While Einstein considered that sub specie astern the correct philosophical position regarding geometry was that of the conventionality of geometry, he felt that provisionally it was necessary to adopt a non-conventional stance that he called practical geometry. here we will make the case that even when adopting Einstein’s views we must conclude that practical geometry is conventional after all. Einstein missed the fact that the conventionality of simultaneity leads to a conventional element in the chrono-geometry, since it (...) corresponds to the possibility of different space-time metrics. (shrink)

In his first paper on the special theory of relativity, Einstein indicated that the question of whether or not two spatially separated events were simultaneous did not necessarily have a definite answer, but instead depended on the adoption of a convention for its resolution. Some later writers have argued that Einstein's choice of a convention is, in fact, the only possible choice within the framework of special relativistic physics, while others have maintained that alternative choices, although perhaps less convenient, are (...) indeed possible. (shrink)

The conventionality of simultaneity thesis as established by Reichenbach and Grünbaum is related to the partial freedom in the definition of simultaneity in an inertial reference frame. An apparently altogether different issue is that of the conventionality of spatial geometry, or more generally the conventionality of chronogeometry when taking also into account the conventionality of the uniformity of time. Here we will consider Einstein’s version of the conventionality of geometry, according to which we (...) might adopt a different spatial geometry and a particular definition of equality of successive time intervals. The choice of a particular chronogeometry would not imply any change in a theory, since its “physical part” can be changed in a way that, regarding experimental results, the theory is the same. Here, we will make the case that the conventionality of simultaneity is closely related to Einstein’s conventionality of chronogeometry, as another conventional element leading to it. (shrink)

After describing a new method of synchronizing spatially separated clocks by means of clock transport, this paper discusses the philosophical import of the existence of such methods, including those of Ellis and Bowman and of Bridgman, with special reference to the Ellis-Bowman claim that "the thesis of the coventionality of distant simultaneity... is thus either trivialized or refuted." I argue that the physical facts do not support this philosophical conclusion, and that a substantial part of their argument against Reichenbach, (...) in particular, is misdirected. Finally, I suggest that Ellis and Bowman employ seriously unclear notions of triviality and "good physical reasons" that tend to obscure rather than clarify the basic philosophical issues. An objective criterion of nontriviality of conventions is advanced. (shrink)

An important epistemological lesson can be learned from the impossibility to determine the one-way velocity of light and the immediate implication that simultaneity is conventional. The vicious circle -- to determine whether two distant events are simultaneous we need to know the one-way velocity of light between them, but to determine the one-way velocity of light we need to know that the two events are simultaneous -- is an indication of the need for a profound change of our view (...) on reality. (shrink)

In 1977, David Malament proved the valuable technical result that the simultaneity relation of standard synchrony $\epsilon=\frac{1}{2}$ with respect to an inertial observer O is uniquely definable in terms of the relation κ of causal connectibility. And he claimed that this definability undermines my own version of the conventionality of metrical simultaneity within an inertial frame.But Malament’s proof depends on the imposition of several supposedly “innocuous” constraints on any candidate for the simultaneity relation relative to O. (...) Relying on Allen I. Janis’s 1983 challenge to one of these constraints, I argue that Malament’s technical result did not undermine my philosophical construal of the ontological status of relative metrical simultaneity. Furthermore, I show that (a) Michael Friedman’s peremptorily substantivalist critique of my conception, which Malament endorses, is ill-founded, and (b) if Malament had succeeded in discrediting my own conventionalist version of metrical simultaneity, he would likewise have invalidated Einstein’s pioneering version of it. (shrink)

Kant’s three Analogies of Experience, in his Critique of Pure Reason, represent a highly condensed attempt to establish the metaphysical foundations of Newtonian physics. His strategy is to show that the organization of experience in terms of a world of enduring substances undergoing mutual causal interaction is a necessary condition of the temporal ordering even of one’s own subjective states, and thus of coherent experience itself. In his Third Analogy—an examination of the necessary conditions of judgments of simultaneous existence—he argues (...) that certain conceptual presuppositions consistent with Newtonian physics are necessary to time-awareness. His argument, however, appears to be undermined by conventionalism in natural science generally, and by the conventionality of simultaneity in particular. In this paper I discuss Kant’s claims in light of contemporary relativity theory. I suggest that, while his project is obsolete in major respects, there may still be useful insights into time-awareness to be drawn from his work. (shrink)

In this paper, I elucidate the main points involved in the question of the non-triviality of the conventionality of simultaneity within the kinematics of special relativity. I argue that there is an important distinction to be made between the inherited component and the sui generis component of the conventionality of simultaneity. The factual core of the kinematics of special relativity is explored, and it is shown that the Round-Trip Clock Retardation effect obtains if, and only if (...) Winnie's Passage Time Principle holds. Some consequences of this fundamental fact are then explored. In particular, Grunbaum's view that the epistemological conventionality of simultaneity is logically prior to the physical inter-frame relativity of simultaneity is found to be based largely on what I call the inherited component of the former. Finally, a question is raised as to the very self-consistency of the claim, made by Ellis and Bowman, that standard signal synchrony and slow-transport synchrony are logically independent. In some concluding remarks, the author's general agreement with Grunbaum's conception of bridled conventionalism is indicated. (shrink)

Despite a broad-range title the paper settles for the related issue of whether the Special Theory of Relativity necessarily advocates the demise of an ontological difference between past and future events, between past and future in general. In the jargon of H. Stein: are we forced, within the framework of the STR, to choose only between ‘solipsism’ and ‘determinism’ exclusively? A special emphasis is placed on the role that the conventionality of simultaneity plays in the STR with regards (...) to this question. The standard arguments rely on the relativity of simultaneity, the claim that the STR negates the existence of a universal ‘present’ that divides the ‘past’ and the ‘future’, so as to conclude that there is no ontological difference between past and future events, that both are equally determined/real. This often neglects the fact that to establish the ontological claims related to relativity of simultaneity, one must first resolve the issues of conventionality of simultaneity within the STR. The paper will aim to show that by addressing the issue of conventionality from Dummett’s ‘purely philosophical’ determination of the difference between the past and the future, we develop an understanding of the said difference, within the framework of the STR, beyond the strict ontological dichotomy of ‘solipsism/determinism’, given that the criterion that is provided by the STR is understood as epistemic and not ontological. (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)

To date, both sides in the conventionality of simultaneity debate grant that transformations from "standard" to "nonstandard" coordinates are possible without any empirically significant effects. However, it is argued here that the very possibility of defining nonstandard coordinates vanishes if one represents special relativity, not by real four-vectors (as has been the case so far in the debate), but by complex spinors as used in the representation of half-integer spin. Thus, in the topologically simplest representation of the Lorentz (...) group, the transformation over which the debate has been fought does not exist and one of the most basic foundations of the conventionalist thesis is challenged. (shrink)

In this work we will consider gauge interpretations of the conventionality of simultaneity as developed initially by Anderson and Stedman, and later by Rynasiewicz. We will make a critical reassessment of these interpretations in relation to the “tradition” as developed in particular by Reichenbach, Grünbaum, and Edwards. This paper will address different issues, including: the relation between these two gauge interpretations; what advantages or defects these gauge approaches might have; how “new” Rynasiewicz’s approach in relation to the previous (...) ones is; how much of the gauge interpretation Rynasiewicz actually applies to deal with objections to the conventionality of simultaneity thesis. The conclusion is that the gauge interpretations, in their current formulation, do not provide a better “rationale” of the conventionality of simultaneity thesis that supersedes the “tradition”. (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)

In recent articles, Zangari (1994) and Karakostas (1997) observe that while an &unknown;-extended version of the proper orthochronous Lorentz group O + (1,3) exists for values of &unknown; not equal to zero, no similar &unknown;-extended version of its double covering group SL(2, C) exists (where &unknown;=1-2&unknown; R , with &unknown; R the non-standard simultaneity parameter of Reichenbach). Thus, they maintain, since SL(2, C) is essential in describing the rotational behaviour of half-integer spin fields, and since there is empirical evidence (...) for such behaviour, &unknown;-coordinate transformations for any value of &unknown;<>0 are ruled out empirically. In this article, I make two observations:(a)There is an isomorphism between even-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions of such spinor fields.(b)There is a 2-1 isomorphism between odd-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions for such spinor fields up to a sign. Evidence that the components of such fields do take unique values is not decisive in favour of the realist in the debate over the conventionality of simultaneity in so far as such fields do not play a role in clock synchrony experiments in general, and determinations of the one-way speed of light in particular.I claim that these observations are made clear when one considers the coordinate-independent 2-spinor formalism. They are less evident if one restricts oneself to earlier coordinate-dependent formalisms. I end by distinguishing these conclusions from those drawn by the critique of Zangari given by Gunn and Vetharaniam (1995). (shrink)

A synchrony-free, velocity-independent formulation of the Lorentz transformation is derived in a very simple manner with the help of thek-calculus. The dependence of the well-known relativistic effects on the choice of simultaneity metric is put forth, and the significance of the possibility of eliminating these effects is explored. This leads to a simple analysis of the clock paradox, or round-trip clock retardation. The doctrine of the conventionality of simultaneity is brought to bear on the interpretation of this (...) effect. It is argued that such a round-trip effect constitutes a physical realization not only of the conventionality of simultaneity but of that of temporal congruence as well. Some physics perhaps vindicates a little philosophy. (shrink)

1. Introduction Dirac's theory of the electron was the first widely accepted relativistic quantum theory, and it later provided the basis for constructing the modern electromagnetic theory of quantum electrodynamics. Whereas Dirac's theory in its simplest form describes relativistic freely-propagating massive non-chiral particles of spin-½, QED describes how such particles interact with one another electromagnetically, via a dynamical quantum field.

We take another look at Reichenbach’s 1920 conversion to conventionalism, with a special eye to the background of his ‘conventionality of distant simultaneity’ thesis. We argue that elements of Reichenbach earlier neo-Kantianism can still be discerned in his later work and, related to this, that his conventionalism should be seen as situated at the level of global theory choice. This is contrary to many of Reichenbach’s own statements, in which he declares that his conventionalism is a consequence of (...) the arbitrariness of coordinative definitions. (shrink)

This paper is a response to the "panel discussion of simultaneity by slow clock transport in the special and general theories of relativity" ("philosophy of science", 36, (march, 1969), Pp. 1-81) which arose out of a paper by brian ellis and peter bowman on "conventionality in distant simultaneity", ("philosophy of science", 34, (june, 1967), Pp. 116-36). It is argued that the basic disagreement between the pittsburgh panel and us is an epistemological one. In particular, Our concept of (...) a good physical reason is radically different from the pittsburgh panel's. For us the known existence of a number of concordant, Isotropic, And logically independent criteria for distant simultaneity, And the non-Existence of any known discordant but isotropic criteria for distant simultaneity is a good physical reason for choosing one of these criteria. For the pittsburgh panel it is not. (shrink)

The conventionality of simultaneity at distant points is defended partly by reference to Einstein's 1905 paper founding special relativity. His famous light-signaling definition takes the transit time of light in one direction to be equal to that in the other. Conventionalists such as Reichenbach and Grunbaum argue that he could have made them unequal without denying any physical fact. However, Einstein's more detailed treatment in the 1910 Archives des sciences runs counter to this thesis. There he required that (...) the two signal-paths be physically equivalent and thus that whatever the signals travel through have no perturbing affect on their motions. (shrink)

The debate on the conventionality of simultaneity and the debate on the dimensionality of the world have been central in the philosophy of special relativity. The link between both debates however has rarely been explored. The purpose of this paper is to gauge what implications the former debate has for the latter. I show the situation to be much more subtle than was previously argued, and explain how the ontic versus epistemic distinction in the former debate impacts the (...) latter. Despite claims to the contrary, I conclude that special relativity leaves the debate on the dimensionality of the world underdetermined. (shrink)

I examine the development of Reichenbach's ideas concerning the conventionality of simultaneity in connection with his ``epsilon''-definition of simultaneity. It does not appear that he ever considered non-standard choices of ``epsilon'' that yield the same ``light-geometry'' as that of special relativity. Rather, it appears he believed that non-standard choices, though always epistemically justified, lead to different ``light-geometries'' (e.g., classical space-time) and thus would necessitate more complicated ``matter axioms'' than those postulated in his axiomatization of relativity.

The present paper pursues two aims. First to show that the experiment proposed by Stolakis [1986] does not lead to absolute synchronization in a single frame of reference and therefore also to the measurement of one-way velocity of light. Second, by consecutively considering the problems of the conventionality of simultaneity and of existence to show that the simultaneity of distant events can be a matter of convention only in a four-dimensional world. * I am grateful to the (...) anonymous referees for their useful suggestions on an earlier version of this paper. (shrink)

Thought experiments are described in which the one-way velocity of light appears as a physical quantity. A rotating shaft is used to define distant synchrony for a system of clocks along the shaft. In this context Einstein's definition of distant simultaneity is seen as based on a physical assumption (and not merely on an overwhelmingly sensible choice in a range of conventional possibilities).

The paper defends the thesis of conventionality in distant simultaneity within the special theory of relativity. The thesis can be expressed in the following way: There is no method independent of standard synchronization by which the one-way velocity of light can be measured if all empirical consequences of the special theory of relativity are to be accepted. Three methods which have recently been suggested are investigated. It is shown that they all depend on the method of standard synchronization. (...) It is finally claimed that nobody has suggested a method which cannot be shown to depend on the method of standard synchronization. (shrink)

In this paper we examine Ellis and Bowman's argument, that simultaneity in inertial frames of reference is not conventional, from the axiomatic point of view. In Part I we examine the role of conventions in an axiomatic physical theory, and in Part II the relation of simultaneity in Reichenbach's axiomatization of the space-time theory of special relativity.

In his original paper of 1905, "On the Electrodynamics of Moving Bodies", Einstein described a procedure for synchronizing distant clocks at rest in any inertial system K. Clocks thus synchronized may be said to be in standard signal synchrony in K. It has often been claimed that there are no logical or physical reasons for preferring standard signal synchronizations to any of a range of possible non-standard ones. In this paper, the range of consistent non-standard signal synchronizations, first for any (...) one inertial system, and second for any set of such systems, is investigated, and it is shown that the requirement of consistency leaves much less room for choice than is commonly supposed. Nevertheless consistent non-standard signal synchronizations appear to be possible. However, it is also shown that good physical reasons for preferring standard signal synchronizations exist, if the Special Theory of Relativity yields correct predictions. The thesis of the conventionality of distant simultaneity espoused particularly by Reichenbach and Grunbaum is thus either trivialized or refuted. (shrink)

My aim in this note is to disambiguate various senses of ‘conventional’ that in the philosophy of physics have been frequently conflated. As a case study, I will refer to the well-known issue of the conventionality of simultaneity in the special theory of relativity, since it is particularly in this context that the above mentioned confusion is present.

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)

Barrett and others have used Lewis-style evolutionary games to argue that we ought not to trust our scientific languages to inform us about ontology. More specifically, Barrett has shown that in some simple evolutionary contexts the best descriptive languages need not cut nature at its joints, that they may guide action as successfully as possible while simultaneously being deeply conventional. The present article expands upon Barrett’s argument, exploring the space for conventionalism in more metaphysically robust causal evolutionary models. By using (...) evolutionary prediction games, the present article examines the range of metaphysical facts in these models and shows how Barrett’s sceptical argument may be both challenged and expanded to cover these systems, resulting in a more thoroughgoing scepticism about what metaphysical conclusions may be drawn from linguistic and theoretical structure. (shrink)

Eternalism is the view that the past, the present and the future exist simpliciter. A typical argument in favor of this view leans on the relativity of simultaneity. The ‘equally real with’ relation is assumed to be transitive between spacelike separated events connected by hyperplanes of simultaneity. This reasoning is in tension with the conventionality of simultaneity. Conventionality indicates that, even within a specific frame, simultaneity is based on the choice of the synchronization parameter. (...) Hence the argument for eternalism is compromised. This paper lays out alternative eternalist strategies which do not hinge on hyperplanes. While we lack a rigorous proof for eternalism, there are still cogent reasons to prefer eternalism over presentism. (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)

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.

Frank Jackson and Robert Pargetter propose a method for synchronizing clocks at rest at distant points of an inertial system in Euclidean space, which, they claim, does not depend on Einstein's signalling method and provides a basis for denying the conventionality of distant simultaneity. I am afraid, however, that the new method presupposes that the simultaneity of distant events relatively to the chosen inertial system has been already determined by Einstein's or some other method. Jackson and Pargetter (...) describe their method as follows: Let UA, UB be clocks at A, B, respectively. Let XY be an axis perpendicular to AB, passing through C, the midpoint of AB. Take a rigid straight rod A′B′ with midpoint C′ and length equal to the length AB. Move A′B′ with uniform velocity such that C′ travels along XY towards C, and A′B′ is perpendicular to XY ; then if the reading … on UA just when A′ coincides with A is the same as the reading … on UB just when B′ coincides with B, clocks UA and UB will be synchronous.. (shrink)

Transnational higher education (TNHE) has been characterised as a crude form of market-driven internationalisation, often targeting immobile student populations in countries with high demand for international academic degrees. In response to recent scholarship on the role of higher education internationalisation in facilitating and producing diasporic networks, this study examines its inverse: how TNHE services existing diasporic communities in situ by mobilising institutions across borders rather than student bodies. It specifically examines these dynamics within the United Arab Emirates (UAE), simultaneously host (...) to one of the largest concentrations of TNHE globally and a five million-member diasporic community of long-term, yet impermanent residents from South Asia. Drawing on interviews with South Asian students in undergraduate degree programmes at three British international branch campuses (IBCs), it explores how students perceive their IBCs as strategic sources of valuable degree capitals for enhancing employment opportunities in the UAE and securing against precarity and uncertain futures as perpetually impermanent residents. The research implicates the role of TNHE in diaspora policymaking, asking how IBCs function as an extension of a limited social contract between a diasporic community and its ‘host’ state. (shrink)

In their article, “Relative Simultaneity in the Special Theory of Relativity,” Jackson and Pargetter have offered a method to determine distant simultaneity which they claim to be independent of any assumptions concerning one-way velocities and thus a basis for denying the conventionality of distant simultaneity within the framework of the Special Theory. In what follows, I shall argue that the case they make to support the claim to independence is mistaken.

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

One of the most debated problems in the foundations of the special relativity theory is the role of conventionality. A common belief is that the Lorentz transformation is correct but the Galilean transformation is wrong. It is another common belief that the Galilean transformation is incompatible with Maxwell equations. However, the “principle of general covariance” in general relativity makes any spacetime coordinate transformation equally valid. This includes the Galilean transformation as well. This renders a new paradox. This new paradox (...) is resolved with the argument that the Galilean transformation is equivalent to the Lorentz transformation. The resolution of this new paradox also provides the most straightforward resolution of an older paradox which is due to Selleri in. I also present a consistent electrodynamics formulation including Maxwell equations and electromagnetic wave equations under the Galilean transformation, in the exact form for any high speed, rather than in low speed approximation. Electrodynamics in rotating reference frames is rarely addressed in textbooks. The presented formulation of electrodynamics under the Galilean transformation even works well in rotating frames if we replace the constant velocity v\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {v}$$\end{document} with v=ω×r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {v}=\varvec{\omega }\times \mathbf {r}$$\end{document}. This provides a practical tool for applications of electrodynamics in rotating frames. When electrodynamics is concerned, between two inertial reference frames, both Galilean and Lorentz transformations are equally valid, but the Lorentz transformation is more convenient. In rotating frames, although the Galilean electrodynamics does not seem convenient, it could be the most convenient formulation compared with other transformations, due to the intrinsic complex nature of the problem. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

An often repeated account of the genesis of special relativity tells us that relativity theory was to a considerable extent the fruit of an operationalist philosophy of science. Indeed, Einstein’s 1905 paper stresses the importance of rods and clocks for giving concrete physical content to spatial and temporal notions. I argue, however, that it would be a mistake to read too much into this. Einstein’s operationalist remarks should be seen as serving rhetoric purposes rather than as attempts to promulgate a (...) particular philosophical position --- in fact, Einstein never came close to operationalism in any of his philosophical writings. By focussing on what could actually be measured with rods and clocks Einstein shed doubt on the empirical status of a number of pre-relativistic concepts, with the intention to persuade his readers that the applicability of these concepts was not obvious. This rhetoric manoeuvre has not always been rightly appreciated in the philosophy of physics. Thus, the influence of operationalist misinterpretations, according to which associated operations strictly define what a concept means, can still be felt in present-day discussions about the conventionality of simultaneity. The standard story continues by pointing out that Minkowski in 1908 supplanted Einstein’s approach with a realist spacetime account that has no room for a foundational role of rods and clocks: relativity theory became a description of a four-dimensional ‘absolute world’. As it turns out, however, it is not at all clear that Minkowski was proposing a substantivalist position with respect to spacetime. On the contrary, it seems that from a philosophical point of view Minkowski’s general position was not very unlike the one in the back of Einstein’s mind. However, in Minkowski’s formulation of special relativity it becomes more explicit that the content of spatiotemporal concepts relates to considerations about the form of physical laws. If accepted, this position has important consequences for the discussion about the conventionality of simultaneity. (shrink)

Summary A recurrent theme in the philosophical literature on the special theory of relativity is the question as to the reality of the Lorentz contraction. It is often suggested that there is a difference between the Lorentz-FitzGerald contraction in the pre-relativistic ether theory and the Lorentz contraction from special relativity in the sense that the former is a real contraction of matter conditioned by dynamical laws, whereas the latter should be compared with the apparent changes in the size of objects (...) when the perspective of the observer changes. It is here shown, however, that the same laws of nature which are operative in the Lorentz-FitzGerald contraction also condition the relativistic Lorentz contraction. The relevant distinction therefore is not between the reality of the two contractions. What is at issue is the difference in explanatory structure of the pre-relativistic theory on the one hand and the special theory of relativity on the other. In the course of the argument the question of the conventionality of simultaneity is also discussed. (shrink)

The Conventionality of Simultaneity espoused by Reichenbach, Grunbaum, Edwards, and Winnie is herein extended to mechanics and electrodynamics. The extension is seen to be a special case of a generally covariant formulation of physics, and therefore consistent with Special Relativity as the geometry of flat space-time. Many of the quantities of classical physics, such as mass, charge density, and force, are found to be synchronization dependent in this formulation and, therefore, in Reichenbach's terminology, "metrogenic." The relationship of these (...) quantities to 4-vectors and their physical significance is discussed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Philosophy of PhysicsMartin CurdRoberto Torretti. The Philosophy of Physics. Cambridge: Cambridge University Press, 1999. Pp. xvi + 512. Cloth, $64.95. Paper, $23.95.This is the first volume in a new Cambridge series, "The Evolution of Modern Philosophy." It is a historical work, tracing the interaction between physics and philosophy from the scientific revolution of the seventeenth century through general relativity and quantum mechanics in the twentieth century. The (...) emphasis is on the philosophy in physics (rather than philosophizing about physics) and, with the exceptions noted below, the focus is on scientists (scientist-philosophers in many cases) rather than philosophers outside of science. Most of the book is about the conceptual and mathematical development of the core branches of physics (mainly mechanics, but also geometry, thermodynamics, and field theory). There are seven chapters plus three supplements giving the mathematical essentials of vector analysis, lattice theory, and topology.The hero of chapter one is Galileo who, more than anyone else prior to Newton, set physics on its modern path towards mathematization and away from Aristotle. Also discussed in chapter one are Descartes, Huyghens, and Leibniz. Chapter two is devoted to Newton (both the foundations of Newtonian mechanics and the derivation of the law of universal gravitation) and follows the development of analytical mechanics up to Lagrange and Hamilton. Chapter three, appropriately entitled "Kant," is the only chapter devoted to a philosopher. After a brief discussion of Leibniz, Berkeley, and Kant's pre-critical writings, it covers the important scientific topics in the Critique of Pure Reason (space, time, the three Analogies) but avoids the Metaphysical Foundations of Natural Science (referring the reader to Michael Friedman's Kant and the Exact Sciences). Chapter four looks at scientific developments in three areas that proved to be important for twentieth-century physics: non-Euclidean geometry from Lobachevsky to Riemann, electromagnetic field theory (Maxwell), and thermal physics (classical thermodynamics, the kinetic theory, and statistical mechanics) from Carnot to Boltzmann. The chapter concludes, somewhat untidily, with a section on four philosophers of science (Whewell, Peirce, Mach, and Duhem), selected, we are told, because of their influence on philosophy of science in the second half of the twentieth century. (For the "two great philosopher-scientists" Helmholtz and Poincaré, the reader is referred to Torretti's earlier books, Philosophy of Geometry from Riemann to Poincaré, and Relativity and Geometry.) Chapter five covers both the special and general theory of relativity. After a masterful exposition of the special theory and its Minkowski spacetime representation, the usual topics of philosophical interest are discussed; these include the conventionality of simultaneity thesis, the twin paradox, the relativistic concept of mass, and determinism. The rather brief treatment of the general theory is, unavoidably, mathematically demanding and carries the subject through to recent inflationary cosmological models. Chapter six (also mathematically demanding at times) examines the development and structure of quantum mechanics, aptly praised as "one of the most elegant creations of the human spirit" (340). Torretti wisely ignores the complexities of quantum field theory since the philosophical problems discussed—measurement, the EPR paradox, the interpretation of the y-function—remain when quantum mechanics is made Lorentz invariant; but he urges philosophers of science to follow the lead of Michael Redhead and [End Page 602] Paul Teller in exploring its metaphysical ramifications. Of special note are the author's trenchant criticisms of attempts to solve the quantum mysteries by Bohr (complementarity), Bohm (hidden variables), Putnam (quantum logic), and Everett (the many worlds interpretation). The book concludes with the author's reflections on issues in the philosophy of science. Torretti defends the structuralist explication of physical theories (more familiarly known as the semantic conception or the model-theoretic view) that informs much of his book, arguing that it succeeds where the "received view" of logical empiricism failed while avoiding Kuhnian incommensurability—"a pseudoproblem that made philosophy of science the laughing stock of practicing physicists" (404). The chapter ends with an attack on inductive logic: "one of the blindest alleys in twentieth-century philosophy" (437).The writing is admirably clear and the author has done a commendable job of explaining the arguments of historical scientists while presenting their theories in a clear... (shrink)