arXiv subjects

Grzegorz M. Koczan

Publications and source records attributed to Grzegorz M. Koczan.

6 recordsLinked to original sources

arXiv2025

The photon position operator (non-commuting) and its string-like eigenstates

The paper provides three main definitions of the Cartesian photon position operator based on: boost generator, the transversality condition and the helicity operator. In each case, the correctness of the definition and Hermitianness of the operator in the domain of physical states are proven. All considered definitions lead to the same form of the Cartesian position operator in the domain of physical states. Radial photon position operators were also defined, but they turned out to be non-equivalent. Nevertheless, the most useful two radial operators turned out to be twin counterparts in the sense of the transformation to the helical representation, which is an alternative positional representation. The components of the photon position operator do not commute, but in analogy to the problem of eigenangular momentum, its eigenstates do exist. The eigenstates of the two components of the position operator (including the radial component) are called photon strings. Photon strings on a straight line and on a circle have been studied. The usual, previously known photon string states were named electric strings, but new magnetic strings were also introduced. Exact helical photon strings on a straight line, as well as hybrid helical photon strings on a circle, were also considered. On the other hand, infinitely short photon magnetic strings turned out to be flat photon vortices on planes with a normalization formula looks like as point-localized particles.

physics.gen-ph↗

arXiv2025

On regularizations of the integral representation of Dirac delta function -- elementary approach

The article presents, in an elementary way, but with mathematical precision and without harm to the intuition, the path from the integral representation to the Dirac delta, starting with Schwartz's functional approach. Next, the considered representation is presented in a more intuitive sequential approach, formulated by Mikusiński and Sikorski. Finally, we present the third regularization that can be related to Sato's approach to distributions.

math.HO↗

arXiv2022

Relative binary and ternary 4D velocities in the Special Relativity in terms of manifestly covariant Lorentz transformation

Zbigniew Oziewicz was a pioneer of the 4D space-time approach to covariant relative velocities. In the 1980s (according to private correspondence) he discovered two types of 4D relative velocities: binary and ternary, along with the rules for adding them. They were first published in conference materials in 2004, and the second time in a peer-reviewed journal in 2007. These physically logical and mathematically precise concepts are so subtle that Oziewicz's numerous preprints have yet to receive the recognition they deserve. This work was planned to be a more review, but a thorough review of the little-known results was made in an original synthetic manner with numerous generalizations. The Part I presents the Oziewicz-Świerk-Bolós (and Matolsci or Bini-Carini-Jantzen) binary relative velocity and the Oziewicz-Ungar-Dragan (also Celakoska-Chakmakov-Petrushevski on the basis of Urbantke, as well as Wyk) ternary relative velocity. The Einstein-Oziewicz and Einstein-Minkowski velocities, which are a four-dimensional generalization of Einstein velocities addition, also have a ternary character. This also applies to Oziewicz-Minkowski relative velocity, which is a time-like equivalent (generalization) of the canonical ternary velocity. It turns out that the Lorentz transformation of velocity itself is already ternary anchored. This fact is explicitly revealed by the manifestly covariant Lorentz transformation of velocity, which is the main tool of the work.

physics.gen-ph↗

arXiv2021

Relativistic relative velocities and relativistic acceleration

It turns out that the standard application of the four-vector SR formalism does not include the concept of relative velocity. Only the absolute velocity is described by the four-vector, and even the Lorentz transformation parameters is described by the three-dimensional velocity. This gap in the development of the SR formalism reflects the lack of some significant velocity subtraction operations. The differential application of these operations leads to a relativistic acceleration.

physics.gen-ph↗

arXiv2020

Research on rolling friction's dependence on ball bearings' radius

There are two alternative historical laws of rolling resistance formulated by French scientist Coulomb and Dupuit. It has been decided to verify experimentally again, which of these laws describes freely rolling ball bearings on a hard surface better. An inducement to carrying out the measurements was the idea of the constant thickness of roadbed, which is consistent with Dupuit's theory. Measurements have been done using the damped oscillations in the pendulum bearings. Results have shown better consistency with the Coulomb's theory with small, but measurable deviations. These deviations were successfully explained by the so called "Cobblestones model". Parameters designated by this model have been successfully verified by the surface roughness's profile measurement. An additional theoretical aspect of this work is distinguishing two types of rolling friction force: dynamical and kinematical in an analogy to two types of specific heat capacity in the thermodynamics of gases.

physics.pop-ph↗

arXiv2020

Defining of three-dimensional acceleration and inertial mass leading to the simple form F=MA of relativistic motion equation

Newton second law of dynamics is a law of motion but also a useful definition of force (F=MA) or inertial mass (M=F/A), assuming a definition of acceleration and parallelism of force and acceleration. In the special theory of relativity, out of these three only the description of force (F=dp/dt) does not raise doubts. The greatest problems are posed by mass, which may be invariant rest mass or relativistic mass or even directional mass like longitudinal mass. This results from breaking the assumption of parallelism of force and standard acceleration. It turns out that these issues disappear if the relativistic acceleration A is defined as a relativistic velocity subtraction formula. This basic fact is obscured by some subtlety related to the calculation of the relativistic differential of velocity. It is based on the direction of force rather than on transformation to a resting system. The reference to a non-resting system generates a (seemingly) different velocity subtraction formula. Thus, the relativistic three-dimensional acceleration is neither rest acceleration, nor four-acceleration, nor standard acceleration. As a consequence, inertial mass in any direction of the force has the same value as relativistic mass. In other words, the concepts of transverse mass and longitudinal mass, which depend on velocity, have been unified. In this work a full relativistic equation is derived for the motion of a body with variable mass whose form confirmed the previously introduced definitions. In addition, these definitions are in line with the general version of the principle of mass and energy equivalence. The work presents a detailed review and discussion of different approaches to the subject in relation to original historical and contemporary texts. On this basis, a proposal is made for consistent definition of relativistic quantities associated with velocity change.

physics.hist-ph↗