arXiv subjects

Krzysztof Rębilas

Publications and source records attributed to Krzysztof Rębilas.

4 recordsLinked to original sources

arXiv2013

Lorentz-invariant three-vectors and alternative formulation of relativistic dynamics

Besides the well known scalar invariants, there exist also vectorial invariants in the realm of special relativity. It is shown that the three-vector $\left(\frac{d\vec{p}}{dt}\right)_{\parallel v}+γ_v\left(\frac{d\vec{p}}{dt}\right)_{\perp v}$ is invariant under the Lorentz transformation. The indices $_{\parallel v}$ and $_{\perp v}$ denote the respective components established with respect to the direction of the velocity of body $\vec{v}$, and $\vec{p}$ is the relativistic momentum. We prove that this vector is equal to a force of $\vec{F}_R$ satisfying the classical Newtonian law $\vec{F}_R=m\vec{a}_R$ in the instantaneous inertial rest frame of an accelerated body. Therefore the equation $\vec{F}_R=\left(\frac{d\vec{p}}{dt}\right)_{\parallel v}+γ_v\left(\frac{d\vec{p}}{dt}\right)_{\perp v}$, based on the Lorentz-invariant vectors, may be used as a truly invariant (not merely a covariant) relativistic equation of motion in any inertial system of reference. An alternative approach to classical electrodynamics based on the invariant three-vectors is proposed.

physics.class-ph↗

arXiv2013

Origin of the thermodynamic time arrow demonstrated in a realistic statistical system

Emergence of one-time-direction macroscopic evolution of a classical system of two mixed gases having different temperatures is derived and explained. The analysis performed at the microscopic level, where the time-symmetric laws of mechanics govern the particles collisions, leads to a time-asymmetric macroscopic heat transfer equation and a theorem analogous to the Boltzmann H-theorem. Some statistical symmetries in the velocity distribution that should be satisfied by the incoming and outgoing particles are pointed out. The time reversed evolution is shown to be highly improbable because in this case these typical symmetries are broken. Additionally, some remarks explaining implicit time-asymmetry of the Boltzmann \emph{Stosszahlansatz} are made.

physics.class-ph↗

arXiv2013

Derivation of the relativistic momentum and relativistic equation of motion from Newton's second law and Minkowskian space-time geometry

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 $\vec{F}=d\vec{p}/dt$, where $\vec{p}$ is the relativistic momentum. The relativistic momentum is then derived without referring to any additional assumptions concerning elastic collisions of bodies. Lorentz-invariance of the relativistic law is proved without tensor formalism. Some new method of force transformation is also presented.

physics.gen-ph↗

arXiv2013

A way to discover Maxwell's equations theoretically

The Coulomb force, established in the rest frame of a source-charge $Q$, when transformed to a new frame moving with a velocity $\vec{V}$ has a form $\vec{F}= q\vec{E} + q\vec{v} \times \vec{B}$, where $\vec{E}=\vec{E}'_\parallel + γ\vec{E}'_\perp $ and $\vec{B}= \vec{\frac{V}{c^2}} \times \vec{E}$ and $\vec{E}'$ is the electric field in the rest frame of the source. The quantities $\vec{E}$ and $\vec{B}$ are then manifestly interdependent. We prove that they are determined by Maxwell's equations, so they represent the electric and magnetic fields in the new frame and the force $\vec{F}$ is the well known from experiments Lorentz force. In this way Maxwell's equations may be discovered theoretically for this particular situation of uniformly moving sources. The general solutions of the discovered Maxwell's equations lead us to fields produced by accelerating sources.

physics.class-ph↗