Related papers: Scaffolding of Spacetime
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The…
We show that the quantized free relativistic point particle can be understood as a string in a Clifford space which generates the space-time coordinates through its inner product. The generating algebra is preserved by a unitary symmetry…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
We present a new quantum algebraic description of an electron localized in space-time. Positions in space and time, mass and Clifford generators are defined as quantum operators. Commutation relations and relativistic shifts under frame…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
A Clifford algebra over the binary field 2 = {0,1} is a second-order classical logic that is substantially richer than Boolean algebra. We use it as a bridge to a Clifford algebraic quantum logic that is richer than the usual Hilbert space…
The Clifford algebra over the three-dimensional real linear space includes its linear structure and its exterior algebra, the subspaces spanned by multivectors of the same degree determine a gradation of the Clifford algebra. Through these…
In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to construct a fully relativistic version of the…
We develop a new concept of quantum mechanics which is based on a generalized space-time and on an action vector space similar to it. Both spaces are provided by algebraic properties. This allows to calculate the Dirac matrixes and to…
We investigate using Clifford algebra methods the theory of algebraic dotted and undotted spinor fields over a Lorentzian spacetime and their realizations as matrix spinor fields, which are the usual dotted and undotted two component spinor…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
Geometric number systems, obtained by extending the real number system to include new anticommuting square roots of +1 and -1, provide a royal road to higher mathematics by largely sidestepping the tedious languages of tensor analysis and…
Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine…
The most familiar formalism for the description of geometry applicable to physics comprises operations among 4-component vectors and complex real numbers; few people realize that this formalism has indeed 32 degrees of freedom and can thus…
A linear vector model of gravitation is introduced in the context of quantum physics as a generalization of electromagnetism. The gravitoelectromagnetic gauge symmetry corresponds to a hyperbolic unitary extension of the usual complex phase…
We demonstrate the emergence of the conformal group SO(4,2) from the Clifford algebra of spacetime. The latter algebra is a manifold, called Clifford space, which is assumed to be the arena in which physics takes place. A Clifford space…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
Perhaps the most significant, if not the most important, achievements in chemistry and physics are the Periodic Table of the Elements in Chemistry and the Standard Model of Elementary Particles in Physics. A comparable achievement in…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…