Spacetime Symmetries and Classical Mechanics

Abstract

Physics students are rarely exposed to the style of thinking that goes into theoretical developments in physics until late in their education. In this work, we present an alternative to the traditional statement of Newton’s second law that makes theory questions accessible to students early in their undergraduate studies. Rather than a contrived example, the model considered here arises from a popular framework for testing Lorentz symmetry used extensively in contemporary experiments. Hence, this work also provides an accessible introduction to some key ideas in ongoing tests of fundamental symmetries in physics.

Lorentz Violation at the Level of Undergraduate Classical Mechanics

“…Our second example is a block on an inclined plane. This has already been studied by others [15], so we restrict our attention for a few new observations. Finally, we consider a binary star system in the presence of Lorentz violation.…”

“…. , 3) [15]. In the limit of non-relativistic classical mechanics, this model's Lagrangian for a single massive particle is given by…”

“…In this section, we consider some aspects of a block on a frictionless inclined place on Earth's surface in the presence of a Lorentz violation, in particular the Lorentz-violating effects described by Lagrangian (2). This system has already been analyzed in [15]; we briefly summarize their findings and then add a few comments.…”

“…As in Ref. [15], we restrict attention to the case where c jk , and hence the effective mass matrix m jk , are diagonal in our chosen coordinate system. To first order in c jk , they found the acceleration down the ramp to be…”

“…In this work, we employ the classical limit of the SME [14,15] to analyze several macroscopic systems. First, we outline the general classical model.…”