Mach's principle

"... the theory of relativity makes it appear probable that Mach was on the right road in his thought that inertia depends upon a mutual action of matter. For we shall show in the following that, according to our equations, inert masses do act upon each other in the sense of the relativity of inertia, even if only very feebly. What is to be expected along the line of Mach's thought? 1. The inertia of a body must increase when ponderable masses are piled up in the neighborhood. 2. A body must experience an accelerating force when neighbouring masses are accelerated, and, in fact, the force must be in the same direction as that acceleration. 3. A rotating hollow body must generate inside itself a "Coriolis field," which deflects moving bodies in the sense of the rotation, and a radial centrifugal field as well. We shall now show that these three effects, which are to be expected in accordance with Mach's ideas, are actually present according to our theory, although their magnitude is so small that confirmation of them by laboratory experiments is not to be thought of."

"Mach's profound critique of the foundations of Newtonian mechanics played a key role in Einstein's development of . Mach's principle has also guided other developments in gravitation theory such as the ... It has inspired interesting experiments, such as the ... and continues to be of current interest ... Mach identified the essential epistemological shortcoming of the Newtonian foundations of physics, namely, that the intrinsic state of a particle in Newtonian mechanics, i.e. its mass, has no immediate connection with its extrinsic state in space and time, i.e. its position and velocity. Mach's observation can be re-stated in terms of the a priori independence of position (x) and momentum (p) of a particle in Newtonian mechanics."

"Most terrestrial motions are of such brief duration and extent, that it is wholly unnecessary to take into account the earth's rotation and the changes of its progressive velocity with respect to the celestial bodies. This consideration is found necessary only in the case of projectiles cast great distances, or in the case of the vibrations of , and in similar instances. When now Newton sought to apply the mechanical principles discovered since Galileo's time to the planetary system, he found that, so far as it is possible to form any estimate at all thereof, the planets, irrespectively of dynamic effects, appear to preserve their direction and velocity with respect to bodies of the universe that are very remote and as regards each other apparently fixed, the same bodies moving on the earth do with respect to the fixed bodies of the earth. The comportment of terrestrial bodies with respect to the earth is reducible to the comportment of the earth with respect to the remote heavenly bodies. If we were to assert that we knew more of moving objects than this their last-mentioned, experimentally-given comportment with respect to the celestial bodies, we should render ourselves culpable of a falsity. When, accordingly, we say, a body preserves unchanged its direction and velocity in space, our assertion is nothing more or less than an abbreviated reference to the entire universe. The use of such an abbreviated expression is permitted the original author of the principle, because he knows, that as things are no difficulties stand in the way of carrying out its implied directions. But no remedy lies in his power, if difficulties of the kind mentioned present themselves; if, for example, the requisite, relatively fixed bodies are wanting."

"The so-called Mach's Principle is surely one of the most elusive concepts in physics. On one hand, Machian aspects have been present either explicitly or implicitly in theoretical astronomy, general physics, and dynamics from their Greek infancy up the present day ... On the other hand, most of practical physics is done, and successfully done, without ever thinking of the 'deep questions' connected with Mach's Principle. (The situation is similar in quantum theory, which functions extremely well using established prescriptions notwithstanding deep and unresolved questions about its interpretation, its measuring process, and its classical limit.)"