Related papers: Why 3 + 1 metric rather than 4 + 0 or 2 + 2?
Position and momentum enter at the same level of importance in the formulation of classical or quantum mechanics. This is reflected in the invariance of Poisson brackets or quantum commutators under canonical transformations, which I regard…
In the History of Ideas, a succession of philosophical and scientific achievements, concerning the concept of space and its dimensionality, were essential to contribute, after a long period, to the theoretical possibility of thinking…
In the context of metric structures introduced by Ben Yaacov, Berenstein, Henson, and Usvyatsov, we exhibit an explicit encoding of metric structures in countable signatures as pure metric spaces in the empty signature, showing that such…
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…
For any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by a non-zero element are shown to form an invariant of A, called its double sign. The…
A physical theory of the world is presented under the unifying principle that all of nature is laid out before us and experienced through the passage of time. The one-dimensional progression in time is opened out into a multi-dimensional…
Minkowski's concept of a four-dimensional physical space is a central paradigm of modern physics. The three-dimensional Maxwellian electrodynamics is uniquely generalized to the covariant four-dimensional form. Is the (1+3) decomposition of…
Finsler spacetimes have become increasingly popular within the theoretical physics community over the last two decades. Because physicists need to use pseudo-Finsler structures to describe propagation}of signals, there will be nonzero null…
While our natural intuition suggests us that we live in 3D space evolving in time, modern physics presents fundamentally different picture: 4D spacetime, Einstein's block universe, in which we travel in thermodynamically emphasized…
A metric space is said to be strongly rigid if no positive distance is taken twice by the metric. In 1972, Janos proved that a separable metrizable space has a strongly rigid metric if and only if it is zero-dimensional. In this paper, we…
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…
Why would anyone wish to generalize the already unappetizing subject of rigid body motion to an arbitrary number of dimensions? At first sight, the subject seems to be both repellent and superfluous. The author will try to argue that an…
We study some aspects when one consider the existence of one extra-dimension in addition to a non-commutative space-time. We present here two different examples, where the first one provides a scenario were it is possible to relate the…
We present some interesting observations on the 3x+1 problem. We propose a new algorithm which eliminates certain steps while we check the action of 3x+1 procedure on a number. Also, we propose a reason why many numbers follow a similar…
Pairs of metrics in a two-dimensional linear vector space are considered, one of which is a Minkowski type metric. Their simultaneous diagonalizability is studied and canonical presentations for them are suggested.
The metric dimension of a graph is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. Bailey and Meagher obtained an upper bound on the…
Any three-dimensional Riemannian metric can be locally obtained by deforming a constant curvature metric along one direction. The general interest of this result, both in geometry and physics, and related open problems are stressed.
Paralleling the formal derivation of general relativity as a flat spacetime theory, we introduce in addition a preferred temporal foliation. The physical interpretation of the formalism is considered in the context of 5-dimensional…
We consider cosmological models in which a homogeneous isotropic universe is embedded as a 3+1 dimensional surface into a 4+1 dimensional manifold. The size of the extra dimension depends on time. It is small compared to the size of the…
The anomaly cancellation condition of the Standard Model may be unnatural in theories with extra dimensions as an anomaly of a low-energy 4-dimensional theory can be canceled by an inflow from a bulk. This inflow may give rise to an…