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The special theory of relativity holds significant interest for scientific perspectivists. In this paper, I distinguish between two related meanings of “perspectival,” and argue that reference frames are perspectives, provided that perspectival means “being conditional” rather than “being partial.” Frame-dependent properties such as length, time duration, and simultaneity, are not partially measured in a reference frame, but their measurements are conditional on the choice of frame. I also discuss whether the constancy of the speed of light depends on perspectival factors such as the idealized definition of the speed of light in a perfect vacuum and the Einstein synchronization convention. Furthermore, I argue for the view that the constancy of its speed is a robust property of light according to the conditions of currently acceptable experimental setups pertaining to special relativity, and conclude that this view supports perspectivism.

International audience; There are three kinds of sources available to reconstruct the reflections that led Einstein to special relativity: a few contemporary letters and documents, his impersonal accounts of the genesis of this theory, and recollections of his own path. At first glance, contradictions within and between these sources hamper the reliability of Einstein’s accounts. Yet, a closer analysis reveals much more consistency than foreseen and helps eliminate the dubious, contradictory elements. It then becomes possible to combine the three kinds of sources to produce a minimally speculative and yet fairly coherent account of the genesis of special relativity.

To model static shapes in the plane, the ancient Greeks introduced Euclidean geometry. To model motion, on the other hand, Newton added a new time axis, perpendicular to the plane. This may help model a force, applied to an object from the outside to accelerate its original motion.

On Earth, we always measure the constant velocity c of electromagnetic radiation. Einstein assumed the velocity c of light to be constant in all inertial frames and developed his theory of special relativity by considering a light beam that moves back and forth, whereby he derived transformations between the coordinates of two reference frames: A moving reference frame represented by the coordinate system k and the coordinate system k that is at rest with respect to k. However, by applying Einstein’s theory of relativity, with its postulates of relativistic time dilation and length contraction, to electromagnetic radiation that moves only in one direction, either in the direction of or in the opposite direction to a moving inertial frame, it is demonstrated that the constancy of the velocity c of light is not compatible with Einstein’s theory of special relativity. It becomes obvious that Einstein’s relativistic physics must be an unrealistic theory, and consequently, we need an alternative, nonrelativistic, explanation of the constancy of the velocity c of electromagnetic radiation measured on Earth, and for the special and general “relativistic” phenomena.

By deriving the Lorentz transformation from the absolute speed of light, Einstein demonstrated the relativistic variability of space and time, enabling him to explain length contraction and time dilation without recourse to a "luminiferous ether" or preferred frame of reference. He also showed that clocks synchronized at a distance via light signals are not synchronized in a frame of reference differing from that of the clocks. However, by mislabeling the relativity of synchrony the "relativity of simultaneity," Einstein implied that this effect concerns an actual difference in times from one frame to another rather than merely a failure of clock synchronization across frames. As a theory of length contraction and time dilation on the basis of relative motion in the context of the absolute speed of light, special relativity is the definitive interpretation of the Lorentz transformation and the correct explanation of relativistic phenomena. The relativity of simultaneity, as I demonstrate, plays no role in this explanation but instead provides apparent justification for a view of time in which the present moment is frame-dependent. In contrast to its legitimate application, special relativity fails as a theory of time on the basis of the relativity of simultaneity.

In this paper, the authors introduce the (p,q)-trapezoidal integral inequalities, which are the (p,q)-analogues of the recently introduced q-trapezoidal integral inequalities. We derive a new (p,q)-integral identity for twice (p,q)-differentiable function. Utilizing this as an auxiliary result, we establish several new (p,q)-trapezoidal type integral inequalities for the function whose absolute value of twice (p,q)-derivative is (η1,η2)-convex functions. Some special means of real numbers are also given. At the end, we give brief conclusion. It is expected that this method which is very useful, accurate, and versatile will open a new venue for the real-world phenomena of special relativity and quantum theory.

On the basis of all commutation relations of the $$\kappa $$ -deformed phase space incorporating the $$\kappa $$ -Minkowski space-time, we have derived in this paper an extended first approximation of both Maxwell’s equations and Lorentz force in doubly (or deformed) special relativity (DSR). For this purpose, we have used our approach of the special relativistic version of Feynman’s proof by which we have established the explicit formulations of electric and magnetic fields. As in Fock’s nonlinear relativity (FNLR), the laws of electrodynamics depend on the particle mass which therefore constitutes a common point between the two extended forms of special relativity. As one consequence, the corresponding equation of motion contains two different types of contributions. In addition to the usual type, another one emerges as a consequence of the coexistence of mass and charge which are coupled with the $$\kappa $$ -deformation and electromagnetic field. This new effect completely induced by the $$\kappa $$ -deformed phase space is interpreted as the gravitational-type Lorentz force. Unlike FNLR, the corrective terms all depend on the electromagnetic field in DSR.

The time transformation governing the operation of the global positioning system (GPS) clocks and the time corrections required to ensure sustained clock synchronization are determined to be the Selleri time transformation and not the Lorentz time transformation. This condition, as well as GPS-demonstrated light speed anisotropy, falsifies the Lorentz transformations and special relativity.

A non-solipsist form of presentness is usually thought to require the non-relative co-presentness of space-like separated events, where this requirement further implies the non-relative simultaneit...

We review the Thomas precession exhibiting the exact form of the Thomas rotation in the axis-angle parameterization. Assuming three inertial frames S, S′, and S″ moving with arbitrary velocities and with S and S″ having their axes parallel to the axes of S′, we focus our attention on the two essential elements of the Thomas precession: (i) there is a rotation between the axes of frames S and S″ and (ii) the combination of two Lorentz transformations from S to S′ and from S′ to S″ fails to produce a pure Lorentz transformation from S to S″. The physical consequence of (i) and (ii) refers to the impossibility of arbitrary frames S, S′, and S″ moving with non-parallel relative velocities having their axes mutually parallel. Then, we reexamine the validity of (i) and (ii) under the conjecture that time depends on the state of motion of the frames and we show that the Thomas precession assumes a different form as formulated in (i) and (ii).

The GPS satellite clock corrections (along with gravitational redshift) which are necessary for the proper operation of the GPS are fully described without invoking relativity theory as is the practice today.

In the spring of 2020, the schools and universities in the Netherlands were closed for the first time. Urgently and unexpectedly, teaching had to be organised differently. At the time, our students at Utrecht University were well in their third quarter already.

The Carmeli Cosmological Special Relativity theory (CSR) is used to study the universe at early times after the big bang. The universe temperature vs. time relation is developed from the mass density relation. It is shown that CSR is well suited to analyze the nucleosynthesis of the light elements up to beryllium, equivalent to the standard model.

This brief note introduces the conceptual framework of special and general relativity isoclocks and isoframes. Isoclocks and isoframes, as defined herein, can be used to create geometrical maps of space and time (“space-time”) with and without matter embedded. They are useful for having a mental picture of space-time relationships without having to picture 4-dimensional manifolds, which very few students and scientists are able to do. With the aid of the optical lensing definition of curvature as inverse radius, a new gravitational force equation is derived, which also incorporates Einstein’s mass/energy relation in the mx term. Thus, one may see how it is that gravitational force correlates with its time-embedded curvature-squared (Cx2) space in a more accurate formulation than could be envisioned by Newton. This becomes more apparent in high gamma fields, such as found near a black hole horizon. It is hoped that probability theories, such as quantum field theories in curved space-time, might be adaptable to the general relativity isoframe concept introduced herein.

In this paper, a simple test of special relativity involving light transmission through a uniformly moving medium and Fresnel’s drag coefficient is discussed. It is shown using Fresnel drag that there is a difference in propagation time of two light beams travelling in opposite directions in such a medium and that this time difference is independent of the index of refraction of the medium. This result has been experimentally confirmed by Wang et al. but cannot be explained by special relativity. Fresnel drag in the context of ether theory provides a full and accurate explanation that is consistent with the existence of a preferred frame.

Although Einstein’s special theory of relativity (STR) is more than a century old, the relation to reality of its predictions, such as length contraction, for instance, still seems obscure. Here, it is argued that the STR, by reason of observer-dependence and the contradicting nature of its predictions, describes a particular relationship of an observer to reality. Thus, it is concluded that the STR should be looked at as an account for a special kind of optical illusion.

The appropriate placements of the four-dimensional spacetimes of different universes make their coexistence possible, such that corresponding points in spacetimes within the universes are not separated in space or time. The corresponding points do not touch, because they are points in separate spacetimes. The different universes are described heuristically as existing in separate spacetime ‘compartments’. This new conception of many worlds (or universes) is therefore entitled compartment worlds (or universes) in this article. Compartment universes is a potential platform for many-world interpretations and uniform formulation of the natural laws. The two-world background of the special theory of relativity (SR) (involving two compartment universes), demonstrated elsewhere, is re-interpreted as four-world background (involving four compartment universes) in this article.

A new spacetime is isolated and added to the existing spacetime, yielding a pair of co-existing spacetimes, which are four-dimensional inversions of each other. The separation of the spacetimes by the special-relativistic event horizon, compels an interpretation of a pair of symmetrical worlds (or universes) in nature. Furthermore, a two-dimensional intrinsic spacetime that underlies the four-dimensional spacetime in each universe is introduced. The four-dimensional spacetime is the outward manifestation of the two-dimensional intrinsic spacetime, just as the special theory of relativity (SR) on flat four-dimensional spacetime is the outward manifestation of the intrinsic special theory of relativity (∅SR) on flat two-dimensional intrinsic spacetime in each universe. A new set of spacetime/intrinsic spacetime diagrams in the two-world picture is developed, from which intrinsic Lorentz transformation in ∅SR and Lorentz transformation in SR are derived and intrinsic Lorentz invariance and Lorentz invariance are validated in each universe. The SR remains unchanged, but the exposition of its two-world background, the isolated parallel new theory ∅SR and other isolated new features in this article, allow a broader view of SR. This article includes a new addition to the conceptions of many worlds (or universes) in physics and it is effectively a review (in the two-world picture) of the existing geometrical representations of the Lorentz transformation (in a one-world picture).

We critically revisit the definition of thermal equilibrium, in its operational formulation, provided by standard thermodynamics. We show that it refers to experimental conditions which break the covariance of the theory at a fundamental level and that, therefore, it cannot be applied to the case of moving bodies. We propose an extension of this definition which is manifestly covariant and can be applied to the study of isolated systems in special relativity. The zeroth law of thermodynamics is, then, proven to establish an equivalence relation among bodies which have not only the same temperature, but also the same center of mass four-velocity., 15 pages, 0 figures

Space-time symmetries and the principle of relativity alone suffice to obtain Lorentz-like coordinate transformations, in which a free parameter, k, plays the part of c − 2 in special relativity. Several authors have concluded that special relativity does not need the postulate of the constancy of the speed of light (the “second postulate”). I oppose this claim and argue that the transformations have no physical content unless different observers can ensure that they use the same units. The relativity of lengths and durations makes this non-trivial. One usually assumes boostability to solve this problem. I analyze this concept and show it is also non-trivial and cannot be assumed in general. The second postulate offers a way around this, as well as an economical method to match both time and length units. Without it, additional postulates are necessary to ground the physical meaning of the transformations.

A new model is constructed for the Big Bang and the expansion of the Universe, based on a description of a spread of a finite mass of ideal (nonviscous and non-heat-conducting) gas from a point (“initial hot singularity”) to empty space in the framework of general and special relativity (GR and SR). That is, the expansion began inside the sphere with the gravitational radius of the Universe. At first sight, such a spread, like a spread of the singularity of a black hole, is impossible. However, a fundamental difference is that a black hole results from a collapse of a massive star after complete burning of its thermonuclear fuel. Therefore, although at a collapse the temperature, pressure and density grow infinitely, this growth is such that the gravitational forces in the course of compression are always larger than the resisting high pressure. Everything is the opposite at a spread of the initial hot singularity because of the huge (at the beginning of the spread) energy and pressure of all kinds of massless (with zero rest mass) and massive particles and antiparticles, under a negligible contribution of the excess (over antibaryons and positrons) baryons and electrons. In the process of spreading, the situation changes, and the energy of the atoms formed by these baryons and electrons becomes dominant.

This paper analyses magnetosphere-ionosphere (MI) coupling from a perspective that is independent of inertial reference frame, explicitly acknowledging the role of special relativity in MI coupling...

The formulation of special relativity by Albert Einstein in 1905 was based on a symmetry assumption, namely that the laws of physics must be the same for all non-accelerating (i.e. inertial) observers. This simple and very sensible assumption, called the Fundamental Postulate of special relativity, led to one of the most important paradigm shifts in Science. We introduce some of the basic ideas and consequences of special relativity. Inertial frames, which are relevant to both Newtonian mechanics and special relativity, are first defined. Next we show how the Fundamental Postulate leads the conclusion that the speed of light must be the same for all inertial observers. The remarkably consequences resulting from the constancy of the speed of light are then described. These include the unification of space and time into a single spacetime continuum, the relativity of simultaneity, time dilation and Lorentz contraction. Spacetime diagrams are a valuable tool for deciphering and utilizing the consequences of special relativity. We introduce spacetime diagrams and show how to use them to solve simple problems. Finally, we present the “Death Star Betrayal” conundrum as an example of the potential importance of understanding fully the implications of special relativity.

With the mass-energy \(m=E(v=0)/c^{2}\) relation, all pivotal properties of special relativity have been now derived and we consider the related status of SR tests. 1) There are direct tests exploring i) the speed of light in different context, ii) the time dilation, iii) the body contraction, and iv) mass-energy relation. 2) The Michelson-Morley experiment tests indirectly body-contraction and more generally the relativity principle and aether properties. 3) Another family of tests addresses the verification of the Lorentz coordinate transformation. 4) We describe the Doppler effect tests which test relativity per se. We close with a discussion of time and how it is different from space.

Eternalism is the view that all times are equally real. The relativity of simultaneity in special relativity backs this up. There is no cosmically extended, self-existing 'now'. This leads to a tricky problem. What makes statements about the present true? I shall approach the problem along the lines of perspectival realism and argue that the choice of the perspective does. To corroborate this point, the Lorentz transformations of special relativity are compared to the structurally similar equations of the Doppler effect. The 'now' is perspectivally real in the same way as a particular electromagnetic spectrum frequency. I also argue that the ontology of time licensed by perspectival realism is more credible in this context than its current alternative, the fragmentalist interpretation of special relativity., Comment: 24 pages, 3 figures

Quantum mechanics for describing the behavior of microscopic entities and thermodynamics for describing macroscopic systems exhibit separate time concepts. Whereas many theories of modern physics interpret processes as reversible, in thermodynamics, an expression for irreversibility and the so-called time arrow has been developed: the increase of entropy. The divergence between complete reversibility on the one hand and irreversibility on the other is called the paradox of time. Since more than hundred years many efforts have been devoted to unify the time concepts. So far, the efforts were not successful. In this paper a solution is proposed on the basis of matter-energy equivalence with an energetic distinction between matter and mass. By refraining from interpretations predominant in modern theoretical physics, the first and second laws of thermodynamics can be extended to fundamental laws of nature, which are also valid at quantum level.

The successful results of the relativistic form of a quantum field theory that is derived from aLagrangian density justify its general usage. The significance of the Euler-Lagrange equations of a quantum particle is analysed. Many advantages of this approach, like abiding by the conservation laws of energy, momentum, angular momentum, and charge are well known. The merits of this approach also include other properties that are still not well known. For example, it is shown that a quantum function of the form ψ(t, r) describes a pointlike particle. Furthermore, the Lagrangian density and the Hamiltonian density take a different relativistic form – the Lagrangian density is a Lorentz scalar, whereas the Hamiltonian density is the T00 component of the energy-momentum tensor. It is proved that inconsistencies in the electroweak theory stem from negligence of the latter point.

Background : Given the importance of working on Modern Physics in the classroom and considering the great difficulty of understanding by students, it is important to investigate efficient ways to develop the theme. Objective: Identify if there was learning after using a didactic material built using animated gifs and specially after using computer simulations, and to investigate if there is a difference in learning between students who interacted and did not interact with the computer simulations. Design: The design is based on a quantitative analysis made by comparing the results of pre-tests and post-tests of the control and experimental groups. Setting and participants: The research was carried out with 82 students from the third year of high school from a public school. Of these students, 62 form the experimental group, while 20 make up the control group. Data collection and analysis: The activities were developed during the curricular classes of the Physics discipline, with the application of questionnaires immediately before and after the activities. The activities contemplated the four types of mediations (according the CNMT referential), and the control group did not use hypercultural mediation. Results: The outcome of the analysis shows a significant difference in the results of the control and experimental groups, and the experimental group showed a statistically superior growth. Conclusions: Using the four types of mediations, especially hypercultural , students' learning is enhanced for Special Relativity concepts and problem-solving.

Aynştayn Nazariyyesi: Mekân, Zaman ve Kütle Mefhumlarının Tebeddülü, Mehmet Refik Fenmen’in (1882-1951) Einstein’ın Görelilik Teorisini tanıtmak için kaleme aldığı bir eserdir. Mühendis Mektebi ve Darülfünun fizik hocalarından, Mühendis Mektebi müdürlerinden elektrik mühendisi Mehmet Refik’in bu eserinin ilk baskısı 1922’de, ikinci baskısı 1924 yılında yapılmıştır. İki baskı arasında, gerek yöntem gerekse muhteva açısından belirgin farklılıklar vardır. Latin harflerine aktardığımız bu ilk baskıda “medhal” başlığı altında bir giriş yazısı ve “fasıl” başlıklı 13 bölüm yer almaktadır. Herkesin anlayacağı bir şekilde kaleme alınan eser, bazı kusur ve noksanlıklarına rağmen Einstein’ın teorisi hakkında bildiğimiz kadarıyla Türkçe yazılmış ilk müstakil eser olması bakımından önemlidir. Eserin ilk altı bölümü özel görelilik, geri kalan yedi bölümü ise genel görelilik teorisi ile ilgilidir. Bu çalışmada Mehmet Refik’in Aynştayn Nazariyyesi adlı kitabı, ilk defa Latin harflerine harflere aktarılarak sunulmuştur. Yazarın üslubuna riayet etmek için Osmanlıca terimlerde sadeleştirme yapılmamış; çalışmanın sonunda okuyucuya kolaylık sağlaması için seçme bir sözlüğe yer verilmiştir.

A rational approach to the Fermi-Walker transport equation is proposed by deriving it from a condition of “non-rotation”. First, the condition is applied to a tetrad basis and then generalized to an arbitrary space-time four-vector. The method is conceptually simple and apart from the use of tetrad bases in four-dimensional space-time, does not require the effort of visualizing abstract geometrical constructs in spaces of more than three dimensions. The argument develops in the context of the flat space-time of special relativity theory but the final result can be immediately extended to curved space-time.

The purpose of this paper is to show how the result of an erroneous experiment and the lack of understanding of the basic laws of Newtonian mechanics and its application diverted the progress of an important branch of theoretical physics from its true path and led to the creation of the theory of relativity (SR). Every year, many new papers regarding this theory are published that show its many contradictions and anomalies. This paper shows why Einstein's theory of relativity is theoretically and fundamentally incorrect and why, despite its problems, the theory gives some empirical predictions. A more logical solution based on Newtonian mechanics and on experiments and observations plus the concept of ether, leading to the same results, is proposed. As an example, mass-energy equivalence E ≅ m c 2 is derived to show that Newtonian mechanics is adequate in the domain of high-speed particles. The derivation in this paper is by a similar technique to what has been previously published by the same author but with a different method of calculation. The paper also shows that SR does not explain, as claimed by Einstein, the null result of the Michelson and Morley experiment, which is the basis for the theory. It explains why the error in the experiment is hidden and difficult to detect. It also gives more information about the three previously published papers by the same author and endeavors to give a more comprehensive explanation as to what went wrong in this branch of theoretical physics.

20th century physics experimentally established beyond doubt the fact that moving clocks read differently from “static” clocks. This fact is typically interpreted as support for special relativity. On the other hand, the same century produced proof that clocks at various locations in the gravitational field also read differently, and this fact is explained by general relativity, which is, in general, not Lorentz transformable. This paper establishes a common framework for the physics of clocks in these different situations.

The nature and origin of the photon and elementary rest masses are some of the challeng-ing problems that physics face. The approaches used to solve these problems are complex and time-consuming. Specifically, the photon rest mass pays attention to theoretical physi-cists. Many experimental works show that the photon rest mass is non zero. This problem can be solved using generalized potential dependent special relativity, which has been de-rived using simple arguments, and Maxwell’s equations, besides the conventional Einstein energy-momentum relation. The results obtained show that the rest mass of photons and elementary particles are strongly dependent on the vacuum energy and a universal con-stant. This result conforms with the models that predict time decaying vacuum energy as-sociated with production of smaller rest mass particles followed by larger masses. The two potential dependent mass expressions conform with the cosmological models that suggest the photon is generated first by assuming the universe consisting of total constant vacuum with decaying cosmological part and mass generating part. Using Maxwell’s equations, beside plank and De Broglie hypothesis together with special relativity energy-momentum relation the photon rest mass is estimated. It was shown that the photon rest mass is ex-tremely small compared to the electron mass.

By experimental measurements and theoretical analyses, this paper investigates the variation of the Sun’s visual shape and figures out the reasons for the variation of its shape. First, the method of image processing, the method of moments and the least-square method are combined to perform experimental measurements and calculations, and the features of the Sun’s visual shape are extracted from the photos of the Sun. Second, theoretical analyses are conducted based on atmospheric refraction and the Einstein’s special relativity theory. The relationship model is established between the zenith and azimuth angles of the Sun, the velocity of the Sun relative to the Earth, and the observation time and position; the refraction index of the atmosphere is expressed as a function of altitude and wavelength of light; an iterative algorithm is constructed to trace rays of light in the atmosphere; a set of formulas is derived to determine the contraction ratio and contraction direction of the Sun’s visual shape. Finally, the theoretical and experimental results are compared; their relative errors are less than 0.3%, which verifies the theoretical analyses. Both theoretically and experimentally, this research proves that the Sun’s visual shape is an ellipse; its shape variation mainly results from atmospheric refraction effects; and the length contraction effect of the Einstein’s special relativity also contributes a little, except at the time of sunrise and sunset.

What is simultaneous with an event is what can interact with it; events have duration; therefore, any given event has distant events simultaneous with it, even according to Special Relativity. Consequently, the extension of our pre-relativistic judgments of distant simultaneity are largely preserved.

The question of how best to explain magnetic forces between uniformly moving charges has divided physicists. A fictitious dialogue styled on David Hume's Dialogues Concerning Natural Religion (1779) crystallises the various views expressed in the literature around three positions: a) special relativity can explain such forces as a relativistic aspect of electricity; b) special relativity cannot explain such forces and no explanation is required; c) special relativity cannot explain such forces and an alternative explanation is required. The arguments deployed suggest that it is possible to achieve a deeper understanding of the forces between moving charges than is commonly assumed.

The twin paradox, which evokes from the the idea that two twins may age differently because of their relative motion, has been studied and explained ever since it was first described in 1906, the year after special relativity was invented. The question can be asked: "Is there anything more to say?" It seems evident that acceleration has a role to play, however this role has largely been brushed aside since it is not required in calculating, in a preferred reference frame, the relative age difference of the twins. Indeed, if one tries to calculate the age difference from the point of the view of the twin that undergoes the acceleration, then the role of the acceleration is crucial and cannot be dismissed. In the resolution of the twin paradox, the role of the acceleration has been denigrated to the extent that it has been treated as a red-herring. This is a mistake and shows a clear misunderstanding of the twin paradox., Comment: 16 pages, 5 figures

Special relativity theory (SRT) is an iconic physics theory and prototypical for how new knowledge develops in this field. Therefore, learning SRT can be valuable for secondary school students. SRT was introduced in the Dutch pre-university level secondary physics curriculum (VWO) as an elective topic in 2013. However, learning relativistic concepts gives rise to some robust misconceptions and little is known on how to teach this topic at the secondary level. This research project aims to contribute to the scientific knowledge base of learning SRT in secondary physics education through the design and evaluation of a teaching and learning sequence (TLS). The first study deals with students’ pre-instructional reasoning on the light postulate, which states that the speed of light is the same regardless of the state of motion of its source or the observer. We developed a reasoning tool, the Event Diagram, that supports secondary students to perform relativistic thought experiments. We found that students used one of two different models for light propagation. Some of them switched models when they experienced a mismatch between different reference frames. The second study presents an educational reconstruction of SRT, yielding a TLS introducing the light postulate by presenting such a mismatch. Evaluation in small groups showed students developed confidence in the light postulate and used it to derive relativistic concepts. In the final study, the TLS was adapted for the classroom and evaluated in seven classes. Also in this context, the TLS resulted in productive reasoning with the light postulate.

For randomly-moving-particle swarm, the past researches only focused on its whole behavior and few people have studied the special particle swarm formed in it, which leading to the phenomenon and reasons for the spontaneous aggregation of particles in the special particle swarm being still unknown. For such a special particle swarm, we have previously studied the causes of its special relativity phenomenon. Here we show the causes of spontaneous aggregation of “randomly moving” particles. The diffusion kinetics of particles in a special circumstance (that is, in a moving reference frame $\mathcal{R}_u$ relative to the stationary reference frame $\mathcal{R}_0$) are studied theoretically. For the first time, the effects of the location aggregation and velocity direction aggregation of randomly moving particles on the diffusion coefficient are considered, and the corresponding generalized diffusion equation is deduced employing concise mathematical logic and Mathematica software.

Length contraction predicted by special relativity, requiring that two observers in different inertial frames measure each other's rods shorter than his own, is shown to be a logical contradiction and therefore invalid.

An axiomatic theory is proposed that reconciles the existence of an absolute scale for time (Planck time) and special relativity. According to this theory speed of light c becomes a variable which is proposed to be taken as the fifth dimension.

We study the effect of the generation of the mechanical transverse wave (MTW) travelling in the opposite direction (OD) to a moving medium (MM) on the relativistic energy conservation law (RECL). From the viewpoint of the relativity of simultaneity (RS), the time on the coordinate coinciding with the advance end of the wave (AEW) travelling toward the rear of the MM passes faster than that on the coordinate coinciding with the wave source (WS). Then the AEW in the MM travels forward compared to that in the rest frame of reference (RFR) which is stationary relative to the medium when the time on the coordinate coinciding with the WS is same for each inertial frame of reference (IFR). Hence, the coordinate interval (CI) between the AEW and WS in the MM is observed to be larger than that between them in the RFR. We show that this difference holds true for the CI of any portion having transverse velocities mutually converted by the Lorentz transformation (LT). This difference in the CI leads to that in the rest mass (RM). We demonstrate that the RM included in wave motion (WM) in the MM is larger than one included in WM in the RFR when comparing the portions having transverse velocities mutually converted by the LT. This relation holds true for all portions in WM. Therefore, the total coordinate interval of the portion (CIP) and total RM (TRM) included in WM in the MM (WMMM) are large compared to them included in WM in the RFR. Furthermore, we compare the relativistic kinetic energy (RKE) of the MTW travelling in the OD to the MM (ODMM) with that of the MTW propagating in the direction vertical to the moving direction of the medium. We prove that the CIP and RM included in the former MTW are larger than them included in the latter MTW when comparing each portion with the same transverse velocity (TV). Moreover, the total CIP and TRM included in the former MTW are also large compared to them included in the latter MTW. The reason for these is that the latter CIP and RM are equal to them in the RFR when comparing the portions having transverse velocities mutually converted by the LT. On the other hand, the energy supplied to generate each MTW is the same. From these, we demonstrate that the RKE of the MTW travelling in the ODMM can be larger than the total relativistic energy (TRE) of the MTW propagating in the direction vertical to the moving direction of the medium. Consequently, we propose a violation of the RECL and Einstein’s principle of relativity (EPR) because the TRE is not necessarily conserved in the IFR in which the medium is moving.

This chapter uses gold as a vehicle for showing the relevance of Einsteinian physics. Special relativity combined with quantum mechanics explains the unique color and properties of gold. It is intended for teachers who look for material for a middle-to-upper senior school module on Einsteinian physics that combines relativity, nuclear physics, atomic physics and astrophysics. The chapter summarizes the discoveries that finally gave satisfactory answers to all questions. Gold is no longer a mystery. Instead, it is a wonderful case study for the importance of Einsteinian physics to understand the universe. Electrons have an important property called quantum spin, discussed more in the chapter on atoms. The Einstein-First project has used the mystery story in the chapter to motivate classroom instruction from year 3 to year 9. The e-resources contain examples of relevant classroom activities.

This chapter suggests a view towards physics education that reflects Einstein's perspective on the purpose, content, and methods of teaching physics. It introduces how the people practice Einsteinian physics education in South Korea, which can help their students see the forest of physics and deeply understand the nature of physics. The chapter is intended for readers who wish to obtain historical and philosophical background knowledge in Einsteinian physics education, and also, for those who wish to further their cultural content knowledge in special and general relativity. Einstein emphasised that the concept of inertial frames, which is assumed in Newtonian mechanics and even in special relativity, has been abolished in general relativity. Einsteinian physics education in the Korean context is a physics education that reflects Einstein's perspective on physics education, which concerns the purpose, the contents, and the methods of teaching physics.

This paper pinpoints a severe infirmity of the Lorentz Transformation in the Special Theory of Relativity. Even if it were true, its ambit is very much limited. Out of infinite events happening in the universe, it covers only the events of detecting light signals at the spatial points lying on a straight line in the direction of the relative velocity between the two inertial frames. This paper points out that the slowing down of moving clocks is not a prediction of Lorentz Transformation and hints at the possibility of attributing the observed slowing down of fast-moving clocks to the Relativistic Variation of Mass with Velocity. This paper concludes that from the fact that the same Reality is perceived differently by the observers in different inertial frames, we can draw a straightforward explanation for the constancy of light's speed in all inertial frames without any need for bringing in narrow-scoped and unrealistic Lorentz Transformation.