Relativity allegedly contradicts presentism, the dynamic view of time and reality, according to which temporal passage is conceived of as an existentially distinguished ‘moving’ now. Against this common belief, the paper motivates a presentist interpretation of spacetime: It is argued that the fundamental concept of time—proper time—cannot be characterized by the earlier-later relation, i.e., not in the B-theoretical sense. Only the presentist can provide a temporal understanding of the twins’ paradox and of universes with closed timelike curves.

The twin paradox (i.e. the reasoning made by the traveling twin, reversing the reasoning made by the earthbound twin, by which it is he who should be older) can be resolved by taking into account the relativity of simultaneity. However, simultaneity depends on a convention about the one-way velocity of light provided that the Reichenbach-Grünbaum hypothesis, is time. So far the resolution has been presented only for the Einstein convention. We show that for all possible choices (...) of the relevant synchronization parameters the calculations performed by both twins yield the same final results when carefully taking into account the relativity of simultaneity according to the conventions they have chosen. Since the final results do not depend on any of the synchronization parameters, the Reichenbach-Grünbaum hypothesis is thereby supported. (shrink)

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of (...) accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND. (shrink)

The Twin Paradox is not a new topic. What is new in this article is that it is an exercise toward interpretation that is functional, in the sense discovered by Lonergan in Method in Theology. The author being interpreted is P. Tipler; and the primary document is taken from his well known textbook. I try to lay out the basic argument in a way that reveals the operative insights, as well as the significant oversights. As it turns out, (...) it would seem that there is neither theoretical basis nor experimental evidence for the alleged “slowing of time” for the high speed traveler. (shrink)

In a recent paper in this journal, McCall and Lowe (2003) argue that an understanding of Special Relativity reveals that the A theorist’s notion of temporal passage is consistent with the B theory of time. They arrive at this conclusion by considering the twins’ paradox, where one of two twins (T) travels to Alpha Centauri and back and upon her return has aged 30 years, while her earth-bound twin (S) has aged 40 years.Does this reconcile the A theoretic (...) notion of temporal passage with the B theory of time? I argue not. (shrink)

According to McCall and Lowe (2003) interpreting the twins’ paradox reconciles the A-theorist’s notion of temporal passage or flow with the special theory of relativity. Miller, however, recalls that “the B-theorist never denied that there was temporal passage in some sense of the term” (Miller 2004, 204), and argues convincingly that McCall and Lowe stipulate nothing other than this B-theorist’s sense of temporal succession. But, as I want to show, we need in fact the A-theorist’s or even presentist’s account (...) of temporal passage in the sense of a ‘moving now’ in order to preserve the temporal content of the twins’ paradox. It is essential, I think, that for a temporal understanding of the twins’ paradox proper times and coordinate times have to be combined in a way that only the presentists can cope. (shrink)

Alternate View Column AV-38 Keywords: special relativity, twin paradox, time dilation, starship, Einstein, Lorentz factor Published in the March-1990 issue of Analog Science Fiction & Fact Magazine; This column was written and submitted 8/20/89 and is copyrighted © 1989, John G. Cramer. All rights reserved. No part may be reproduced in any form without the explicit permission of the author.

The thesis of 3D/4D equivalence states that every three-dimensional description of the world is translatable without remainder into a four-dimensional description, and vice versa. In representing an object in 3D or in 4D terms we are giving alternative descriptions of one and the same thing, and debates over whether the ontology of the physical world is "really" 3D or 4D are pointless. The twins paradox is shown to rest, in relativistic 4D geometry, on a reversed law of triangle inequality. (...) But considering the twins as 3D beings who age through time, the paradox implies that time passes at different rates in different reference frames, and therefore that the concept of a single global or Absolute time is unsustainable. (shrink)

The resolution of the Langevin paradox for an out-and-return journey gives rise to a result which appears to violate the underlying basis of special relativity. The resolution of this second paradox, due to G. Builder, leads to a physically-intelligible interpretation of Einstein's theory and reconciles it with the cosmologically-based fundamental reference frame revealed by modern astronomy.

The amount of information that can be transmitted through a noisy channel is affected by relativistic effects. Under the presence of a fixed noise at the receiver, there appears an asymmetry between “slowly aging” and “fast aging” observers which can be used to have private information transmission. We discuss some models for users inside gravitational wells and in the twin paradox scenario.

This paper responds briefly to the criticism of Rodrigues and Rosa on my earlier analysis of the twin paradox. The main point that I have emphasized (and that the authors have not refuted, either logically or mathematically) is the error in directly identifying anabstract measure relative to a reference frame [and its transformations to all other possible reference frames in which the laws of nature are to be compared (such as temporal and spatial measures)], with aphysical extension and (...) duration of a material body. (shrink)

The purpose of the present paper is to reply to a misleading paper by M. Sachs entitled “Einstein's later view of the Twin Paradox” (TP) (Found. Phys. 15, 977 (1985)). There, by selecting some passages from Einstein's papers, he tried to convince the reader that Einstein changed his mind regarding the asymmetric aging of the twins on different motions. Also Sachs insinuates that he presented several years ago “convincing mathematical arguments” proving that the theory of relativity does not (...) predict asymmetrical aging in the TP. Here we give a definitive treatment to the clocks problem showing that Sachs' “convincing mathematical arguments” are non sequitur. Also, by properly quoting Einstein, we show that his later view of the TP coincides with the one derived from the rigorous theory of time developed in this paper. (shrink)

The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent to the assumption of the slowing down of moving clocks, and the lack of TwP is not logically equivalent to the Newtonian assumption of absolute time. The logical connection between TwP and a symmetry axiom of special (...) relativity is also studied. (shrink)

The aging of the two brothers in the “twins paradox” is analyzed through the space-time evolution of the densities that correspond to their internal complex structure. Taking into account their relative motion, it is shown that the traveling brother evolves over a shorter interval of time than his twin, which makes him younger than his brother.

Recently a suggestion has been made that standard textbook representations of hypersurfaces of simultaneity for the travelling twin in the twin 'paradox' are incorrect. This suggestion is false: the standard textbooks are in agreement with a proper understanding of the relativity of simultaneity.

It is shown that Einstein abandoned his earlier view that there are material consequences, such as asymmetric aging, implied by the space-time transformations of transformations of relativity theory.

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity somehow relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a space-time (...) coordinate system in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein's rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to but that is either false or trivial. (shrink)

The twin paradox of relativity theory is reviewed. A distinction is made between physical clocks and biological ones. It is suggested that metabolic activity might be a better measure of aging than physical time. Further it is suggested that entropy changes representing metabolic activity would be a good way to describe aging. Using the above criterion it appears that a traveling twin will be older than his brother.

This paper provides an account of the paradoxes of teaching democracy, the paradoxes of being a citizen in a liberal democracy, and the insights that can be gained from the model of citizenship that T.H. Green promoted. Green thought citizenship was predicated on the twin foundations of the community and the common good. Freedom for Green means individual self-determination coupled with recognition of the dependency relations between individuals and the community. Green is noteworthy not only as a theorist but (...) also as an active contributor to the development of public schools in England. A consideration of his arguments provides a model for educating citizens, addresses the paradoxes of democracy in education, and reveals elements of his philosophy that are relevant to educational issues today. (shrink)

Beginning with the paradoxes of zombie twins, we present an argument that dualism is both true and false. We show that avoiding this contradiction is impossible. Our diagnosis is that consciousness itself engenders this contradiction by producing contradictory points of view. This result has a large effect on the realism/anti-realism debate, namely, it suggests that this debate is intractable, and furthermore, it explains why this debate is intractable. We close with some comments on what our results mean for metaphysics and (...) philosophy, in general. (shrink)

This is a somewhat simplistic introduction to some of the topics related to the so called ‘paradox of liberalism’. It tries to serve the twin purpose of facilitating access to the papers printed in this issue of Analyse & Kritik and putting them into a broader perspective.

Rousseau’s life and his work are notoriously paradoxical. This certainly applies to his work on property which includes one of the most powerful of all denunciations of private property (the Second Discourse) and an affirmation of private property as ‘the most sacred of all citizens’ rights, and in some respects more important than freedom itself’ (in the essay on political economy in the Encyclopedie). In this paper, I explore the reasons for this seeming paradox, focusing upon Rousseau’s twin (...) concerns with inequality (rather than equality) and sincerity. In the end, Rousseau’s treatment is not entirely consistent, but it does make sense. (shrink)

This “fun, brain-twisting book... will make you think” as it explores more than 75 paradoxes in mathematics, philosophy, physics, and the social sciences (Sean Carroll, New York Times–bestselling author of Something Deeply Hidden) Paradox is a sophisticated kind of magic trick. A magician’s purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn’t require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and (...) symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind, Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts—and how reason can dispel the illusion of contradiction. The journey begins with “a most ingenious paradox” from Gilbert and Sullivan’s Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform “supertasks”; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world—and much more. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Michael’s Story or the Paradox of NormalcyMichael KreuzerI was born in Montreal in 1974. My parents were both “older.” My mother was almost 45; my father was in his 50’s. I have a sister who is six years older than me. What I know about my mother’s prenatal care is that it was quite basic.I was premature. My mother’s due date was in mid–August, however I showed up (...) about three weeks earlier. I know that initially upon my birth I was declared male. However, upon closer examination, a few “abnormalities” of my genitals were found. I urinated through a small hole at the base of my penis; adjacent to this hole was another opening, barely big enough for a Q–tip. My scrotum was empty; my gonads had not descended.The doctors who examined me decided that they could not assign a gender without further testing. They told my mother I would need to remain in the hospital until such testing was completed. Apparently not being able to determine sex/gender is a life–threatening condition that requires hospitalization.It was determined that I had a uterus and it was presumed that my undescended gonads were ovaries (not verified by biopsy). There was a small vaginal opening behind my small urethral opening. Structures such as the labia were not developed. I found out later my vagina had fistulated into both my urethra and my perineum. Karyotyping was performed resulting in 46,XX with a diagnosis of female pseudo–hermaphroditism. My parents were informed that in spite of my external genitalia I was female and I would never develop as a male. I would require “corrective surgeries” which should be performed as soon as possible so I would not have any issues with my gender identity. They were even told that I would be able to become pregnant if I had the surgeries. In fact, I never ovulated and I have a small unicornuate uterus.My father refused all surgeries on my behalf most likely because he was a full–blooded Navajo who had suffered from abuse in an Indian boarding school during his childhood in New Mexico. His family was traditional, and because they didn’t adapt to prevailing Christian values, he and several of his siblings were removed from their parents. My dad was the oldest of 12 children and by the time his youngest siblings were born, the practice to take children away from their families had been changed.I think my father was deeply traumatized by his childhood and did not associate much with his family, nor did he want to visit the reservation. He spoke the language but never encouraged us to learn it. He did teach us some of the traditions. He told me about the nadleh, which is the other gender besides male and female in the Navajo tradition. There are two kinds of nadleh, which are almost like male–to–female and female–to–male transsexuals. Mostly I educated myself later and learned about the Navajo belief system in which the creation story is an important part. In the Navajo tradition, the creation story tells of First Man and First Woman; the first children born to them are the Hermaphrodite Twins. [End Page E7]My father was a US Army Master Sergeant, which was an unusual career for a man of his origins; he was a veteran of the Second World War. After he left the army he took his family to Montreal where he had a job in security. I think he preferred to live outside the U.S. He used to say that in Germany, where he had managed to stay for a long time while serving in the Army, he was just another American soldier. In spite of his career, he had a deep mistrust for “white people.” I remember he used to say that he was in the Army because this was his country long before the white people came and he loved it. He did not love the people who governed it. All this very much played into the decision not to listen to the doctors’ recommendations about surgery. My... (shrink)

Why should all human beings have certain rights simply by virtue of being human? One justification is an appeal to religious authority. However, in increasingly secular societies this approach has its limits. An alternative answer is that human rights are justified through human dignity. This paper argues that human rights and human dignity are better separated for three reasons. First, the justification paradox: the concept of human dignity does not solve the justification problem for human rights but rather aggravates (...) it in secular societies. Second, the Kantian cul-de-sac: if human rights were based on Kant’s concept of dignity rather than theist grounds, such rights would lose their universal validity. Third, hazard by association: human dignity is nowadays more controversial than the concept of human rights, especially given unresolved tensions between aspirational dignity and inviolable dignity. In conclusion, proponents of universal human rights will fare better with alternative frameworks to justify human rights rather than relying on the concept of dignity. (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)

Yablo’s Paradox, an infinite-sentence version of the Liar Paradox, aims to show that semantic paradox can emerge even without circularity. I will argue that the lack of meaning/content of the sentences involved is the source of the paradoxical outcome.I will introduce and argue for a Moderate Antirealist approach to truth and meaning, built around the twin principles that neither truth nor meaning can outstrip knowability. Accordingly, I will introduce a MAR truth operator that both forges an (...) explicit connection between truth and knowability and distinguishes between truth and factuality. I will also argue that the meaning/content of propositions should be identified not with the set of possible worlds in which the propositions are true/factual, but rather in which they are known.I will show that our MAR framework dissolves Yablo’s Paradox and also confirms our intuition that these sentences are all devoid of content/meaning. (shrink)

Two physical "paradoxes" (the paradox of twins in special relativity and that of Einstein, Podolsky, and Rosen in quantum mechanics) are considered philosophically from a common viwepoint. Its essence is the unification of "measurement" and "motion". an idea for the generalization of the concept of reference fram is suggested.

Old and recent ideas concerning the nature of time are reviewed, starting from Mach's refusal of Newton's absolute time. Many experiments show that the slowing down of moving clocks is a real phenomenon. Such must then also be the so-called “twin paradox,” which owes its name to its evident incompatibility with the philosophy of relativism (not to be confused with the theory of relativity). The Lorentz reformulation of special relativity started by postulating physical effects of the ether, but (...) accepted Einstein's clock synchronization. Only because of this Lorentz could not understand the advantages of an easily deducible different theory. As stressed by Popper, one of the main problems of the usual approach is the introduction of a superdeterministic universe. Recent results obtained by the author show that a theory is possible, based on relative time but on absolute simultaneity, in which the conceptual difficulties of relativity are avoided. (shrink)

This book is dedicated to the first ten years of Chaos and Complexity Letters - International Journal of Dynamical Systems Research. This journal was born to collect and disseminate complexity science related information to anybody interested in the topic; to speed up the evolutionary development of complexity science; to extend its interactions crossing over disciplines, levels of knowledge and geography; and to foster finding new pathways in research and new applications. The structure of CCL was specifically designed to add value (...) to the trans-disciplinary approach while, at the same time, differentiating the epistemology of different contributions. In this enterprise we were sustained and inspired by two great companions that in different ways shared our project during its prehistory: Ilya Prigogine and Francisco Varela. This book collects 16 papers appeared on the first ten volumes of Chaos and Complexity Letters. They range from the life sciences, to STEM and economy, in accordance with the interdisciplinary mission of the journal. A special highlight starts with Acceleration and entropy: a macroscopic analogue of the twin paradox, possibly the last paper written by the Nobel Prize Ilya Prigogine with Gonzalo Ordonez. Important academic specialists who wrote in our scientific journal passed away. For example, Walter Freeman, Tullio Minelli, Ilya Prigogine, and Joseph P. Zbilut. This special issue is also dedicated to them. We are in opinion that their trajectories in life and research designed some contours of the shape of a new science to come. (shrink)

This concise book introduces nonphysicists to the core philosophical issues surrounding the nature and structure of space and time, and is also an ideal resource for physicists interested in the conceptual foundations of space-time theory. Tim Maudlin's broad historical overview examines Aristotelian and Newtonian accounts of space and time, and traces how Galileo's conceptions of relativity and space-time led to Einstein's special and general theories of relativity. Maudlin explains special relativity using a geometrical approach, emphasizing intrinsic space-time structure rather than (...) coordinate systems or reference frames. He gives readers enough detail about special relativity to solve concrete physical problems while presenting general relativity in a more qualitative way, with an informative discussion of the geometrization of gravity, the bending of light, and black holes. Additional topics include the Twins Paradox, the physical aspects of the Lorentz-FitzGerald contraction, the constancy of the speed of light, time travel, the direction of time, and more.Introduces nonphysicists to the philosophical foundations of space-time theory Provides a broad historical overview, from Aristotle to Einstein Explains special relativity geometrically, emphasizing the intrinsic structure of space-time Covers the Twins Paradox, Galilean relativity, time travel, and more Requires only basic algebra and no formal knowledge of physics. (shrink)

This book gives an excellent introduction to the theory of special relativity. 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)

In Minkowski spacetime, because of the relativity of simultaneity to the inertial frame chosen, there is no unique world-at-an-instant. Thus the classical view that there is a unique set of events existing now in a three dimensional space cannot be sustained. The two solutions most often advanced are that the four-dimensional structure of events and processes is alone real, and that becoming present is not an objective part of reality; and that present existence is not an absolute notion, but is (...) relative to inertial frame; the world-at-an-instant is a three dimensional, but relative, reality. According to a third view, advanced by Robb, Capek and Stein, what is present at a given spacetime point is, strictly speaking, constituted by that point alone. I argue here against the first of these views that the four-dimensional universe cannot be said to exist now, already, or indeed at any time at all; so that talk of its existence or reality as if that precludes the existence or reality of the present is a non sequitur. The second view assumes that in relativistic physics time lapse is measured by the time co-ordinate function; against this I maintain that it is in fact measured by the proper time, as I argue by reference to the Twin Paradox. The third view, although formally correct, is tarnished by its unrealistic assumption of point-events. This makes it susceptible to paradox, and also sets it at variance with our normal intuitions of the present. I argue that a defensible concept of the present is nonetheless obtainable when account is taken of the non-instantaneity of events, including that of conscious awareness, as that region of spacetime comprised between the forward lightcone of the beginning of a small interval of proper time t and the backward lightcone of the end of that interval. This gives a serviceable notion of what is present to a given event of short duration, as well as saving our intuition of the “reality” or robustness of present events. (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)

This is a short, nontechnical introduction to features of time in classical and relativistic physics and their representation in the four-dimensional geometry of spacetime. Topics discussed include: the relativity of simultaneity in special and general relativity; the ‘twin paradox’ and differential aging effects in special and general relativity; and time travel in general relativity.

Einstein, in his “Zur Elektrodynamik bewegter Körper”, gave a physical (operational) meaning to “time” of a remote event in describing “motion” by introducing the concept of “synchronous stationary clocks located at different places”. But with regard to “place” in describing motion, he assumed without analysis the concept of a system of co-ordinates.In the present paper, we propose a way of giving physical (operational) meaning to the concepts of “place” and “co-ordinate system”, and show how the observer can define both the (...) place and time of a remote event. Following Einstein, we consider another system “in uniform motion of translation relatively to the former”. Without assuming “the properties of homogeneity which we attribute to space and time”, we show that the definitions of space and time in the two systems are linearly related. We deduce some novel consequences of our approach regarding faster-than-light observers and particles, “one-way” and “two-way” velocities of light, symmetry, the “group property” of inertial reference frames, length contraction and time dilatation, and the “twin paradox”. Finally, we point out a flaw in Einstein’s argument in the “Electrodynamical Part” of his paper and show that the Lorentz force formula and Einstein’s formula for transformation of field quantities are mutually consistent. We show that for faster-than-light bodies, a simple modification of Planck’s formula for mass suffices. (Except for the reference to Planck’s formula, we restrict ourselves to Physics of 1905.). (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.

This useful anthology comprises seventy-nine selections arranged under three headings. Part I is titled "Ancient and Classical Ideas of Space"; part II, "The Classical and Ancient Concepts of Time"; part III, "Modern Views of Space and Time and their Anticipations." According to the general editors of the Boston series, R. S. Cohen and Marx W. Wartofsky, Capek’s choice of contents was governed by the desire to show that "parts of our view of nature greatly and mutually influence other parts, and (...) that our conception of the world keeps evolving. Thus, ideas of time intertwine with ideas of space, and both with ideas of matter and force." F. M. Cornford’s essays, "The Invention of Space" and "The Elimination of Time by Parmenides," introduce parts I and II respectively. In part I, while Descartes, Pascal, Gassendi, Newton, etc., speak for themselves, the ancients and medievals are given other mouthpieces—Duhem’s monumental Le système du monde, for Plato, Aristotle, and the medievals; C. Bailey, for Leucippus, Epicurus and Lucretius; Koyré, Höffding, Jammer, for the period from Bradwardine to William Gilbert. On the subject of time, however, both ancient and classical authors are allowed to express their opinions in their own words, with the understandable exception of the Stoics. Part III begins with the prerelativistic critique of Newton as well as the well-known Clarke-Leibniz discussion on the nature of space and time. This third part, however, is dominated largely by the implications of Einstein’s general and special relativity theories. For instance, we have Minkowski’s "Union of Space and Time." Four items, at least, are devoted to the twin-paradox. Some argue for a static, subjective, or even idealistic conception of space-time whereas positivists like Frank attack Sir James Jeans’ and other idealistic interpretations of relativity as instances of meaningless metaphysics. Part III concludes with Weyl’s objectivistic interpretation of quantum-mechanical indeterminacy. While it is difficult to find an anthology that will please all readers or teachers, this work goes far towards dealing comprehensively with the subject of space and time. As Cohen and Wartofsky note, what is distinctive of Capek’s approach within the field of philosophy of nature and its history is that "he is greatly appreciative of Bergson, James, Peirce and Whitehead" and though influenced by them, he is also critical because of the "understanding of the philosophical import that contemporary physics brings into our picture of the world." In a lengthy introduction, the editor explains his rationale for each item he includes. In general this is very helpful, but in some instances the suggested historical connections are misleading at best, if not simply false or questionable. Einstein for instance is said to have "rejected any absolute frame of reference which would be a substrate of absolutely simultaneous events... within the context of Michelson’s vain search for the absolute motion of the earth." This seems to imply—as many others have claimed—that the negative results of the ether-drift experiment influenced Einstein in formulating his relativity theory, whereas historians have pointed out that if Einstein referred to the experiment, it would have to be as a confirmation of his theory, since he did not learn of the results obtained by Michelson and Morley until after the publication of his revolutionary paper in 1905. Though there are other generalizations in the introduction which might be open to dispute, Capek’s prefatory remarks are in general helpful, and the essay collection as a whole stands on its own feet. It is valuable, if for no other reason, that a number of the selections appear in English translation for the first time.—A.B.W. (shrink)

It is generally believed that an invariant notion of a global present or "Now" cannot be defined in special relativity, because of the relativity of optical simultaneity. I argue that this may be a non sequitur since it is not necessarily the case that the psychological "Now" should be thought of as associated with constant time slices in spacetime. By considering a science fictional version of the Twin Paradox due to Robert A. Heinlein, I argue that it is (...) psychologically plausible to associate the common specious present of several observers in relative motion with certain hypersurfaces of proper time of those observers corrected for acceleration history and relative motion in an obvious way. If this is correct then the relativity of optical simultaneity may be simply irrelevant to the question of the relativity of a globally distinguished "present". (shrink)

The main purpose of this paper is to demonstrate that the analysis of the kinematical effects of special relativity holds the key to answering the question of the dimensionality of the world. It is shown that these effects and the experiments which confirmed them would be impossible if the world were three-dimensional. Section 2 shows that relativity of simultaneity, conventionality of simultaneity, and the existence of accelerated observers in special relativity would be impossible if the world were three-dimensional. Section 3 (...) deals with the dimensionality of physical objects and demonstrates that the relativistic length contraction and the twin paradox would be impossible if the physical bodies involved in these relativistic effects were three-dimensional objects. (shrink)

The Theory of Relativity has been portrayed as a theory that redefined the way we look at the cosmos, enabling us to unlock the reality we live in. Its proponents are constantly reminding us of how Einstein managed to reveal the true nature of the universe with his groundbreaking theory, which has been proved multiple times until now. Yet, philosophy of science teaches us that no theory has any privileged connection with what we call reality per se. The role of (...) science is to formulate models of the cosmos we see and not to try to interpret or reveal reality. This paper tries to show how this holds true even for the famous relativity theory, by showing specific objections to the connection of the theory with the Holy Grail of philosophers. By analyzing various subjects related to the theory, from the twins’ paradox to the GPS satellites, this paper illustrates that relativity is much less connected to reality than what we would like to think. At the end, what Einstein’s theory provides is nothing more than a way to formalize the interactions of the world but without being able to make any claims whatsoever regarding the ‘reality’ of its conclusions. (shrink)

Untimely -- "More Einsteinian than Einstein" -- Science or philosophy? -- The twin paradox -- Bergson's achilles' heel -- Worth mentioning? -- Bergson writes to Lorentz -- Bergson meets Michelson -- The debate spreads -- Back from Paris -- Two months later -- Logical positivism -- The immediate aftermath -- An imaginary dialog -- "Full-blooded" time -- The previous spring -- The church -- The end of universal time -- Quantum mechanics -- Things -- Clocks and wristwatches -- (...) Telegraph, telephone, and radio -- Atoms and molecules -- Einstein's films: reversible -- Bergson's movies: out-of-control -- Microbes and ghosts -- One new point: recording devices -- Bergson's last comments -- Einstein's last thoughts. (shrink)

The disk that rotates in an inertial frame in special relativity has long been analysed by assuming a Lorentz contraction of its peripheral elements in that frame, which has produced widely varying views in the literature. We show that this assumption is unnecessary for a disk that corresponds to the simplest form of rotation in special relativity. After constructing such a disk and showing that observers at rest on it do not constitute a true rotating frame, we choose a “master” (...) observer and calculate a set of disk coordinates and spacetime metric pertinent to that observer. We use this formalism to resolve the “circular twin paradox”, then calculate the speed of light sent around the periphery as measured by the master observer, to show that this speed is a function of sent-direction and disk angle traversed. This result is consistent with the Sagnac Effect, but constitutes a finer analysis of that effect, which is normally expressed using an average speed for a full trip of the periphery. We also use the formalism to give a resolution of “Selleri’s paradox”. (shrink)