Gyro precession and mach's principle

The precession of a gyroscope is calculated in a nonrelativistic theory due to Harbour which satisfies Mach's principle. It is shown that the theory predicts both the geodetic and motional precession of general relativity to within factors of order 1. The significance of the gyro experiment is discussed from the point of view of metric theories of gravity and this is contrasted with its significance from the point of view of Mach's principle.     

Axioma for Mach's Mechanics

We present an axiomatic framework for what we call Mach's mechanics, inspired on the ideas by A. K. T. Assis and P. Graneau about relational mechanics. We show that, in contrast to a suggestion of these authors, Mach's principle does not need to be committed with any Weber's like gravitational force. Actually it is possible to settle an axiomatic framework for non-relativistic classical particle mechanics which incorporates Mach's principle and is still consistent with any force that obeys the Newtonian action-reaction principle. We make further criticisms concerning relational mechanics.     

Further studies in aesthetic field theory VII

In this paper we discuss the clock paradox within the framework of the general theory of relativity. It is shown that in generalthe aging asymmetry exists. We also argue that the clock paradox, according to Mach's principle, is essentially a cosmological problem.     

Cosmological models in general relativity and brans-dicke theories: a comparison

We review general relativistic and Brans-Dicke cosmological models of the early universe and for the present phase. Both theories render similar results, in general, as far as Mach's principle is concerned. There is some difference in the stability problem for the inflationary phase, and we point out how to test one theory against the other experimentally.     

Machian Mechanics with Isotropic Inertia

A nonrelativistic theory is discussed here which contains an interaction which produces isotropic inertia for anisotropic matter distributions. The interaction is a 4-body interaction and it is explained why it is necessary to have this type of interaction. The consequences of the theory are discussed for celestial mechanics including the predicted perihelion precession. Frame dragging effects are calculated and compared with other theories. Possible ways to extend the theory to noninstantaneous interactions are briefly discussed. This theory demonstrates that Mach's principle in the form considered here is not necessarily inconsistent with isotropic inertia.     

An axiomatization of general relativity

An axiomatization of the general theory of relativity is proposed. The assumed philosophical background is critical realism. None of the principles commonly considered as founding the theory, such as (a) the equality of inertial and gravitational mass, (b) the principle of equivalence, (c) the principle of general covariance, (d) the geodesic postulate, and (e) Mach's principle, are taken as axioms in our system.     

Elementary physical approach to Mach's principle and its observational basis

It is shown that Mach's principle and the general principle of relativity are logical consequences of a materialistic postulate and that general relativity implies the validity of Mach's principle for a static (or quasistatic) homogeneous and isotropic universe, spatially self-enclosed. The finite velocity of propagation of gravitational field does not imply a retardation of inertial forces due to the distant masses and therefore does not exclude the validity of Mach's principle. Similarly, the experimentally verified isotropy of inertia is compatible with this principle. The recent observational evidence of very high isotropy of the actual universe proves that the anti-Machian Gödel world model must be rejected as a nonphysical one. This suggests the possibility of a renaissance of Einstein's first cosmological model by considering-in the spirit of an older idea of Herbert Dingle-a superlargescale quasistatic universe consisting of an unknown number of statistically oscillating regions similar to our own, momentarily expanding, metagalaxy.     

Mach's principle. Part 1. Initial state of the universe the universe

The integral formulation of equations of general relativity proposed earlier as a mathematical tool for Mach's principle forbids the conventional singular cosmologies but is compatible with the de Sitter initial space.     

Mach's Principle and Model for a Broken Symmetric Theory of Gravity

We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that gravitational coupling may be the result of a spontaneous symmetry breaking. In this model matter is taken to be coupled with a metric which is different but conformally related to the metric appearing explicitly in the vacuum sector. We show that after the spontaneous symmetry breaking the resulting theory is consistent with Mach's principle in the sense that inertial masses of particles have variable configurations in a cosmological context. Moreover, our analysis allows to construct a mechanism in which the resulting large vacuum energy density relaxes during evolution of the universe.     

Machian Inertia and the Isotropic Universe

This paper addresses the origin of the forces of inertia. It proposes a Newton-Mach particle interaction force between all pairs of particles that depends on their relative acceleration and is proportional to the gravitational force between them. The motion of all objects therefore becomes directly influenced by all of the matter in the universe, as prescribed by Mach's principle. The effect of the observed hierarchical structure of the universe is considered and is used to ensure that the inertial force on an object is finite and isotropic. The instantaneous matter interaction force is justified and both Einstein's and Mach's objections to a Newtonian framework are discussed and shown to be absorbed by the proposed universal law of inertia.     

Translational inertial dragging

The electrical field inside a uniformly charged, slowly accelerated spherical shell is calculated. The result is used to find the inertial translational dragging field inside a slowly accelerated spherical shell of dust particles, according to the linearized gravitational field equations. The relevance of this effect in connection with Mach's principle and the principle of relativity is discussed.     

Mach's principle,mass, and the fine structure constant

A modified form of Mach's principle is proposed, and its consequences are discussed.Work supported in part by the U.S. Atomic Energy Commission.     

Classical and relativistic forces of inertia

It is shown that — in contrast to the classical physics and special relativity — the self-consistency of general relativity requires that the forces of inertia follow unambiguously from the field equations as inductive gravitational effects of the cosmic matter and that this requirement is perfectly satisfied, without supplementary hypotheses, for the Einstein universe, in full agreement with Mach's principle.     

Some remarks on nonlocal field theory and space-time quantization

From the point of view that the charge and mass of an electron is of dynamical origin and quantization of charge in units ofe is related to the space-time quantization as developed in an earlier paper, we here show that it is possible to consider that the internal space within the elementary domain of the quantized space-time world is not governed by Lorentz invariance. This helps us to develop a consistent theory of nonlocal fields for extended particles where the infinite mass degeneracy is avoided. Moreover, this ensures the convergence of nonlocal field theories and suggests that massless particles like photons and neutrinos, though they may be taken to be of extended structure, will appear only as point particles in the physical world. In this picture, Lorentz invariance appears to be a consequence of the distribution of matter and energy in the Universe, and this may be taken to be another interpretation of Mach's principle.     

A background-dependent approach to the theory of gravitation

On the basis of a Machian view of nature we find a covariant formulation of Newton's gravitational equation in a general frame which satisfies the requirements (i) of being singular if the density of mass is zero everywhere and (ii) of depending on the parallel transport of the four-momentum density of matter (from the three-space point in which it is defined to any other three-space point, at any fixed time) in such a way that it incorporates the idea that the frame has to be fixeddirectly in connection with the distribution and motion of matter. In Paper II we will use such an equation as starting point in order to find relativistic gravitational equations which are supposed to hold in any conceivable universe, describe a purely geometrical theory of gravitation, and explicitly incorporate Mach's principle.     

Nonlocal forces of inertia in cosmology

This paper reviews the origin of inertia according to Mach's principle and Weber's law of gravitation. The resulting theory is based on simultaneous nonlocal gravitational interactions between particles in the solar system and others in the remote universe beyond the Milky Way galaxy. It explains the precession of the perihelion of Mercury. A most important implication of the Mach-Weber theory of the force of inertia is the necessity for a large amount of uniformly distributed matter in the galactic universe. This matter could be the source of the cosmic background radiation. Nonlocal inertia forces are compatible with a static universe and also with an expanding universe but the latter would demand slow changes in the mass of particles and the gravitational constant.     

Mach's Principle revisited

In this essay, we review first Mach's Principle and then the notion of an isotropic singularity. We give evidence to support a formulation of the cosmological part of Mach's Principle as the requirement that the initial singularity of space-time is an isotropic singularity, and we suggest that Mach's Principle may become a theorem of quantum gravity.     

On the Foundation of the Principle of Relativity

The relation of the special and the general principle of relativity to the principle of covariance, the principle of equivalence and Mach's principle, is discussed. In particular, the connection between Lorentz covariance and the special principle of relativity is illustrated by giving Lorentz covariant formulations of laws that violate the special principle of relativity: Ohm's law and what we call Aristotle's first and second laws. An Aristotelian universe in which all motion is relative to absolute space is considered. The first law: a free particle is at rest. The second law: force is proportional to velocity. Ohm's law: the current density is proportional to the electrical field strength. Neither of these laws fulfills the principle of relativity. The examples illustrate, in the context of Lorentz covariance and special relativity, Kretschmann's critique of founding Einstein's general principle of relativity on the principle of general covariance. A modification of the principle of covariance is suggested, which may serve as a restricted criterium for a physical law to satisfy Einstein's general principle of relativity. Other objections that have been raised to the validity of Einstein's general principle of relativity are based upon the preferred state of inertial frames in the general, as well as in the special theory, the existence of tidal effects in true gravitational fields, doubts as to the validity of Mach's principle, whether electromagnetic phenomena obey the principle, and, finally, the anisotropy of the cosmic background radiation. These objections are reviewed and discussed.     

Mach's principle,relative motion,and fundamental numbers of physics

Mach's principle is discussed as a fundamental statement on kinematics, and an apparent contradiction is identified in the Lorentz-Minkowski form of the inertial metric. To resolve the incompatibility, length is redefined so that the speed of light is a field-dependent variable, although still constant for all inertial observers at a point in space-time. Gravitational theories with variableG are considered, and it is shown that a redefinition of length and time results in constantG and variablec.     

Test of the gravitomagnetic field via laser-ranged satellites

We describe a new experiment to measure the gravitomagnetic field of the Earth. This field, a consequence of the general relativistic formulation of Mach's principle (WEM—Wheeler-Einstein-Mach principle), has never been detected. The idea is to measure the Lense-Thirring precession of the nodal lines of two laser-ranged satellites with supplementary inclinations. In this way it is possible to separate the relativistic nodal precession from the classical nodal precession due to the multipole moments of the Earth.