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.

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.

The Incompatibinty between Lorentz Transformations and the Inertial Frame of Reference

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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.

Deriving of the Generalized Special Relativity (GSR) by Using Mirror Clock and Lorentz Transformations

Einstein relativity theory shows its high capability of promoting itself to solve the long stand physical problems. The so-called generalized special relativity (GSR) was derived later, using the beautiful Einstein relation between field and space-time curvature. In this work we re-derive (GSR) expression of time by incorporating the field effect in it, and by using mirror clock and Lorentz transformations. This expression reduces to that of (GSR) the previous conventional one, besides reducing to special relativistic expression. It also shows that the speed of light is constant inside the field and is equal to C. This means that the observed decrease of light in matter and field is attributed to the strong interaction of photons with particles and mediates which causes successive absorption and reemission processes that lead to time delay. This absorption process makes some particles appear to move faster than light within the field or medium. This new expression, unlike that of GSR, can describe time and coordinate relativistic expressions for strong as well as weak fields at constant acceleration.

Elastic Collisions in Minkowski Momentum Space with Lorentz Transformations

We reexamined the elastic collision problems in the special relativity for both one and two dimensions from a different point of view. In order to obtain the final states in the laboratory system of the collision problems, almost all textbooks in the special relativity calculated the simultaneous equations. In contrast to this, we make a detour through the center-of-mass system. The two frames of references are connected by the Lorentz transformation with the velocity of the center-of-mass. This route for obtaining the final states is easy for students to understand the collision problems. For one dimensional case, we also give an example for illustrating the states of the particles in the Minkowski momentum space, which shows the whole story of the collision.

Classical Derivation of Auxiliary Lorentz Transforms: Their Relations with Special Relativity

In this paper we have given a direct deduction of the auxiliary Lorentz transforms from the consideration of Maxwell. In the Maxwell’s theory, if c is considered to be the speed of light in ether space, his equations should be affected on the surface of the moving earth. But curiously, all electromagnetic phenomena as measured on the surface of the moving earth are independent of the movement of this planet. To dissolve this problem, Einstein (1905) assumes that Maxwell’s equations are invariant to all measurers in steady motion which acts as the foundation of Special Relativity. This assumption of Einstein is possible when all four auxiliary Lorentz transforms are real. There is not a single proof that could properly justify Einstein’s assumption. On the contrary it is now known that classical electrodynamics could easily explain all relativistic phenomena rationally.

Reply to “A Simple Derivation of the Lorentz Transformation”

The theory of Relativity is consistent with the Lorentz transformation. Thus Pr. Lévy proposed a simple derivation of it, based on the Relativity postulates. A reply is provided: Some related results (five ones) are found and developed step by step which would invalid it. So Lorentz transformation would not be simply derived by this way. Finally an alternative demonstration of Lorentz transformation is reminded, consistent with Quantum Mechanics.

Measurement Method of Graviton Velocity and Thought on Correcting Lorentz Transformation——The Superluminal Neutrino’s Influence on Special Relativity and Other Physical Theories

After discovery of the superluminal particle and consideration on development of contemporary physical theory research, also on the existing errors and omissions, the principle of constant light speed is found not a necessary condition in derivation of Lorentz Transformation;instead, this thesis proposes the velocity of graviton may feature superluminal, constant velocity in different directions, and independence of inertial reference frame speeds. This is an optional thought of correction. According serial hypothesis, an equation of graviton’s motion trace, i.e., the central curve of nebula density, is established for spiral galaxy. Thus we gain the method to measure velocity of graviton. If to totally avoid problem of limit speed, we have to search for independent of inertia frames, and relevant to space-time properties. Regarding current difficulties of singular points in the Theory of Limited Universe, this thesis points out that the document [1] is the best solution to these difficulties.

Change of Space-Time Structure under Lorentz Transformation

When we study Lorentz transformation in the framework of quantum gauge theory of gravity, we will find that the vacuum gravitational gauge field will be changed under gravitational gauge transformation, which will change the structure of the physical space-time and cause clock dilation effect. The study in this paper provides us with new insights to understand the essential and intrinsic relation between special relativity and general relativity. It provides us with a new way to unify special relativity and general relativity.

Lorentz Transform in Multi-Dimensional Space

It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.

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.

LORENTZ TIME-SPACE TRANSFORMATION IS A APPROXIMATE CALCULATION METHOD IN AERODYNAMICS FOR COMPRESSIBILITY

Between the transformations, witch can transform the compressible wave equation to the incompressible flow, a kind of relativity character can be found, which have the almost equal character as Lorenz time and space relation. This result leads to a new inference: incompressible wave equation with time and space structure of sonic special relativity is only different description of approximate compressible flow. This conclusion can be extended to Euler equation, and arise the interest of "compressible expression" of Maxwell equation. To study the rule of compressibility and thermodynamic character of metastructure field, a try is made by the using Kaman Tsian virtual gas method, this would give the relation, similar as mass and energy of special relativity theory. At first searching a transformation, witch can transform the compressible wave equation to the incompressible flow, but it is almost equal Lorenz time and space relation. So arrive to the conclusion: incompressible wave equation with approximate Lorentz transformation is only different description of compressible flow. This conclusion is expected be used to Maxwell equation, because its wave equation is also perfectly equal form. To search the rule of electromagnet and gravity field, by the using of Kaman Tsian virtual gas method, the relation of mass and energy of relativity theory is given.

Fractional Fourier transform of Lorentz beams

This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields.The fractional Fourier transform （FRFT） is applied to treat the propagation of Lorentz beams.Based on the definition of convolution and the convolution theorem of the Fourier transform,an analytical expression for a Lorentz beam passing through a FRFT system has been derived.By using the derived formula,the properties of a Lorentz beam in the FRFT plane are illustrated numerically.

Lorentz’s Transformations and Gravitation in the Granular Space Theory

Research into the read structure of space at ways leads to the conclusion on the existence of a privileged (absolute) system of reference, with all the equations remaining invariant about Lorentz’s transformations. The expansion of these transformations makes it possible to obtain easily the Schwarzshild matrix and, also, all the results of Einstein’s theory of gravity. The untangling of the physical meaning of velocity as a measure of relative deformation of elementary space cells eliminates, at last, all the paradoxes of Lorentz’s transformations and allows visual observation of the mechanism of gravity and Coulomb interaction in imaginary experiments.

狭义相对论时空观的图像解译

狭义相对论的时空观之所以抽象且难以理解,一方面是因为狭义相对论所涉及的时空效应,如同时性的相对性、长度收缩和时间延缓等,在实际中都很难被观测到;另一方面是因为我们很难将这些时空效应同时直观形象地描述出来,并且给出不同参考系各自观测到的时空效应之间的对应关系。本文针对这一问题,利用图示法将两个参考系在不同时刻观测到的时空图像表示出来,并结合具体数值对他们间的对应关系进行讨论。在图示法中同时考虑了同时性的相对性、长度收缩和时间延缓这三个狭义相对论重要的时空效应,这样可直观形象地看到在一个参考系中得到的观测结果会被另一个参考系所认同,正是这些彼此认同的观测结果构成了狭义相对论的时空观。通过对不同参考系中观察到的时空图像及其相互联系的讨论,可以加深学生对狭义相对论时空效应及洛伦兹变换的物理意义的理解。

德布罗意物质波关系式的推导

本文通过2种直观的方式推导出物质波动量-波长关系式.第1种方式利用洛伦兹变换得出运动粒子“首尾”两端固有时间差,进而通过其对应的相位差以及粒子在空间占据的长度得出相应的物质波波长;第2种方式通过计算与粒子相位变化相适配的行波,得出物质波动量-波长关系式.这两种推导方式较为直观,有助于初学者理解物质波的物理图像.

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. .