Special Relativity-on-a-Photonic-Chip: Applying Circuits’ Analysis to Characterize Einstein Velocity Addition Law

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We demonstrate, for the first time to best of our knowledge, the usefulness of the analytical toolbox developed from a disparate field like Photonic Integrated Circuits (PICs) and now applied in the study of the Einstein Velocity Addition (EVA) in Special Relativity (SR). EVA is a central concept in SR that underlies many relativistic effects. The recently established analogy between the EVA and the PICs-based Optical Add-drop Filter (OADF) [J. Modern Optics 66, 679, (2019)] allows us to apply the “Critical Coupling, Over-Coupling and Under-Coupling” (or CC-OC-UC) analytical toolbox to systematically categorize, analyze, and visualize the different behaviors of EVA. We focus on the (i) relative magnitude and (ii) relative direction of the two non-collinear velocities of EVA. This analysis uncovers “not-too-obvious” features that are overlooked or would not have been discussed, otherwise, in the normal treatment of EVA in SR. Other important consequences are briefly discussed.