A dual first-postulate basis for special relativity
Brian Coleman
2003
European journal of physics
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
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... dundant. 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.
doi:10.1088/0143-0807/24/3/311
fatcat:yjj6f7e4xreovn5nazlb4yns34