Spatial-Causal Geometry (SCG) — D. J. Hallman

Introduction

In 1843, William Rowan Hamilton solved a problem he had been working on for years while walking near Brougham Bridge in Dublin: how to carry a scalar inside a vector expression without losing it. He carved the result into the stone on the spot. The mathematical object he found is called a quaternion.

James Clerk Maxwell used quaternions to write his field equations. A decade earlier, Wilhelm Weber and Rudolf Kohlrausch had made a purely electrical measurement — no light, no optics — and found it produced a velocity. That velocity was c.

Maxwell saw the number and drew what looked like the obvious conclusion: light must be electromagnetic. It was a reasonable inference. The number was right. What it meant — why a purely electrical measurement produces the speed of light — is a question Maxwell's own equations contained the answer to, in the scalar term he left open.

In writing his equations in quaternion form, Maxwell was left with a scalar term he could not close. He noted it appeared to be gravitational in character, declared it open, and stopped — because the geometric tool that would have closed it wouldn't be discovered for another fifty years.

In the 1880s, Oliver Heaviside reformulated Maxwell's equations for practical engineering use. The scalar wasn't needed for electromagnetics, so he set it to zero. The four vector equations now taught in every physics course as "Maxwell's Equations" are what remained.

What was set to zero is \(\varepsilon_0\mu_0\) — the product of the electric permittivity and magnetic permeability of free space. It carries gravity. It carries the origin of mass. It carries what light actually is, which is not electromagnetic.

This site follows the scalar Maxwell left open.

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About

D. J. Hallman is an independent researcher. All works are published open-access through Zenodo under a CC BY 4.0 license. Full publication list: Zenodo · ORCID 0009-0000-1710-3549 · Contact: SCG@azfn.com