On Essential Incompleteness of Hertz's Experiments on Propagation of Electromagnetic Interactions

The historical background of the 19th century electromagnetic theory is revisited from the standpoint of the opposition between alternative approaches in respect to the problem of interactions. The 19th century electrodynamics became the battle-field of a paramount importance to test existing conceptions of interactions. Hertz's experiments were designed to bring a solid experimental evidence in favor of one of them. The modern scientific method applied to analyze Hertz's experimental approach as well as the analysis of his laboratory notes, dairy and private letters show that Hertz's "\textit{crucial}" experiments cannot be considered as conclusive at many points as it is generally implied. We found that alternative Helmholtz's electrodynamics did not contradict any of Hertz's experimental observations of transverse components as Maxwell's theory predicted. Moreover, as we now know from recently published Hertz's dairy and private notes, his first experimental results indicated clearly on infinite rate of propagation. Nevertheless, Hertz's experiments provided no further explicit information on non-local longitudinal components which were such an essential feature of Helmholtz's theory. Necessary and sufficient conditions for a decisive choice on the adequate account of electromagnetic interactions are discussed from the position of modern scientific method

On Two Complementary Types of Total Time Derivative in Classical Field Theories and Maxwell's Equations

Close insight into mathematical and conceptual structure of classical field theories shows serious inconsistencies in their common basis. In other words, we claim in this work to have come across two severe mathematical blunders in the very foundations of theoretical hydrodynamics. One of the defects concerns the traditional treatment of time derivatives in Eulerian hydrodynamic description. The other one resides in the conventional demonstration of the so-called Convection Theorem. Both approaches are thought to be necessary for cross-verification of the standard differential form of continuity equation. Any revision of these fundamental results might have important implications for all classical field theories. Rigorous reconsideration of time derivatives in Eulerian description shows that it evokes Minkowski metric for any flow field domain without any previous postulation. Mathematical approach is developed within the framework of congruences for general 4-dimensional differentiable manifold and the final result is formulated in form of a theorem. A modified version of the Convection Theorem provides a necessary cross-verification for a reconsidered differential form of continuity equation. Although the approach is developed for one-component (scalar) flow field, it can be easily generalized to any tensor field. Some possible implications for classical electrodynamics are also explored.Comment: no figure

The phase free, longitudinal, magnetic component of vacuum electromagnetism

A charge $q$ moving in a reference laboratory system with constant velocity {\bf V} in the $X$-axis produces in the $Z$-axis a longitudinal, phase free, vacuum magnetic field which is identified as the radiated ${\bf B}^{(3)}$ field of Evans, Vigier and others.Comment: ReVTeX file, 7pp., no figure

Brownian dynamics approach to interacting magnetic moments

The question how to introduce thermal fluctuations in the equation of motion of a magnetic system is addressed. Using the approach of the fluctuation-dissipation theorem we calculate the properties of the noise for both, the fluctuating field and fluctuating torque (force) representation. In contrast to earlier calculations we consider the general case of a system of interacting magnetic moments without the assumption of axial symmetry. We show that the interactions do not result in any correlations of thermal fluctuations in the field representation and that the same widely used formula can be used in the most general case. We further prove that close to the equilibrium where the fluctuation-dissipation theorem is valid, both, field and torque (force) representations coincide, being different far away from it

Helmholtz theorem and the v-gauge in the problem of superluminal and instantaneous signals in classical electrodynamics

In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called v-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light c and the other one (irrotational) with an arbitrary finite velocity $v$ (including a velocity more than c . We show also that the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously.Comment: This variant has been accepted for publication in Found. Phys. Letter

Search for a common baryon source in high-multiplicity pp collisions at the LHC

We report on the measurement of the size of the particle-emitting source from two-baryon correlations with ALICE in high-multiplicity pp collisions at s=13 TeV. The source radius is studied with low relative momentum p–p, p‾–p‾, p–Λ, and p‾–Λ‾ pairs as a function of the pair transverse mass mT considering for the first time in a quantitative way the effect of strong resonance decays. After correcting for this effect, the radii extracted for pairs of different particle species agree. This indicates that protons, antiprotons, Λ s, and Λ‾ s originate from the same source. Within the measured mT range (1.1–2.2) GeV/c2the invariant radius of this common source varies between 1.3 and 0.85 fm. These results provide a precise reference for studies of the strong hadron–hadron interactions and for the investigation of collective properties in small colliding systems. © 2020 CERN for the benefit of the ALICE CollaborationPeer reviewe

Long- and short-range correlations and their event-scale dependence in high-multiplicity pp collisions at 1as = 13 TeV

Two-particle angular correlations are measured in high-multiplicity proton-proton collisions at s = 13 TeV by the ALICE Collaboration. The yields of particle pairs at short-( 06\u3b7 3c 0) and long-range (1.6 < | 06\u3b7| < 1.8) in pseudorapidity are extracted on the near-side ( 06\u3c6 3c 0). They are reported as a function of transverse momentum (pT) in the range 1 < pT< 4 GeV/c. Furthermore, the event-scale dependence is studied for the first time by requiring the presence of high-pT leading particles or jets for varying pT thresholds. The results demonstrate that the long-range \u201cridge\u201d yield, possibly related to the collective behavior of the system, is present in events with high-pT processes as well. The magnitudes of the short- and long-range yields are found to grow with the event scale. The results are compared to EPOS LHC and PYTHIA 8 calculations, with and without string-shoving interactions. It is found that while both models describe the qualitative trends in the data, calculations from EPOS LHC show a better quantitative agreement for the pT dependency, while overestimating the event-scale dependency. [Figure not available: see fulltext.