Related papers: Relative mechanical quantities in spaces with a tr…
In this paper the physical systems consisting of relatively moving subsystems are considered in the "true transformations relativity." It is found in a manifestly covariant way that there is a second-order electric field outside stationary…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without…
Physical quantities and physical dimensions are among the first concepts encountered by students in their undergraduate career. In this pedagogical review, I will start from these concepts and, using the powerful tool of dimensional…
A challenge in teaching about special relativity is that a number of the theory's effects are at odds with the intuition of classical physics, as well as student's everyday experience. The relativity of simultaneity, time dilation and…
Given two observers, we define the "relative velocity" of one observer with respect to the other in four different ways. All four definitions are given intrinsically, i.e. independently of any coordinate system. Two of them are given in the…
The study of the evolution of the dynamics of a massive or massless particle shows that in special relativity theory, the energy is not conserved. From the law of evolution of the velocity over time of a particle subjected to a constant…
We show that the relativistic expressions for momentum and energy as well as the way in which they transform could be derived without involving collisions and conservation laws. Our approach involves relativistic kinematics via the addition…
We proved that under quantum mechanics a momentum-energy and a space-time are dual vector spaces on an almost complex manifold in position representation, and the minimal uncertainty relations are equivalent to the inner-product relations…
The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum…
Special relativity theory is generalized to two or more ``maximal'' signalling speeds. This framework is discussed in three contexts: (i) as a scenario for superluminal signalling and motion, (ii) as the possibility of two or more ``light''…
We discuss the motion of extended objects in a spacetime by considering a gravitational field created by these objects. We define multipole moments of the objects as a classification by Lie group SO(3). Then, we construct an energy-momentum…
Gravity stands apart from other fundamental interactions in that it is locally equivalent to an accelerated frame and can be transformed away. Again it is indistinguishable from the geometry of space-time (which is an arena for all other…
General Principle of Relativity unequivocally supports the notion of momentum-less energy for bodies (energy-quanta) moving at the {\em same} or {\em constant} speed relative to all the reference systems. In this communication, we point out…
The theory of transport of charged particles in cosmic magnetic fields is at the very center of the investigation of non-thermal phenomena in the universe, ranging from our local neighborhood to supernovae, clusters of galaxies or distant…
These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…
Although special relativity limits the actual velocity of a particle to $c$, the velocity of light, the observed velocity need not be the same as the actual velocity as the observer is only aware of the position of a particle at the time in…
We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…
What does it mean to ``add'' velocities relativistically -- clarification of the conceptual problems, new derivations of the related formulas, and identification of the source of the non-associativity of the standard vector version of the…
The relationship between the intrinsic motion of gravity, light, and time is explored in terms of the principles of entropy, causality, energy, and symmetry conservation. A conceptual mechanism for gravity and the gravitational connection…