The series hosts a seminar every other week on current research topics. The seminar often features an invited guest speaker and occasionally local faculty members, students or others affiliated with the department. The usual time of the seminar is 3:30-4:30 pm on Fridays. Professors Tatiyana V Apanasovich (firstname.lastname@example.org), Qing Pan (email@example.com) and Emre Barut (firstname.lastname@example.org ) are the Seminar Series Coordinators.
Date: Friday, February 13th, 3:30-4:30pm
Location: Duques Hall, Room 251
Title: Central Limit Theorems in Special Relativity and Quantum Mechanics
Speaker: Dr. Ian McKeague, Department of Biostatistics, Mailman School of Public Health, Columbia University
Abstract: The Maxwell-Boltzmann distribution describes the energy of large systems of particles that interact through elastic collision and are at thermal equilibrium. Numerous relativistic extensions have been proposed, but they do not explain the observed lognormal tail-behavior of the flux distribution of various astrophysical sources, especially those that expand into an infinite surrounding space (e.g., cosmic rays, quasars, gamma ray bursts, and X-rays from black hole objects). Motivated by this question, I develop extensions of some classical central limit theorems under the conditions of special relativity. The results are related to general CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior. There have been numerous attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the interaction of finitely many classical ``worlds." The wave function is then recovered (as a secondary object) from observations of particles in these worlds, without knowing the world from which any particular observation originates. Hall, Deckert and Wiseman (2014) have introduced an explicit many-interacting-worlds harmonic oscillator model to provide support for this approach. I will present a proof of their claim that the particle configuration is asymptotically Gaussian, thus matching the stationary ground-state solution of Schroedinger's equation when the number of worlds goes to infinityt.