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)

Some of the problems associated with the construction of a manifestly covariant relativistic quantum theory are discussed. A resolution of this problem is given in terms of the off mass shell classical and quantum mechanics of Stueckelberg, Horwitz and Piron. This theory contains many questions of interpretation, reaching deeply into the notions of time, localizability and causality. A proper generalization of the Maxwell theory of electromagnetic interaction, required for the well-posed formulation of dynamical problems of systems with electromagnetic interaction is (...) discussed, and some of the significance of recently found (classical) relativistic chaotic behavior is pointed out. Many results of a technical nature have been achieved in this framework; in this paper, some of these are reviewed, but I shall concentrate on a discussion of the basic ideas and foundations of the theory. (shrink)

The requirement of gauge invariance for the Schwinger-DeWitt equations, interpreted as a manifestly covariant quantum theory for the evolution of a system in spacetime, implies the existence of a five-dimensional pre-Maxwell field on the manifold of spacetime and “proper time” τ. The Maxwell theory is contained in this theory; integration of the field equations over τ restores the Maxwell equations with the usual interpretation of the sources. Following Schwinger's techniques, we study the Green's functions for the five-dimensional hyperbolic field equations (...) for both signatures ± [corresponding to O(4, 1) or O(3, 2) symmetry of the field equations] of the proper time derivative. The classification of the Green's functions follows that of the four-dimensional theory for “massive” fields, for which the “mass” squared may be positive or negative, respectively. The Green's functions for the five-dimensional field are then given by the Fourier transform over the “mass” parameter. We derive the Green's functions corresponding to the principal part ΔP and the homogeneous function Δ 1 ; all of the Green's functions can be expressed in terms of these, as for the usual field equations with definite mass. In the O(3, 2) case, the principal part function has support for x2⩾τ2, corresponding to spacelike propagation, as well as along the light cone x2=0 (for τ=0). There can be no transmission ofinformation in spacelike directions, with this propagator, since the Maxwell field, obtained by integration over τ, does not contain this component of the support. Measurements are characterized by such an integration. The spacelike field therefore can dynamically establish spacelike correlations. (shrink)

In a pair of very important papers, namely “Space, Time and Individuals” in the Journal of Philosophy for October 1955 and “The Indestructibility and Immutability of Substances” in Philosophical Studies for April 1956, Professor N. L. Wilson began something which badly needed beginning, namely the construction of a logically rigorous “substance-language” in which we talk about enduring and changing individuals as we do in common speech, as opposed to the “space-time” language favoured by very many mathematical logicians, perhaps most notably (...) by Quine. This enterprise of Wilson's is one with which I could hardly sympathize more heartily than I do; and one wishes for this logically rigorous “substance-language” not only when one is reading Quine but also when one is reading many other people. How fantastic it is, for instance, that Kotarbinski1 should call his metaphysics “Reism” when the very last kind of entity it has room for is things —instead of them it just has the world-lines or life-histories of things; “fourdimensional worms”, as Wilson says. Wilson, moreover, has at least one point of superiority to another rebel against space-time talk, P. F. Strawson; namely he does seriously attempt to meet formalism with formalism—to show that logical rigour is not a monopoly of the other side. At another point, however, Strawson seems to me to see further than Wilson; he is aware that substance-talk cannot be carried on without tenses, whereas Wilson tries to do without them. Wilson, in short, has indeed brought us out of Egypt; but as yet has us still wandering about the Sinai Peninsula; the Promised Land is a little further on than he has taken us. (shrink)

I hear the patter of little feet around the house, I expect Bruce. What I expect is a cat, a particular cat. If I heard such a patter in another house, I might expect a cat but no particular cat. What I expect then seems to be a Meinongian incomplete cat. I expect winter, expect stormy weather, expect to shovel snow, expect fatigue---a season, a phenomenon, an activity, a state. I expect that someday mankind will inhabit at least five planets. (...) This time what I expect is a state of affairs. If we let surface grammar be our guide, the objects of expectation seem quite a miscellany. The same goes for belief, since expectation is one kind of belief. The same goes for desire: I could want Bruce, want a cat but no particular cat, want winter, want stormy weather, want to shovel snow, want fatigue, or want that someday mankind will inhabit at least five planets. The same goes for other attitudes to the extent that they consist partly of beliefs or desires or lacks thereof. But the seeming diversity of objects might be an illusion. Perhaps the objects of attitudes are uniform in category, and it is our ways of speaking elliptically about these uniform objects that are diverse. That indeed is our consensus. We mostly think that the attitudes uniformly have propositions as their objects. That is why we speak habitually of "propositional attitudes.". (shrink)

"This is an important book, and no one interested in issues which touch on the free will will want to ignore it."--Ethics. In this stimulating and thought-provoking book, the author defends the thesis that free will is incompatible with determinism. He disputes the view that determinism is necessary for moral responsbility. Finding no good reason for accepting determinism, but believing moral responsiblity to be indubitable, he concludes that determinism should be rejected.

Perry argues that certain sorts of indexicals are 'essential', in the sense that they cannot be eliminated in favor of descriptions. This paper also introduces the influential idea that certain sorts of indexicals play a special role in thought, and have a special connection to action.

Quentin Smith offers powerful arguments against the New Theory of Reference propounded by leading thhinkers in the philosophy of language. Smith defends the tensed theory of time and argues that the simultaneity is absoltue, basing this position on the theory that all propositions exist in time. Using detailed propostitions and a theory of cognitive significance, he introduces an alternative interpretation of reference that will be relevant to metaphysicians, philosophers of science and philosophers of language and may come to be recognised (...) as the definitive statement on the tensed theory of time. (shrink)

The dynamical equations of relativistic quantum mechanics prescribe the motion of wave packets for sets of events which trace out the world lines of the interacting particles. Electromagnetic theory suggests thatparticle world line densities be constructed from concatenation of event wave packets. These sequences are realized in terms of conserved probability currents. We show that these conserved currents provide a consistent particle and antiparticle interpretation for the asymptotic states in scattering processes. The relation between current conservation and unitarity is used (...) to establish relations between pair production and annihilation amplitudes and scattering. The discrete symmetriesC, T, P are studied and it is shown that no Dirac sea (for fermions where such a construction is possible, or bosons where it is not) is required for consistency of the theory. These currents, furthermore, represent the discrete symmetries in a way consistent with their interpretation as particle currents. (shrink)

WHAT do we mean by saying that a being, God for example, is omniscient? One way of answering this question is to translate ‘God is omniscient’ into some slightly more formalised language than colloquial English, e.g. one with variables of a number of different types, including variables replaceable by statements, and quantifiers binding thes.

We analyze the correspondence between a five-dimensional U(1)gauge invariant theory and four-dimensional scalar QED, where the fifth dimension (τ)is an invariant parameter of evolution of the manifestly covariant one-particle sector as well as for the full Fock space. The correspondence is represented by the limit in which the width of the photon mass distribution Δs tends to zero and large τ correlations occur. In the limiting procedure, calculation of a twopoint diagram shows that the PauliVillars regularization is intrinsically related to (...) these longrange correlations. (shrink)

The new tenseless theory of time, Developed primarily by j j c smart and d h mellor, States that tensed sentence-Utterances cannot be translated by tenseless ones but nevertheless have tenseless truth conditions. Smart and mellor infer from this that the tenseless theory of time is true. The author argues, However, That the rules of use of tensed sentence-Utterances entail that these utterances also have tensed truth conditions. This implies that the tensed theory of time is true.

Gauge invariance of a manifestly covariant relativistic quantum theory with evolution according to an invariant time τ implies the existence of five gauge compensation fields, which we shall call pre-Maxwell fields. A Lagrangian which generates the equations of motion for the matter field (coinciding with the Schrödinger type quantum evolution equation) as well as equations, on a five-dimensional manifold, for the gauge fields, is written. It is shown that τ integration of the equations for the pre-Maxwell fields results in the (...) usual Maxwell equations with conserved current source. The analog of the O (3, 1) symmetry of the usual Maxwell theory is found to be O (3, 2) or O (4, 1), depending on the space-time Fourier spectrum of the field. We argue that the structure that is relevant to the description of radiation in interaction with matter evolving in a timelike sense is that of O (3, 2). The noncovariant form of the field equations is given; there are two fields of electric type and one (divergenceless) magnetic type field. The Noether currents are studied, and some remarks are made on second quantization. (shrink)

All Christian theologians agree that God is without beginning and without end. The vast majority have held, in addition, that God is eternal, existing outside of time. Only a small minority have contended that God is everlasting, existing within time. In what follows I shall take up the cudgels for that minority, arguing that God as conceived and presented by the biblical writers is a being whose own life and existence is temporal.

A physical framework has been proposed which describes manifestly covariant relativistic evolution using a scalar time τ. Studies in electromagnetism, measurement, and the nature of time have demonstrated that in this framework, electromagnetism must be formulated in terms of τ-dependent fields. Such an electromagnetic theory has been developed. Gravitation must also use of τ-dependent fields, but many references do not take the metric's dependence on τ fully into account. Others differ markedly from general relativity in their formulation. In contrast, this (...) paper outlines steps towards a τ-dependent classical intrinsic formulation of gravitation, patterned after general relativity, which we call parametrized general relativity (PGR). Given the existence of a preferred foliation, the Hamiltonian constraint is removed. We find that some nonmetricity in the connection is allowed, unlike in general relativity. Conditions on the allowable nonmetricity are found. Consideration of the initial value problem confirms that the metric signature should normally be O(3, 2) rather than O(4, 1). Following the lead of earlier works, we argue that concatenation (integration over τ) is unnecessary for relating parametrized physics to experience, and propose an alternative to it. Finally, we compare and contrast PGR with other relevant gravitational theories. (shrink)

In a framework describing manifestly covariant relativistic evolution using a scalar time τ, consistency demands that τ-dependent fields be used. In recent work by the authors, general features of a classical parametrized theory of gravitation, paralleling general relativity where possible, were outlined. The existence of a preferred “time” coordinate τ changes the theory significantly. In particular, the Hamiltonian constraint for τ is removed From the Euler-Lagrange equations. Instead of the 5-dimensional stress-energy tensor, a tensor comprised of 4-momentum density mid flux (...) density only serves as the source. Building on that foundation, in this paper we develop a linear approximate theory of parametrized gravitation in the spirit of the flat spacetime approach to general relativity. Using a modified form of Kraichnan's flat spacetime derivation of general relativity, we extend the linear theory to a family of nonlinear theories in which the flat metric and the gravitational field coalesce into a single effective curved metric. (shrink)

Despite the many successes of the relativistic quantum theory developed by Horwitz et al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical. Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics with evolution paratmeter τ, off-shell electrodynamics constitutes a dynamical theory of ppacetime events, interacting through five τ-dependent pre-Maxwell potentials. We present a straightforward solution of the classical (...) equations of motion, for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical levels. We then offer a new model of the particle current—as a certain distribution of the event currents on the worldline—which eliminates these difficulties and permits comparison of classisical off-shell electrodynamics with the standard Maxwell theory. In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions, and are seen to coincide when λ≳10−6 seconds, providing an initial estimate of this parameter. It is also demonstrated that the proposed model provides a natural interpretation for the photon mass cut-off required for the renormalizability of the off-shell quantum electrodynamics. (shrink)

The contemporary view of the fundamental role of time in physics generally ignores its most obvious characteric, namely its flow. Studies in the foundations of relativistic mechanics during the past decade have shown that the dynamical evolution of a system can be treated in a manifestly covariant way, in terms of the solution of a system of canonical Hamilton type equations, by considering the space-time coordinates and momenta ofevents as its fundamental description. The evolution of the events, as functions of (...) a universal invariant world, or historical, time, traces out the world lines that represent the phenomena (e.g., particles) which are observed in the laboratory. The positions in time of each of the events, i.e., the time of their potential detection, are, in this framework, controlled by this universal parameter τ, the time at which they are generated (and may proceed in the positive or negative sense). We find that the notion of thestate of a system requires generalization; at any given τ, it involves information about the system at timest(τ) ≠ τ. The correlation of what may be measured att(τ) with what is generated at τ is necessarily quite rigid, and is related covariantly to the spacelike correlations found in interference experiments. We find, furthermore, that interaction with Maxwell electromagnetism leads back to a static picture of the world, with no real evolution. As a consequence of this result, and the requirement of gauge invariance for the quantum mechanical evolution equation, we conclude that electromagnetism is described by a pre-Maxwell field, whose τ-integral (or asymptotic behavior as τ → ∞) may be identified with the Maxwell field. We therefore consider the world of events in space time, interacting through τ-dependent pre-Maxwell fields, as far as electrodynamics is concerned, as the objective dynamical reality. Our perception of the world, through laboratory detectors and our eyes, are based onintegration over τ over intervals sufficiently large to obtain an aposteriori description of the phenomena which coincides with the Maxwell theory. Fundamental notions, such as the conservation of charge, rest on this construction. The decomposition of the common notion of time into two essentially different aspects, one associated with an unvarying flow, and the second with direct observation subject to dynamical modification, has profound philosophical consequences, of which we are able to explore here only a few. (shrink)

We claim that physics has been constructed because three “philosophical” principles have been respected, namely, realism, locality, and consistency. These principles lead to an interpretation of quantum mechanics (QM) in terms of local hidden-variables theories (LHV). In order to prove that LHV have not been refuted, we analyze the empirical proofs of Bell's inequalities and we argue that none is loophole-free. Then we propose a restricted QM that does not contain measurement postulates and that does not claim that all state (...) vectors (self-adjoint operators) are states (observables). The contradiction of such restricted QM with Bell's inequality cannot be shown as a theorem, but only by the design of a loophole-free experiment. Finally, we argue that noise has been underestimated in quantum theory. It does not appear in QM, but it is essential in quantum field theory. We conjecture that noise will prevent the violation of Bell's inequality. (shrink)

This paper consists of two parts. Firstly, we shall clarify the connections existing between Clauser-Horne's inequalities and the conditions established by Pitowsky expressing the Kolmogorovian nature of a probability vector. We shall discuss afterwards three possible interpretations of the experimental violation of these inequalities.

We further develop a recent new proof (by Greenberger, Horne, and Zeilinger—GHZ) that local deterministic hidden-variable theories are inconsistent with certain strict correlations predicted by quantum mechanics. First, we generalize GHZ's proof so that it applies to factorable stochastic theories, theories in which apparatus hidden variables are causally relevant to measurement results, and theories in which the hidden variables evolve indeterministically prior to the particle-apparatus interactions. Then we adopt a more general measure-theoretic approach which requires that GHZ's argument be modified (...) in order to produce a valid proof. Finally, we motivate our more general proof's assumptions in a somewhat different way from previous authors in order to strengthen the implications of our proof as much as possible. After developing GHZ's proof along these lines, we then consider the analogue, for our proof, of Bohr's reply to the EPR argument, and conclude (pace GHZ) that in at least one respect (viz. that of most concern to Bohr) the proof is no more powerful than Bell's. Nevertheless, we point out some new advantages of our proof over Bell's, and over other algebraic proofs of nonlocality. And we conclude by giving a modified version of our proof that, like Bell's, does not rely on experimentally unrealizable strict correlations, but still leads to a testable “quasi-algebraic” locality inequality.“... to admit things not visible to the gross creatures that we are is, in my opinion, to show a decent humility, and not just a lamentable addiction to metaphysics.”J. S. Bell. (shrink)

A recent analysis by de Barros and Suppes of experimentally realizable GHZ correlations supports the conclusion that these correlations cannot be explained by introducing local hidden variables. We show, nevertheless, that their analysis does not exclude local hidden variable models in which the inefficiency in the experiment is an effect not only of random errors in the detector equipment, but is also the manifestation of a pre-set, hidden property of the particles ("prism models"). Indeed, we present an explicit prism model (...) for the GHZ scenario; that is, a local hidden variable model entirely compatible with recent GHZ experiments. (shrink)

We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction (Section 1), we briefly review the conceptual problems of the ingredient theories (Section 2) and introduce the enterprise of quantum gravity (Section 3). We then describe how three main research programmes in quantum (...) gravity treat four topics of particular importance: the scope of standard quantum theory; the nature of spacetime; spacetime diffeomorphisms, and the so-called `problem of time' (Section 4). These programmes are the old particle-physics approach, superstring theory, and canonical quantum gravity. By and large, these programmes accept most of the ingredient theories' treatment of spacetime, albeit with a metric with some type of quantum nature; but they also suggest that the treatment has fundamental limitations. This prompts the idea of going further: either by quantizing structures other than the metric, such as the topology; or by regarding such structures as phenomenological. We discuss this in Section 5. (shrink)

But there is considerable consensus, even among writers who disagree radically about the ultimate significance of time so understood, that time as ...