May 09, 2025
The assertion that "Relativity does not have a mathematical explanation for why the speed of light is c" is fundamentally correct. In special relativity, the invariance of the speed of light is not derived from first principles but postulated as a foundational axiom. While Maxwell’s equations predict that electromagnetic waves propagate at a fixed speed c in vacuum, these equations are formulated within particular reference frames and do not inherently explain why this speed should remain invariant across all inertial observers. Special relativity adopts this invariance as its second postulate: that the speed of light in a vacuum is the same for all observers, regardless of their relative motion. As such, the value of c is not mathematically deduced from within relativity—it is assumed.
In standard relativity, photons are treated as massless (rest mass m = 0), yet they carry energy and momentum, implying an effective inertial influence. In Extended Classical Mechanics (ECM), this leads to a re-interpretation: photons and other massless particles can exhibit negative apparent mass (Mᵃᵖᵖ < 0) due to their kinetic energy characteristics. This challenges the conventional notion of masslessness by introducing a dynamical interpretation tied to acceleration and force. Similarly, in cosmological contexts, dark energy—such as that inferred in studies by A. D. Chernin et al. on the Coma Cluster—is interpreted as having negative effective mass, a view consistent with ECM’s framework.
Within ECM, particles exhibiting negative apparent mass—such as photons emitted from gravitationally bound systems—tend toward unbounded propagation speeds. This provides an alternative explanation for the observed superluminal recession of distant galaxies, where the recession is not merely a relativistic artifact of metric expansion, but a real, force-driven phenomenon resulting from gravitational–antigravitational interaction. Specifically, such recession occurs when the negative effective mass component dominates over the matter mass, producing a net repulsive dynamic. Here, "unbounded" refers to the mathematical tendency of speed to diverge as apparent mass becomes increasingly negative or frequency increases without bound.
However, ECM also acknowledges that physical unboundedness is constrained by fundamental quantum limits. The Planck scale introduces the smallest meaningful physical quantities—the Planck length (Lₚ) and Planck time (Tₚ)—which naturally impose an upper bound on velocity. This bound is expressed through the ratio:
c = Lₚ / Tₚ
This expression does not emerge from relativity itself but from dimensional considerations in quantum gravity. It defines the maximum attainable speed for any propagation process, including those involving particles with Mᵃᵖᵖ < 0. While mathematical models may suggest speeds approaching infinity, the Planck scale sets a physical boundary, beyond which further acceleration or frequency increase ceases to be meaningful or measurable. In this way, ECM preserves causal consistency and enforces a speed limit—not as a postulate of relativity or a consequence of spacetime curvature, but as a boundary arising from the discrete, physical limits imposed by the Planck scale.
