It will be shown that, in comparison with the pre-relativistic Galileo-invariant conceptions, specialrelativity tells us nothing new about the geometry of spacetime. It simply calls something else "spacetime", and this something else has different properties. All statements of specialrelativity about those features of reality that correspond to the original meaning of the terms "space" and "time" are identical with the corresponding traditional pre-relativistic statements. It will be also argued that specialrelativity and (...) Lorentz theory are completely identical in both senses, as theories about spacetime and as theories about the behavior of moving physical objects. (shrink)
In the established space-time coordinate-transformation (STCT) interpretation of specialrelativitytheory, relativistic changes are consequent upon the Lorentz transformation of coordinate clocks and rods between relatively moving systems. In the proposed alternative interpretation, relativistic changes occur only in association with physical interactions, and are direct alterations in the variables of the observed system. Since space-time and momentum-energy are conjugate four-vectors, transformation of a space or time variable of a system is to be expected only if there is (...) a concomitant transformation of the corresponding momentum or energy variable. The Lorentz invariance of the scalar entropy functionS supports the interaction interpretation; timet=f(S) of a macroscopic, entropy clock should give a Lorentz-invariant time measure, and an illustrative entropy clock is discussed. Noninteracting physical processes may be called Clausius processes, in contrast to Lorentz processes for which there is interaction and associated Lorentz transformation. Changes of energy and frequency, withE=hv, are instances of the parallel relativistic transformations. Likewise, the variation with velocity in decay time of mesons follows directly from the relativistic energy transformation of decay products; this relationship is shown for muons by a simple calculation with β-decay theory. (shrink)
The interaction interpretation of specialrelativitytheory (elaborated in Part I) is discussed in relation to quantum theory. The relativistic transformations (Lorentz processes) of physical variables, on the interaction interpretation, are observation-interaction dependent, just as are the physical values (eigenvalues) of systems described by quantum-theoretic state functions; a common, basic structure of the specialrelativity and quantum theories can therefore be presented. The constancy of the light speed is shown to follow from interaction-transformations of (...) frequency and wavelength variables. A parallelism is suggested between, on the one hand, the Lorentz-Clausius distinction for relativistic transformations, and, on the other, the distinction between observation-dependent and observation-independent natural processes. The empirical study of rates of macroscopic clocks can provide a critical test of the interaction interpretation and of a possible extension to gravitational time changes; the role of time as prior determinant of natural process is at issue. The Hafele-Keating observations are of general relativity effects on clocks in accelerated motion. (shrink)
Neither special nor general relativity make any use of a notion of absolute simultaneity. Since A-Theories about time do make use of such a notion, it is natural to suspect that relativity and A-Theory are inconsistent. Many authors have argued that they are in fact not inconsistent, and I agree with that diagnosis here. But that doesn’t mean, as these authors seem to think, that A-Theory and relativity are happy bedfellows. I argue that (...) class='Hi'>relativity gives us good reason to reject the A-Theory, even though strict inconsistency isn’t that reason. (shrink)
Im vierdimensionalen Raum-Zeit-Kontinuum der Speziellen Relativitätstheorie gibt es dreidimensionale geometrische Objekte, sogenannte Hyperebenen, die für die Theorie von zentraler Bedeutung sind. Jede solche Hyperebene kann zum einen als raumartig charakterisiert werden und zum anderen als Gleichzeitigkeitsebene. Dasselbe geometrische Objekt ist also je nach Betrachtungsweise raumartig oder räumlich. Während der Ausdruck „raumartige Hyperebene“ ein lorentzinvariantes, absolutes Objekt bezeichnet, ist mit „Gleichzeitigkeitsebene“ etwas Beobachterabhängiges benannt. Daher läßt sich sagen: Dasselbe, das in seiner Beobachterabhängigkeit als räumlich charakterisiert ist, ist in seiner Beobachterunabhängigkeit betrachtet (...) raumartig. Ganz ähnlich argumentiert auch Kant bezüglich empirischer Objekte: Dasselbe ist auf zwei verschiedene Weisen betrachtbar – nämlich zum einen „als Erscheinung“ und zum anderen „an sich selbst“. Es als Erscheinung zu betrachten, bedeutet, es in seiner Subjektabhängigkeit zu erfassen, es an sich selbst zu betrachten, heißt, in ihm auch Subjektunabhängiges zu erblicken. Daß dies keine bloße Analogie ist, soll im ersten Teil gezeigt werden. Hier wie dort geht es letztlich um denselben Zweck – nämlich um die Charakterisierung empirischer Objekte als wirklicher: Ein wirkliches Objekt ist nach Kant subjektabhängig, aber nicht subjektiv. Weil subjektabhängig, ist es als Erscheinung betrachtbar; aber weil nicht subjektiv, auch immer an sich selbst. In der SRT wiederum ist ein empirisches Objekt in seiner Wirklichkeit nur dann voll erfaßt, wenn man es sowohl als räumliches wie als raumartiges betrachtet. Als bloß räumliches wäre es nämlich für verschieden bewegte Beobachter nicht zugleich gegenwärtig und nicht in allen seinen Teilen gleichzeitig; als bloß raumartiges hingegen wäre es noch gar nicht inhaltlich, sondern bloß formal bestimmt. Die SRT gibt mithin dem kantischen „an sich selbst“ einen neuen Namen, was man als eine Konkretisierung ansehen kann. (shrink)
Summary The present paper constitutes an elaboration of a previous work by one of us which, among other things, proposed some modifications of Popper's tetradic schema. Here, in the first part, we consider critically and develop further these modifications and elaborate on methods which prove more satisfactory for the mapping of the problem solving processes in Physics. We also find the opportunity to make some comments on Physics and on its relation to Mathematics. In the second part, there is an (...) attempt to test the above ideas on the genesis and development of the SpecialRelativityTheory. In doing this, we concentrate mainly on Einstein's 1905 paper and try to explicitate its relation with the situation Physics found itself in that period as well as to clarify the epistemological status of Einstein's two postulates. (shrink)
To comprehend the specialrelativity genesis, one should unfold Einstein’s activities in quantum theory first . His victory upon Lorentz’s approach can only be understood in the wider context of a general programme of unification of classical mechanics and classical electrodynamics, with relativity and quantum theory being merely its subprogrammes. Because of the lack of quantum facets in Lorentz’s theory, Einstein’s programme, which seems to surpass the Lorentz’s one, was widely accepted as soon as (...) quantum theory became a recognized part of physics. A new approach to specialrelativity genesis enables to broaden the bothering “Trinity” group of its creators to include Gilbert N. Lewis. Notwithstanding that the links necessarily existing between all the 1905 papers were obscured by Einstein himself due to the reasons discussed below, Lewis revealed from the very beginning the connections between specialrelativity and quasi-corpuscular theory of light, as he punctuated: “The consequences which one of us obtained from a simple assumption as to the mass of a beam of light, and the fundamental conservation of mass, energy and momentum, Einstein has derived from the principle of relativity and the electromagnetic theory” (Lewis G.N.& Tolman R.C. “The Principle of Relativity and Non-Newtonian Mechanics”, Philosophical Magazine, 1908). (shrink)
This book gives an excellent introduction to the theory of specialrelativity. Professor Resnick presents a fundamental and unified development of the subject with unusually clear discussions of the aspects that usually trouble beginners. He includes, for example, a section on the common sense of relativity. His presentation is lively and interspersed with historical, philosophical and special topics (such as the twin paradox) that will arouse and hold the reader's interest. You'll find many unique features (...) that help you grasp the material, such as worked-out examples,summary tables,thought questions and a wealth of excellent problems. The emphasis throughout the book is physical. The experimental background, experimental confirmation of predictions, and the physical interpretation of principles are stressed. The book treats relativistic kinematics, relativistic dynamics, and relativity and electromagnetism and contains special appendices on the geometric representation of space-time and on general relativity. Its organization permits an instructor to vary the length and depth of his treatment and to use the book either with or following classical physics. These features make it an ideal companion for introductory courses. (shrink)
This survey article is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativitytheory. 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". (shrink)
Endurantism is not inconsistent with the theory of specialrelativity, or so I shall argue. Endurantism is not committed to presentism, and thus not committed to a metaphysics that is at least prima facie inconsistent with specialrelativity. Nor is specialrelativity inconsistent with the idea that objects are wholly present at a time just if all of their parts co-exist at that time. For the endurantist notion of co-existence in terms of which (...) “wholly present” is defined, is not, I will argue, a notion according to which co-existence is transitive. Although an absence of absolute simultaneity presents some problems for the endurantist claim that objects are wholly present whenever they exist, there are a number of ways that the endurantist can respond to this difficulty. Thus, I conclude, considerations pertaining to the theory of specialrelativity certainly do not rule out endurantism as a metaphysics of persistence. (shrink)
This white paper aims to identify an open problem in 'Quantum Physics and the Nature of Reality' -namely whether quantum theory and specialrelativity are formally compatible-, to indicate what the underlying issues are, and put forward ideas about how the problem might be addressed.
In this paper I expound an argument which seems to establish that probabilism and specialrelativity are incompatible. I examine the argument critically, and consider its implications for interpretative problems of quantum theory, and for theoretical physics as a whole.
Are specialrelativity and probabilism compatible? Dieks argues that they are. But the possible universe he specifies, designed to exemplify both probabilism and specialrelativity, either incorporates a universal "now" (and is thus incompatible with specialrelativity), or amounts to a many world universe (which I have discussed, and rejected as too ad hoc to be taken seriously), or fails to have any one definite overall Minkowskian-type space-time structure (and thus differs drastically from (...) class='Hi'>specialrelativity as ordinarily understood). Probabilism and specialrelativity appear to be incompatible after all. What is at issue is not whether "the flow of time" can be reconciled with specialrelativity, but rather whether explicitly probabilistic versions of quantum theory should be rejected because of incompatibility with specialrelativity. (shrink)
In a comparison of the principles of specialrelativity and of quantum mechanics, the former theory is marked by its relative economy and apparent explanatory simplicity. A number of theorists have thus been led to search for a small number of postulates - essentially information theoretic in nature - that would play the role in quantum mechanics that the relativity principle and the light postulate jointly play in Einstein's 1905 specialrelativitytheory. The (...) purpose of the present paper is to resist this idea, at least in so far as it is supposed to reveal the fundamental form of the theory. It is argued that the methodology of Einstein's 1905 theory represents a victory of pragmatism over explanatory depth; and that its adoption only made sense in the context of the chaotic state state of physics at the start of the 20th century - as Einstein well knew. (shrink)
N. Maxwell (1985) has claimed that specialrelativity and "probabilism" are incompatible; "probabilism" he defines as the doctrine that "the universe is such that, at any instant, there is only one past but many alternative possible futures". Thus defined, the doctrine is evidently prerelativistic as it depends on the notion of a universal instant of the universe. In this note I show, however, that there is a straightforward relativistic generalization, and that therefore Maxwell's conclusion that the special (...)theory of relativity should be amended is unwarranted. I leave open the question whether or not probabilism (or the related doctrine of the flow of time) is true, but argue that the specialtheory of relativity has no fundamental significance for this question. (shrink)
The Reichenbach-Grunbaum thesis of the conventionality of simultaneity is clarified and defended by developing the consequences of the SpecialTheory when assumptions are not made concerning the one-way speed of light. It is first shown that the conventionality of simultaneity leads immediately to the conventionality of all relative speeds. From this result, the general-length-contraction and time-dilation relations are then derived. Next, the place of time-dilation and length-contraction effects within the SpecialTheory is examined in the light (...) of the conventionality thesis. The slow-transport method of synchrony is then examined in the light of these results and is shown not to provide an adequate method of uniquely determining the one-way speed of light. Finally, the general ε -Lorentz transformations for events along the x-axis are derived from three principles: the round-trip light principle, the principle of equal passage times, and the linearity principle. These principles are shown to be independent of one-way velocity assumptions, and thus may form the basis of a SpecialTheory of Relativity without distant simultaneity assumptions. (shrink)
In this paper, I defend a theory of local temporality, sometimes referred to as a point-present theory. This theory has the great advantage that it allows for the possibility of an open future without requiring any alterations to our standard understanding of specialrelativity. Such theories, however, have regularly been rejected out of hand as metaphysically incoherent. After surveying the debate, I argue that such a transformation of temporal concepts (i) is suggested by the indexical (...) semantics of tense in a relativistic universe, (ii) when properly understood easily withstands the usual accusations of metaphysical incoherence and (iii) leads naturally to a meta-philosophical position from which we can understand and escape the increasing sterility of debates between radical Parmenideans and radical Heracliteans in the philosophy of time. (shrink)
According to a widespread view, Einstein’s definition of time in his specialrelativity is founded on the positivist verification principle. The present paper challenges this received outlook. It shall be argued that Einstein’s position on the concept of time, to wit, simultaneity, is best understood as a mitigated version of concept empiricism. He contrasts his position to Newton’s absolutist and Kant’s transcendental arguments, and in part sides with Hume’s and Mach’s empiricist arguments. Nevertheless, Einstein worked out a concept (...) empiricism that is considerably more moderate than what we find in the preceding empiricist tradition and early logical positivism. He did not think that the origin of concepts is in observations, but in conventions, and he also maintained a realist ontology of physical events, which he thought is necessary for his theory. Consequently, his philosophy of time in specialrelativity is not couched in terms of an anti-metaphysical verificationism. (shrink)
With the interaction interpretation, the Lorentz transformation of a system arises with selection from a superposition of its states in an observation-interaction. Integration of momentum states of a mass over all possible velocities gives the rest-mass energy. Static electrical and magnetic fields are not found to form such a superposition and are to be taken as irreducible elements. The external superposition consists of those states that are reached only by change of state of motion, whereas the internal superposition contains all (...) the states available to an observer in a single inertial coordinate system. The conjecture is advanced that states of superposition may only be those related by space-time transformations (Lorentz transformations plus space inversion and charge conjugation). The continuum of external and internal superpositions is examined for various masses, and an argument for the unity of the super-positions is presented. (shrink)
It has been repeatedly argued, most recently by Nicholas Maxwell, that the specialtheory of relativity is incompatible with the view that the future is in some degree undetermined; and Maxwell contends that this is a reason to reject that theory. In the present paper, an analysis is offered of the notion of indeterminateness (or "becoming") that is uniquely appropriate to the specialtheory of relativity, in the light of a set of natural (...) conditions upon such a notion; and reasons are given for regarding this conception as (not just formally consistent with relativitytheory, but also) philosophically reasonable. The bearings upon Maxwell's program for quantum theory are briefly considered. (shrink)
Specialrelativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation (...) laws’ violations are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Specialrelativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work. (shrink)
The Reichenbach-Grunbaum thesis of the conventionality of simultaneity is clarified and defended by developing the consequences of the SpecialTheory when assumptions are not made concerning the one-way speed of light. It is first shown that the conventionality of simultaneity leads immediately to the conventionality of all relative speeds. From this result, the general-length-contraction and time-dilation relations are then derived. Next, the place of time-dilation and length-contraction effects within the SpecialTheory is examined in the light (...) of the conventionality thesis. The slow-transport method of synchrony is then examined in the light of these results and is shown not to provide an adequate method of uniquely determining the one-way speed of light. Finally, the general ε -Lorentz transformations for events along the x-axis are derived from three principles: the round-trip light principle, the principle of equal passage times, and the linearity principle. These principles are shown to be independent of one-way velocity assumptions, and thus may form the basis of a SpecialTheory of Relativity without simultaneity assumptions. (shrink)
We present a streamlined axiom system of specialrelativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of specialrelativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
It is widely believed that the principal difference between Einstein's specialrelativity and its contemporary rival Lorentz-type theories was that while the Lorentz-type theories were also capable of “explaining away” the null result of the Michelson-Morley experiment and other experimental findings by means of the distortions of moving measuring-rods and moving clocks, specialrelativity revealed more fundamental new facts about the geometry of space-time behind these phenomena. I shall argue that specialrelativity tells us (...) nothing new about the geometry of space-time, in comparison with the pre-relativistic Galileo-invariant conceptions; it simply calls something else "space-time", and this something else has different properties. All statements of specialrelativity about those features of reality that correspond to the original meaning of the terms "space" and "time" are identical with the corresponding traditional pre-relativistic statements. It will be also argued that specialrelativity and Lorentz theory are completely identical in both senses, as theories about space-time and as theories about the behavior of moving physical objects. (shrink)
Recently we presented a new specialrelativitytheory for cosmology in which it was assumed that gravitation can be neglected and thus the bubble constant can be taken as a constant. The theory was presented in a six-dimensional hvperspace. three for the ordinary space and three for the velocities. In this paper we reduce our hyperspace to four dimensions by assuming that the three-dimensional space expands only radially, thus one is left with the three dimensions of (...) ordinary space and one dimension of the radial velocity. (shrink)
In these inspiring lectures David Bohm explores Albert Einstein’s celebrated _Theory of Relativity_ that transformed forever the way we think about time and space. Yet for Bohm the implications of the theory were far more revolutionary both in scope and impact even than this. Stepping back from dense theoretical and scientific detail in this eye-opening work, Bohm describes how the notion of relativity strikes at the heart of our very conception of the universe, regardless of whether we are (...) physicists or philosophers. (shrink)
It is shown that the combination of unitary quantum theory and specialrelativity may lead to a contradiction when considering the EPR correlations in different inertial frames in a Gedankenexperiment. This result seems to imply that either unitary quantum theory is wrong or if unitary quantum theory is right then there must exist a preferred Lorentz frame.
In this paper I argue that the case of Einstein׳s specialrelativity vs. Hendrik Lorentz׳s ether theory can be decided in terms of empirical evidence, in spite of the predictive equivalence between the theories. In the historical and philosophical literature this case has been typically addressed focusing on non-empirical features. I claim that non-empirical features are not enough to provide a fully objective and uniquely determined choice in instances of empirical equivalence. However, I argue that if we (...) consider arguments proposed by Richard Boyd, and by Larry Laudan and Jarret Leplin, a choice based on non-entailed empirical evidence favoring Einstein׳s theory can be made. (shrink)
In recent work, David Chalmers argues that “Edenic shapes”—roughly, the shape properties phenomenally presented in spatial experience—are not instantiated in our world. His reasons come largely from the theory of SpecialRelativity. Although Edenic shapes might have been instantiated in a classical Newtonian world, he maintains that they could not be instantiated in a relativistic world like our own. In this essay, I defend realism about Edenic shape, the thesis that Edenic shapes are instantiated in our world, (...) against Chalmers’s challenge from SpecialRelativity. I begin by clarifying the notion of an Edenic shape by reference to Chalmers’s notion of the “Edenic” content of perceptual experience. I then reconstruct Chalmers’s argument that Edenic shapes could not be instantiated in a relativistic world. His reasoning proceeds from two assumptions. The first is that the only shape properties instantiated in a relativistic world are those which somehow involve relations to frames of reference. This is thought to follow from the phenomenon of Lorentz contraction, a consequence of SpecialRelativity. The second assumption is that Edenic shapes do not involve relations to frames of reference. One reason to accept the second assumption is that it seems that Edenic shapes could be instantiated in a classical Newtonian world, where the notion of a frame-relative shape has no meaningful application. I then proceed to defend RES against Chalmers’s argument by arguing that SpecialRelativity, properly understood, provides no support for Chalmers’s first assumption. More generally, I argue, by way of a careful analysis of the geometric structure of Minkowski space–time and Galilean space–time Newtonian physics), that Edenic shapes are no less at home in a relativistic world than in a classical Newtonian world. (shrink)
Are probabilism and specialrelativity compatible? Dieks argues that they are. But the possible universe he specifies, designed to exemplify both probabilism and specialrelativity, either incorporates a universal “now”, or amounts to a many world universe, or fails to have any one definite overall Minkowskian-type space-time structure. Probabilism and specialrelativity appear to be incompatible after all. What is at issue is not whether “the flow of time” can be reconciled with special (...)relativity, but rather whether explicitly probabilistic versions of quantum theory should be rejected because of incompatibility with specialrelativity. (shrink)
B- theorists frequently argue that the A- theoretic views are incompatible with the SpecialTheory of Relativity (STR) and that this is a problem for the A- theoretic views. however, the B- theory needs to be revised in light of implications of STR. in particular, it follows from STR that some events stand in genuine temporal relations to each other while others do not. Consequently, there isn’t a single temporal order of all events. instead, there are (...) multiple B- series. Some B- theorists defend a view of the passage of time according to which passage is simply temporal succession. This paper argues that, in Minkowski spacetime, time passes in each of the multiple B- series, but there is no passage spanning across all events because some events stand in no genuine temporal relations to each other. (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, specialrelativity 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, specialrelativity fails as a theory of time on the basis of the relativity of simultaneity. (shrink)
Within SpecialRelativity accelerated systems can be described as those systems in which standard clock synchronism does not hold. Therefore, the ε -generalized Lorentz equations derived by Winnie are the equations governing accelerated systems. The ε -generalized equation for time is used in analyzing two cases of the clock paradox: (1) the case in which a clock travels in a straight line, stops, and returns, and (2) the case in which a clock travels with uniform velocity in a (...) circular path. The treatment of case (1) of the paradox within this generalization of the SpecialTheory is compared with Møller's treatment of it within the General Theory. (shrink)
A recent paper suggested that if Galilean covariance was extended to signals and interactions, the resulting theory would contain such anomalies as would have impelled physicists towards specialrelativity even without empirical prompts. I analyze this claim. Some so-called anomalies turn out to be errors. Others have classical analogs, which suggests that classical physicists would not have viewed them as anomalous. Still others, finally, remain intact in specialrelativity, so that they serve as no impetus (...) towards this theory. I conclude that Galilean covariance is insufficient to derive specialrelativity. (shrink)
Concise, well-written treatment of epochal theory of modern physics covers classical relativity and the relativity postulate, time dilation, the twin paradox, momentum and energy, particles of zero mass, electric and magnetic fields and forces and more. Only high school math needed. Replete with examples, ideal for self-study.
Relativity is the most important scientific idea of the twentieth century. Albert Einstein is the unquestioned founder of modern physics. His Special and General theories of Relativity introduced the idea to the world. In this classic short book he explains clearly, using the minimum amount of mathematical terms, the basic ideas and principles of his theory of Relativity. Unsurpassed by any subsequent books on Relativity, this remains the most popular and useful exposition of Einstein's (...) immense contribution to human knowledge. (shrink)
In a recent paper, Howard Stein makes a number of criticisms of an earlier paper of mine ('Are Probabilism and SpecialRelativity Incompatible?', Phil. Sci., 1985), which explored the question of whether the idea that the future is genuinely 'open' in a probabilistic universe is compatible with specialrelativity. I disagree with almost all of Stein's criticisms.
McTaggart distinguished two conceptions of time: the A-series, according to which events are either past, present or future; and the B-series, according to which events are merely earlier or later than other events. Elsewhere, I have argued that these two views, ostensibly about the nature of time, need to be reinterpreted as two views about the nature of the universe. According to the so-called A-theory, the universe is three dimensional, with a past and future; according to the B-theory, (...) the universe is four dimensional. Given specialrelativity (SR), we are obliged, it seems, to accept (a modified version of) the B-series, four dimensional view, and reject the A-series, three dimensional view, because SR denies that there is a privileged, instantaneous cosmic "now" which seems to be required by the A-theory. Whether this is correct or not, it is important to remember that the fundamental problem, here, is not "What does SR imply?", but rather "What is the best guess about the ultimate nature of the universe in the light of current theoretical knowledge in physics?". In order to know how to answer this question, we need to have some inkling as to how the correct theory of quantum gravity incorporates quantum theory, probability and time. This is, at present, an entirely open question. String theory, or M-theory, seems to evade the issue, and other approaches to quantum gravity seem equally evasive. However, if probabilism is a fundamental feature of ultimate physical reality, then it may well be that the A-theory, or rather a closely related doctrine I call “objectism”, is built into the ultimate constitution of things. (shrink)
The two-component spinor theory of van der Waerden is put into a convenient matrix notation. The mathematical relations among various types of matrices and the rule for forming covariant expressions are developed. Relativistic equations of classical mechanics and electricity and magnetism are expressed in this notation. In this formulation the distinction between time and space coordinates in the four-dimensional space-time continuum falls out naturally from the assumption that a four-vector is represented by a Hermitian matrix. The indefinite metric of (...) tensor analysis is a derived result rather than an arbitrary ad hoc assumption. The relation to four-component spinor theory is also discussed. (shrink)
The open future view is the common-sense view that there is an ontological difference between the past, the present, and the future in the sense that the past and the present are real, whereas the future is not yet a part of reality. In this paper we develop a theory in which the open future view is consistently combined with specialrelativity. Technically, the heart of our contribution is a logical conservativity result showing that, although the open (...) future view is not definable inside the causal geometry of Minkowski space-time, it can be conservatively added to it. (shrink)