arXiv subjects
Publications and source records attributed to Paul S. Wesson.
A new method involving the effective wave function is used to define the mass of a particle in a standard five-dimensional extension of general relativity. The mass is inversely proportional to the magnitude of the scalar field of the extra dimension. Since the scalar field is global and depends on the coordinates, this definition for the particle mass agrees with Machs Principle.
We give a new, wave-like solution of the field equations of five-dimensional relativity. In ordinary three-dimensional space, the waves resemble de Broglie or matter waves, whose puzzling behaviour can be better understood in terms of one or more extra dimensions. Causality is appropriately defined by a null higher-dimensional interval. It may be possible to test the properties of these waves in the laboratory.
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such theories smoothly embed general relativity, ensuring recovery of the latter's observational support. When the embedding of spacetime is carried out in accordance with Campbell's theorem, the resulting 5D theory naturally explains the origin of classical matter and vacuum energy. Also, constraints on the equations of motion near a high-energy surface or membrane in the 5D manifold lead to quantization and quantum uncertainty. These are major returns on the modest investment of one extra dimension. Instead of fruitless bickering about whether it is possible to "see" the fifth dimension, it is suggested that it be treated on par with other concepts of physics, such as time. The main criterion for the acceptance of a fifth dimension (or not) should be its usefulness.
The cosmological constant (lambda) of general relativity is a natural consequence of embedding Einstein's theory in a five-dimensional theory of the type needed for unification. The exact 5D solution for lambda less than 0 shows waves in ordinary 3D space with properties similar to those of de Broglie or matter waves. Here the dispersion relation is derived for matter waves in a toy two-phase model, where regions with lambda less than 0 and lambda greater than 0 average on the large scale to lambda = 0, thus providing in principle a resolution of the cosmological-constant problem. A striking result of the analysis is that the dispersion relation is bimodal, with a well-defined window of high-frequency transmission which effectively defines the speed of light.
In cosmologies with more than four dimensions, of the type required for unification, it is possible for signals to have velocities in excess of that of light. Using a five-dimensional model which otherwise agrees with observations, two subjects are reviewed: (a) An exact solution of the field equations which describes a 4D spacetime with a large cosmological constant and waves travelling in ordinary 3D space with velocities exceeding lightspeed. (b) An example where the 4D interval or proper time is modulated by the systematic variation of the scalar field associated with the fifth dimension, providing a simple signalling method. These and related consequences of higher-dimensional cosmology have significant implications for astrophysics, and especially the Search for Extraterrestrial Intelligence.
When the cosmological "constant" is derived from modern five-dimensional relativity, exact solutions imply that for small systems it scales in proportion to the square of the mass. However, a duality transformation implies that for large systems it scales as the inverse square of the mass.
To better understand the scalar field typical of higher-dimensional extensions of general relativity, we analyse three classes of solutions. In all, the field equation for the extra dimension resembles the Klein-Gordon equation, and we evaluate the strength of the source. Our results show that the scalar field is coupled to matter, and may be regarded as generating it.
In unified field theories with more than four dimensions, the form of the equations of physics in spacetime depends in general on the choice of coordinates in higher dimensions. The reason is that the group of coordinate transformations in (say) five dimensions is broader than in spacetime. This kind of gauge dependence is illustrated by two examples: a cosmological model in general relativity and a matter wave in quantum theory. Surprisingly, both are equivalent by coordinate transformations to flat featureless five-dimensional space. This kind of transformity is of fundamental significance for the philosophy of physics.
Replacing 4D Minkowski space by 5D canonical space leads to a clearer derivation of the main features of wave mechanics, including the wave function and the velocity of de Broglie waves. Recent tests of wave-particle duality could be adapted to investigate whether de Broglie waves are basically 4D or 5D in nature.
Five-dimensional relativity as an extension of general relativity has field equations that simplify considerably given the adoption of a new gauge. The result is a scalar field governed by the Klein-Gordon equation, in an empty spacetime with a cosmological constant governed by Einstein's equations. The main application is to the properties of massive particles in a vacuum-dominated universe.
Astronomy is a precise and relatively simple science because objects accelerate in a gravitational field at the same rate, irrespective of their composition. Galileo knew this, and Einstein took it as the basis for general relativity. Surprisingly, it is also a consequence of new theories that use a fifth dimension.
As an example of the unification of gravitation and particle physics, an exact solution of the five-dimensional field equations is studied which describes waves in the classical Einstein vacuum. While the solution is essentially 5D in nature, the waves exist in ordinary 3D space, and may provide a way to test for an extra dimension.
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for spherically-symmetric systems, in a particularly convenient form that aids their application to astrophysics. New ideas in research are also outlined, notably involving extra dimensions.
Since the 5D canonical metric embeds all 4D vacuum solutions of Einstein's equations, I review its application to the cosmological 'constant', quantized particles, deBroglie waves, scalar fields and wave-particle duality. There are several ways to ra-tionalize these things using an extra dimension. A possible explanation of wave-particle duality is that an observed particle manifests two isometries of flat 5D space in different 4D ways, one with waves and one without.
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 particle has a local cosmological 'constant' whose magnitude is proportional to the square of the mass.
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.
The basic quasi-Schwarzschild 5D objects known as solitons have a long history, which is reviewed. Then some material is added, leading to the inference that a soliton is a singularity in the geometry which represents a bivalent source of gravitational and scalar mass.
In 5D, I take the metric in canonical form and define causality by null-paths. Then spacetime is modulated by a factor equivalent to the wave function, and the 5D geodesic equation gives the 4D Klein-Gordon equation. These results effectively show how general relativity and quantum mechanics may be unified in 5D.