Related papers: Spacetime geometry of spin, polarization, and wave…
There are many examples where geometry and gravity are concepts that emerge from a theory of quantum mechanics without gravity. This suggests thinking of gravity as an exotic phase of matter. Quantifying this phase in the Landau paradigm…
The problem is posed of further extending the axiomatic construction proposed in Part 1 for non-local point transformations mapping in each other different curved space times. The new transformations apply to curved space times when…
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…
Plane-based Geometric Algebra (PGA) has revealed points in a $d$-dimensional pseudo-Euclidean space $\mathbb{R}_{p,q,1}$ to be represented by $d$-blades rather than vectors. This discovery allows points to be factored into $d$ orthogonal…
In a recent paper (arXiv:1412.6000) a general mechanism for emergence of cosmological space-time geometry from a quantum gravity setting was devised and departure from standard dispersion relations for elementary particle were predicted. We…
Singularity theorems demonstrate the inevitable breakdown of the concept of continuous, classical spacetime under highly general conditions. Quantum gravity is expected to intervene to avoid singularities and models so far hint towards…
We study propagation of high-frequency electromagnetic waves in a curved spacetime. We demonstrate how a modification of the standard geometric optics allows one to include the helicity dependent corrections into the equations of motion of…
We consider a quantum test particle in the background of a Newtonian gravitational field in the framework of Cartan's formulation of nonrelativistic spacetimes. We have proposed a novel quantization of a point particle which amounts to…
By incorporating spinning particles into the framework of classical General Relativity, the theory is changed insofar, as, though using holonome coordinates, the connexion becomes asymmetrical. This implies, that partial derivatives do not…
Quantum mechanics ordinarily describes particles as being pointlike, in the sense that the uncertainty $\Delta x$ can, in principle, be made arbitrarily small. It has been shown that suitable correction terms to the canonical commutation…
We complete the program of spectral geometry, in the sense that we show that a manifold's shape, i.e., its metric, can be reconstructed from its resonant sound when tapped lightly, i.e., from its spectrum, -- if in addition we also record…
Newtonian gravity arises as the nonrelativistic, static, weak-field limit of some Lorentzian spacetime geometry solving the generally covariant Einstein equations for a given matter field configuration. Spacetime geometry has a local…
We extend vector formalism by including it in the algebra of split octonions, which we treat as the universal algebra to describe physical signals. The new geometrical interpretation of the products of octonionic basis units is presented.…
In arXiv:1105.5629, equations of the modified geometrical optics for circularly polarized photon trajectories in a stationary spacetime are derived by using a (1+3)-decomposed form of Maxwell's equations. We derive the same results by using…
The quantized canonical space-time coordinates of a relativistic point particle are expressed in terms of the elements of a complex Clifford algebra which combines the complex properties of SL(2.C) and quantum mechanics. When the quantum…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…
We develop a generalized projective gauge theory of gravity and spinorial matter, incorporating both non-metricity and torsion. The work is divided into three parts. Part I provides a thorough review of General Relativity, Metric-Affine…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…