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)

The fundamental open questions of general relativity theory are the unification of the gravitational field with other fields, aiming at a unified geometrization of physics, as well as the renormalization of relativistic gravitational theory in order to obtain their self-consistent solutions. These solutions are to furnish field-theoretic particle models—a problem first discussed by Einstein. In addition, we are confronted with the issue of a coupling between gravitational and matter fields determined (not only) by Einstein's principle of equivalence, and also with (...) the question of the geometric meaning of a gravitational quantum theory. In our view, all these problems are so closely related that they warrant a general solution. We treat mainly the concepts suggested by Einstein and Weyl. (shrink)

The physicist's conception of space-time underwent two major upheavals thanks to the general theory of relativity and quantum mechanics. Both theories play a fundamental role in describing the same natural world, although at different scales. However, the inconsistency between them emerged clearly as the limitation of twentieth-century physics, so a more complete description of nature must encompass general relativity and quantum mechanics as well. The problem is a theorists' problem par excellence. Experiment provide little guide, and the inconsistency mentioned above (...) is an important problem which clearly illustrates the intermingling of philosophical, mathematical, and physical thought. In fact, in order to unify general relativity with quantum field theory, it seems necessary to invent a new mathematical framework which will generalise Riemannian geometry and therefore our present conception of space and space-time. Contemporary developments in theoretical physics suggest that another revolution may be in progress, through which a new kind of geometry may enter physics, and space-time itself can be reinterpreted as an approximate, derived concept. The main purpose of this article is to show the great significance of space-time geometry in predetermining the laws which are supposed to govern the behaviour of matter, and further to support the thesis that matter itself can be built from geometry, in the sense that particles of matter as well as the other forces of nature emerges in the same way that gravity emerges from geometry. Scientific research is not a process of steady accumulation of absolute truths, which has culminated in present theories, but rather a much more dynamic kind of process in which there are no final theoretical concepts valid in unlimited domains. (David Bohm). (shrink)

We analyzed remarkable stories linked to the famous Anatoly Vlasov equations in plasma physics. Their creation, modification, and application are interesting from a scientific viewpoint. We also show the relations between those equations dealing with electromagnetism and analogous Jeans equations describing, in particular, gravitational instability in astrophysics. The second half of the essay is devoted to the controversies and political struggle in Soviet (before 1991) and Russian (after 1991) physical communities related to Vlasov’s personality, career, and posthumous recognition. The never-ending (...) destructive influence of Russian totalitarianism on science is demonstrated. (shrink)

A general sketch on how the problem of space dimensionality depends on anthropic arguments is presented. Several examples of how life has been used to constraint space dimensionality (and vice-versa) are reviewed. In particular, the influences of three-dimensionality in the solar system stability and the origin of life on Earth are discussed. New constraints on space dimensionality and on its invariance in very large spatial and temporal scales are also stressed.

Diffeomorphism invariance is sometimes taken to be a criterion of background independence. This claim is commonly accompanied by a second, that the genuine physical magnitudes (the ``observables'') of background-independent theories and those of background-dependent (non-diffeomorphism-invariant) theories are essentially different in nature. I argue against both claims. Background-dependent theories can be formulated in a diffeomorphism-invariant manner. This suggests that the nature of the physical magnitudes of relevantly analogous theories (one background free, the other background dependent) is essentially the same. The temptation (...) to think otherwise stems from a misunderstanding of the meaning of spacetime coordinates in background-dependent theories. (shrink)

Does the gravitational field described in general relativity possess genuine stress-energy? We answer this question in the affirmative, in a weak sense applicable in a certain class of frames of a certain class of models of the theory, and arguably also in a strong sense, applicable in all frames of all models of the theory. In addition, we argue that one can be a realist about gravitational stress-energy in general relativity even if one is a relationist about spacetime ontology. In (...) each case, our reasoning rests upon a functionalist approach to the definition of physical quantities. (shrink)

Coordinate-based approaches to physical theories remain standard in mainstream physics but are largely eschewed in foundational discussion in favour of coordinate-free differential-geometric approaches. I defend the conceptual and mathematical legitimacy of the coordinate-based approach for foundational work. In doing so, I provide an account of the Kleinian conception of geometry as a theory of invariance under symmetry groups; I argue that this conception continues to play a very substantial role in contemporary mathematical physics and indeed that supposedly ``coordinate-free'' differential geometry (...) relies centrally on this conception of geometry. I discuss some foundational and pedagogical advantages of the coordinate-based formulation and briefly connect it to some remarks of Norton on the historical development of geometry in physics during the establishment of the general theory of relativity. (shrink)

Laws of mechanics, quantum mechanics, electromagnetism, gravitation and relativity are derived as “related mathematical identities” based solely on the existence of a joint probability distribution for the position and velocity of a particle moving on a Riemannian manifold. This probability formalism is necessary because continuous variables are not precisely observable. These demonstrations explain why these laws must have the forms previously discovered through experiment and empirical deduction. Indeed, the very existence of electric, magnetic and gravitational fields is predicted by these (...) purely mathematical constructions. Furthermore these constructions incorporate gravitation into special relativity theory and provide corrected definitions for coordinate time and proper time. These constructions then provide new insight into the relationship between manifold geometry and gravitation and present an alternative to Einstein’s general relativity theory. (shrink)

It is assumed that the motion of a particle in spacetime does not depend on the motion relative to it of any observer or of any frame of reference. Thus if the particle has an internal vibration of the type hypothesized by de Broglie, the phase of that vibration at any point in spacetime must appear to be the same to all observers, i.e., the same in all frames of reference. Each observer or reference frame will have its own de (...) Broglie wave for the particle. The phase of the particle's vibration must, by definition, be the same as that of all possible de Broglie waves at the point where the particle is. By superimposing all these possible de Broglie waves, a wave packet is formed centered in space on the particle. The formation of such a packet is discussed with the help of spacetime diagrams; the packet does not spread with time. The relevance of this packet to the wave mechanics of Schrödinger is discussed; it is also pointed out that any vibration can lead to such a packet. (shrink)

Pauli's five-dimensional Dirac equation in projective space, which results in an anomalous magnetic moment term in four dimensions, is related to the Schuster-Blackett law of the magnetic field of rotating bodies and to the recent results on the gyromagnetic ratio in Kaluza-Klein theories.

Why is space 3-dimensional? The fi rst answer to this question, entirely based on Physics, was given by Ehrenfest, in 1917, who showed that the stability requirement for n-dimensional two-body planetary system very strongly constrains space dimensionality, favouring 3-d. This kind of approach will be generically called "stability postulate" throughout this paper and was shown by Tangherlini, in 1963, to be still valid in the framework of general relativity as well as for quantum mechanical hydrogen atom, giving the same constraint (...) for space{dimensionality. In the present work, before criticizing this methodology, a brief discussion has been introduced, aimed at stressing and clarifying some general physical aspects of the problem of how to determine the number of space dimensions. Then, the epistemological consequences of Ehrenfest's methodology are critically reviewed. An alternative procedure to get at the proper number of dimensions, in which the stability postulate - and the implicit singularities in three-dimensional physics - are not an essential part of the argument, is proposed. In this way, the main epistemological problems contained in Ehrenfest's original idea are avoided. The alternative methodology proposed in this paper is realized by obtaining and discussing the n-dimensional quantum theory as expressed in Planck's law, de Broglie relation and the Heisenberg uncertainty relation. As a consequence, it is possible to propose an experiment, based on thermal neutron di raction by crystals, to directly measure space dimensionality. Finally the distinguished role of Maxwell's electromagnetic theory in the determination of space dimensionality is stressed. (shrink)

In previous work the author was able to derive the Schrödinger equation by an analytical approach built around a physical model that featured a special diffusion process in an ensemble of particles. In the present work, this approach is extended to include the derivation of the Dirac equation. To do this, the physical model has to be modified to make provision for intrinsic electric and magnetic dipoles to be associated with each ensemble particle.

We investigate the possibility of inducing the cosmological constant from extra dimensions by embedding our four-dimensional Riemannian space-time into a five-dimensional Weyl integrable space. Following the approach of the space-time-matter theory we show that when we go down from five to four dimensions, the Weyl field may contribute both to the induced energy-tensor as well as to the cosmological constant Λ, or more generally, it may generate a time-dependent cosmological parameter Λ(t). As an application, we construct a simple cosmological model (...) in which Λ(t) has some interesting properties. (shrink)

The equivalence principle as well as the spin-two character of the weak gravitational field lead to difficulties in the measurability analysis of this field which are not encountered in Bohr and Rosenfeld's corresponding inquiry into the electromagnetic field. To meet these difficulties, atomic elastic structures are proposed as gravitational field detectors whose parameters (masses, total volumes, lattice and elastic constants) are adjustable. The limitations imposed by the uncertainty principle and by the radiation reaction of the detectors on the determination of (...) the amplitude, frequency, and direction of the field are then exhibited. Finally, the relevance of the present work to the investigation of DeWitt and to Einstein's full theory of gravitation is briefly considered. (shrink)

In preparation for the treatment of the gravitational field at spatial infinity, this paper deals with the electromagnetic field at spatial infinity. The field equations on this three-dimensional(1+2) manifold can be obtained from an action principle, which in turn lends itself to a Hamiltonian formulation. Quantization is formally straightforward, but some thought is given to the physical interpretation of the results.

The aim of this paper is to address, from a fresh perspective, the question of whether Newtonian mechanics can legitimately be regarded as a limiting case of the special theory of relativity, or whether the two theories should be deemed so radically different as to be incommensurable in the sense of Feyerabend and Kuhn. Firstly, it is argued that focusing on the concept of mass and its transformation across the two varieties of mechanics is bound to leave the issue unsettled. (...) On the one hand, the idea of a speed-dependent ‘relativistic mass’, which has been invoked in support of incommensurability claims, results from a particular, often innocuous but unnecessary and inappropriate reading of certain basic formulae. On the other hand, the existence of an invariant rest mass in STR does not warrant its identification with the Newtonian mass, be it in a suitable limit. This invariant notwithstanding, those who follow Feyerabend and Kuhn can still uphold their views with regard to the two theories. It is shown, however, that the two mechanics embody relativistic frameworks that are direct consequences of the same set of assumptions. As a result, if Newton’s mechanics cannot simply be regarded as a limiting case of STR, the possibility of ‘recovering’ from the latter some elements of the former can be traced to a common source, belying claims of logical disconnection between the two theories. (shrink)

The objection that Einstein's principle of general covariance is not a relativity principle and has no physical content is reviewed. The principal escapes offered for Einstein's viewpoint are evaluated.

The ArgumentIn this paper it will be shown that Newton'sPrincipiagives an explication of and an argument for the first Law of Motion, that seems to be outside the scope of today's philosophy of science but was familiar to seventeenth-century commentators: The foundation of classical mechanics is possible only by recurrence to results of a successful technical practice. Laws of classical mechanics gain their meaning as well as their claims to validity only when considered as statements about artifacts whose production belongs (...) to the shared know-how of a scientific community. (shrink)

On a macroscopic level we take general relativity as the appropriate theory of space-time and gravity. We will argue that, on a more microscopic level, in the Compton wavelength regime of elementary particles, there are good reasons for suspecting the presence of a torsion of space-time. A corresponding gaugetheoretical formalism related to the Poincaré group is reviewed, and the kinematical consequences of the presence of a torsion are worked out. In particular we discuss the operational meaning and the measurability of (...) torsion. The dynamics of torsion is left for a forthcoming article. (shrink)

It is shown that the covariance together with the quantum principle speak for an affinely connected structure which, for distances greater than Planck’s length, goes over in a metrically connected structure of space-time.

In this paper I discuss some philosophical problems concerning the geometrization of physics, and propose that geometrization and unification are strongly combined.

In Kaluza's five-dimensional unified field theory the restriction for the 55 component of the metric tensor γ55=1 demands that the 15 equations for the unified field be weakened. Equations which have been proposed have identically vanishing trace. The equations then admit only a radiation field as source of the gravitational field. By relaxing the condition, this limitation is avoided, while retaining the striking successes of the five-dimensional approach. A scalar function, determined by the 15th field equation apart from integration constants, (...) provides source terms for both the gravitational and electromagnetic fields, in the latter case of polarization type. (shrink)

In discussing fundamentals of general-relativistic irreversible continuum thermodynamics, this theory is shown to be characterized by the feature that no thermodynamical degrees of freedom are ascribed to gravitation. However, accepting that black hole thermodynamics seems to oppose this harmlessness of gravitation one is called on to consider other approaches. Therefore, in brief some gravitational and thermodynamical alternatives are reviewed.