In this paper a method is proposed for empirically determining simultaneity at a distance within the special theory of relativity. It is argued that this method is independent of Einstein's signalling method and provides a basis for denying the conventionality of distant simultaneity.

In their recent paper, Jackson and Pargetter have attempted to prove that simultaneity is not a matter of convention. They attempt to show that it is an empirical fact whether or not a moving rod A′B′ is perpendicular to a plane XY. If it is an empirical fact, then such a perpendicular rod can be used to synchronize clocks. We shall show that it is not an empirical fact, but it is in fact synchronization dependent.

The General Theory of Relativity (GR) and the Dynamic Universe (DU) are evaluated in how they explain frequencies of atomic clocks. DU and GR predict the frequencies with equal accuracy, but their explanations, the postulates they apply in the explanations and the word-views that come along with them are entirely different. The central argument is that if unified and under- standable physics is appreciated, then DU deserves to be taken as a viable alternative to GR. In GR different frequencies of (...) identical atomic clocks are explained by letting rates of the flow of time in their frames of reference vary as functions of the clocks’ states of motion and gravitation. The GR- based world-view is nonunderstandable because GR violates absolute simultaneity, and disunified because quantum mechanics is built on different postulates than GR. In DU different frequencies of identical atomic clocks are explained by letting their frequencies vary as functions of their states of motion and gravitation. As DU commits to absolute simultaneity and as the postulates of DU suffice as the ontological ground of quantum mechanics at least partially, DU provides an under- standable and unified scientific world-view. -/- Résumé: La théorie de la relativité générale (RG) et de l’univers dynamique (UD) sont évalués sur la fac ̧on dont ils expliquent les fréquences des horloges atomiques. La RG et l’UD prédisent les fréquences avec une précision égale, mais leurs explications, les postulats qu’ils appliquent aux explications et les visions du monde qui les accompagnent sont entie`rement différents. L’argument central est que si l’on reconnaˆıt la physique unifiée et compréhensible, alors l’UD mérite d’ être considéré comme une alternative viable à la RG. En RG, différentes fréquences d’horloges atomiques identiques sont expliquées en faisant varier les vitesses de l’écoulement du temps dans leurs cadres de référence en fonction des états de mouvement et de la gravitation des horloges. La vue du monde basée sur la RG est incompréhensible parce que la RG viole la simultanéité absolue, et est désunifiée parce que la mécanique quantique est construite sur des postulats différents de ceux de la RG. Dans l’UD, différentes fréquences d’horloges atomiques identiques sont expliquées en laissant leurs fréquences varier en fonction de leurs états de mouvement et de gravitation. Comme l’UD s’engage à la simultanéité absolue et que les postulats de l’UD suffisent, au moins en partie, comme fondements ontologiques de la mécanique quantique, l’UD fournit une vision du monde scientifique compréhensible et unifiée. (shrink)

Ellis and Bowman's account of nonstandard signal synchronizations is examined as a prolegomenon to this paper. Attention is called to some consequences of an important ambiguity in their account of the transitivity of nonstandard synchrony. Then an analysis is given of the principle of relativity to assess E & B's claim that this principle either restricts nonstandard signal synchronisms or rules them out altogether. It is argued that the latitude for choices of nonstandard synchronisms is not circumscribed by the factual (...) content of the principle of relativity; instead, the exclusion of such synchronisms by this principle depends on a tacit appeal to the particular conventions implicit in certain formulations of the principle. Hence E & B's claim is rejected as an argument against the factual tenability of nonstandard synchronisms. (shrink)

Ever since the now infamous comments made by Hermann Minkowski in 1908 concerning the proper way to view space-time, the debate has raged as to whether or not the universe should be viewed as a four-dimensional, unified whole wherein the past, present, and future are equally real or whether the views espoused by the possibilists, historicists, and presentists regarding the unreality of the future (and, for presentists, the past) are best. Now, a century after Minkowski’s proposed blockworld first sparked debate, (...) we seek a more conclusive argument in favor of the eternalist picture of space-time. Utilizing an argument based on the relativity of simultaneity in the tradition of Putnam and Rietdijk and novel but reasonable assumptions as to the nature of “reality”, we will show that the past, present, and future are equally real, thus ruling out presentism and other theories of time that bestow special ontological status to the past, present, or future as untenable. Finally, we will respond to our critics who would suggest that: 1) there is no metaphysical difference between the positions of eternalism and presentism, 2) the present must be defined as the “here” as well as the “now”, or 3) presentism is correct and our understanding of relativity is incomplete because it does not incorporate a preferred frame. We call eternalist response 1 deflationary since it purports to dissolve or deconstruct the age-old debate between the two views and response 2 compatibilist because it does nothing to alter special relativity (SR) arguing instead that SR unadorned has the resources to save presentism. Response 3 we will call incompatibilism because it adorns SR in some way in order to save presentism a la some sort of preferred frame. We will show that neither move 1 nor 2 can save presentism and move 3 is not well motivated at this juncture except as an ad hoc device to refute eternalism. (shrink)

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.

Einstein, Relativity and Absolute Simultaneity is an anthology of original essays by an international team of leading philosophers and physicists who have come together to reassess the contemporary paradigm of the relativistic concept of time. A great deal has changed since 1905 when Einstein proposed his Special Theory of Relativity, and this book offers a fresh reassessment of Special Relativity’s relativistic concept of time in terms of epistemology, metaphysics, and physics.

In this journal, Brogaard and Marlow recently argued that the relativity of simultaneity is an illusion. We claim their argument is fallacious.

The picture which one naturally presents of the situation is that which would arise before an observer placed outside the earth, who could watch the light wave starting from the central mirror and pursuing the distant mirror, catching up with it at some distance beyond the point at which it was when the light wave started. In this case the observer is able to locate the points at which the parts of the apparatus were at different moments and to measure (...) the distances between. We could simulate this situation on the earth by assuming an enclosed square car, from some point in which two balls were shot out in directions at right angles to each other to the walls of the car, bounding back to the point at which they started. We will assume that the balls move with uniform velocity going and coming, and we will assume that the car is moving. An observer outside the car who marked the point on the rail directly over the starting point and the points reached by the balls when they struck the sides of the car, and then measured the distances which the balls travelled, would find that the ball which travelled with the car covered a greater distance than that traversed by the ball which went at right angles to the direction of the train, and yet the balls would return to the starting point at the same moment, provided they travelled over both their paths at the same velocity during their entire trajects, i.e., the same velocity measured within the car. The observer would be at no difficulty to explain this, for he would see that the velocity in the direction of its motion of the car had to be added to that of balls within the car. That is not the case of the light wave. The velocity of a moving shining body is not added to that of the light wave. The wave motion being set up in ether travels with its own uniform velocity of approximately 300,000 kilometers a second. The light waves then, from the standpoint of the observer outside the earth, traverse through the stagnant ether different distances at a uniform velocity and yet the ether waves exhibit on their return none of the evidence which they should exhibit in the interferometer. (shrink)

I challenge the assumption in the debate on the conventionality of simultaneity that a simultaneity relation of special relativity should be defined relative to a single inertial observer, not relative to multiple inertial observers as such. I construct an example of a simultaneity relation relative to two inertial observers, and demonstrate that it is explicitly definable in terms of the causal connectibility relation and the world lines of the two observers. I argue that, consequently, (...) thesimultaneity relation of special relativity is not uniquely definable from the causal connectibility relation. (shrink)

RésuméLe raisonnement selon lequel la simultanéité est relative du point de vue de l'observateur est fondamental dans la Relativité restreinte. Pourtant, l'analyse de ce raisonnement mène aux critiques suivantes:1. Le raisonnement appartient à la physique classique plutǒt qu'à la physique relativiste, en ce qu'il adopte la conception classique de la propagation de la lumière et ignore le principe de la constance de la vitesse de la lumière.2. Il entre en conflit avec l'évidence empirique, car son hypothèse de base et (...) son mode de raisonnement sont presque exactement analogues à ceux qui amenèrent Michelson et Morlay à attendre un résultat positif lors de leur expérience d'interférence.3. Il est logiquement inacceptable, car il repose à la fois sur l'affirmation et sur la négation d'un système de référence privilégié.Bien plus, on montre que l'application correcte des transformations de Lorentz mène non pas à la conclusion que la simultanéité est relative, mais plutǒt à celle qu'elle est absolue.The argument that simultaneity is relative to the viewpoint of an observer, is fundamental to Special Relativity. However, analysis of this argument leads to the following strictures: the argument belongs to classical physics rather than to relativity physics, in that it adheres to the classical view of the propagation of light, and ignores altogether the relativistic principle of the constancy of the velocity of light; the argument conflicts with empirical evidence, in that its basic assumption and mode of reasoning are almost exactly analogous to those which led Michelson and Morley to expect a positive result from their interferometer experiment; the argument is logically untenable, in that it rests on both the affirmation, and the denial, of a privileged frame of reference. Furthermore, it is shown that proper application of the Lorentz transformation, in actually transforming data from one system to another, must lead, not to the conclusion that simultaneity is relative, but rather to the conclusion that it is absolute. (shrink)

In a recent issue of this journal Berit Brogaard and Kristian Marlow claim that an absolute frame of reference is compatible with Einstein’s Special Relativity. To achieve this they tweak Einstein’s famous train and embankment thought experiment and unjustifiably attribute, to Einstein, Hans Reichenbach’s claim that cause and effect are always temporally separated. Their conclusion is incompatible with the proper Lorentz transformations to show how time dilates from one frame of reference to another; transformations they show no evidence of having (...) done. I refute their conclusion by doing the calculations. (shrink)

In connection with the special theory of relativity, Einstein made use of a now familiar thought experiment1 involving two lightning flashes, a railway train, and an embankment. Whether he used it merely to help explain the theory to others or whether it played a role in the theory's very generation as well is perhaps a matter of conjecture. However, physicist Richard Feynman, for one, believes that Einstein first conceived his theories in the visualizations of thought experiments and developed their mathematical (...) formulations afterwards. According to a recent magazine essay, ‘Einstein came to an understanding about relativity by imagining people going up in elevators and beaming light back and forth between rocket ships. (shrink)

A-theoretic presentness is commonly regarded as non-solipsist and non-relative. The non-solipsism of a non-relative, A-theoretic presentness requires at least two space-like separated things to be present simpliciter together – this co-presentness further implies the global, non-relative, non-conventional simultaneity of them. Yet, this implication clashes with the general view that there is no global, non-relative, non-conventional simultaneity in Minkowski space-time. In order to resolve this conflict, this paper explores the possibility that the non-solipsism of a (...) non-relative, A-theoretic presentness does not require at least two space-like separated things to be present simpliciter together. This can be done by holding exclusive disjunctivism –that mutually space-like separated things are present simpliciter exclusively disjunctively, and each one of them gets to be present simpliciter in a non-successive way (just like mutually time-like related things are present simpliciter exclusively disjunctively, and each one of them gets to be present simpliciter, but in a successive way). (shrink)

Tensism holds that the present moment has a special status that sets it apart from the past and the future, independently of perceivers. One of the main objections to this view has been Einstein’s argument from special relativity, which aims at showing that absolute simultaneity is a myth. We argue that the moving observer in a causal variant of Einstein’s original thought experiment is subject to a temporal illusion. Owing to the analogy of the cases, this casts doubt on (...) the conjectures that there is no privileged frame of reference and that special relativity poses a problem for tensism. (shrink)

Starting from the special theory of relativity it is argued that the structure of an experience is extended over time, making experience dynamic rather than static. The paper describes and explains what is meant by phenomenal parts and outlines opposing positions on the experience of time. Time according to he special theory of relativity is defined and the possibility of static experience shown to be implausible, leading to the conclusion that experience is dynamic. Some implications of this for the relationship (...) of phenomenology to the physical world are considered. (shrink)

상대성이론의 역사에서 베르그손과 푸앵카레는 주목받지 못했다. 두 인물은 상대성이론이 제시하는 개념들에 대해 표준적인, 즉 아인슈타인과 다른 해석을 제시했다는 공통점을 지닌다. 논문에서 나는 우선 베르그손이 어떻게 특수상대성이론의 핵심적인 논변으로부터 유일하고 보편적인 시간이라는 공통관념을 이끌어내고 또 이론의 핵심 개념 중 하나인 동시성을 이해하는지 보인다. 다음으로는 푸앵카레가 어떻게 자신의 공간론에서 상대공간의 개념과 그 적용으로서 상대시간 개념을 이끌어내고 또 그 전제가 되는 상대성원리를 이해하는지 살핀다. 이로부터 상대성이론의 형성 및 해석의 역사에서 베르그손과 푸앵카레의 위치를 재평가하고, 나아가 두 철학의 비교 연구를 위한 초석을 마련하는 것이 이 (...) 논문의 목적이다. (shrink)

The A-theory of time has intuitive and metaphysical appeal, but suffers from tension, if not inconsistency, with the special and general theories of relativity (STR and GTR). The A-theory requires a notion of global simultaneity invariant under the symmetries of the world's laws, those ostensible transformations of the state of the world that in fact leave the world as it was before. Relativistic physics, if read in a realistic sense, denies that there exists any notion of global simultaneity (...) that is invariant under the symmetries of the world's laws. If physics is at least a decent guide to metaphysics--as sympathies for scientific realism would suggest--then relativistic physics supports the B-theory. If there were a physically natural way to modify the symmetries of the physical laws so as to remove those that are repugnant to the A-theory, while retaining empirical adequacy, then such an altered physics might be attractive to the A-theorist and would weaken the support given by relativity to the B-theory. I exhibit a way to do so here, displaying a Lagrangian density explicitly containing distant simultaneity, yet implying Einstein's field equations. The modification involves a change in the nature of the lapse function and makes use of the Dirac-Bergmann formalism of constrained dynamics, which recently has been discussed much by John Earman. Here this formalism is adapted slightly to permit both local and global generalized coordinates. A classification of senses in which time might be absolute or not is made along the way. Some suggestions for extending the work by finding a first principles motivation are made. An appendix outlines an argument why many local presents are insufficient and a global present is attractive, while two more appendices review the Dirac-Bergmann apparatus for GTR and then apply it to the theory at hand. (shrink)

In this paper the classical topic of “conventionality” in defining the simultaneity (or synchrony) of distant events is tackled again, and the validity of Reichenbach's view is carefully circumscribed. In particular, the role of “one-way” assumptions in the foundations of special relativity is emphasized. The restriction by the round-trip isotropy condition on the admissible distance functions in inertial frames is studied, and its relevance to several issues (absolute simultaneity, the interpretation of Michelson–Morley type experiments, the self-measured speed of (...) a clock) is shown. Two “clock transport” synchronizations in an inertial frame, using self-measured speed and “proper distance,” are presented in detail, and the agreement of the synchronies so established with standard synchrony is proven to be non- circular. By assuming a reasonable concept of “convention” this result is shown to dissolve several objections by supporters of a strong version of conventionalism. Throughout, a number of common misapprehensions in the literature are pointed out. (shrink)

It is routinely assumed that Einstein discovered the relativity of simultaneity by thinking about how clocks can be synchronized by light signals, much in accord with the analysis he gave in his 1905 special relativity paper. Yet that is just supposition. We have no real evidence that it actually happened this way. In later recollections, Einstein stressed the importance of several thought experiments in the thinking that led up to the final theory. They include his chasing a light beam (...) thought experiment and his magnet and conductor thought experiment. They do not include thought experiments on clocks and their synchronization. My goal here is to show that other pathways to the relativity of simultaneity are quite plausible. In several places Einstein stressed the importance in his discovery of special relativity of stellar aberration and Fizeau's measurement of the speed of light in moving water. The results can be seen as direct observational expressions of the relativity of simultaneity, if one knows how to read them. I will suggest that, thanks to his knowledge of Lorentz's 1895 Versuch, Einstein did know how to read them, and that it is quite possible that these observations first led Einstein to the relativity of simultaneity. (shrink)

David Malament's (1977) well-known result, which is often taken to show the uniqueness of the Poincare-Einstein convention for defining simultaneity, involves an unwarranted physical assumption: that any simultaneity relation must remain invariant under temporal reflections. Once that assumption is removed, his other criteria for defining simultaneity are also satisfied by membership in the same backward (forward) null cone of the family of such cones with vertices on an inertial path. What is then unique about the Poincare-Einstein convention (...) is that it is independent of the choice of inertial path in a given inertial frame, confirming a remark in Einstein 1905. Similarly, what is unique about the backward (forward) null cone definition is that it is independent of the state of motion of an observer at a point on the inertial path. (shrink)

The question of the simultaneity of relatives is one of the most debated aspects of Aristotle’s theory of relational properties. Are they exceptions to the rules of co-introduction and co-suppression for a pair of relatives? The present article studies a particular chapter of the long history of this problem, the contribution of three Byzantine thinkers of the ninth century. Their discussion is embedded in the complex phenomenon of the Iconoclast crisis. For reinvigorating their discourse on icons, these iconophiles thinkers (...) deployed Aristotelian logic, notably by treating the model and the image as Aristotelian relatives. This move implies tackling the issue of the simultaneity of relatives. Metrophanes, Nicephorus and Theodore solved it in three different ways which the present article reconstructs. (shrink)

This paper deals with the concept of simultaneity in classical and relativistic physics as construed in terms of group-invariant equivalence relations. A full examination of Newton, Galilei and Poincaré invariant equivalence relations in ℝ4 is presented, which provides alternative proofs, additions and occasionally corrections of results in the literature, including Malament’s theorem and some of its variants. It is argued that the interpretation of simultaneity as an invariant equivalence relation, although interesting for its own sake, does not cut (...) in the debate concerning the conventionality of simultaneity in special relativity. (shrink)

I develop Special Relativity with backward-light-cone simultaneity, which I call, for reasons made clear in the paper, ‘Apparent Simultaneity’. In the first section I show some advantages of this approach. I then develop the kinematics in the second section. In the third section I apply the approach to the Twins Paradox: I show how it removes the paradox, and I explain why the paradox was a result of an artificial symmetry introduced to the description of the process by (...) Einstein’s simultaneity definition. In the fourth section I discuss some aspects of dynamics. I conclude, in a fifth section, with a discussion of the nature of light, according to which transmission of light energy is a form of action at a distance. -/- deposited in Pittsburgh PhilSci-Archive, March 2007. (shrink)

Some elementary properties of tachyons are described and then it is argued that the claim that (T) Tachyons exist, is incompatible with the truth of the Special Theory of Relativity (STR). First it is argued that from T, STR, and the negation of the principle that (Pl) Effect never precedes cause, one can derive a paradoxical conclusion, one of the so-called "causal paradoxes". An obvious response is to affirm (Pl), but then it is argued that (Pl) and (T) entail that (...) STR is false. (shrink)

An ideal choice for undergraduate students of science and engineering, this book presents a thorough exploration of the basic concepts of relativity. The treatment provides more than the typical coverage of introductory texts, and it offers maximum flexibility since many sections may be used independently, in altered order, or omitted altogether. Numerous problems -- most with hints and answers -- make this volume ideal for supplementary reading and self-study. Nearly 300 diagrams illuminate the three-part treatment, which examines special relativity in (...) terms of kinematics and introductory dynamics as well as general relativity. Specific topics include the speed of light, the relative character of simultaneity, the Lorentz transformation, the conservation of momentum and energy, nuclei and fundamental particles, the principle of equivalence and curved space-time, Einstein's equations, and many other topics. (shrink)

Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the 'principle theory' approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein's treatment of the relativistic behaviour of rigid bodies and clocks in motion in (...) the kinematical part of his great paper, and suggested that the dynamical understanding of length contraction and time dilation intimated by the immediate precursors of Einstein is more fundamental. Harvey Brown both examines and extends these arguments, after giving a careful analysis of key features of the pre-history of relativity theory. He argues furthermore that the geometrization of the theory by Minkowski in 1908 brought illumination, but not a causal explanation of relativistic effects. Finally, Brown tries to show that the dynamical interpretation of special relativity defended in the book is consistent with the role this theory must play as a limiting case of Einstein's 1915 theory of gravity: the general theory of relativity.Appearing in the centennial year of Einstein's celebrated paper on special relativity, Physical Relativity is an unusual, critical examination of the way Einstein formulated his theory. It also examines in detail certain specific historical and conceptual issues that have long given rise to debate in both special and general relativity theory, such as the conventionality of simultaneity, the principle of general covariance, and the consistency or otherwise of the special theory with quantum mechanics. Harvey Brown' s new interpretation of relativity theory will interest anyone working on these central topics in modern physics. (shrink)

Max Jammer's Concepts of Simultaneity presents a comprehensive, accessible account of the historical development of an important and controversial concept -- which played a critical role in initiating modern theoretical physics -- from the days of Egyptian hieroglyphs through to Einstein's work in 1905, and beyond. Beginning with the use of the concept of simultaneity in ancient Egypt and in the Bible, the study discusses its role in Greek and medieval philosophy as well as its significance in Newtonian (...) physics and in the ideas of Leibniz, Kant, and other classical philosophers. The central theme of Jammer's presentation is a critical analysis of the use of this concept by philosophers of science, like Poincaré, and its significant role in inaugurating modern theoretical physics in Einstein's special theory of relativity. Particular attention is paid to the philosophical problem of whether the notion of distant simultaneity presents a factual reality or only a hypothetical convention. The study concludes with an analysis of simultaneity's importance in general relativity and quantum mechanics. (shrink)

We show that true colors as defined by Chevreul (1839) produce unsuspected simultaneous brightness induction effects on their immediate grey backgrounds when these are placed on a darker (black) general background surrounding two spatially separated configurations. Assimilation and apparent contrast may occur in one and the same stimulus display. We examined the possible link between these effects and the perceived depth of the color patterns which induce them as a function of their luminance contrast. Patterns of square-shaped inducers of a (...) single color (red, green, blue, yellow, or grey) were placed on background fields of a lighter and a darker grey, presented on a darker screen. Inducers were always darker on one side of the display and brighter on the other in a given trial. The intensity of the grey backgrounds varied between trials only. This permitted generating four inducer luminance contrasts, presented in random order, for each color. Background fields were either spatially separated or consisted of a single grey field on the black screen. Experiments were run under three environmental conditions: dark-adaptation, daylight, and rod-saturation after exposure to bright light. In a first task, we measured probabilities of contrast, assimilation, and no effect in a three-alternative forced-choice procedure (background appears brighter on the ‘left’, on the ‘right’ or the ‘same’). Visual adaptation and inducer contrast had no significant influence on the induction effects produced by colored inducers. Achromatic inducers produced significantly stronger contrast effects after dark-adaptation, and significantly stronger assimilation in daylight conditions. Grouping two backgrounds into a single one was found to significantly decrease probabilities of apparent contrast. Under the same conditions, we measured probabilities of the inducers to be perceived as nearer to the observer inducers. These, as predicted by Chevreul’s law of contrast, were determined by the luminance contrast of the inducers only, with significantly higher probabilities of brighter inducers to be seen as nearer, and a marked asymmetry between effects produced by inducers of opposite sign. Implications of these findings for theories which attempt to link simultaneous induction effects to the relative depth of object surfaces in the visual field are discussed. (shrink)

This survey article is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative simultaneity relation in the context of Minkowski spacetime; (ii) the ``geometrized" version of Newtonian gravitation theory (also known as Newton-Cartan theory); and (iii) the possibility of recovering the global geometric structure of spacetime from its ``causal structure".

Bergson's central contention is that time is not measurable by any objective standard; in Duration and Simultaneity, that position is tried out against the major movement in physics of the day - Relativity. Bergson argues that Relativity fails to live up to the promise of a truly relative physics, and counter to its own spirit retains some of the objectivist assumptions of previous world views. Duration and Simultaneity was conceived in the desire to make good the new (...) paradigm to which Relativity was bound to lay claim; in the desire to be more Einsteinian than Einstein. (shrink)

We consider the problem of uniqueness of certain simultaneity structures in flat spacetime. Absolute simultaneity is specifiled to be a non-trivial equivalence relation which is invariant under the automorphism group Aut of spacetime. Aut is taken to be the identity-component of either the inhomogeneous Galilei group or the inhomogeneous Lorentz group. Uniqueness of standard simultaneity in the first, and absence of any absolute simultaneity in the second case are demonstrated and related to certain group theoretic properties. (...) Relative simultaneity with respect to an additional structure X on spacetime is specified to be a non-trivial equivalence relation which is invariant under the subgroup in Aut that stabilises X. Uniqueness of standard Einstein simultaneity is proven in the Lorentzian case when X is an inertial frame. We end by discussing the relation to previous work of others. (shrink)

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. (shrink)