A dual first-postulate basis for special relativity

TL;DR

This paper derives a universal limit speed in special relativity from velocity reciprocity and a cosmic invariant, suggesting the second postulate is redundant and enabling new measurement approaches.

Contribution

It introduces a new ratio-based invariant that defines the universal speed limit without relying on the second postulate of relativity.

Findings

Identifies a cosmic invariant related to relative velocities

Shows the limit speed can be measured independently of signals

Derives the invariant as a function of signal response times

Abstract

An overlooked straightforward application of velocity reciprocity to a triplet of inertial frames in collinear motion identifies the ratio of their cyclic relative velocities' sum to the negative product as a cosmic invariant, whose inverse square root corresponds to a universal limit speed. A logical indeterminacy of the ratio equation establishes the repeatedly observed unchanged speed of stellar light as one instance of this universal limit speed. This formally renders the second postulate redundant. The ratio equation furthermore enables the limit speed to be quantified, in principle, independently of a limit speed signal. Assuming negligible gravitational fields, two deep-space vehicles in non-collinear motion could measure with only a single clock the limit speed against the speed of light, without requiring these speeds to be identical. Moreover, the cosmic invariant (from dynamics, equal to the mass-to-energy ratio) emerges explicitly as a function of signal response time ratios between three collinear vehicles, multiplied by the inverse square of the velocity of whatever arbitrary signal might be used.