The Interplay of Gravity and Lorentz Transformation Collaborating with ChatGPT

This paper presents a short exploration of the phenomena of mass and heat increase, shedding light on the remarkable notion of an expanding universe. Aimed at physicists and mathematicians, this investigation draws on an innovative collaboration with ChatGPT, an AI language model trained using scientific knowledge, to enrich our understanding of these fundamental concepts. By delving into the Gravitational Constant, we unveil compelling evidence for an increase in mass and heat for all celestial objects within an isotropic and homogenous universe as a result of the Lorentz Transformation of mass energy (LTME). Traditionally, LTME has been considered relevant primarily for subatomic particles at high velocities. However, this study posits that LTME is equally applicable to celestial bodies, even at relatively low velocities. The journey commences with an examination of the Gamma Factor in the LTME, illuminating its significance in comprehending the expansion of the cosmos. Ultimately, this paper offers a comprehensive validation of “Expanding Matter” with responses from ChatGPT, illuminating the ever-growing nature of our universe. As physicists, embarking on this journey will lead to new perspectives on the profound mysteries that shape cosmic reality. This pursuit contemplates the possibility of an infinitely energetic universe, where energy metamorphoses into mass through M = E/c2. This interpretation proposes the existence of a Process of Continuously Created Matter, manifesting as an ongoing accretion, augmentation, and expansion, harmonizing with the universe’s ever-expansive nature. The study further incorporates state-of-the-art observational technologies to substantiate its claims, thereby opening new avenues for future research in both theoretical physics and cosmology.

The Equations of Lorentz Transformation

This work consists of two parts. The first part: The Lorentz transformation has two derivations. One of the derivations can be found in the references at the end of the work in the “Appendix I” of the book marked by number one. The equations for this derivation [1]: The other derivation of the Lorentz transformation is the traditional hyperbolic equations:; ; For these equations we found new equations: , . The second part: In the second part is the equation by which we derive Minkowski’s equation. It will be proved that Minkowski’s equation is the integral part of the Lorentz transformation.

Invariance of the Electromagnetic Field Vectors Obtained in Course of the Lorentz Transformation Characteristic for the Relativistic Theory

The invariance of several new component electromagnetic-field vectors with respect to the Lorentz transformation has been demonstrated in the paper. The formalism of the classical relativistic mechanics has been applied in examining both the time-square variable of the field, as well as the square-values of the position coordinates of a moving particle.

The Incompatibinty between Lorentz Transformations and the Inertial Frame of Reference

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On Lorentz Transformations and the Theory of Relativity

In the course of a research study on Lorentz transformations and the theory of relativity, the fundamentals of the relativistic concepts of space and time, the relations of those concepts to Lorentz transformations, and equivalence of mass and energy were studied. Many important references on the said subjects were reviewed. This paper draws attention to some critical questions that have risen in the course of that research study on the concepts of expansion of time and unbounded increase of a particle’s mass with velocity.

Lorentz Transformation Derived from Relativity of Time

The principles of special relativity and Einstein’s simple derivation of the Lorentz transformation are reviewed. A new simple derivation of the Lorentz transformation is developed in this paper, by a new approach of light-pulse observation or time-dilation observation. Therefore, under the two principles of special relativity, there exist two equivalent simple derivations of or two equivalent approaches to the Lorentz transformation. Einstein’s approach emphasizes or highlights relativity of space while our approach emphasizes or highlights relativity of time. This research reveals, in a particular way, the equivalence of relativity of space and relativity of time in special relativity. Combination of Einstein’s approach and the approach developed in this paper makes the methodology of simple derivation of the Lorentz transformation complete and perfect.

Lorentz transformation of three dimensional gravitational wave tensor

Recently there has been more and more interest in the gravitational wave(GW) of moving sources. This paper introduces a Lorentz transformation problem of GWs. Although the BondiMetzner-Sachs(BMS) theory has in principle already included the Lorentz transformation of GWs, the transformation of the three-dimensional GW tensor has not been explicitly calculated before. Within four-dimensional spacetime, GWs have the properties of ‘boost weight zero’ and‘spin weight 2’. This fact makes the Lorentz transformation of GWs difficult to understand. In the current paper, we adopt the traditional three-dimensional tensor description of a GW. Such a transverse-traceless tensor describes the GW freedom directly. We derive the explicit Lorentz transformation of the GW tensor. The transformation is similar to the Lorentz transformation for an electric field vector and a magnetic field vector which are three-dimensional vectors. Based on the deduced Lorentz transformation of the GW three-dimensional tensor, we can construct the gravitational waveform of a moving source with high speed if only the waveform of the corresponding rest waveform is given.

Einstein’s Concept of Clock Synchronization Conflicts with the Second Relativity Postulate

Einstein defined clock synchronization whenever photon pulses with timetags traverse a fixed distance between two clocks with equal time spans ineither direction. Using the second relativity postulate, he found clocksmounted on a rod uniformly moving parallel with the rod’s length cannot besynchronized, but clocks attached to a stationary rod can. He dismissed thisdiscrepancy by claiming simultaneity and clock synchronization were not commonbetween inertial frames, but this paper proves with both Galilean and Lorentztransformations that simultaneity and clock synchronization are preservedbetween inertial frames. His derivation means moving clocks can never besynchronized in a “resting” inertial frame. Ultraprecise atomic clocks intimekeeping labs daily contradict his results. No algebraic error occurred inEinstein’s derivations. The two cases of clocksattached to a rod reveal three major conflicts with the currentsecond postulate. The net velocity between a photon source and detector plusthe “universal” velocity c is mathematically equivalent toEinstein’s clock synchronization method. As the ultraprecise timekeepingcommunity daily synchronizes atomic clocks on the moving Earth withultraprecise time uncertainty well below Einstein’s lowest limit ofsynchronization, the theoretical resolution of the apparent conflict isaccomplished by expanding the second relativity postulate to incorporate thenet velocity between the photon source and detector with the emitted velocity c as components of the total velocity c. This means the magnitudeof the total photon velocity can exceed the speed limit (299792458 m/s) set by the standard velocity c. .

The Vertical Projection Model of Hyperbolic Space and Geometric Illustration of Special Relativity

In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry.

ARCADE 2 Spatial Roar, What Theory of Relation Reveals

The theory of Relation provides an explanation for the Arcade 2 excess. It assumes that the isotropic radio emission measured by the Arcade 2 Collaboration, which is 5 - 6 times brighter than the expected contributions from known extra-galactic sources, is the residue of an immense primitive energy of ordinary matter released by a relativistic bang almost 100 million years after the big bang, which gave the mass-energy the missing gravity to activate contraction. This relativistic bang, via a Lorentz energy transformation, would have released enormous energy held to be the source of the powerful radio noise detected by the NASA researchers. This transformation would have simultaneously triggered the formation of the first stars from dense gas and the reionization of less dense neutral gas. This departs from the idea that continuous reionization began after the formation of the first stars. We emphasize the importance of primordial magnetic fields, which would have generated significant density fluctuations during recombination and acted as a direct seed for cosmic structures. The first stars and galaxies were bathed in strong magnetic fields that gave rise to the radio microwave din (boom) discovered by Arcade 2. These intense magnetic fields alter the trajectory of charged particles zooming near the speed of light, triggering the space roar and emitting radiation that forms a synchrotron radio background. The theory of Relation offers an alternative to the Lambda-CDM cosmological model, which has become the standard model of the big bang, which leads straight to the vacuum catastrophe.

On the Existence of a Minimum Universal Speed of Physical Transmissions Associated with Matter Wave in Special Relativity

In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.

Relativity and the Solar Wind: The Maxwell-Equation Origins of the Solar-Wind Motional Electric Field

The motional electric field of the solar wind as seen by the Earth is examined theoretically and with spacecraft measurements. As it flows outward from the sun, the solar-wind plasma carries a spatially structured magnetic field with it. To calculate the motional electric field of the solar wind the spatially structured magnetic field is Lorentz transformed;for a full physical understanding, it is also necessary to Lorentz transform the current densities and charge densities in the solar wind. Referring to Maxwell’s equations, two related questions are asked: 1) Is the source of the solar-wind motional electric field charge density in the solar wind, time derivatives of current densities in the solar wind, or both? 2) Is the solar-wind motional electric field at Earth an electrostatic field, an induction field, or a superposition of the two? A Helmholtz decomposition of the motional electric field of the solar wind is made into a divergence-origin (electrostatic) and a curl-origin (induction) electric field. The global electric field associated with the outward advection of the global Parker-spiral magnetic field is found to be electrostatic with its origin being a distributed charge density in the solar-wind plasma. The electrostatic versus induction nature of the time-varying electric field associated with the advection of mesoscale magnetic structure varies with time as differently shaped magnetic structures in the solar-wind plasma pass the Earth;the mesoscale structure of the solar-wind plasma contains sheets of space charge and sheets wherein the current density has nonzero time derivatives.

Has the Twin Paradox Really Been Resolved?

Despite several attempts that have been made to explain the twin paradox, which are based on asymmetry and acceleration, it is shown that none of these explanations can resolve the paradox in the general case. Three specific examples of the twin paradox are provided in which the system is completely symmetric;consequently the existing explanations are not able to resolve the paradox.

Relativistic Reduction of the Electron-Nucleus Force in Bohr’s Hydrogen Atom and the Time of Electron Transition between the Neighbouring Quantum Energy Levels

The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.

The Nature of Inertial and Vacuum Gravitational Field

The uniformly accelerated motion is studied in the framework of gauge theory of gravity. It is found that, when an inertial reference system is transformed into a uniformly accelerated system by a local gravitational gauge transformation, a non-trivial gravitational gauge field appears. If there is a mass point in the new reference frame, there will be a non-trivial gravitational force acting on it. The nature and the characteristic of this new force are completely the same as those of the traditional inertial force. This new gravitational force is considered to be the inertial force. Therefore, the nature of inertial force is gravity, which is the basic idea of the equi-valence principle.

A Fractal Menger Sponge Space-Time Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy

The 95.5 percent of discrepancy between theoretical prediction based on Einstein’s theory of relativity and the accurate cosmological measurement of WMAP and various supernova analyses is resolved classically using Newtonian mechanics in conjunction with a fractal Menger sponge space proposal. The new energy equation is thus based on the familiar kinetic energy of Newtonian mechanics scaled classically by a ratio relating our familiar three dimensional space homology to that of a Menger sponge. The remarkable final result is an energy equation identical to that of Einstein’s E=mc2 but divided by 22 so that our new equation reads as . Consequently the energy Lorentz-like reduction factor of percent is in astonishing agreement with cosmological measurements which put the hypothetical dark energy including dark matter at percent of the total theoretical value. In other words our analysis confirms the cosmological data putting the total value of measured ordinary matter and ordinary energy of the entire universe at 4.5 percent. Thus ordinary positive energy which can be measured using conventional methods is the energy of the quantum particle modeled by the Zero set in five dimensions. Dark energy on the other hand is the absolute value of the negative energy of the quantum Schrodinger wave modeled by the empty set also in five dimensions.

The Golden Ratio

The Lorentz transformation (if x = ct) is the same the golden ratio: .

Recent Progress on the Maxwell’s Equations for Describing a Mechano-Driven Medium System with Multiple Moving Objects/Media

Maxwell’s equations for a mechano-driven media system(MEs-f-MDMS)have been used to characterize the electromagnetism of multislow-moving media that may be accelerated with complex trajectories.Such an approach starts from the integral forms of the four physics laws and is different from the classical approach of using the Lorentz transformation for correlating the electromagnetic phenomena observed in two inertial reference frames with relative motion.The governing equations inside the moving object/medium are the MEs-f-MDMS,and those in vacuum are the classical Maxwell’s equations;the full solutions of both reconcile at the medium surface/interface and satisfy the boundary conditions.This paper reviews the background,physical principle,and mathematical derivations for formulating the MEs-f-MDMS.Strategies are also presented for mathematically solving the MEs-f-MDMS.The unique advances made by the MEs-f-MDMS have been systematically summarized,as are their potential applications in engineering.We found that the Lorentz transformation is perfect for treating the electromagnetic phenomena of moving point charges in vacuum;however,for moving objects,the covariance of Maxwell’s equations may not hold,and use of the MEs-f-MDMS may be required if the velocity is low.Finally,recent advances for treating the boundary conditions at the nanoscale without assuming an abrupt boundary are also reviewed.

An Approach to Differential Geometry of Fractional Order via Modified Riemann-Liouville Derivative

In order to cope with some difficulties due to the fact that the derivative of a constant is not zero with the commonly accepted Riemann-Liouville definition of fractional derivative, one （Jumarie） has proposed recently an alternative referred to as （local） modified Riemann-Liouville definition, which directly, provides a Taylor＇s series of fractional order for non differentiable functions. We examine here in which way this calculus can be used as a framework for a differential geometry of fractional or- der. One will examine successively implicit function, manifold, length of curves, radius of curvature, Christoffel coefficients, velocity, acceleration. One outlines the application of this framework to La- grange optimization in mechanics, and one concludes with some considerations on a possible fractional extension of the pseudo-geodesic of thespecial relativity and of the Lorentz transformation.

Uniform-velocity spacetime crystals

We perform a comprehensive analysis of uniform-velocity bilayer spacetime crystals,combining concepts of conventional photonic crystals and special relativity.Given that a spacetime crystal consists of a sequence of spacetime discontinuities,we do this by solving the following sequence of problems:(1)the spacetime interface,(2)the double spacetime interface,or spacetime slab,(3)the unbounded crystal,and(4)the truncated crystal.For these problems,we present the following results:(1)an extension of the Stokes principle to spacetime interfaces,(2)an interference-based analysis of the interference phenomenology,(3)a quick linear approximation of the dispersion diagrams,a description of simultaneous wavenumber and frequency bandgaps,and(4)the explanation of the effects of different types of spacetime crystal truncations and the corresponding scattering coefficients.This work may constitute the foundation for a virtually unlimited number of novel canonical spacetime media and metamaterial problems.