Abstract

In a previous web conference in December, we outlined a rough field theory reinterpretation of gravity based upon inverted integrals and the Poisson equation. This presentation is an update on the research. Between 1912 and 1914, Gunnar Nordstr?m theorized that a covariant scalar theory of gravity could be had from simply extending Newtonian gravity into four dimensions. Before the paper was even published though, Einstein notified Nordstr?m that he had already attempted this previously and had given up on it as an impossible dead end. To Einstein?s complete surprise, Nordstr?m then modified the equation by using the d?Alembertian operator instead. This new formulation was at the time exciting since it apparently presented a covariant field equation that could be interpreted as the trace of the stress-energy tensor R=kT. Although this was the last covariant scalar theory to present a serious alternative to General Relativity, it is now considered as nothing more than an occasional teaching aid in the development of GR.

In this presentation, we will demonstrate that efficient calculus notation is based on Euclidean geometry (derivative-of-a-function notation is simpler than writing out the redundant derivative-of-an-integral). We will show there is strong evidence that one cannot base non-Euclidean mathematics upon this efficient notation and that differential topology, the foundation of General Relativity (derivatives/tangents of lines), is most likely based upon a fundamental misunderstanding of non-Euclidean integrals and should be discarded after reviewing Riemann sums and the covariant d?Alembertian operator (Nordstr?m?s second theory). As preliminary evidence of this, we will demonstrate that whereas differential topology cannot combine the linearized gravitational equation ((1-2𝝓)?, 1-2𝝓, 𝝓->0 at infinity) with the cosmological constant Ʌ (constant of integration under unimodular conditions), the tangent ((C-f)?) of a linearized and normalized non-Euclidean integral (C-f=C(1-f/C), f->C at infinity) most certainly can and does not lead to mathematical artifacts such as black holes. Based upon this, we will consider that the scalar equation attempted in Nordstr?m?s theory was arbitrarily restricted and that the best physical model is to consider baryonic energy density as a delta of vacuum energy density leading to a tensor, rather than two separate tensors summed together. These physical model ?densities? will be founded upon the same perfect fluid analogies that lead to Max von Laue?s stress-energy tensor, but in this case is sensibly called the Aether. In other words, differential topology (derivatives of lines) only works because it mimics the derivative of an integral, and that the need for a mysterious tiny vacuum energy that ?repulses? attractive gravity stretches the credibility of mainstream models beyond the breaking point. Based upon this logical solution to the ?worst theoretical prediction in physics?, we will be proposing that empirical evidence overwhelmingly suggests most physical mathematical laws are ?backwards? due to this fundamental misunderstanding of the derivation of calculus notation.