Related papers: Particle Mechanics from Local Energy Conservation
The formalism of classical particle dynamics is reinvestigated according to the basic requirement of causal consistency, and a new equation of particle dynamics, which is more general and more in line with classical mechanics experiments…
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.…
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…
Newton's law of motion relative to an inertial frame ("the laboratory") for a particle subject to a force acting at a certain time may be interpreted in either of two ways: (1) The force acting on the particle during an infinitesimal time…
It is shown that the force in relativistic mechanics is not only the cause of acceleration of particle relative to an inertial frame of reference, but also the cause of change of the course of time along the particle's trajectory. Therein…
Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion…
It is generally expected from intuition that the electromagnetic force exerted on a charged particle should remain unchanged when observed in different reference frames in uniform translational motion. In the special relativity, this…
On the basis of a manifestly covariant formalism of non-relativistic quantum mechanics in general coordinate systems, proposed by us recently, we derive general expressions for inertial forces. The results enable us further to discuss, and…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
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…
Riemann's principle "force equals geometry" provided the basis for Einstein's General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The…
According to this principle (EEP), in order that the local physical laws cannot change, after changes of velocity and potentials of a measuring system, the relativistic changes of any particle and any stationary radiation (like those used…
Viewing gravitational energy-momentum $p_G^\mu$ as equal by observation, but different in essence from inertial energy-momentum $p_I^\mu$ naturally leads to the gauge theory of volume-preserving diffeormorphisms of an inner Minkowski space…
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…
Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…
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,…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
. The inertia property of matter is discussed in terms of a type of induction law related to the extended charged particle's own vector potential. Our approach is based on the Lagrangian formalism of canonical momentum writing Newton's…