Mach's Principle
Mach's principle is the proposal that inertia is not a property a body possesses on its own, but an effect of that body's relation to all the other matter in the universe — so that local inertial frames are determined by the distant stars rather than by absolute space.
The standard account
The idea originates with the Austrian physicist and philosopher Ernst Mach (1838–1916), whose Die Mechanik in ihrer Entwicklung (1883) attacked Newton's use of absolute space. Newton had argued from his rotating-bucket experiment that the curved surface of the water reveals rotation with respect to space itself. Mach replied that the experiment shows nothing of the kind: the water rotates with respect to the fixed stars, and nobody has performed — or could perform — the experiment with the rest of the universe removed. On Mach's reading, inertial resistance is a relational quantity, produced by the surrounding masses.
Einstein was strongly influenced by this argument and coined the term "Mach's principle" in 1918, hoping General Relativity would embody it. It does so only partially. General relativity does predict genuine relational effects — the Lense–Thirring frame dragging of 1918, measured by the LAGEOS satellites and by Gravity Probe B in 2011 — but it also admits solutions that are plainly non-Machian, notably Gödel's 1949 rotating universe and the empty Minkowski spacetime, in which inertial frames exist with no matter at all to define them. Brans and Dicke proposed their scalar–tensor theory in 1961 explicitly to make gravitation more Machian by tying the gravitational "constant" to the mass distribution; solar-system tests have since pushed its coupling parameter to values where it is observationally close to general relativity.
There is no agreed formulation of the principle. Physicists have catalogued a dozen or more inequivalent statements travelling under the same name, and whether general relativity satisfies any of them remains genuinely disputed inside mainstream relativity, not only outside it.
On this wiki
Mach's principle is a live thread here rather than a historical curiosity, and it is one of the few points where dissident and mainstream research overlap heavily. See Category:Mach's Principle for the full collection.
The most fully developed programme is Andre K T Assis's relational mechanics, which implements Mach's principle quantitatively using Weber's velocity-dependent force law. His Relational Mechanics and Implementation of Mach's Principle with Weber's Gravitational Force (2014) derives inertia from the gravitational interaction of a body with the distant matter of the cosmos, so that Newton's second law becomes a theorem rather than an axiom; The Relationship Between Mach's Principle and the Principle of Physical Proportions (2002) sets out the underlying methodological commitment that only ratios of quantities are physically meaningful. Jorge A Guala-Valverde examines the resulting notion of mass in Inertial Mass in Mach-Weber-Assis Theory (Apeiron, 1999).
Amitabha Ghosh pursues a related but distinct route in Origin of Inertia: Extended Machs Principle and Cosmological Consequences (2000), adding a velocity-dependent inertial induction term to Newtonian gravity and drawing out cosmological consequences from it. Mendel Sachs, who worked on deriving inertia from within general relativity itself, is represented by Mach's Principle and the Origin of Inertia (2003), the proceedings of the Kharagpur workshop he helped shape. Julian B Barbour's edited volume Mach's Principle: From Newton's Bucket to Quantum Gravity (1995) is the standard scholarly survey and is catalogued here as well.
Several contributors treat Mach's principle as a rival to relativity rather than a component of it. Lars Wåhlin argues the case directly in Mach's Principle vs. Einstein's Relativity (Galilean Electrodynamics, 1993), tying it to the interpretation of cosmic redshifts. Robert D Sadykov applies it to the classic test of general relativity in Mach's Principle and Mercury's Perihelion Shift (2009). Peter Graneau, whose work on Ampère's force law runs through this wiki, connects the principle to nonlocality in Mach's Principle & Nonlocal Mass Interactions (2009).
There are also proposals for testing it. Hoff Lu and Shi-Ming Wang propose a direct observational test using the transverse Doppler effect in A Direct Test of Mach's Principle (Galilean Electrodynamics, 1995). James F Woodward takes the principle in an experimental and propulsive direction in Mach's Principle, Mass Fluctuations, And Rapid Spacetime Transport (1998), arguing that Machian mass fluctuations are physically real and manipulable. David F Roscoe reports that a Machian starting point led him to new phenomenology in spiral galaxy discs in A Perspective on Mach's Principle and the Consequent Discovery of Major New Phenomenology in Spiral Discs (2002) — a result that bears directly on the Dark Matter question. Harry E Mongold takes up the philosophical genealogy in Was Einstein a Berkeleian? (1979).