Mach's principle

Mach's principle
Name	Mach's principle
Caption	Ernst Mach, 1889
Field	Physics, History of science, Philosophy of physics
Introduced	19th century
Notable proponents	Albert Einstein, Ernst Mach, Julian Barbour
Related concepts	Inertia, Principle of relativity, General relativity

Mach's principle is a contested hypothesis about the origin of inertia and the relational character of motion, proposing that local inertial frames are determined by the large-scale distribution of mass–energy in the universe. It influenced debates among figures such as Ernst Mach, Albert Einstein, Hugo von Seeliger, Gustav Kirchhoff, and later contributors like Dennis Sciama, Felix Klein, and Julian Barbour. The idea shaped developments in classical mechanics, stimulated revisions of Newtonian mechanics and guided attempts to formulate alternatives to general relativity and proposals in cosmology and philosophy of science.

Introduction

Mach’s principle emerged from 19th-century critiques of Isaac Newton’s notions of absolute space and absolute motion, articulated by Ernst Mach and taken up by scientists and philosophers across Europe and the United States. It asserts a relational linkage among bodies such that local inertial properties depend on the mass distribution of distant stars and galaxies like those catalogued by William Herschel, Edwin Hubble, and Heber Curtis. This relational stance influenced research agendas at institutions including the University of Vienna, the Kaiser Wilhelm Society, and later centers such as Princeton University and Cambridge University.

Historical background

Discussions trace to debates between Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century, later advanced by critics including Ernst Mach and commentators such as Arthur Eddington, Hermann Weyl, and Henri Poincaré. In the 19th century, astronomers like Simon Newcomb and theoreticians like George Stokes and William Thomson, Lord Kelvin weighed in on absolute vs. relative motion. By the early 20th century, exchanges among Albert Einstein, Michele Besso, Max Planck, and Paul Ehrenfest integrated Machian concerns into the emergence of general relativity and discussions at forums like the Solvay Conference.

Formulations and interpretations

Various formulations exist, from strong versions positing complete determination of inertia by the universe’s matter (advocated by Ernst Mach, Julian Barbour) to weak versions asserting influence or boundary conditions (advanced by Dennis Sciama, Andrzej Trautman). Interpretations range across proposals by Albert Einstein in correspondence with Tullio Levi-Civita and Marcel Grossmann, to later mathematical treatments by Hermann Bondi, John Wheeler, and Robert Dicke. Competing frameworks include relational mechanics of Gottfried Leibniz and Erwin Schroedinger’s early critiques, contrasted with background-dependent theories like those of Isaac Newton and the field-theoretic approach of James Clerk Maxwell.

Role in classical mechanics and Newtonian gravity

In Newtonian mechanics, absolute space provided a fixed inertial backdrop, a view defended by Newton in the Principia and criticized by Ernst Mach and later by Pierre-Simon Laplace’s successors. Machian ideas influenced reformulations such as Leibnizian relationalism and efforts by Ernst Mach to reinterpret inertia in terms of interactions with distant masses catalogued in surveys by Fritz Zwicky and Harlow Shapley. Attempts to render Newtonian gravity Machian include the work of Hugo von Seeliger, Carl Neumann, and later modifications like those proposed by Dennis Sciama that sought to derive inertial mass from gravitational potentials.

Mach's principle in general relativity and alternative theories

Albert Einstein was inspired by Mach while developing general relativity, corresponding with Hermann Minkowski and Marcel Grossmann about the role of matter in determining spacetime geometry. However, solutions of Einstein’s field equations — such as the Schwarzschild solution, Kerr metric, de Sitter space, and Gödel metric — reveal both Machian and non‑Machian behavior, prompting analysis by Kurt Gödel, Arthur Eddington, Felix Pirani, and John Synge. Alternative theories explicitly addressing Machian aims include scalar–tensor theories by Carl Brans and Robert Dicke, formulations by Dennis Sciama, shape dynamics advanced by Julian Barbour and Bruno Bertotti, as well as proposals in conformal gravity and teleparallel gravity explored by researchers at University of Cambridge, Caltech, and CERN.

Empirical tests and observational implications

Empirical implications connect to cosmology and tests of local inertial frames using gyroscopes, ring laser experiments, and satellite missions such as Gravity Probe B and proposals invoking Lunar Laser Ranging and Very Long Baseline Interferometry. Observations of cosmic microwave background anisotropies by COBE, WMAP, and Planck inform constraints on global mass–energy distributions influencing local inertial properties. Measurements of frame dragging around Earth and Neutron stars tested frame-dependent predictions tied to Machian ideas, with analyses contributed by Leland Wilkinson, Jim Peebles, and Bryan Gaensler.

Philosophical and foundational issues

Mach’s principle raises questions in the philosophy of physics about relationalism vs. substantivalism debated by philosophers such as Bertrand Russell, Ernest Nagel, John Nortons, and Michael Friedman. Issues include the status of absolute structures like spacetime in Immanuel Kant’s framework, the epistemology of reference frames discussed by Henri Poincaré and W.V.O. Quine, and implications for ontology debated at workshops involving scholars from Princeton University, University of Oxford, and the Institute for Advanced Study. Contemporary debates intersect with research programs in quantum gravity pursued by groups at Perimeter Institute, MIT, and ETH Zurich.

Category:Physics