arXiv subjects
Publications and source records attributed to Paul S. Wesson.
Campbell's theorem enables the embedding of 4D anti-deSitter space in 5D canonical space, so a particle becomes a wave in the extra dimension, running through spacetime. This model of wave-particle duality provides a new approach to particle mass.
When the proper time of general relativity is adjusted to reflect the possible existence of higher dimensions, small dynamical effects appear in spacetime of the sort usually associated with the cosmological constant, Hubble's Law and Heisenberg's relation.
Einstein theory can be embedded in Kaluza-Klein theory, and in particular all 4D vacuum solutions can be embedded in 5D (pure) canonical space where spacetime is independent of the extra coordinate. The uniqueness of 5D canonical space is quickly reproven, and its history and implications briefly reviewed. For 4D anti-deSitter space, the 5D space involves a wave running around spacetime, with an associated particle that has a local value of the cosmological 'constant' proportional to the square of the mass.
Astronomically, there are viable mechanisms for distributing organic material throughout the Milky Way. Biologically, the destructive effects of ultraviolet light and cosmic rays means that the majority of organisms arrive broken and dead on a new world. The likelihood of conventional forms of panspermia must therefore be considered low. However, the information content of dam-aged biological molecules might serve to seed new life (necropanspermia).
When four-dimensional general relativity is embedded in an unconstrained man-ner in a fifth dimension, the physical quantities of spacetime can be interpreted as geometrical properties related to the extra dimension. It has become widespread to view the ten Einstein equations and the source terms of the energy-momentum tensor in this way. We now assign physical meanings to the other five equations involved. The scalar field acts like gravity, but concerns inertial as opposed to gravitational mass. The other four equations are conservation laws for 4D dynamics, but where the mass of a test particle is related to a local value of the cosmological 'constant'. Ways of testing these identifications are suggested.
The main results are reviewed of relating the scalar field of noncompactified Kaluza-Klein gravity to the Higgs field of particle physics. The embedding of 4D spacetime in a 5D manifold can result in a variable cosmological 'constant' and particle masses tiny compared to the Planck value.
The group of coordinate transformations for 5D noncompact Kaluza-Klein theory is broader than the 4D group for Einstein's general relativity. Therefore, a 4D quantity can take on different forms depending on the choice for the 5D coordinates. We illustrate this by deriving the physical consequences for several forms of the canonical metric, where the fifth coordinate is altered by a translation, an inversion and a change from spacelike to timelike. These cause, respectively, the 4D cosmological 'constant' to become dependent on the fifth coordinate, the rest mass of a test particle to become measured by its Compton wavelength, and the dynamics to become wave-mechanical with a small mass quantum. These consequendes of 5D covariance -- whether viewed as positive or negative -- help to determine the viability of current attempts to unify gravity with the interactions of particles.
We review the idea, due to Einstein, Eddington, Hoyle and Ballard, that time is a subjective label, whose primary purpose is to order events, perhaps in a higher-dimensional universe. In this approach, all moments in time exist simultaneously, but they are ordered to create the illusion of an unfolding experience by some physical mechanism. This, in the language of relativity, may be connected to a hypersurface in a world that extends beyond spacetime. Death in such a scenario may be merely a phase change.
All objects in 4D spacetime may in principle travel on null paths in a 5D mani-fold. We use this, together with a change in the extra coordinate and the signature of the metric, to construct a simple model of a classical universe and a quantized particle. There are notable implications for the Weak Equivalence Principle and the cosmological constant, and for astrophysics.
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 general relativity, and leads to several new effects which can be tested.
Massive particles on timelike paths in spacetime can be viewed as moving on null paths in a higher-dimensional manifold. This and other consequences follow from the use of Campbell's theorem to embed 4D general relativity in non-compactified 5D Kaluza-Klein theory. We now show that it is possible in principle to obtain the standard rule for quantization in 4D from the canonical metric with null paths in 5D. Particle mass can be wavelike, as suggested originally by Dirac, and other 4D/5D consequences are outlined.
We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of book-keeping device, their number increasing as required by advances in physics. The world almost certainly has more than the four dimensions of space and time, but the introduction of the fifth and higher dimensions requires a careful approach wherein known results are embedded and new ones are couched in the most productive manner.
By using a massless scalar field we examine the effect of an extra dimension on black hole radiation. Because the equations are coupled, we find that the structure of the fifth dimension (as for membrane and induced-matter theory) affects the nature of the radiation observed in four-dimensional spacetime. In the case of the Schwarzschild-de Sitter solution embedded in a Randall-Sundrum brane model, the extension of the black hole along the fifth dimension looks like a black string. Then it is shown that, on the brane, the potential barrier surrounding the black hole has a quantized as well as a continuous spectrum. In principle, Hawking radiation may thus provide a probe for higher dimensions.
Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle becomes a geometrical symmetry which can be broken, perhaps at a level detectable by new tests in space.
Using exact solutions, we show that it is in principle possible to regard waves and particles as representations of the same underlying geometry, thereby resolving the problem of wave-particle duality.
The Campbell-Magaard theorem is widely seen as a way of embedding Einstein's 4D theory of general relativity in a 5D theory of the Kaluza-Klein type. We give a brief history of theorem, present a short account of it, and show that it provides a geometrical frame for new physics related to the unification of the forces. Anderson's recent vituperative attack on Campbell's theorem (gr-qc/0409122)is errant.
We present an exact solution to the Einstein field equations which is Ricci and Riemann flat in five dimensions, but in four dimensions is a good model for the early vacuum-dominated universe.
We review the implications of modern higher-dimensional theories of gravity for astrophysics and cosmology. In particular, we discuss the latest developments of space-time-matter theory in connection with dark matter, particle dynamics and the cosmological constant, as well as related aspects of quantum theory. There are also more immediate tests of extra dimensions, notably involving perturbations of the cosmic 3K microwave background and the precession of a supercooled gyroscope in Earth orbit. We also outline some general features of embeddings, and include pictures of the big bang as viewed from a higher dimension.