No Arabic abstract
The tight connection between mass and energy unveiled by Special Relativity, summarized by the iconic formula $E = mc^2$, has revolutionized our understanding of nature and even shaped our political world over the past century through its military application. It is certainly one of the most exhaustively-tested and well-known equations of modern science. Although we have become used to its most obvious implication -- mass-energy equivalence --, it is surprising that one of its subtle -- yet, inevitable -- consequences is still a matter of confusion: the so-called hidden momentum. Often considered as a peculiar feature of specific systems or as an artifact to avoid paradoxal situations, here we present a new relativistic paradox which exposes the true nature and ubiquity of hidden momentum. We also show that hidden momentum can be forced to reveal itself through observable effects, hopefully putting an end to decades of controversy about its reality.
Relativistic kinematics is usually considered only as a manifestation of pseudo-Euclidean (Lorentzian) geometry of space-time. However, as it is explicitly stated in General Relativity, the geometry itself depends on dynamics, specifically, on the energy-momentum tensor. We discuss a few examples, which illustrate the dynamical aspect of the length-contraction effect within the framework of Special Relativity. We show some pitfalls associated with direct application of the length contraction formula in cases when an extended object is accelerated. Our analysis reveals intimate connections between length contraction and the dynamics of internal forces within the accelerated system. The developed approach is used to analyze the correlation between two congruent disks - one stationary and one rotating (the Ehrenfest paradox). Specifically, we consider the transition of a disk from the state of rest to a spinning state under the applied forces. It reveals the underlying physical mechanism in the corresponding transition from Euclidean geometry of stationary disk to Lobachevskys (hyperbolic) geometry of the spinning disk in the process of its rotational boost. A conclusion is made that the rest mass of a spinning disk or ring of a fixed radius must contain an additional term representing the potential energy of non-Euclidean circumferential deformation of its material. Possible experimentally observable manifestations of Lobachevskys geometry of rotating systems are discussed.
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the individual layers. We find that these correlations are strong in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate: (i) the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers; (ii) accurate trans-layer link prediction, where connections in one layer can be predicted by observing the hidden geometric space of another layer; and (iii) efficient targeted navigation in the multilayer system using only local knowledge, which outperforms navigation in the single layers only if the geometric correlations are sufficiently strong. Our findings uncover fundamental organizing principles behind real multiplexes and can have important applications in diverse domains.
Which non-local hidden variables could complement the description of physical reality? The present model of extended Newtonian dynamics (MEND) is generalize but not alternative to Newtonian Dynamics because its extended Newtonian Dynamics to arbitrary reference frames. It Is Physics of Arbitrary Reference Frames. Generalize and alternative is not the same. MEND describes the dynamics of mechanical systems for arbitrary reference frames and not only for inertial reference frames as Newtonian Dynamics. Newtonian Dynamics can describe non-inertial reference frames as well introducing fiction forces. In MEND we have fiction forces naturally and automatically from new axiomatic and we neednt have inertial reference frame. MEND is differs from Newtonian Dynamics in the case of micro-objects description.
Newtonian physics is describes macro-objects sufficiently well, however it does not describe microobjects. A model of Extended Mechanics for Quantum Theory is based on an axiomatic generalization of Newtonian classical laws to arbitrary reference frames postulating the description of body dynamics by differential equations with higher derivatives of coordinates with respect to time but not only of second order ones and follows from Mach principle. In that case the Lagrangian $L(t,q,dot{q},ddot{q},...,dot {q}^{(n)},...)$ depends on higher derivatives of coordinates with respect to time. The kinematic state of a body is considered to be defined if n-th derivative of the body coordinate with respect to time is a constant (i.e. finite). First, kinematic state of a free body is postulated to invariable in an arbitrary reference frame. Second, if the kinematic invariant of the reference frame is the n-th order derivative of coordinate with respect to time, then the body dynamics is describes by a 2n-th order differential equation. For example, in a uniformly accelerated reference frame all free particles have the same acceleration equal to the reference frame invariant, i.e. reference frame acceleration. These bodies are described by third-order differential equation in a uniformly accelerated reference frame.
Recently BESIII collaboration discovered a charged strange hidden-charm state $Z_{cs}$(3985) in the $D_s^-D^{*0} + D_s^{*-}D^{0}$ spectrum. A higher $Z_{cs}$ state coupling to $bar{D}_s^{*-}D^{*0}$ is expected by SU(3)-flavor symmetry, and their bottom partners are anticipated by heavy quark flavor symmetry. Here we study the photoproduction of these exotic states and investigate carefully the background from Pomeron exchange. Our results indicate that the maximal photoproduction cross section of strange partner is around 1 $sim$ 2 orders of magnitude smaller than that of the corresponding non-strange states. The possibility of searching for them in future electron-ion colliders (EIC) is briefly discussed.