In this work a new mechanics will be studied which is based on the hypothesis that the change of linear momentum of a particle happens as a discrete pulses. By using this hypothesis and by considering Newton's relation between energy and momentum, and the law of mass and energy conservation as a priori, the Einstein dispersion relation can be derived as a zero approximation without using Lorentz transformations. Other terms will be derived as a corrections to this relation. It will be shown that the effect of the corrections will be smaller and smaller with the increase of momentum. The work will offer an explanation of why the velocity of light seems to be constant regardless of the velocity of the source, and under which condition this will be changed. Also a prediction is made that faster than light transition could happen theoretically under certain conditions, and a nonzero mass photon can exist in nature. The work is purely classical in the sense that it doesn't involve any uncertainty relations.
We describe an interference setup which seems to defy the No-Communication theorem. We discuss its potential flaw and derive a relation implied by quantum mechanics that limits the size of the detector given the particle's state width.
For steady-state and some other types of mechanical waves of an arbitrary form, intensity and nature, propagating in a free uniform waveguide, we present the following. Relations for the axial momentum as it directly follows from the conservation laws. The mass associated with the wave. The connection between the wave energy and momentum. The structure of a binary wave which possesses a self-equilibrated momentum, in particular, a transverse-longitudinal wave formed upon excitation of flexural waves. Conditions under which longitudinal sinusoidal waves can carry momentum and the physical meani…
We show the value of mass-momentum diagrams for analyzing collision problems in classical mechanics in one dimension. Collisions are characterized by the coefficient of restitution and the momentum of the interacting particles both before and after the collision. All those quantities are presented in the mass-momentum diagrams without the need to do any calculations. We also show that the same diagrams can be used to investigate collisions with respect to the center-of-mass system. In this case, also, we do not need to do any calculations to obtain the momentum. Since we give an alternative wa…
The quantum mechanics is considered to be a partial case of the stochastic system dynamics. It is shown that the wave function describes the state of statistically averaged system $<\mathcal{S}_{st}>$, but not that of the individual stochastic system $\mathcal{S}_{st}$. It is a common practice to think that such a construction of quantum mechanics contains hidden variables, and it is incompatible with the von Neumann's theorem on hidden variables. It is shown that the original conditions of the von Neumann's theorem are not satisfied. In particular, the quantum mechanics cannot describe the pa…
I present a new group-theoretical approach to the interaction mechanism of elementary particle physics. Within an irreducible unitary two-particle representation of the Poincare group, the commutation relations of the Poincare group require that the two-particle states be momentum entangled. As in gauge theories, momentum entanglement defines a correlation between two particles that can be described as an interaction provided by the exchange of virtual (gauge) quanta. The coupling constant of this interaction is uniquely determined by the structure of the irreducible two-particle state space. …
We first define the functions which ensure the transformation of momentum and energy of a tardyon, the transformation of the wave vector and the frequency of the associated wave. Having done this, we show that they ensure the relativistic invariance of the quotient between momentum and wave vector and between energy and frequency if the product between particle velocity u and phase velocity w is a relativistic invariant (uw=c^2), a condition which is a natural combination of special relativity theory and quantum mechanics.
An important methodological problem of theoretical mechanics related to inertia is discussed. Analysis Inertia is performed in four-dimensional Minkowski space-time based on the law of conservation of energy-momentum. This approach allows us to combine the laws of conservation of momentum and angular momentum into a single law and separate the forces of inertia that actually exist in nature from the imaginary forces introduced to simplify calculations or arising from the transition from one frame of reference to another. From the energy-momentum tensor, in a non-relativistic approximation, the…
The equilibrium distribution function of a relativistic ideal gas has been derived to include the effect of angular momentum. The result agrees with the one obtained from kinetic theory, and consistent with relativistic thermodynamics. The role of angular momentum becomes transparent in this derivation, and the equilibrium distribution can be generalized to accommodate the effect of intrinsic angular momentum. The results here is for a flat spacetime, however, same approach can be applied to static curved spacetimes.
A fundamental belief is that the formulism of relativistic quantum mechanics equations (RQMEs) should remain in low momentum motion. However, it is found that some formulas from RQMEs were lost in Schrödinger equation. For example, a free relativistic particle has positive and negative energy branches. The former includes positive kinetic energy (PKE) and the latter negative kinetic energy (NKE). The latter should be treated on an equal footing as the former. Nevertheless, from Schrödinger equation, a free particle can have only PKE. Starting from RQMEs and taking low momentum approximation, w…
Most of the logical objections against the classical laws of motion, as they are usually presented in textbooks, centre on the fact that defining force in terms of mass and acceleration, the first two laws are mere assertions of concepts to be introduced in the theory; conversely, the third law expresses the experimental fact that the ratio of masses is inversely proportional to the ratio of accelerations, but it is known to fail when the interacting bodies are rapidly accelerated or far apart, leading to objections at the research level, particularly when electromagnetic phenomena is present.…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described by the wave function is subatomic particle moving randomly. Therefore, the characteristics of quantum mechanics have a dual nature, one of them is the deterministic nature carried on from classical physics, and the other is the probabilistic nature coined by particle's random motion. Based on this model, almost all of open questions in quantum mechanics can…
Various approaches to quantum gravity suggest that the fundamental volume of the phase space of the given space for representative points, means !0, should be modified. In this paper, we study the effects of this modification on the thermodynamics of an ideal gas within the micro canonical ensemble. For this end, we use a Generalized Uncertainty Principle (GUP) that admits both a minimal measurable length and a maximal momentum. Using this GUP causes decreasing the total number of the microstates of the system. In the first step, we calculate these reductions for classical ideal gas, and in th…
Mechanics can be founded in a principle stating the uncertainty in the position of an observable particle delta-q as a function of its motion relative to the observer, expressed in a trajectory representation . From this principle, p.delta-q=const., being p the q-conjugated momentum, mechanical laws are derived and the meaning of the Lagrangian and Hamiltonian functions are discussed. The connection between the presented principle and Hamilton's Least Action Principle is examined. For a particle hidden from direct observation, the position uncertainty is determined by the enclosing boundaries,…
The version of electrodynamics is constructed in which faster-than-light motions of fields and particles with real masses are possible. Transformational properties of 3-velocity, momentum, energy and electromagnetic field are presented in addition to the paper physics/0405085.
It is shown that for a central potential that is an injective function of the radial coordinate, a second central potential can be found that leads to trajectories in the configuration space and the momentum space coinciding, respectively, with the trajectories in the momentum space and the configuration space produced by the original potential.
Quantum mechanics with quaternionic mass is considered. The momentum eigen-value equation with quaternionic mass yields the Klein-Gordon equation with a mass consisting of longitudinal and traverse masses. The scalar field total mass is found to be a sum of these masses. This field appears to be connected with two subfields conserving linear momentum. It is found that a particle with real mass satisfies the quantum Telegraph equation, whereas that one with quaternionic mass satisfies the Klein-Gordon equation. A quantum force acting on the particle is found to be proportional to its velocity. …
Fundamental and applied concepts concerning the ability of light beams to carry a certain mechanical angular momentum with respect to the propagation axis are reviewed and discussed. Following issues are included: Historical reference; Angular momentum of a paraxial beam and its constituents; Spin angular momentum and paradoxes associated with it; Orbital angular momentum; Circularly-spiral beams: examples and methods of generation; Orbital angular momentum and the intensity moments; Symmetry breakdown and decomposition of the orbital angular momentum; Mechanical models of the vortex light bea…
This paper inspects more closely the problem of the momentum and energy of a bound (non-radiating) electromagnetic (EM) field. It has been shown that for an isolated system of non-relativistic mechanically free charged particles a transformation of mechanical to EM momentum and vice versa occurs in accordance with the requirement PG=const, where PG is the canonical momentum. If such a system contains bound charges, fixed on insulators then, according to the assumption of a number of authors, a so-called "hidden" momentum can contribute into the total momentum of the system. The problem of "hid…
