# Mach Principle

Also found in: Wikipedia.

## Mach principle

[′mäk ‚prin·sə·pəl]
(relativity)
The principle that the motion of a particle is only meaningful when referred to the rest of the matter in the universe; this motion is thus determined by the distribution of this matter and is not an intrinsic property of an absolute space.

## Mach Principle

the assertion that the inertial properties of a body arise from the interaction of that body with infinitely distant large masses of the universe. (This is one of the simplest formulations of the Mach principle, which often differ significantly from one another.) All formulations of the Mach principle, from the “experimental principles” advanced by E. Mach in The Science of Mechanics (1883) to the current ones, develop or refine the concepts of inertia, mass, and inertial frame of reference and relate them to the properties of the universe as a whole. Mach sought to give the laws of mechanics such a form that they would be independent not only of uniform and rectilinear translational motion of the frame of reference (this had been already done by Galileo) but also of its rotation.

Rejecting Newtonian concepts of absolute space, absolute time, absolute motion, and mass as a measure of the quantity of substance, Mach made the first attempt to construct a mechanics based on the fact that only relative motions, time intervals, velocities, and accelerations are experimentally observable. Consequently, according to Mach, the motions of bodies (including accelerations) can be determined only with respect to other bodies. Mach proposed to define the accelerations of bodies with respect to the center of mass of the bodies that fill the entire universe: if it is assumed that there are large masses that are sufficiently (“infinitely”) distant from the observed body, then a fixed frame of reference (an inertial frame of reference after Newton) may be related to their center with a high degree of accuracy. The uniform and rectilinear motion of a body in such a frame means that it is possible to neglect the effect of masses located at finite distances as compared with the effect of the infinitely distant bodies.

The Mach principle played an important heuristic role in the building up of the general theory of relativity by A. Einstein. Einstein subsequently rejected the Mach principle because it did not satisfy the gravitational theory that he had developed. However, the Mach principle continues to be used extensively in theoretical works whose goal is the elucidation of the structure and properties of the universe as a whole. Here, the problem of coordinating the principle with the conclusions of cosmology, originating either in Einstein’s general theory of relativity or in other gravitational theories, encounters serious contradictions; the latter suggest that the Mach principle is either invalid or experimentally unverifiable. The most important contradictions are (1) the noncoincidence in arbitrary cosmological models of the locally inertial frame of reference with the frame of reference of the “fixed stars”; (2) the existence of nontrivial solutions of the gravitational equations in a vacuum, which signify that bodies have inertia relative to empty space; and (3) the ambiguity of the correspondence between the gravitational field (and, by virtue of the equivalence principle, the field of inertial forces) and the distribution of masses throughout the universe. One of the major contradictions between the Mach principle and observational data is the absence of anisotropy of masses on the earth, despite the asymmetric positioning of the solar system in our galaxy.

### REFERENCES

Zel’dovich, Ia. B., and M. Novikov. Reliativistskaia astrofizika. Moscow, 1967.
Gravitatsiia i otnositel’nost’. Edited by H. Chiu and W. Hoffman. Moscow, 1965. (Translated from English.)
Reinhard, M. “Mach’s Principle: A Critical Review.” Zeitschrift fur Naturforschung, 1973, vol. 28a, nos. 3-4.

N. P. KONOPLEVA

Mentioned in ?
References in periodicals archive ?
This proves that gravity by the entire expanding universe is the root cause of inertia, which is evidence for the intuitive Mach principle [1-4].
"The scientific parallel to Transtromer's metaphor of 'the great unknown' he holds steady can well be the so-called Mach principle, which states that every single inertial movement, let us say the spinning of a whirligig, is dependent on the total mass of matter in the universe.
When the author was reading a paper [19] about the Mach principle and Brans-Dicke theory of gravity to develop his electric redshift mechanism in accord with the five-dimensional fully covariant Kaluza-Klein theory with a scalar field [20], an idea that the universe is a black hole came to his mind [21].
According to the Mach principle, the inertia of an object re sults as the interaction by the rest of the universe.
In [24], Sciama developed a theoretical model to incorporate the Mach principle and obtained [GM.sub.EF] /([c.sup.2] [R.sub.EF]) ~ 1, where [M.sub.EF] and [R.sub.EF] are the effective mass and radius of the universe (see also [19, 25]).
Principle II (extended Mach principle) shows that the stars and galaxies of the universe are essential to the laws of Nature and to the existence of the Earth and ourselves.
This is called the extended Mach principle, after Ernst Mach who suggested in the nineteenth century that the inertia of any body is caused by its interaction with the rest of the universe.
An aether theory, the extended Mach principle as well as pushing gravity, takes the line that smaller particles (like gravitons) that we cannot yet detect do exist.
The tired light model can be combined with an aether theory, the extended Mach principle and pushing gravity.
Thus, the Mach principle establishes a) that the Universe-as-a-whole influences the mechanical behavior of every body in the Universe, and b) that one of mechanical properties, namely inertia is not innate in a body, but arises from its relation ...
The consideration made above leads to the conclusion that the part (a) of Mach principle for the human thinking, i.
The question remains whether the part (b) of Mach principle can be generalized correspondingly?--that there is only one human being in the whole Universe.

Site: Follow: Share:
Open / Close