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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]

Reciprocal length contraction and time dilation, as enshrined in the Lorentz transformation, are the bulwark of the special relativity theory. Reciprocal time dilation is typically discussed (in the context of its apparent contradiction) and usually explained away as the result of differing synchronization in inertial reference frames and the relativity of simultaneity. Further, it is generally suggested that time is an abstract concept, and its perceptions may differ with context. However, we suggest that regarding length measurements no such abstraction can be envisaged. In this manuscript, we examine the reciprocal length contraction in detail to assess whether it leads to any contradiction. [ABSTRACT FROM AUTHOR]

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]

Introductory textbooks for the theory of special relativity discuss the time dilation effect after introducing the Lorentz transformations. Reading the dictum 'moving clocks run slow' a student is likely to have the impression that this is a measured effect. On the other hand, after considering the relativistic Doppler effect the same student might be puzzled that this effect depends on the relative emitter-observer direction, contrary to Einstein's time dilation. Simple thought experiments are presented here where the inferred time dilation and the observed relativistic Doppler effect give quite opposite answers. Before solving the puzzle, we show how easily one can get confused and obtain apparently contradictory results. [ABSTRACT FROM AUTHOR]

The importance of synchronization of spatially separated clocks in observing event coordinates cannot be overemphasized. We illustrate this with a real-world example. The results show the dependence of both length contraction and time dilation on the adopted synchronization convention. It is illustrated that a change in synchronization convention completely alters the appearance of the physical world. This is to be viewed in the context of the stated position in physics that synchronization of spatially separated clocks in any inertial frame depended on the adoption of a convention for its resolution. The preferred method of synchronization of spatially separated clocks is the standard convention recommended by the theory of relativity; however, it still remains a convention. [ABSTRACT FROM AUTHOR]

A Lorentz transformation may involve the changes in a three-dimensional fixed reference frame when given a constant boost velocity v in a moving reference frame as measured by an observer in a specified fixed reference frame. A Lorentz transformation may also involve changes in the size and shape of a material object when given a constant boost velocity v in a moving (Galilean) reference frame as measured by an observer in a specified fixed reference frame receiving light signals along the straight axis of a connecting ether rope. The mass of the flux of primordial fluid moving with a boost velocity is increased by the Lorentz gamma factor so that the measured time is reduced by the factor gamma. This is known as time dilation. [ABSTRACT FROM AUTHOR]

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Asymmetrical time dilation in the Global Positioning System (GPS) invalidates the relativity principle of special relativity since it confirms the existence of a preferred frame that is prohibited by the principle. It also contradicts symmetrical time dilation predicted by special relativity [ABSTRACT FROM AUTHOR]

According to the special theory of relativity (STR), when the velocity of a moving body increases, the length of the body contracts in the direction of motion, and the passage of time slows down in its coordinate system. This conclusion can be derived from the equations of the Lorentz transformation. Inside the atom, however, potential energy must be taken into account, and the equations of the Lorentz transformation cannot be applied. In situations where the transformation equations newly derived by the author can be applied, if the velocity of a moving body increases, then the body elongates in the direction of motion, and the passage of time speeds up in its coordinate system. At the same time, the relativistic energy and mass of the body decrease. In the special theory of relativity, it is the relative velocity between the stationary frame and moving frame which determines length in the direction of motion of the moving body, and the tempo of the time which passes in the body's coordinate system. However, this paper rejects the claim that relativistic velocity is the factor which determines the body's length and the time which passes. Instead it concludes that the true cause is the ratio of the body's rest mass energy and relativistic energy--a ratio which varies as the velocity of the moving body increases and decreases. [ABSTRACT FROM AUTHOR]

A model of gravitational waves is proposed using a complex Yukawa potential which is non-singular and predicts a dual wave structure composed of incoming and outgoing waves. Using this potential, a fundamental gravitational wave frequency associated with the mass of the universe is calculated to be equal to Hubble's Constant. The characteristic out-wave frequency of the Earth is calculated to be 3.38 x 10-5 Hz, which is in good agreement with the range of frequency of gravitation waves predicted by Hawking and Israel. Also, the Lorentz transformation of the outgoing wave speed to the incoming wave speed predicts the same time dilation as the G44 solution from the Einstein field equations. Measurements with an accelerometer sampled at 200 Hz over a period of 16 hours demonstrates the signals with the expected frequencies of the Earth and Moon mass. [ABSTRACT FROM AUTHOR]

We examine the Lorentz factor and the Schwarzschild solution in relation to the estimation and verification of time dilation in particular from Global Positioning System data. As a result, we detect the possible occurrence of a proportionality between the time dilation effects of special and general relativity in free-fall motion in Keplerian orbits. This observation is then proved mathematically. The results show that gravitational time dilation during free fall in Keplerian orbits must be exactly double that caused in special relativity due to linear velocity. We propose that a law be enunciated in view of the proof provided, and of the experimental and technological verification of time dilation effects during the past six to seven decades. The importance of this finding as a universal phenomenon and in the further development of stable clocks and satellite technology is highlighted. [ABSTRACT FROM AUTHOR]

The case of two rockets approaching each other with constant velocity is used to underscore a common misconception in relativity theory. Since each rocket is an inertial system (IS), it has been argued that a clock located on either one of them must be running faster in each case than an identical clock on the other (symmetry principle). This conclusion is based on the Lorentz transformation (LT) of Einstein's special theory of relativity (STR). There has never been an experimental verification of this prediction, however. On the contrary, experiments with atomic clocks carried onboard airplanes and rockets have demonstrated that their rates can be computed in a simple manner just by knowing their speed relative to the Earth's non-rotating polar axis. After accounting for gravitational effects, it has always been found that the rates of these clocks are slower than those of identical counterparts located on the polar axis. These results can be predicted quantitatively by defining an objective rest system (ORS), the Earth's polar axis in the present case, from which to uniquely apply Einstein's time dilation formula for clocks moving relative to it. On this basis it is concluded that measurement is objective (rational) rather than symmetric, and that the LT therefore does not correctly predict the rates of atomic clocks on a sufficiently general basis. A key result of the ORS formulation is that the lifetime of meta-stable particles on the Earth's surface measured by an observer moving at high speed relative to them is shorter than the value he finds for the identical particles when they are at rest in his laboratory. More generally, this approach underscores the advantages of introducing a set of physical units that is dependent on the state of motion of the observer. [ABSTRACT FROM AUTHOR]

The article discusses about simplifying time dilation and length contraction to students through a thought experiment. Topics include the Lorentz transformations; experiments conducted using a light clock, the period of oscillation of the photons, and explaining the students about special relativity.

Special relativity is a half-baked theory in which Lorentz transformation only considers the outbound or departing motion where speed and distance change in the same direction. This paper considers the inbound or approaching motion where speed and distance change in the opposite direction. This paper derived a new form of transformation along with the new Lorentz factor, according to which, in addition to well-known time dilation caused by outbound motion, there would be time contraction caused by inbound motion. [ABSTRACT FROM AUTHOR]

Deformed relativistic kinematics is a framework which captures effects, that are expected from particles and fields propagating on a quantum spacetime, effectively. They are formulated in terms of a modified dispersion relation and a modified momentum conservation equation. In this work we use Finsler geometry to formulate deformed relativistic kinematics in terms of particle velocities. The relation between the Finsler geometric velocity dependent formulation and the original momentum dependent formulation allows us to construct deformed Lorentz transformations between arbitrary frames. Moreover, we find the corresponding compatible momentum conservation equation to first order in the Planck scale deformation of special relativity based on the κ-Poincaré algebra in the bicrossproduct basis. We find that the deformed Lorentz transformations, as well as the deformed time dilation factor, contain terms that scale with the energy of the particle under consideration to the fourth power. We derive how the distributions of decay products are affected when the deformed relativity principle is satisfied and find, for the case of a pion decaying into a neutrino and a muon, that the ratio of expected neutrinos to muons with a certain energy is just slightly modified when compared to the predictions based on special relativity. We also discuss the phenomenological consequences of this framework for cosmic-ray showers in the atmosphere. [ABSTRACT FROM AUTHOR]

Rotational transformations describe relativistic effects in rotating frames. There are four major kinematic rotational transformations: the Langevin metric; Post transformation; Franklin transformation; and the rotational form of the absolute Lorentz transformation. The four transformations exhibit different combinations of relativistic effects and simultaneity frameworks, and generate different predictions for relativistic phenomena. Here, the predictions of the four rotational transformations are compared with recent optical data that has sufficient resolution to distinguish the transformations. We show that the rotational absolute Lorentz transformation matches diverse relativistic optical and nonoptical rotational data. These include experimental observations of length contraction, directional time dilation, anisotropic one-way speed of light, isotropic two-way speed of light, and the conventional Sagnac effect. In contrast, the other three transformations do not match the full range of rotating-frame relativistic observations. [ABSTRACT FROM AUTHOR]

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We present a comprehensive discussion of the formulation of the kinematics of special relativity, i.e., the Lorentz transformation. We begin with a concise new proof that the principle of relativity implies that the transformation of event coordinates between inertial reference frames is linear. We then give a clear derivation of the pre-Lorentz transformation, which follows from the principle of relativity. We then show that the pre-Lorentz transformation and the inertial invariance of the speed of light together result in the Lorentz transformation. This, of course, is essentially the traditional formulation. We next present two additional formulations, one using Lorentz–Fitzgerald contraction and one using time dilation, instead of inertial invariance. This is reasonable since Lorentz–Fitzgerald contraction and time dilation are about as well established as and are arguably less abstract than inertial invariance, and thus may profitably be used instead of inertial invariance to complete the formulation. We then present a complete proof that the pre-Lorentz transformation and the requirement of closure upon composition together imply that the transformation is either a Galilean transformation or a generalized Lorentz transformation. This is noteworthy in that it gets ever so close to the Lorentz transformation without invoking light. In the course of this, we obtain a generalized velocity addition rule, which reduces to the velocity addition rule of special relativity. We next show that the generalized Lorentz transformation, together with inertial invariance, Lorentz–Fitzgerald contraction, and time dilation, used one at a time, yields three more formulations. We then show that the unspecified, nonzero, constant speed in the generalized Lorentz transformation can be determined without any reference to light, thereby obtaining a seventh formulation. Light plays no explicit role in the four formulations employing Lorentz–Fitzgerald contraction and time dilation and plays no role whatsoever in the seventh formulation. Thus, and this is a fact which should be strongly emphasized, the formulation of special relativity in no way depends upon the nature of electromagnetic radiation. We conclude by briefly discussing these seven formulations of the kinematics of special relativity and some associated implications. [ABSTRACT FROM AUTHOR]

The article focuses on relativistic addition of parallel velocities. It states that there are several publications, on different derivations of the formula for the relativistic addition of parallel velocities that do not require the use of Lorentz transformation. It stresses that these derivations has gained favorable response, especially for a first course in special relativity, for the fact that time dilation and Lorentz transformation are complicated to use. The article cites a derivation of the relativistic velocity addition formula which is based on Lorentz contraction and time dilation. It claims that this derivation is simpler because time dilation are scaled down into two, "rod enters the detector" and "rod leaves the detector."

Special relativity (SR) determines the properties of synchrotron radiation, but the corresponding mechanisms are frequently misunderstood. Time dilation is often invoked among the causes, whereas its role would violate the principles of SR. Here it is shown that the correct explanation of the synchrotron radiation properties is provided by a combination of the Doppler shift, not dependent on time dilation effects, contrary to a common belief, and of the Lorentz transformation into the particle reference frame of the electromagnetic field of the emission-inducing device, also with no contribution from time dilation. Concluding, the reader is reminded that much, if not all, of our argument has been available since the inception of SR, a research discipline of its own standing. [ABSTRACT FROM AUTHOR]

A review of the predictions of Einstein's Special Theory of Relativity (STR) shows that two of them, remote non-simultaneity and time dilation, are incompatible with each other. It is claimed thereby that two numbers, time differences for the same event that are measured by observers in different states of motion, always occur with a fixed ratio, but that one of them can be zero (simultaneous observation) without the other being so as well. It is impossible that both of these conditions can each be met in any given case, and this constitutes proof that the Lorentz transformation (LT), from which both effects are derived in STR, is not a physically valid set of space-time equations. It is further pointed out that a clock moving through space in the complete absence of unbalanced external forces, in accordance with Newton's Law of Inertia and the Law of Causality, must be expected to have a constant rate. As a consequence, elapsed times Δt and Δt' measured by two such (inertial) clocks for the same event should always occur in a fixed ratio, as expressed by the following relation: Δt'=Δt/Q, where Q is a constant fully determined by the above ratio. [ABSTRACT FROM AUTHOR]

The so called modern physics is at present included in the curricula of high school. Therefore, we often organize in-depth lessons on quantum mechanics and on the special theory of relativity (SR). In the following sections, we want to show a lesson given by the first author of this paper. He proposes to students a proportion to deduce relativistic time dilation and length contraction without knowing the Lorentz transformations. [ABSTRACT FROM AUTHOR]

This was six years after the publication of Einstein's special theory of relativity, but several years before the general theory, and in his book he includes Langevin's original account in English translation. Benguigui himself is strongly of the opinion that the acceleration must be involved, and that this involves considerations of general relativity. The author of the present book, Lucien Benguigui, recounts this and traces the original tale back to a talk by the French physicist Paul Langevin in 1911. There are few topics in physics that have excited so many different contrary opinions as Einstein's so-called "Twin Paradox", otherwise known as the "Clock Paradox". [Extracted from the article]

The author’s previous papers on superluminal time dilation [E. J. Betinis, Phys. Essays 11, 81 (1998)] and the superluminal Schrödinger equation [E. J. Betinis, Phys. Essays 11, 311 (1998)] are mentioned in order to inform the reader of the existence of the superluminal theories developed to date. The superluminal time dilation is utilized in the derivation of the Lorentz transformations in order to show as a first step that the superluminal theory for physics is valid and can maintain the invariance of the metric. Next the most general Einstein equation of gravitation is reduced to the special case of finding the weak and static fields of the gravitational potential for the universe and one receding galaxy. This case is further simplified by assuming that the receding galaxy is only moving radially from the center of the universe. It is found that by restricting the moving galaxy to having a velocity less than the speed of light c (the subluminal case), the turning point or “stopping point” of the receding galaxy would fall far short of the distance of the known observed outermost galaxy. By Hubble’s law, it is shown that the outermost galaxy would have a velocity greater than the speed of light, so the subluminal restriction also contradicts Hubble’s law as well. The superluminal formulation shows that the turning point if it exists can occur at the present assumed location of the outermost galaxy where its velocity is greater than the velocity of light. However, since observations presently show that the outermost galaxy is still receding at a velocity greater than the velocity of light c, the universe does not, at present, seem to be contracting or to be oscillatory. In addition, then the superluminal treatment for finding the gravitational potential as it allows a velocity greater than the velocity of light is also consistent with the Hubble’s law calculation of the velocity of the outermost receding galaxy. In the above formulation of the weak and static gravitational fields of the Einstein equation, spacetime is not really totally flat but is slightly curved. In addition, the group theory aspects of the Lorentz transformations for both the subluminal and superluminal cases are demonstrated. [ABSTRACT FROM AUTHOR]

The paper concludes that the net proper time difference between two observers in relative motion does not exist. The twin paradox is only an illusion due to misunderstandings. [ABSTRACT FROM AUTHOR]

The change in the reading on a distant Earth clock from the point of view of a traveling twin who instantaneously reverses direction is calculated by considering the behavior of the Earth clock during the turnaround, performing an integral, and taking a limit. [ABSTRACT FROM AUTHOR]

We provide three examples of the use of geometric reasoning with three-dimensional spacetime diagrams, rather than algebraic manipulations using three-dimensional Lorentz transformations, to analyze problems in special relativity. The examples are the "rising manhole" paradox, the "moving spotlight" problem, and Einstein's light-clock derivation of time dilation. [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 conventional methods, Lorentz transformation equations are derived by considering the motion of light wave front perceived by two observers, one stationary and other one moving. But, as per the new theory of reaction-at-a-distance proposed in our recent paper [B. Dikshit, Phys. Essays 24, 4 (2011)] that establishes a unified picture explaining the two surprising characteristics of light, viz., invariance of speed and wave-particle duality, propagation of light in intermediate space between the source and detector is ruled out. So, there is a need to rederive the Lorentz transformation equations using this theory of reaction-at-a-distance without considering the motion of light wave front in space in any step of the derivations. Using this basic Lorentz transformation, all other conventional relations, viz., length contraction, time dilation, etc., can be proved. A notable advantage of this approach is that it is valid for all types of interactions (electromagnetic and gravitational) between the observer and the body being observed. Dans les méthodes conventionnelles, les équations de transformation de Lorentz sont calculées en considérant le mouvement du front d'onde lumineux perçue par deux observateurs, un stationnaire et l'autre en mouvement. Mais, selon la nouvelle théorie de la réaction-à-distance proposée dans notre récent article [B. Dikshit, Phys. Essays 24, 4 (2011)] qui établit une image unifiée expliquant les deux caractéristiques surprenantes de la lumière, c'est-à-dire l'invariance de la vitesse et la dualité onde-particule, la propagation de la lumière dans l'espace intermédiaire entre la source et le détecteur est exclue. Donc, il ya un besoin de re-dériver les équations de transformation de Lorentz en utilisant cette théorie de la réaction au-distance sans considérer le mouvement du front d'onde de lumière dans l'espace à n'importe quel stade des dérivations. En utilisant cette transformation fondamentale de Lorentz, tous les autres, à savoir: les relations conventionnelles, contraction des longueurs, dilatation du temps, etc. peut être prouvées. Un avantage remarquable de cette approche est qu'elle est valable pour tous les types d'interactions (électromagnétique et gravitationnel) entre l'observateur et le corps observé. [ABSTRACT FROM AUTHOR]

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Accelerated motion is considered as a successive presence of an observer in accompanying inertial reference frames (AIRF) with jumps between them. A formula comprising two terms has already been derived to explain the twin paradox. The first term of this formula describes the time dilation in the reference frame associated with the twin at rest, while the moving twin is in the chosen AIRF. The second term describes a jump of readings of the clock of the twin at rest observed by the accelerated twin who jumps in the next AIRF. In the present study, this formula is used to derive the relative velocity and the distance passed by the accelerated twin by the scale associated with the twin at rest from a noninertial reference frame (NRF). Uniformly accelerated motion followed by uniformly decelerated motion to the stop in the initial inertial reference frame is examined. Readings of any clocks at rest, including clocks of the twin at rest, are derived from the NRF. [ABSTRACT FROM AUTHOR]

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In this paper, Special Relativity Search (SRS) is developed for solving engineering problems. The interaction of particles in a magnetic field is considered as an optimizer model of the SRS in which the magnetic field is the feasible search space and the particles in this field are the possible design vectors. Particles interaction is investigated using the Lorentz force, velocity and distance between particles. Charged particles that move in opposite directions produce an inverse force and repel each other while charged particles that move in the same direction attract each other. The special relativity theory is implemented in an applicable way to develop SRS. In SRS, using the angular frequency, centripetal force, and inverse Lorentz transformations, main equations of the algorithm are developed. The design variables are randomly selected as a candidate for optimal answers from the initial population and updated their position in each iteration. This process continues until the global optimum is obtained. In this paper, to validate the SRS performance in solving engineering problems, total twenty-nine CEC-2017 Boundary Constraint (BC) problems and 12 engineering problems are optimized. To evaluate the superiority of the SRS algorithm, the results are compared with other well-known metaheuristic methods. Friedman's test is also used to rank the best algorithm. The results show a good performance of the SRS in most problems with the lowest computational cost. [Display omitted] • Special Relativity Search is developed. • Lorentz inverse transformations, the phenomenon of length contraction, and time dilation are main steps. • The new algorithm is utilized to solve real-world mechanical and structural engineering problems. [ABSTRACT FROM AUTHOR]

The article focuses on the derivation of relativistic velocity addition law based on a machine gun-target analogy of the acoustic Doppler effect. The process is considered from the rest frame of the machine gun and from the rest frame of the target. It provides a detailed derivation of the relativistic addition law of parallel velocities without prior knowledge of Lorentz transformations. It notes that the derivation involves special relativity via the time dilation effect formula.

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Since the Lorentz boost is symmetric under exchange of x and ct, special relativistic phenomena will also manifest this symmetry. Firstly, simultaneity becomes paired with ‘colocality’ (‘at the same place’), and the ‘Relativity of Colocality’ becomes the dual to the well-known ‘Relativity of Simultaneity’. Further, Lorentz time contraction arises from reversal of the observation conditions pertaining to time dilation, expressible figuratively as ‘Moving clocks run slow, but moving time runs fast’. Symmetry also dictates that the most fundamental observational modes are: (1) the simultaneous observation of length, a process involving both the relativity of simultaneity and length contraction; and (2) the colocal measurement of duration, involving both the relativity of colocality and time contraction. Only the first of these modes is well known. The adoption of this symmetrical lexicon provides a necessary logical basis for interpretational studies of observation and measurement in special relativity. [ABSTRACT FROM AUTHOR]

Contrary to the prevailing lore, the twin paradox is shown to lose its raison d'être when a proper account is taken of the intrinsic role of time in relativity theory. [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.)

We demonstrate a compatibility between the relativity principle and the clock postulate in deformed special relativity, by identifying the relevant deformed Lorentz transformations in position space between arbitrary frames. This result leads to a first-principles correction to the dilated lifetime of fundamental particles. It turns out that these modified time dilations offer a way to scrutinize Lorentz invariance (or deviations thereof) to high precision. [ABSTRACT FROM AUTHOR]

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