On the Challenges Posed by Non-Machian Solutions to Relationalism in General Relativity

Author

Zachary Matthew Zito, Utah State University

Date of Award

5-2025

Degree Type

Thesis

Degree Name

Departmental Honors

Department

Languages, Philosophy and Communication Studies

Abstract

The relationship between Mach’s Principle and solutions to Einstein’s field equations is examined, with special attention to Friedmann-Lematre-Robertson-Walker (FLRW) cosmology. Mach’s Principle is outlined, and the extent to which general relativity fulfills Machs vision is assessed. It is argued that several important solutions to Einsteins equations, particularly the FLRW cosmological models, embody key Machian features. In order to elucidate the FLRW cosmological model, the associated energy-momentum tensor for a perfect fluid under the assumptions of large-scale homogeneity and isotropy is derived and used to obtain the Friedmann equations that govern cosmic expansion. It is shown that FLRW cosmology can be understood as Machian in three important respects: ontologically (inertial structure arises from the global massenergy content of the universe), geometrically (the evolution of the scale factor and the emergence of a preferred foliation tie inertial motion to spacetime geometry), and topologically (in cases where the universe’s spatial curvature is positive, a complete description of inertial frames requires multiple overlapping local charts, emphasizing the relational nature of spacetime). The appendices provide detailed derivations and example calculations related to the mathematical framework supporting these claims.

Recommended Citation

Zito, Zachary Matthew, "On the Challenges Posed by Non-Machian Solutions to Relationalism in General Relativity" (2025). Undergraduate Honors Capstone Projects. 1012.
https://digitalcommons.usu.edu/honors/1012