2023/06/14 by Eitan Bachmat, Bachmat, Eitan, Sveinung Erland +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Mathematics #FOS: Physical sciences #Galaxies: Formation, Evolution, Phenomena #General Relativity and Quantum Cosmology (gr-qc) #Physics and Society (physics.soc-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2306.08307
openalex publication_date 2023/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We mathematically construct focal lenses for positive-mass particles in Minkowski space. Particles emanating from a point source, refocus with synchronized proper time regardless of initial direction and velocity. Minkowski space offers a useful representation of the passenger queue formed during airplane boarding. The blocking relations between passengers coincide with the past-future relation in spacetime, and the boarding time is determined by the longest blocking chain. All blocking chains can be kept equally long if slow passengers are placed according to a lens in Minkowski space. The two media of the lens correspond to a grouping of fast and slow passengers, and the lens specifies the optimal placement of fast and slow passengers in the queue at the gate. Not only the boarding time, but also its variance is minimized.