A Machian definition of particle mass in higher-dimensional gravity

Mach's Principle is usually taken to mean that the mass of a particle as measured locally is determined in some way by the other matter in the universe. This is difficult to formalize in 4D,but is feasible in 5D if the scalar potential of non-compactified Kaluza-Klein theory is interpreted as an inertial field. We therefore review 5D space-time-matter theory, but take the local particle mass to be defined by the integral of a global scalar field. This approach smoothly embeds...

We briefly discuss the current status of Mach's principle in general relativity and point out that its last vestige, namely, the gravitomagnetic field associated with rotation, has recently been measured for the earth in the GP-B experiment. Furthermore, in his analysis of the foundations of Newtonian mechanics, Mach provided an operational definition for inertial mass and pointed out that time and space are conceptually distinct from their operational definitions by means of...

The new interpretation of Mach's principle of mass of a particle being a measure of the interactions of this particle with all other gravitating particles inside its causal spheres is introduced. It is shown that within some alternative model of gravitation that incorporates this principle, the Machian influence of the universe can reduce Planck's scale to the electro-weak scale and the large number that is needed to explain the hierarchy between the scales is the amount of g...

I give metrics and equations of motion in 5D general relativity, and use the conservation of momentum and conformal transformations to study the possible variability of particle masses and the cosmological 'constant'. It is feasible that all particles are photon-like and travel on null paths in 5D, that massive particles are perturbations of the extra dimension which intrude into 4D, and that the cosmological 'constant' is a 5D / 4D gauge term. In the simplest case, a particl...

Cosmological solutions of Einstein equation for a \mbox{5-dimensional} space-time, in the case of a dust-filled universe, are presented. With these solutions we are able to test a hypothetical relation between the rest mass of a particle and the $5^{\rm th}$ dimension. Comparison with experiment strongly refutes the implied dependence of the rest mass on the cosmological time.

Mach's principle is surely one of those tantalizingly beautiful concepts in physics which remain elusive. Though General Relativity (GR) was conceived in the spirit of realizing it, the theory failed to fulfill this expectation. Here a study on the implications of imposing Mach's principle on GR with an insight that spacetime has no independent existence without a material background, is presented. This inclusion of the principle in GR turns out to be unexpectedly rewarding...

Gravity does not provide any scale for matter properties. We argue that this is also the implication of Mach's hypothesis of the relativity of inertia. The most general spacetime compatible with this property of gravity is that admitting three, independent spatial homothetic Killing vectors generating an arbitrary function of each one of the three spatial coordinates. The matter properties for such a spacetime are (spatially) arbitrary and the matter generating the spacetime ...

Mach's Principle says that a particle's inertia is due to some interaction of that particle with all the other masses in the universe. Here we explore the possibility of the gravitational interaction energy of the background quantum vacuum energy playing the role of a global Higg's field (described by a varying cosmological constant) entirely contributing to the local inertial masses of particles in the spirit of Mach's principle.

I outline a model where a massive particle in 4D spacetime follows a null (photon-like) path in 5D canonical (super-spherically-symmetric) space. This leads to wave-particle duality and quantization, along with other effects which show that it is possible to unify general relativity and wave mechanics in a simple fashion, given an extra dimension.

A non-relativistic theory of inertia based on Mach's principle is presented as has been envisaged but not achieved by Ernst Mach in 1872. Central feature is a space-dependent, anisotropic, symmetric inert mass tensor.