Related papers: On Cremonian Dimensions Qualitatively Different fr…
The standard interpretation of the observed redshifted spectra and luminosities towards distant astrophysical objects is that the universe is expanding, an inference which is found to be consistent with other cosmological probes as well.…
An action for a string and a particle with two timelike dimensions is proposed and analyzed. Due to new gauge symmetries and associated constraints, the motion of each system in the background of the other is equivalent to effective motion…
We study the relationship between space-time-matter (STM) and brane theories. These two theories look very different at first sight, and have different motivation for the introduction of a large extra dimension. However, we show that they…
Starting from a completely general standpoint, we find the most general brane-Universe solutions for a three-brane in a five dimensional spacetime. The brane can border regions of spacetime with or without a cosmological constant. Making no…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
Pointwise tangential dimensions are introduced for metric spaces. Under regularity conditions, the upper, resp. lower, tangential dimensions of X at x can be defined as the supremum, resp. infimum, of box dimensions of the tangent sets, a…
We show that if a complete, doubling metric space is annularly linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a question of Bonk and Kleiner: if the boundary of a one-ended…
Two projective varieties are said to be Cremona equivalent if there is a Cremona modification sending one onto the other. In the last decade, Cremona equivalence has been investigated widely, and we now have a complete theory for…
I review the basis and limitations of plausible inference in cosmology, in particular the limitation that it can only provide fundamentally true inferences when the hypotheses under consideration form a set that is exhaustive. They never…
We discuss a formalism where a universe is identified with the support of a wave function propagating through space-time. As opposed to classical cosmology, the resulting universe is not a spacelike section of some space-time, but a…
The large-scale structure of the Universe is well approximated by the Friedmann equations, parametrized by several energy densities which can be observationally inferred. A natural question to ask is: How different would the Universe be if…
We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of…
A particular science is not only defined by its object of study, but also by the point of view and method under which it considers that same object. Taking space and time as an illustrative example, our main aim here is to bring out an…
The universe we see gives every sign of being composed of matter. This is considered a major unsolved problem in theoretical physics. Using the mathematical modeling based on the algebra ${\bf{T}} := {\bf{C}}\otimes{\bf{H}}\otimes{\bf{O}}$,…
While Quantum Gravity remains elusive and Quantum Field Theory retains the interpretational difficulties of Quantum Mechanics, we have introduced an alternate approach to the unification of particles, fields, space and time, suggesting that…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
By means of a simple model we investigate the possibility that spacetime is a membrane embedded in higher dimensions. We present cosmological solutions of d-dimensional Einstein-Maxwell theory which compactify to two dimensions. These…
It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the…
Duality symmetries in M--theory and string theory are reviewed, with particular emphasis on the way in which string winding modes and brane wrapping modes can lead to new spatial dimensions. Brane world-volumes wrapping around Lorentzian…
Multidimensionality of our Universe is one of the most intriguing assumption in modern physics. It follows naturally from theories unifying different fundamental interactions with gravity, e.g. M/string theory. The idea has received a great…