There is a fundamental issue in relativity theory: if all motion is relative, how can we measure the inertia of a body? We must measure the inertia with respect to something else. But what if we imagine a particle completely on its own in the universe? We might hope to still have some notion of its state of motion. Mach's principle is sometimes interpreted as the statement that such a particle's state of motion has no meaning in that case. In Mach's words, the principle is embodied as follows:
Albert Einstein seemed to view Mach's principle as something along the lines of: In this sense, at least some of Mach's principles are related to philosophical
holism. Mach's suggestion can be taken as the injunction that gravitation theories should be
relational theories. Einstein brought the principle into mainstream physics while working on
general relativity. Indeed, it was Einstein who first coined the phrase ''Mach's principle''. There is much debate as to whether Mach really intended to suggest a new physical law since he never states it explicitly. The writing in which Einstein found inspiration was Mach's book
The Science of Mechanics (1883, tr. 1893), where the philosopher criticized
Newton's idea of
absolute space, in particular the argument that Newton gave sustaining the existence of an advantaged reference system: what is commonly called "Newton's
bucket argument". In his
Philosophiae Naturalis Principia Mathematica, Newton tried to demonstrate that one can always decide if one is rotating with respect to the absolute space, measuring the apparent forces that arise only when an absolute rotation is performed. If a bucket is filled with water, and made to rotate, initially the water remains still, but then, gradually, the walls of the vessel communicate their motion to the water, making it curve and climb up the borders of the bucket, because of the centrifugal forces produced by the rotation. This
experiment demonstrates that the centrifugal forces arise only when the water is in rotation with respect to the absolute space (represented here by the earth's reference frame, or better, the distant stars) instead, when the bucket was rotating with respect to the water no centrifugal forces were produced, this indicating that the latter was still with respect to the absolute space. Mach, in his book, says that the bucket experiment only demonstrates that when the water is in rotation with respect to the bucket no centrifugal forces are produced, and that we cannot know how the water would behave if in the experiment the bucket's walls were increased in depth and width until they became leagues big. In Mach's idea this concept of absolute motion should be substituted with a total relativism in which every motion, uniform or accelerated, has sense only in reference to other bodies (
i.e., one cannot simply say that the water is rotating, but must specify if it's rotating with respect to the vessel or to the earth). In this view, the apparent forces that seem to permit discrimination between relative and "absolute" motions should only be considered as an effect of the particular asymmetry that there is in our reference system between the bodies which we consider in motion, that are small (like buckets), and the bodies that we believe are still (the earth and distant stars), that are overwhelmingly bigger and heavier than the former. This same thought had been expressed by the philosopher
George Berkeley in his
De Motu. It is then not clear, in the passages from Mach just mentioned, if the philosopher intended to formulate a new kind of physical action between heavy bodies. This physical mechanism should determine the inertia of bodies, in a way that the heavy and distant bodies of our universe should contribute the most to the inertial forces. More likely, Mach only suggested a mere "redescription of motion in space as experiences that do not invoke the term
space". What is certain is that Einstein interpreted Mach's passage in the former way, originating a long-lasting debate. Most physicists believe Mach's principle was never developed into a quantitative physical theory that would explain a mechanism by which the stars can have such an effect. Mach himself never made his principle exactly clear. Although Einstein was intrigued and inspired by Mach's principle, Einstein's formulation of the principle is not a fundamental assumption of
general relativity, although the
principle of equivalence of gravitational and inertial mass is most certainly fundamental. == Mach's principle in general relativity ==