Related papers: Quaternion Time, Mass, and Particle Velocity
In this article the concept of mass is analyzed based on the special and general relativity theories and particle (quantum) physics. The mass of a particle (m=E(0)/c^2) is determined by the minimum (rest) energy to create that particle…
Examination of the Einstein energy-momentum relationship suggests that simple unbound forms of matter exist in a four-dimensional Euclidean space. Position, momentum, velocity, and other vector quantities can be expressed as Euclidean…
The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition of angular momentum…
In this study, we develop the generalized Dirac like four-momentum equation for rotating spin-half particles in four-dimensional quaternionic algebra. The generalized quaternionic Dirac equation consists the rotational energy and angular…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
Quaternions have an (over a century-old) extensive and quite complicated interaction with special relativity. Since quaternions are intrinsically 4-dimensional, and do such a good job of handling 3-dimensional rotations, the hope has always…
For over a century the definitions of mass and derivations of its relation with energy continue to be elaborated, demonstrating that the concept of mass is still not satisfactorily understood. The aim of this study is to show that, starting…
Formulae relating one and the same force in two inertial frames of reference are derived directly from the Lorentz transformation of space and time coordinates and relativistic equation for the dynamic law of motion in three dimensions. We…
We compute in a relativistic way the time-of-arrival and the traversal time through a region of a free particle with spin 1/2. We do this by applying the relativistic extension of the Event-Enhanced Quantum Theory which we have presented in…
It has been suggested that re-expressing relativity in terms of forces could provide fresh insights. The formalism developed for this purpose only applied to static, or conformally static, space-times. Here we extend it to arbitrary…
We present an operator definition of the collisional energy and momentum loss suffered by an energetic charged particle in the presence of a medium. Our approach uses the energy-momentum tensor of the medium to evaluate the energy and…
We review how reparametrization of space and time, namely the procedure where both are made to depend on yet another parameter, can be used to formulate quantum physics in a way that is naturally conducive to relativity. This leads us to a…
Concept of inertial mass is not well defined in physics. For defining inertial mass of a particle we need to know its acceleration under some force in an inertial reference frame, which itself is defined by the motion of its background…
In particular cases of stationary and stationary axially symmetric space-time passage to non-relativistic limit of Einstein equation is completed. For this end the notions of absolute space and absolute time are introduced due to…
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…
In looking for qualitative differences between quaternionic and complex formulations of quantum physical theories, we provide a detailed discussion of the behavior of a wave packet in presence of a quaternionic time-independent potential…
The expressions of momentum and energy of a particle in special relativity are often derived in a quite unconvincing manner in elementary text, by resorting either to electrodynamic or quantum considerations, or via the introduction of the…
We discuss the definition of particle velocity in doubly relativity theories. The general formula relating velocity and four-momentum of particle is given.
The particle effective mass is often a challenging concept in solid state physics due to the many different definitions of the effective mass that are routinely used. Also, the most commonly used theoretical definition of the effective mass…
In this paper we show how relativistic tensor dynamics and relativistic electrodynamics can be formulated in a biquaternion tensor language. The treatment is restricted to mathematical physics, known facts as the Lorentz Force Law and the…