity Theory the explanation is direct: the Sun is a colossal cluster of in-phase spinning nodes, and they twist the membrane in their neighborhood. Light from a distant star, riding the membrane on its way past, follows the twist.

Galaxy-cluster lensing. The same effect at a larger scale: a galaxy cluster between us and a distant background galaxy bends and even multiplies the image of the background object — sometimes producing arcs and complete Einstein rings. The cluster's billions of in-phase nodes twist the membrane sharply enough to act as a lens. We see this as smoking-gun evidence for both dark matter (because the lensing is stronger than the visible mass would predict) and curved spacetime.

Gravitational waves — the membrane ripples

When two large in-phase clumps (two black holes, two neutron stars) orbit and merge, the local twist of the membrane oscillates and propagates outward. Those propagating ripples are gravitational waves, first directly detected by LIGO in 2015 (Nobel Prize 2017). They travel at $c$ because they ARE membrane updates, and the membrane updates at $c$. Every binary merger detected by LIGO/Virgo since then is a confirmation of this picture: the membrane is real, and its twist can move.

Frame-dragging — when spinning mass twists the surroundings

Spinning massive bodies (rotating stars, spinning black holes) are predicted by GR to drag the local spacetime around them — the Lense-Thirring effect, confirmed in 2011 by Gravity Probe B. In Supreme Polarity Theory, this is direct: the in-phase nodes of a spinning star are themselves spinning together, and their bulk rotation forces the local membrane to rotate with them. A nearby gyroscope feels the membrane's drag.