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The explanation of Einstein’s special theory of relativity in his original 1905 paper is examined. His analysis is confusing, as terms x, y, z, t, etc., have different meanings at various points, and he presents equations based on different and inconsistent assumptions. Adding subscripts clarifies these issues but exposes errors in his reasoning. To calculate his transformation equations, he selects a combination of equations which gives results matching the Lorentz transformation but he ignores other possible valid solutions. Also his calculations contain serious errors. Therefore, he fails to prove that his theory leads to the Lorentz equations as a unique solution. Einstein’s analysis includes “moving” clocks which show “stationary” time t, so the idea that a moving clock should run slower than a stationary clock is incompatible with his theory. Also, his calculation of time dilation contains serious errors. As a result, he fails to provide a theoretical justification for his famous “clocks paradox.” [ABSTRACT FROM AUTHOR]

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For decades, historians have debated the origins of Einstein's special theory of relativity. The derivation of the Lorentz Transformations given by Einstein in 1905 is studied in detail; and it is found to be mathematically inconsistent, and thus in error. Therefore, he must have been aware of the transformations at the time of writing the paper, which is an extremely minority opinion in the general literature. His attempt to rederive them starting from the synchronization condition is incorrect. Though the derivation is flawed, it does not affect many of the concepts he put forth that flow from the Lorentz Transformations. The observations given here will help resolve a long-standing dispute over the priority of the discovery of various parts of the theory. The priority, which is presently concentrated with Einstein, may need to be redistributed between Einstein, Lorentz, Poincare', Larmor, Voigt, and others. [ABSTRACT FROM AUTHOR]

In his groundbreaking 1905 paper on special relativity, Einstein distinguished between local and global time in inertial systems, introducing his famous definition of distant simultaneity to give physical content to the notion of global time. Over the following decade, Einstein attempted to generalize this analysis of relativistic time to include accelerated frames of reference, which, according to the principle of equivalence, should also account for time in the presence of gravity. Characteristically, Einstein's methodology during this period focused on simple, intuitively accessible physical situations, exhibiting a high degree of symmetry. However, in the final general theory of relativity, the a priori existence of such global symmetries cannot be assumed. Despite this, Einstein repeated some of his early reasoning patterns even in his 1916 review paper on general relativity and in later writings. Modern commentators have criticized these arguments as confused, invalid, and inconsistent. Here, we defend Einstein in the specific context of his use of global time and his derivations of the gravitational redshift formula. We argue that a detailed examination of Einstein's early work clarifies his later reasoning and demonstrates its consistency and validity. [ABSTRACT FROM AUTHOR]

A popular physics legend holds that scissors can cut paper with a speed faster than light. Here this counter-intuitive myth is investigated theoretically using four simple examples of scissors. For simplicity, all cases will involve a static lower scissors blade that remains horizontal just under the paper. In the first case, the upper blade will be considered perfectly rigid as it rotates around and through the paper, while in the second case, a rigid upper blade will drop down to cut the paper like a guillotine. In the third case, the paper is cut with a laser rotating with a constant angular speed that is pointed initially perpendicular to the paper at the closest point, while in the fourth case, the uniformly rotating laser is pointed initially parallel to the paper. Although details can be surprising and occasionally complex, all cases allow sections of the paper to be cut faster than light without violating special relativity. Therefore, the popular legend is confirmed, in theory, to be true. [ABSTRACT FROM AUTHOR]

The derivation of mass-energy equivalence, called Einstein's Relation, was derived through different ways by Einstein and appeared in his article published in 1905. In this research paper, the authors present Einstein's method in new ways, where a general method valid to all of the relativistic and non-relativistic phenomena is proposed by applying the physical law and the classical principle of relativity. [ABSTRACT FROM AUTHOR]

A recent paper Pal (2022 Eur. J. Phys. 43 015204) puts into covariant form an extension of relativistic classical electromagnetism from free space to a linearly polarizable medium. The paper is based on the assumption that the relativistic tensor, F μ ν , which is a tensor in free space, will also be a tensor in a linear medium. Pal constructs a proposed covariant formulation that gives F μ ν for a medium moving with constant velocity, v, in terms of F μ ν for the medium at rest. However, although F μ ν has been proven to be a relativistic tensor in free space, we show that it is not a tensor in a linear medium. This means that the covariant extension proposed by Pal fails. [ABSTRACT FROM AUTHOR]

The core of this volume is formed by four chapters (2–5) with detailed reconstructions of the arguments and derivations in four of Einstein's most important papers, the three main papers of his annus mirabilis 1905 (on the light quantum, Brownian motion, and special relativity) and his first systematic exposition of general relativity of 1916. The derivations are given in sufficient detail and in sufficiently modernized notation (without any serious distortion of the originals) for an undergraduate physics major to read and understand them with far less effort than it would take him or her to understand (English translations of) Einstein's original papers. Each of these four papers is accompanied by a detailed introduction, which covers the conceptual development of the relevant field prior to Einstein's contribution to it and corrects some of the myths surrounding these papers that still have not been fully eradicated among physicists. (One quibble: though Kennedy correctly points out that the goal of the light quantum paper was not to explain the photoelectric effect, it is also not quite right to say that 'it was written to explain the Wien region of blackbody radiation' (p. xv). Einstein used this explanatory feat as the central argument for his light quantum hypothesis.) These four chapters then are the most valuable part of the volume. They could be used, independently of one another, but preferably in conjunction with Einstein's original texts, in courses on quantum mechanics, statistical mechanics, electrodynamics, and general relativity, respectively, to add a historical component to such courses. As a historian of science embedded in a physics department who is regularly called upon to give guest lectures in such courses on the history of their subjects, I can highly recommend the volume for this purpose. However, I would not adopt this volume as (one of) the central text(s) for a course on the history of modern physics. For one thing, chapter 1, which in just 26 pages (not counting six pages of notes and references) covers everything from Copernicus, Galileo, Kepler and Newton to Maxwell and Lorentz to Einstein's early biography to a cardboard version of Popper versus Kuhn, is too superficial to be useful for such a course. To a lesser extent, this is also true for chapter 6, which compresses the development of quantum theory after Einstein's 1905 paper into 20 pages (plus seven pages of notes and references) and for chapter 7, a brief epilogue. However, this is not my main worry. One could easily supplement or even replace the bookends of the volume with other richer sources and use this volume mainly for its excellent detailed commentaries on some Einstein classics in the four chapters in between. My more serious reservation about the use of the volume as a whole in a history of physics course, ironically, comes from the exact same feature that made me whole-heartedly recommend its core chapters for physics courses. This is especially true for the chapters on special and general relativity. How useful is it for a student to go through, in as much detail as this volume provides, the Lorentz transformation of Maxwell's equations in vector form? I can see how a student in an E&M class (with a section on special relativity) might benefit from this exercise. The clumsiness of the calculations in vector form by Lorentz and Einstein could help a student encountering Maxwell's equations in tensor form for the first time appreciate the advantages of the latter formalism. Similarly, it would be useful for a student in a GR class to go through the basics of tensor calculus in the old-fashioned but not inelegant mathematical introduction of Einstein's 1916 review article on general relativity. This could reinforce mastery of material that a student in a GR class will have to learn anyway (though Einstein's presentation of the mathematics of both special and gene [ABSTRACT FROM AUTHOR]

'Small-scale cosmology' is a theory designed to incorporate the linear redshift versus distance relation, which is inferred from observations, into the theoretical framework independent of the global Robertson–Walker–Friedman (RWF)-type models. The motivation behind this is that the RWF cosmological models, based on the assumptions of homogeneity and a constant matter density, as well as the concept of expanding space inherent to them are not applicable on the scales of observations from which the linear Hubble law is inferred. Therefore, explaining the Hubble law as the small redshift limit of the RWF model or as an effect of expanding space is inconsistent. Thus, the Hubble linear relation between the redshift of an extragalactic object and its distance should be considered an independent law of nature valid in the range of the distances where the RWF cosmology is not valid. In general, the theory, based on that concept, can be developed in different ways. In the present paper, 'small-scale cosmology' is formulated as a theory operating in the (redshift–object coordinates) space, which allows developing a conceptual and computational basis of the theory along the lines of that of special relativity. In such a theory, the condition of invariance of the Hubble law with respect to a change in the observer acceleration plays a central role. In pursuing this approach, the effectiveness of group theoretical methods is exploited. Applying the Lie group method yields transformations of the variables (the redshift and space coordinates of a cosmological object) between the reference frames of the accelerated observers. In this paper, the transformations are applied to studying the effects of the solar system observer acceleration on the observed shape, distribution and rotation curves of galaxy clusters. [ABSTRACT FROM AUTHOR]

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Aggregative moral theories face a series of devastating problems when we apply them in a physically realistic setting. According to current physics, our universe is likely infinitely large, and will contain infinitely many morally valuable events. But standard aggregative theories are ill-equipped to compare outcomes containing infinite total value. So, applied in a realistic setting, they cannot compare any outcomes a real-world agent must ever choose between. This problem has been discussed extensively, and non-standard aggregative theories proposed to overcome it. This paper addresses a further problem of similar severity. Physics tells us that, in our universe, how remotely in time an event occurs is relative. But our most promising aggregative theories, designed to compare outcomes containing infinitely many valuable events, are sensitive to how remote in time those events are. As I show, the evaluations of those theories are then relative too. But this is absurd; evaluations of outcomes must be absolute! So we must reject such theories. Is this objection fatal for all aggregative theories, at least in a relativistic universe like ours? I demonstrate here that, by further modifying these theories to fit with the physics, we can overcome it. [ABSTRACT FROM AUTHOR]

In 1909, Lewis and Tolman, then physical chemists at the Massachusetts Institute of Technology, wrote a paper which built on an earlier paper by Lewis. This gave a more mechanics-based approach to the subject, in contrast to Einstein's original work which drew on electrodynamics. This work played a significant role in the early development of special relativity theory, then only four years old and still under heated discussion worldwide. This paper with Tolman, though a relatively minor part of Lewis's overall work, has historical and pedagogical value and gives a glimpse of his breadth, early growth and influence as a scientist. The present article outlines the arguments of their 1909 paper, and places it in context. [ABSTRACT FROM AUTHOR]

This paper investigates GPT-4's role as a research partner, particularly its ability to scrutinize complex theories like Einstein's Special Relativity Theory (SRT). GPT-4's advanced capabilities prove invaluable in complex research scenarios where human expertise might be limited. Despite initial biases, an inclination to uphold Einstein's theory, and certain mathematical limitations, GPT-4 validated an inconsistency within the SRT equations, leading to a questioning of the theory's overall validity. GPT-4 contributed significantly to honing the analytical approach and expanding constraints. This paper explores the strengths and challenges associated with the use of GPT-4 in scientific research, with a strong emphasis on the need for vigilance concerning potential biases and limitations in large language models. The paper further introduces a categorization framework for AI collaborations, and specific guidelines for optimal interaction with advanced models like GPT-4. Future research endeavors should focus on augmenting these models' precision, trustworthiness, and impartiality, particularly within complex or contentious research domains. [ABSTRACT FROM AUTHOR]

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This paper proposes an original and thorough analysis of the behavior of electromagnetic waves in the presence of moving bodies by using the finite difference time domain (FDTD) method. Movements are implemented by changing positions of the objects at each time step, through the classical FDTD time loop. This technique is suitable for non-relativistic speeds, thus for most encountered problems in antennas and propagation domain. The numerical aspects that need to be considered are studied. Then, different bodies in motion are examined: plane wave source with matching resistors, observation point, inclined partially reflecting surface (PRS), line source, and metallic cylinder illuminated by a plane wave. The results are compared with those of special relativity which are considered as the references. Some aspects of special relativity are present in the direct FDTD approach, such as the independence of the velocity of electromagnetic wave propagation with the speed of the source and Lorentz local time (with a different physical interpretation). It is shown that the amplitude of the electric field for a moving plane wave source does not increase with the speed of motion, if the impedance of the source is small. Moreover, for a moving scattering metallic wire, one can observe a phenomenon similar to shock waves. [ABSTRACT FROM AUTHOR]

One of the biggest unsolved problems in physics is explaining what time is. The paper explains what time is in kinematics theories. It has been proved that in the kinematics of Special Theory of Relativity (STR) and Special Theory of Ether (STE) time is measured by the light clock. Therefore, all properties of time in kinematics result from the properties of a signal clock. The paper explains the time dilation phenomenon on the basis of STE. The presented explanation is not only a classic description of time dilation but is based on the construction of an innovative technical model of this phenomenon. Time dilation is due to the properties of the light clock. It is a natural property of this clock. The article shows that the claim that the speed of light in a vacuum is the maximum speed in the real world has no theoretical basis. In modern physics, such a doctrine has been adopted as a result of an overinterpretation of the mathematics on which the Special Theory of Relativity is based. The presented model shows how, using atomic clocks, it may be possible to determine the movement in relation to the universal frame of reference in which electromagnetic signals propagate. This article contains only original research. [ABSTRACT FROM AUTHOR]

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This paper develops the approach to special relativity put forward by John S. Bell. The classical dynamics of an electron orbiting a nucleus in uniform motion is solved analytically and compared to numerical simulations for an accelerated nucleus. The relativistic phenomena of length contraction and time dilation are shown to result from the electric and magnetic forces on the electron when its motion is analyzed in a single frame of reference. The relevance of these results for understanding the theory of special relativity is discussed. In this paper, the author explores a suggestion by John Bell for teaching special relativity: to introduce length contraction and time dilation as dynamical phenomena arising from the laws of motion, without reference to the Lorentz transformations. The paper provides historical and philosophical insight into the development of special relativity alongside an analysis of electron orbits in a classical model of an atom. Using only the Lorentz force law, the author illustrates the deformation of orbits of moving and accelerating atoms with approximate, exact, and numerical calculations that reveal time dilation and length contraction. Instructors may find these derivations useful in teaching courses on modern physics, relativity, classical mechanics, electrodynamics, or numerical methods. [ABSTRACT FROM AUTHOR]

It is generally assumed that compatibility with special relativity is guaranteed by the invariance of the fundamental equations of quantum physics under Lorentz transformations and the impossibility of transferring energy or information faster than the speed of light. Despite this, various contradictions persist, which make us suspect the solidity of that compatibility. This paper focuses on collapse theories—although they are not the only way of interpreting quantum theory—in order to examine what seems to be insurmountable difficulties we encounter when trying to construct a space–time picture of such typically quantum processes as state vector reduction or the non-separability of entangled systems. The inescapable nature of such difficulties suggests the need to go further in the search for new formulations that surpass our current conceptions of matter and space–time. [ABSTRACT FROM AUTHOR]

Albert Einstein proposed a unification of mechanics and electrodynamics by his special theory of relativity, which describes point-like particles moving through empty space. We show in this paper that mechanics and electrodynamics can be unified in Euclidean space if we relax the idea of point-like particles by describing fermions and bosons as spatially extended wave objects. Based on the process theory of gases presented in Paper II [Kalies et al., AIP Adv. 13(5), 055317 (2023)] of this series, we consider a confined photon gas and show that the momentum work of photons leads to an analogous description of matter and light and to the insight that electromagnetic energy is momentum energy. We present the unified energy equations, which do justice to the wave nature of matter, and it is the momentum work that links physical theories. Without momentum energy, which is larger in real terms than the kinetic energy of mechanics, the theoretical edifice of modern physics, at the fundamental level, is incomplete. [ABSTRACT FROM AUTHOR]

This paper employs a novel φ6-model expansion approach to get dark, bright, periodic, dark-bright, and singular soliton solutions to the complex Ginzburg-Landau equation with dual power-law nonlinearity. The dual-power law found in photovoltaic materials is used to explain nonlinearity in the refractive index. The results of this paper may assist in comprehending some of the physical effects of various nonlinear physics models. For example, the hyperbolic sine arises in the calculation of the Roche limit and the gravitational potential of a cylinder, the hyperbolic tangent arises in the calculation of the magnetic moment and the rapidity of special relativity, and the hyperbolic cotangent arises in the Langevin function for magnetic polarization. Frequency values, one of the soliton's internal dynamics, are used to examine the behavior of the traveling wave. Finally, some of the obtained solitons' three-, two-dimensional, and contour graphs are plotted. [ABSTRACT FROM AUTHOR]

In the theory of special relativity, energy can be found in two forms: kinetic energy and rest mass. The potential energy of a body is actually stored in the form of rest mass, the interaction energy too, but temperature is not. Information acquired about a dynamical system can be potentially used to extract useful work from it. Hence, the "mass–energy–information equivalence principle" that has been recently proposed. In this paper, it is first recalled that for a thermodynamic system made of non-interacting entities at constant temperature, the internal energy is also constant. So, the energy involved in a variation in entropy ( T Δ S ) differs from a change in the potential energy stored or released and cannot be associated to a corresponding variation in mass of the system, even if it is expressed in terms of the quantity of information. This debate gives us the opportunity to deepen the notion of entropy seen as a quantity of information, to highlight the difference between logical irreversibility (a state-dependent property) and thermodynamical irreversibility (a path-dependent property), and to return to the nature of the link between energy and information that is dynamical. [ABSTRACT FROM AUTHOR]

This paper presents a method for parameterizing new Lorentz spacetime coordinates based on coupled parameters. The role of symmetry in rapidity in special relativity is explored, and invariance is obtained for new spacetime intervals with respect to the Lorentz transformation. Using the Euler–Hamilton equations, an additional angular rapidity and perpendicular rapidity are obtained, and the Hamiltonian and Lagrangian of a relativistic particle are expanded into rapidity spectra. A so-called passage to the limit is introduced that makes it possible to decompose physical quantities into spectra in terms of elementary functions when explicit decomposition is difficult. New rapidity-dependent Lorentz spacetime coordinates are obtained. The descriptions of particle motion using the old and new Lorentz spacetime coordinates as applied to plane laser pulses are compared in terms of the particle kinetic energy. Based on a classical model of particle motion in the field of a plane monochromatic electromagnetic wave and that of a plane laser pulse, rapidity-dependent spectral decompositions into elementary functions are presented, and the Euler–Hamilton equations are derived as rapidity functions in 3+1 dimensions. The new and old Lorentz spacetime coordinates are compared with the Fermi spacetime coordinates. The proper Lorentz groups SO(1,3) with coupled parameters using the old and new Lorentz spacetime coordinates are also compared. As a special case, the application of Lorentz spacetime coordinates to a relativistic hydrodynamic system with coupled parameters in 1+1 dimensions is demonstrated. [ABSTRACT FROM AUTHOR]

The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light always remains the same. Consequently, a wave packet of light exhibits different frequencies, wavelengths, and amplitudes. In this paper, we present a local approach to the relativistic Doppler effect based on relativity, spatial and time translational symmetries, and energy conservation. Afterwards, we investigate the implications of the relativistic Doppler effect for the quantum state transformations of wave packets of light and show that a local photon is a local photon at the same point in the spacetime diagram in all inertial frames. [ABSTRACT FROM AUTHOR]

The study of the interaction between moving plasma-coated objects and electromagnetic (EM) waves is the essential factor for the EM problems of high-speed targets. In this paper, the physical model of a moving dispersive medium is developed based on the principle of special relativity to study the EM properties of highspeed moving targets coated with plasma sheath. First, the Lorentz transform is used to introduce the incident plane wave into moving frame. Second, based on the proposed EM model, the EM problems are solved in moving frame by the shift-operator (SO) FDTD numerical algorithm. Finally, the EM results are further converted back into the laboratory frame to analyze the scattered properties of high-speed plasma coated objects. The validity of the proposed algorithm is verified by comparison with the reference solution. On this basis, the influence of relativistic effects produced by the motion of the object and the EM properties of the plasma on the scattering fields of high-speed targets are investigated. This work expands the applicability of the FDTD method and provides a theoretical foundation for solving the scattering properties of high-speed plasma-coated complex shape objects through numerical methods. [ABSTRACT FROM AUTHOR]

A semantic adjustment to what physicists mean by the terms 'special relativity' and 'general relativity' is suggested, which prompts a conceptual shift to a more unified perspective on physics governed by the Poincaré group and physics governed by the Galilei group. After exploring the limits of a unified perspective available in the setting of 4-dimensional spacetime, a particular central extension of the Poincaré group—analogous to the Bargmann group that is a central extension of the Galilei group—is presented that deepens a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting. The immediate focus of this paper is classical physics on affine 4-dimensional and 5-dimensional spacetimes ('special relativity' as redefined here), including the electrodynamics that gave rise to Poincaré physics in the first place, but the results here may suggest the existence of a 'Galilei general relativity' more extensive than generally known, to be pursued in the sequel. [ABSTRACT FROM AUTHOR]

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Copyright of Physics Essays is the property of Physics Essays Publication and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In special relativity, the time dilation formula has been obtained by particles propagation in a straight line trajectory relative to an observer in motion. Up to now, there are no available formulas for other possible trajectories of particles. However, this paper obtains formulas of time dilation for several trajectories of particle such as parabolic, elliptic, and circular and finds a relatively accurate trajectory. The obtained formulas are employed in order to analyze the time dilation of the muon particles decay. In this paper, it is found that the time dilation of the parabolic and the elliptical trajectories exceed the corresponding results utilizing the standard Lorentz-Einstein time dilation formula. Consequently, if we are able to control the trajectory of unstable particles by some external forces, then their life-times might be increased. Probably, the increase in lifetime via a curved trajectory occurs at lower relative velocity & acceleration energy if compared to the straight line trajectory. In addition, the circular trajectory leads to multiple values of time dilation at certain velocities of an observer in motion, which may give an interpretation of fluctuations of time dilation in quantum mechanics. The result arises from the present relatively accurate formula of time dilation that is very close to the experimental data of muon decay (CERN experiment) when it is compared to the result obtained by the Lorentz-Einstein formula. Finally, it may be concluded that the time dilation not only depends on relative velocity and acceleration energy of particles but also on curved trajectories. The present work may attract other researchers to study different trajectories. [ABSTRACT FROM AUTHOR]

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Gu, continues the author's previous efforts [[11]] to develop a fully "realist" representation - with observer-independent space and time coordinates - of spacetime that is consistent with GR by deriving a representation for the spinor connection within such a spacetime [[12]]. The second paper, by Illuminati, Lambiasi, and Petruzziello, extends previous work [[13]] on the breaking of Lorentz symmetry that results when the Heisenberg uncertainty principle is generalized to account for the effects of long-range spacetime curvature on locally-observable momenta [[14]]. Ng equates the "quanta" of spacetime foam with holographically encoded bits of information, and shows that these quanta must be distinguishable - i.e., must collectively encode macroscopic, multibit information - to generate a macroscopic spacetime. Nicolas Gisin [[1]] has emphasized that, prior to Einstein's imposition of a finite speed of light, and hence of information, in the Special Theory of Relativity, physics was nonlocal. [Extracted from the article]

The paper focuses on applying the octonions to explore the influence of the external torque on the angular momentum of fluid elements, revealing the interconnection of the external torque and the vortices of vortex streets. J. C. Maxwell was the first to introduce the quaternions to study the physical properties of electromagnetic fields. The contemporary scholars utilize the quaternions and octonions to investigate the electromagnetic theory, gravitational theory, quantum mechanics, special relativity, general relativity, curved spaces, and so forth. The paper adopts the octonions to describe the electromagnetic and gravitational theories, including the octonionic field potential, field strength, linear momentum, angular momentum, torque, and force. In case the octonion force is equal to zero, it is able to deduce eight independent equations, including the fluid continuity equation, current continuity equation, and force equilibrium equation. Especially, one of the eight independent equations will uncover the interrelation of the external torque and angular momentums of fluid elements. One of its inferences is that the direction, magnitude, and frequency of the external torque must impact the direction and curl of the angular momentum of fluid elements, altering the frequencies of Karman vortex streets within the fluids. It means that the external torque is interrelated with the velocity circulation, by means of the liquid viscosity. The external torque is able to exert an influence on the direction of downwash flows, improving the lift and drag characteristics generated by the fluids. [ABSTRACT FROM AUTHOR]

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Fragmentalism was first introduced by Kit Fine in his 'Tense and Reality' (Modality and tense: philosophical papers, Oxford University Press, Oxford, pp 261–320, 2005). According to fragmentalism, reality is an inherently perspectival place that exhibits a fragmented structure. The current paper defends the fragmentalist interpretation of the special theory of relativity, which Fine briefly considers in his paper. The fragmentalist interpretation makes room for genuine facts regarding absolute simultaneity, duration and length. One might worry that positing such variant properties is a turn for the worse in terms of theoretical virtues because such properties are not involved in physical explanations and hence theoretically redundant. It will be argued that this is not right: if variant properties are indeed instantiated, they will also be involved in straightforward physical explanations and hence not explanatorily redundant. Hofweber and Lange, in their 'Fine's Fragmentalist Interpretation of Special Relativity' (Noûs 51:871–883, 2017), object that the fragmentalist interpretation is in tension with the right explanation of the Lorentz transformations. It will be argued that their objection targets an inessential aspect of the fragmentalist framework and fails to raise any serious problem for the fragmentalist interpretation of special relativity. [ABSTRACT FROM AUTHOR]

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This paper addresses and proposes to resolve a longstanding problem in the philosophy of physics: whether and in what sense Albert Einstein's Chasing the Light thought experiment was significant in the development of the theory of special relativity. Although Einstein granted this thought experiment pride of place in his 1949 Autobiographical Notes, philosophers and physicists continue to debate about what, if anything, the experiment establishes. I claim that we ought to think of Chasing the Light as Einstein's first attempt to problematize the very idea of the electromagnetic ether frame, and that it thereby contributed to his eventual adoption of one of special relativity's two foundational axioms: the "light postulate". This interpretation requires the assumption that Einstein had presupposed special relativity's other axiom, the "principle of relativity", when initially considering Chasing the Light. This argument is novel insofar as it provides evidence that such a presupposition by Einstein is both conceptually and historically plausible. Moreover, this paper directly challenges John D. Norton's compelling claim that Chasing the Light is best understood as a refutation of emission theories of light propagation; while both interpretations of the experiment are conceptually coherent, I argue that the interpretation found in this paper is supported more straightforwardly by historical evidence. [ABSTRACT FROM AUTHOR]

Metaphysicians who are aware of modern physics usually follow Putnam (1967) in arguing that Special Theory of Relativity is incompatible with the view that what exists is only what exists now or presently. Partisans of presentism (the motto 'only present things exist') had very difficult times since, and no presentist theory of time seems to have been able to satisfactorily counter the objection raised from Special Relativity. One of the strategies offered to the presentist consists in relativizing existence to inertial frames. This unfashionable strategy has been accused of counterfeiting, since the meaning of the concept of existence would be incompatible with its relativization. Therefore, existence could only be relativistically invariant. In this paper, I shall examine whether such an accusation hits its target, and I will do this by examining whether the different criteria of existence that have been suggested by the Philosophical Tradition from Plato onwards imply that existence cannot be relativized. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce a novel argument (the “Region Argument”) that objects do not have frame‐independent shapes in special relativity. The Region Argument lacks vulnerabilities present in David Chalmers' argument for that conclusion based on length contraction. We then examine how views on persistence interact with the Region Argument. We argue that this argument and standard four‐dimensionalist assumptions entail that nothing in a relativistic world has any shape, not even stages or the regions occupied by them. We also argue that endurantists have viable ways of preserving shape despite the Region Argument. The upshot of these arguments is that contrary to conventional wisdom, considerations about shape in relativity support endurantism rather than four‐dimensionalism. We conclude by examining the implications of our discussion for the debate over Edenic shapes, noting that endurantists have a satisfying response to skeptical arguments about Edenic shapes similar to the one they have against the Region Argument. [ABSTRACT FROM AUTHOR]

In this paper, it is argued that there exist different interdisciplinary abductive analogies between Keynes' monetary-production theory and Einstein's theories of relativity. Based on some of the equations in Einstein's special theory of relativity vis-à-vis the fundamental equation describing the equilibrium condition in Keynes' model version of a realistic entrepreneur economy—a complementary scheme to an algebraic-topological interpretation of Keynes' vision is outlined within the Post Keynesian scientific research programme. [ABSTRACT FROM AUTHOR]

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The theory of special relativity is a topic not addressed in theoretical chemistry courses. Einstein's theory of relativity is mainly applied to high‐energy phenomena governed by physical laws not used to describe the chemical bond. Nevertheless, the electrons of heavy elements orbit around the nucleus with relativistic velocities. Here it is, then, the laws that appeared so unusual for chemistry became fundamental tools for investigating the properties of these atoms. Studying the electronic structure of heavy elements is the best place for chemists to learn to tame the pitfalls of a little‐known subject, such as Einstein's theory, and become familiar with its elegant formalism. In this paper, the main relativistic approaches to quantum chemistry are revisited. The problem of the finite nuclear size, the approximation methods used to solve the relativistic equations for k‐shell electrons, and the problem of the negative energy continuum are investigated. Some ansatzes to solve divergence's problem of relativistic corrections near the nucleus are proposed. Finally, a possible connection between the self‐consistent field method and bondonic chemistry is also investigated. [ABSTRACT FROM AUTHOR]

This paper advances the state-of-the-art by extending the study of the analogy between the fabric of spacetime and elasticity. As no prior work exists about a potential spacetime thermal expansion coefficient α , we explore the analogy of general relativity with the theory of elasticity by considering the cosmological constant Λ as an additional space curvature of the structure of space due to a thermal gradient coming from the cosmic web and the cold vacuum and we propose ( α S Δ T e) 2 = (1 R 0 ) 2 = Λ with R 0 being the curvature radius of the space fabric. It follows from this analogy and from the supposed space model consisting of thin sheets of Planck thickness l p curved by this thermal gradient Δ T a possible thermal expansion coefficient of the equivalent elastic medium modeling the space α S = l p Λ Δ T of the order of α space-QFT = 1. 1 6 × 1 0 − 6 K − 1 . As spacetime and not only space must be considered in general relativity, this paper also proposes an innovative approach which consists in introducing into the interval ds2 of special relativity a temperature effect T : d s 2 = (1 ± α t T) 2 c 2 d t 2 − (1 ± α s T) 2 [ d x 2 + d y 2 + d z 2 ] (entropy variations correlated with time laps, based on temperature variations affecting always physically the clocks) based on different thermal expansion coefficients for space and time with for the flow of time t : c t c n τ = k B t n h × Δ T = α t Δ T. With T ≈ 106 K, n = 1 , the associate time interval is 4. 8 × 1 0 − 1 7 s and α t = 1. 0 × 1 0 − 6 K − 1 . The consequence of this hypothesis is that dark energy potentially becomes a thermal spacetime curvature ( α f T l p ) 2 with f equal to s or t depending of the temperature, the thermal entropy variation of the universe, the Planck thickness and time, that increases since the Big bang, depending on thermal expansion coefficients for spacetime α s and α t as a function, respectively, of Λ , k B h × t , in opposition to spacetime curvature gravity due to mass/energy density as described in general relativity. [ABSTRACT FROM AUTHOR]

The projectile motion (PP) in a vacuum is re-examined in this paper, taking into account the relativistic mass in special relativity (SR). In the literature, the mass of the projectile was considered as a constant during motion. However, the mass of a projectile varies with velocity according to Einstein's famous equation m = m 0 1 − v 2 / c 2 , where m 0 is the rest mass of the projectile and c is the speed of light. The governing system consists of two-coupled nonlinear ordinary differential equations (NODEs) with prescribed initial conditions. An analytical approach is suggested to treat the current model. Explicit formulas are determined for the main characteristics of the relativistic projectile (RP) such as time of flight, time of maximum height, range, maximum height, and the trajectory. The relativistic results reduce to the corresponding ones of the non-relativistic projectile (NRP) in Newtonian mechanics, when the initial velocity is not comparable to c. It is revealed that the mass of the RP varies during the motion and an analytic formula for the instantaneous mass in terms of time is derived. Also, it is declared that the angle of maximum range of the RP depends on the launching velocity, i.e., unlike the NRP in which the angle of maximum range is always π / 4 . In addition, this angle lies in a certain interval [ π / 4 , π / 6) for any given initial velocity (

This paper studies the motion of a light signal and a test particle in the field of an infinite flat slab in terms of the general theory of relativity. The two cases of an external solution for a gravitational field in a vacuum corresponding to Rindler and Taub metrics are examined. The time of the motion and the path traveled by a particle before it stops are determined. It is shown that in the Taub geometry, as opposed to a light signal, a material particle does not reach a singularity. The minimum distance from the singularity is determined as a function of the particle energy. Results in terms of the special theory of relativity are given for comparison. [ABSTRACT FROM AUTHOR]

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Time dilation (TD) is a principal concept in the special theory of relativity (STR). The Einstein TD formula is the relation between the proper time t 0 measured in a moving frame of reference with velocity v and the dilated time t measured by a stationary observer. In this paper, an integral approach is firstly presented to rededuce the Einstein TD formula. Then, the concept of TD is introduced and examined in view of the fractional calculus (FC) by means of the Caputo fractional derivative definition (CFD). In contrast to the explicit standard TD formula, it is found that the fractional TD (FTD) is governed by a transcendental equation in terms of the hyperbolic function and the fractional-order α. For small v compared with the speed of light c (i.e., v ≪ c ), our results tend to Newtonian mechanics, i.e., t → t 0 . For v comparable to c such as v = 0.9994 c , our numerical results are compared with the experimental ones for the TD of the muon particles μ + . Moreover, the influence of the arbitrary-order α on the FTD is analyzed. It is also declared that at a specific α , there is an agreement between the present theoretical results and the corresponding experimental ones for the muon particles μ + . [ABSTRACT FROM AUTHOR]