2008/02/29 by Louis Marchildon, Louis Marchildon · 5 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebra over a field #Algebraic number #Calculus (dental) #Classical mechanics #Geometry #Hermitian matrix #Impossibility #Invariant (physics) #Law #Lorentz covariance #Lorentz transformation #Mathematical analysis #Mathematical physics #Mathematical proof #Mathematics #Physics #Pure mathematics #Quantum Mechanics and Applications #Relativity and Gravitational Theory #Theoretical physics #quant-ph
paper · pdf · doi:10.1007/s10701-008-9238-9
published in Foundations of Physics 38(9), 804-817 (Springer Science+Business Media) · Clarifications, reference added; published version
openalex publication_date 2008/09/01 · arxiv created 2008/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Several arguments have been proposed some years ago, attempting to prove the impossibility of defining Lorentz-invariant elements of reality. I find that a sufficient condition for the existence of elements of reality, introduced in these proofs, seems to be used also as a necessary condition. I argue that Lorentz-invariant elements of reality can be defined but, as Vaidman pointed out, they won't satisfy the so-called product rule. In so doing I obtain algebraic constraints on elements of reality associated with a maximal set of commuting Hermitian operators.