Mach's Principle and Higher-Dimensional Dynamics

Abstract

We briefly discuss the current status of Mach's principle in general relativity and point out that its last vestige, namely, the gravitomagnetic field associated with rotation, has recently been measured for the earth in the GP-B experiment. Furthermore, in his analysis of the foundations of Newtonian mechanics, Mach provided an operational definition for inertial mass and pointed out that time and space are conceptually distinct from their operational definitions by means of masses. Mach recognized that this circumstance is due to the lack of any a priori connection between the inertial mass of a body and its Newtonian state in space and time. One possible way to improve upon this situation in classical physics is to associate mass with an extra dimension. Indeed, Einstein's theory of gravitation can be locally embedded in a Ricci-flat 5D manifold such that the 4D energy-momentum tensor appears to originate from the existence of the extra dimension. An outline of such a 5D Machian extension of Einstein's general relativity is presented.

16 pages, accepted for publication in Annalen der Physik; Revised Version: minor improvements

References in corpus (6)

• Gravity Probe B: Final Results of a Space Experiment to Test General Relativity
• Gravitational induction
• Decaying Dark Energy in Higher-Dimensional Gravity
• General Relativity and Quantum Mechanics in Five Dimensions
• An Embedding for General Relativity and its Implications for New Physics
• Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

Cited by in corpus (7)

• Mach's Principle: A Response to Mashhoon and Wesson's Paper arXiv: 1106.6036
• Emergent physics on Mach's principle and the rotating vacuum
• Mach, the Universe, and Foundations of Mechanics
• Waves and causality in higher dimensions
• Review of the Gravitomagnetic Clock Effect
• Machian gravity and a cosmology without dark matter and dark energy
• Mach's Principle and the Origin of Inertia