The Emergent Nature of the Constant Speed of Light: Lorentz Symmetry under the Information-Potential Conversion Framework

Lorentz symmetry is a cornerstone of modern physics—it asserts that the laws of physics are the same in all inertial reference frames, with the speed of light in vacuum as an invariant constant. Yet a fundamental question has remained unresolved: Why does Lorentz symmetry exist? Is it an a priori property of spacetime, or a necessary consequence of some deeper physical mechanism? This paper proposes, within the information-potential conversion framework, that Lorentz symmetry is not an a priori property of spacetime, but a necessary requirement of causal consistency in information-potential conversion—the speed of light c is the maximum rate of information-potential conversion, and if this rate were not held invariant across different consensus protocols, logical contradictions would arise in the causal network. We proceed from the first principles of the causal law of information-potential conversion: first, a finite speed limit is an inevitable consequence of the causal structure of conversion avoiding logical loops; second, the photon, as a zero-mass mediator, must have its speed equal to this speed limit; from this we derive that the existence of a speed limit is equivalent to the linear structure of the Lorentz transformation; finally, the consistency requirement of the consensus protocol promotes this symmetry from local to global. Thus, Lorentz symmetry is an emergent symmetry locked in at the level of the consensus protocol, not a fundamental input of nature. Based on this interpretation, two testable quantitative predictions are proposed: (1) The energy spectrum of ultra-high-energy cosmic rays near the GZK cutoff may exhibit residuals caused by a weak protocol dependence of the conversion rate under extreme energy-momentum conditions; (2) The arrival time delay of extremely high-energy photons relative to low-energy photons should exhibit a directional dependence on the line-of-sight integral of the cosmic information processing density.

Lorentz symmetry, constant speed of light, information-potential conversion, consensus protocol, causal structure, GZK cutoff