Related papers: Quaternions and Special Relativity
We demonstrate a compatibility between the relativity principle and the clock postulate in deformed special relativity, by identifying the relevant deformed Lorentz transformations in position space between arbitrary frames. This result…
We show that the classical algebra of quaternions is a commutative $\Z_2\times\Z_2\times\Z_2$-graded algebra. A similar interpretation of the algebra of octonions is impossible.
The quaternion spaces can be used to describe the property of electromagnetic field and gravitational field. In the quaternion space, some coordinate transformations can be deduced from the feature of quaternions, including Lorentz…
The canonical description is based on the prior choice of a spacelike foliation, hence making a reference to a spacetime metric. However, the metric is expected to be a dynamical, fluctuating quantity in quantum gravity. After presenting…
A construction of the magic square, and hence of exceptional Lie algebras, is carried out using trialities rather than division algebras. By way of preparation, a comprehensive discussion of trialities is given, incorporating a number of…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
In this article, we give the most genaral form of the quaternions algebra depending on 3-parameters. We define 3-parameter generalized quaternions (3PGQs) and study on various properties and applications. Firstly we present the definiton,…
The conceptual evolution of principle of relativity in the theory of special relativity is discussed in detail. It is intimately related to a series of difficulties in quantum mechanics,relativistic quantum mechanics and quantum field…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may…
This work deals with the questions of absolute space and relativity. In particular, an alternative derivation of the effects described by special relativity is provided, which is based on a description that assumes a privileged reference…
In this study, after introducing algebraic properties of real quaternions some characterizations of quaternionic involute-evolute curves in Q are obtained. And some results and theorems for quaternionic w-curves are given. Lastly, we…
Scalar Gauss-Bonnet gravity is the only theory with quadratic curvature corrections to general relativity whose field equations are of second differential order. This theory allows for nonperturbative dynamical corrections and is therefore…
The conventional discussion of apparent distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations of : (i) moving objects of limited lifetime in…
We present an explicit basis for orders of arbitrary level N>1 in definite rational quaternion algebras. These orders have applications to computations of spaces of elliptic and quaternionic modular forms.
A proposal for the matrix model formulation of the M-theory on a space with a boundary is given. A general machinery for modding out a symmetry in M(atrix) theory is used for a Z_2 symmetry changing the sign of the X_1 coordinate. The…
We present some gauge conditions to eliminate all second time derivative terms in the vierbein forms of the ten Einstein equations of general relativity; at the same time, we present the corresponding Lagrangian in which there is not any…
Real Time Relativity is a computer program that lets students fly at relativistic speeds though a simulated world populated with planets, clocks, and buildings. The counterintuitive and spectacular optical effects of relativity are…
We explicitly develop a quaternionic version of the electroweak theory, based on the local gauge group $U(1, q)_{L}\mid U(1, c)_{Y}$. The need of a complex projection for our Lagrangian and the physical significance of the anomalous scalar…
The Principle of Relativity has so far been understood as the {\it covariance} of laws of Physics with respect to a general class of reference frame transformations. That relativity, however, has only been expressed with the help of {\it…