J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial reference frames, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic reference frames. There exist some differences between this theory and Einstein's theory of general relativity.

Newton's kinetic energy equation delineates the laws of motion for objects travelling at speeds much less than the speed of light, an equation extensively validated at these lower velocities. Any new, more complete formulation of kinetic energy must approximate Newton's kinetic energy equation under these conditions. Einstein's special relativity, utilizing the Lorentz factor, introduces a new perspective on spacetime, adhering to the requirement that the Newtonian kinetic energy equation serves as an approximation at low velocities. In this paper, we identify all factor expressions satisfying the condition that their approximate solutions at low velocities align with Newton's kinetic energy equation. We introduce the Yuyunrui factor, incorporating two real number hyperparameters, $\alpha$ and $\beta$, encompassing all potentially correct factors, with the Lorentz factor as a specific instance where $(\alpha=0$, $\beta=1)$. We classify all potentially correct $(\alpha, \beta)$ combinations into six categories based on their distinct scaling effects and present the corresponding scaling effects. The combinations of $(\alpha, \beta)$ values applicable in the real world are necessarily included within these candidates, with the precise values requiring rigorous experimental validation. This work aims to refine our understanding of special relativity beyond the Lorentz factor.

We show that Universe inflation occurs when Einstein's gravity couples to nonlinear electromagnetic fields with cosmic stochastic magnetic fields background. Nonlinear electrodynamics with two parameters is used. The strength of magnetic fields to have the Universe inflation is obtained. It is shown that singularities of the energy density and pressure are absent for any scale factors. At large scale factors one arrives at equation of state for ultra-relativistic case. It is demonstrated that the curvature invariants do not have singularities. By computing the deceleration parameter we show that graceful exit takes place with reasonable e-folding number. The duration of Universe inflation as a function of model parameters is obtained. The classical stability and causality are analyzed by calculating the speed of the sound.

When solving the Einstein's equations for an isolated system of masses, V. Fock introduces harmonic reference frame and obtains an unambiguous solution. Further, he concludes that there exists a harmonic reference frame which is determined uniquely apart from a Lorentz transformation if suitable supplementary conditions are imposed. It is known that wave equations keep the same form under Lorentz transformations. Thus, we speculate that Fock's special harmonic reference frames may have provided us a clue to derive the Einstein's equations in some special class of non-inertial reference frames. Following this clue, generalized Einstein's equations in some special non-inertial reference frames are derived based on the theory of vacuum mechanics. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explain all the experiments which support the theory of general relativity. There exist some differences between this theory and the theory of general relativity.

In 1922, Albert Einstein visited Paris and interacted extensively with an illustrious section of the French academia. In overfilled sessions at the Coll\`{e}ge de France and the Sorbonne, Einstein explained his theories of relativity, and prominent physicists, mathematicians and philosophers listened, debated, questioned and explored facets of relativity. The 1922 visit had its echoes in the life and works of many who participated, particularly decisive for Einstein and the philosopher Henri Bergson. This essay examines that eventful visit, focusing on the physical and logical aspects of Bergson's critique, with physics commentaries, linking prominent French physicists and mathematicians Langevin, Painlev\'{e}, Hadamard, Becquerel, Sagnac, and Kastler. I give particular attention to the logical and empirical accuracy of the physics issues involved, delineating Bergson's exact reasoning for his philosophical enthusiasm in Einstein's theory and for the ensuing critique. Bergson's philosophical stand on duration and simultaneity is reassessed in the context of later developments in cosmological physics as well as the wealth of empirical data involving comparison of atomic clocks. Finally we are led naturally to a surprising completion of the philosopher's program on universal time, duration and simultaneity, in harmony with the time of the physicist. In the appendices after the main text I also give the physics background and easily verifiable proofs for the assertions made in the text, pertaining to relativity, simultaneity and time dilation, clearly distinguishing beliefs and facts.

We study Einstein's gravity coupled to nonlinear electrodynamics with two parameters in Anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space is investigated. We obtain the mass and metric functions, their asymptotic and corrections to the Reissner--Nordstr\"{o}m metric function when the cosmological constant vanishes. The first law of black hole thermodynamics in extended phase space is formulated and the magnetic potential and the thermodynamic conjugate to the coupling are obtained. We proved the generalized Smarr relation. The heat capacity and the Gibbs free energy are computed and phase transitions are studied. It was shown that the electric field of charged objects at the origin and electrostatic self-energy are finite within the nonlinear electrodynamics proposed.

Light can interfere like a wave in a multi-path experiment, but it also has particle properties when interacting with matter. In a closer look, the interference pattern is created by many individual detections ("clicks"), which do not all occur simultaneously. An established assumption is therefore that a single light particle is capable of interfering with itself by superimposing all possibilities to get from the source to the detector. This is in stark contrast to our experience with macroscopic objects, which always "decide" in favour of only one of the alternative paths.In 2010, Jin et al. (Ref. 15) described an event-based model which allowed the authors to show that an interference pattern consisting of clicks can arise in a multi-path experiment even if photons, like macroscopic objects, only follow one path. To do this, photons must be able to transmit the information about their travelling duration to the detector and the detector must have a basic memory. A threshold function uses the message of several light quanta to decide whether a single detection is initiated, which is not the evidence for a single photon. In this "proof of principle", the authors do not claim that the detector function is a realistic one.In the present paper, this detector is replaced by a material consisting of ionizable molecules whose interaction with light takes place according to a modified version of Einstein's radiation laws. Based on this, a photon pair interaction mediated by matter takes place, which in a multi-path experiment generates an interference pattern of clicks at the detector, even if an arbitrary amount of time elapses between the individual detections. In the present model an interference pattern with minima that have less than half the intensity of the maxima is the result of a peculiar behaviour of the detector: In this case, the entirety of its electrons must be described as a unit (a “field”) with many equidistant energy levels. The results of a simulation are presented which enable the model to be tested in experiments.

Light can interfere like a wave in a multi-path experiment, but it also has particle properties when interacting with matter. In a closer look, the interference pattern is created by many individual detections ("clicks"), which do not all occur simultaneously. An established assumption is therefore that a single light particle is capable of interfering with itself by superimposing all possibilities to get from the source to the detector. This is in stark contrast to our experience with macroscopic objects, which always "decide" in favour of only one of the alternative paths.In 2010, Jin et al. (Ref. 15) described an event-based model which allowed the authors to show that an interference pattern consisting of clicks can arise in a multi-path experiment even if photons, like macroscopic objects, only follow one path. To do this, photons must be able to transmit the information about their travelling duration to the detector and the detector must have a basic memory. A threshold function uses the message of several light quanta to decide whether a single detection is initiated, which is not the evidence for a single photon. In this "proof of principle", the authors do not claim that the detector function is a realistic one.In the present paper, this detector is replaced by a material consisting of ionizable molecules whose interaction with light takes place according to a modified version of Einstein's radiation laws. Based on this, a photon pair interaction mediated by matter takes place, which in a multi-path experiment generates an interference pattern of clicks at the detector, even if an arbitrary amount of time elapses between the individual detections. In the present model an interference pattern with minima that have less than half the intensity of the maxima is the result of a peculiar behaviour of the detector: In this case, the entirety of its electrons must be described as a unit (a “field”) with many equidistant energy levels. The results of a simulation are presented which enable the model to be tested in experiments.

Dirac's Large Number Hypothesis (LNH), proposed in 1937, has captivated the scientific community with its exploration of profound correlations between cosmic and atomic scales. This hypothesis delves into the intricate interplay between the infinitesimally small and the vastly large, offering potential insights into the fundamental nature of the universe. As we continue to uncover the mysteries of the cosmos, the LNH oscillates on the precipice of scientific acceptance—neither fully validated nor entirely dismissed. In this review paper, we embark on a comprehensive journey through Dirac's LNH, shedding light on its theoretical underpinnings, its implications for universe models, and its resonance with the Anthropic Principle. We delve into the possibilities of variable gravitational constants and continuous mass creation, inviting further exploration into the intricacies of our cosmic symphony. By embracing the ongoing quest for understanding, we endeavor to unravel the profound harmonies that connect the infinitesimal with the infinite, contributing to the symphony of knowledge in theoretical physics and cosmology.

Dirac's Large Number Hypothesis (LNH), proposed in 1937, has captivated the scientific community with its exploration of profound correlations between cosmic and atomic scales. This hypothesis delves into the intricate interplay between the infinitesimally small and the vastly large, offering potential insights into the fundamental nature of the universe. As we continue to uncover the mysteries of the cosmos, the LNH oscillates on the precipice of scientific acceptance—neither fully validated nor entirely dismissed. In this review paper, we embark on a comprehensive journey through Dirac's LNH, shedding light on its theoretical underpinnings, its implications for universe models, and its resonance with the Anthropic Principle. We delve into the possibilities of variable gravitational constants and continuous mass creation, inviting further exploration into the intricacies of our cosmic symphony. By embracing the ongoing quest for understanding, we endeavor to unravel the profound harmonies that connect the infinitesimal with the infinite, contributing to the symphony of knowledge in theoretical physics and cosmology.