We present a formal derivation of the Mino–Sasaki–Tanaka–Quinn–Wald (MSTQW) equation describing the self-force on a (semi-) classical relativistic point mass moving under the influence of quantized linear metric perturbations on a curved background space–time. The curvature of the space–time implies that the dynamics of the particle and the field is history-dependent and as such requires a non-equilibrium formalism to ensure the consistent evolution of both particle and field, viz., the worldline influence functional and (...) the closed- time-path (CTP) coarse-grained effective action. In the spirit of effective field theory, we regularize the formally divergent self-force by smearing the local part of the retarded Green’s function and employing a quasi-local expansion. We derive the MSTQW–Langevin equations describing the perturbations of the particle’s worldline about its semi-classical trajectory resulting from interactions with the quantum fluctuations of the linear metric perturbations. Finally, we demonstrate that the quantum fluctuations of the field could, in principle, leave imprints on gravitational waveforms expected to be observed by gravitational interferometers, thereby encoding information about tree-level perturbative quantum gravity. (shrink)

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive “outside-inwards approach” in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior. -/- Another consequence (...) of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light-sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi–Metzner–Sachs group. This essay is the second part of a partitioned longer paper. (shrink)

Quantum field theory (QFT) combines quantum mechanics with Einstein's special theory of relativity and underlies elementary particle physics. This book presents a philosophical analysis of QFT. It is the first treatise in which the philosophies of space-time, quantum phenomena, and particle interactions are encompassed in a unified framework. Describing the physics in nontechnical terms, and schematically illustrating complex ideas, the book also serves as an introduction to fundamental physical theories. The philosophical interpretation (...) both upholds the reality of the quantum world and acknowledges the irreducible cognitive elements in its representation. The interpretation is based on an analysis of our ways of thinking as the are embedded in the logical structure of QFT. The author argues that philosophical categories are significant only if they play active and essential roles in our knowledge and hence constitute part of the theories in actual use. Thus she regards physical theories as primary, extracts their categorical structure, and uses it to rethink key philosophical questions. Among the questions this book tries to answer are: What are the quantum properties independent of measurements? How do we refer to individual things in a continuous field? How do theories relate to objects? What are the general conditions of the world and of our ways of thinking that make possible our knowledge of the microscopic realm, which is so intangible and counterintuitive? As a penetrating analysis of vital themes in contemporary science, the book will engage the interest of students and professionals in physics and philosophy alike. (shrink)

The simplest case of quantum field theory on curved spacetime—that of the Klein–Gordon field on a globally hyperbolic spacetime—reveals a dilemma: In generic circumstances, either there is no dynamics for this quantum field, or else there is a dynamics that is not unitarily implementable. We do not try to resolve the dilemma here, but endeavour to spell out the consequences of seizing one or the other horn of the dilemma.

AUTHOR: STAN GUDDER (John Evans Professor of Mathematical Physics, University of Denver, USA) -- -/- We consider a discrete scalar, quantum field theory based on a cubic 4-dimensional lattice. We mainly investigate a discrete scattering operator S(x0,r) where x0 and r are positive integers representing time and maximal total energy, respectively. The operator S(x0,r) is used to define transition amplitudes which are then employed to compute transition probabilities. These probabilities are conditioned on the time-energy (x0,r). (...) In order to maintain total unit probability, the transition probabilities need to be reconditioned at each (x0,r). This is roughly analogous to renormalization in standard quantum field theory, except no infinities or singularities are involved. We illustrate this theory with a simple scattering experiment involving a common interaction Hamiltonian. We briefly mention how discreteness of space-time might be tested astronomically. Moreover, these tests may explain the existence of dark energy and dark matter. (shrink)

The status of the vacuum in relativistic quantum field theory is examined. A sharp distinction arises between the global vacuum and the local vacuum. The concept of local number density is critically assessed. The global vacuum state implies fluctuations for all local observables. Correlations between such fluctuations in space-like separated regions of space-time are discussed and the existence of correlations which are maximal in a certain sense is remarked on, independently of how far apart (...) those regions may be. The analogy with the mirror-image correlations in the singlet state of two spin-1/2 particles is explained. The connection between these maximal correlations and the well-known violation of the Bell inequality in the vacuum state is discussed, together with the way in which the existence of these correlations might be exploited in developing a vacuum version of the Einstein-Podolsky-Rosen argument. The recent relativistic formulation of the Einstein-Podolsky-Rosen argument by Ghirardi and Grassi is critically assessed with particular reference to the vacuum case. (shrink)

Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the principal bundle of orthonormal frames on the 4-dimensional space-time. This leads quite naturally to a new theory which takes place on 10-dimensional manifolds. The fields are pairs of \,\varpi )\), where \\) is a 1-form with coefficients (...) in the Lie algebra of the Poincaré group and \ is an 8-form with coefficients in the dual of this Lie algebra. The dynamical equations derive from a simple variational principle and imply that the 10-dimensional manifold looks locally like the total space of a fiber bundle over a 4-dimensional base manifold. Moreover this base manifold inherits a metric and a connection which are solutions of a system of Einstein–Cartan equations. (shrink)

After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles, the automata theory is (...) quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements, solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (shrink)

An axiomatic foundation of a quantum theory for microsystems in the presence of external fields is developed. The space-time structure is introduced by considering the invariance of the theory under a kinematic invariance group. The formalism is illustrated by the example of charged particles in electromagnetic potentials. In the example, gauge invariance is discussed.

This chapter explores the concept of time itself, as physicists understand it. Einstein's special theory of relativity requires worldlines of physical objects to be timelike; the field equations of his general theory of relativity predict that massive bodies such as stars and black holes distort space‐time and bend worldlines. Suppose space‐time becomes so distorted that some worldlines form closed loops. If one tried to follow such a closed timelike curve (or CTC) exactly, (...) all the way around, one would bump into ones former selves and get pushed aside. But by following part of a CTC, we could return to the past and participate in events there. According to a recent calculation by J. Richard Gott of Princeton, a cosmic string passing rapidly by another would generate CTCs. The chapter concludes that if time travel is impossible, then the reason has yet to be discovered. (shrink)

It is shown that both covariant harmonic oscillator formalism and quantum field theory are based on common physical principles which include Poincaré covariance, Heisenberg's space-momentum uncertainty relation, and Dirac's “C-number” time-energy uncertainty relation. It is shown in particular that the oscillator wave functions are derivable from the physical principles which are used in the derivation of the Klein-Nishina formula.

The mathematical and physical aspects of the conformal symmetry of space-time and of physical laws are analyzed. In particular, the group classification of conformally flat space-times, the conformal compactifications of space-time, and the problem of imbedding of the flat space-time in global four-dimensional curved spaces with non-trivial topological and geometrical structure are discussed in detail. The wave equations on the compactified space-times are analyzed also, and the set of their elementary solutions (...) constructed. Finally, the implications of global compactified space-times for cosmology are discussed. It is argued that the recent discovery of periodic structure of matter distribution on large distances strongly suggests that the global cosmological space-time should be close. Next we analyze the inflation scalar field in the inflationary model of universe evolution considered on the spatially compact Robertson-Walker space-time. It is shown that the energy distribution in this model is periodic and the periods and density decrease with increasing distance, in striking agreement with experimental data. Our model of the universe also provides a definite predictions for the energy distribution, polar and azimuthal, considered as a function of angles θ and φ. These predictions should be tested with the new astronomical data. (shrink)

In relativistic quantum field theory the notion of a local operation is regarded as basic: each open space-time region is associated with an algebra of observables representing possible measurements performed within this region. It is much more difficult to accommodate the notions of events taking place in such regions or of localized objects. But how can the notion of a local operation be basic in the theory if this same theory would not be (...) able to represent localized measuring devices and localized events? After briefly reviewing these difficulties we discuss a strategy for eliminating the tension, namely by interpreting quantum theory in a realist way. To implement this strategy we use the ideas of the modal interpretation of quantum mechanics. We then consider the question of whether the resulting scheme can be made Lorentz invariant. (shrink)

The physical, mathematical, and philosophical foundations of the quantum theory of free Bose fields in fixed general relativistic spacetimes are examined. It is argued that the theory is logically and mathematically consistent whereas semiclassical prescriptions for incorporating the back-reaction of the quantum field on the geometry lead to inconsistencies. Still, the relations and heuristic value of the semiclassical approach to canonical and covariant schemes of quantum gravity-plus-matter are assessed. Both conventional and rigorous formulations of (...) the theory and of its principal predictions, cosmological particle creation and horizon radiation, are expounded and compared. Special attention is devoted to spacetime properties needed for the existence or uniqueness of the relevant theoretical elements , renormalization of the stress tensor). The emergence of unitarily inequivalent representations in a single dynamical context is used as motivation for the introduction of the abstract $\rm C\sp{\*}$-algebraic axiomatic formalism. The operationalist and conventionalist claims of the original abstract algebraic program are criticized in favor of its tempered outgrowth, local quantum physics. The interpretation of the theory as a wave mechanics of classical field configurations, deriving from the Schrodinger representations of the abstract algebra, is discussed and is found superior, at least on the level of analogy, to particle or harmonic oscillator interpretations. Further, it is argued that the various detector results and the Fulling nonuniqueness problem do not undermine the particle concept in the ways commonly claimed. In particular, arguments are offered against the attribution of particle status to the Rindler quanta, against the physical realizability of the Rindler vacuum, and against the more general notion of observer-dependence as to the definition of 'particle' or 'vacuum'. However, the question of the ontological status of particles is raised in terms of the consistency of quantum field theory with non-reductive realism about particles, the latter being conceived as entities exhibiting attributes of discreteness and localizability. Two arguments against non-reductive realism about particles, one from axiomatic algebraic local quantum theory in Minkowski spacetime and one from quantum field theory in curved spacetime, are developed. (shrink)

We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein’s general relativity in a non-Riemannian Finsler space. This approach is based on the geometrization of quantum mechanics proposed in Tavernelli and combines quantum and gravitational effects into a global curvature of the Finsler space induced by the quantum potential associated to the matter quantum fields. In order to (...) make this theory compatible with general relativity, the quantum effects are described in the framework of quantum field theory, where a covariant definition of ‘simultaneity’ for many-body systems is introduced through the definition of a suited foliation of space-time. As in Einstein’s gravitation theory, the particle dynamics is finally described by means of a geodesic equation in a curved space-time manifold. (shrink)

Theories of free fields describing spin zero and1/2 extended particles are derived within the stochastic quantum field theory (SQFT) framework. Covariant SQFT analogs of free Schwinger functions and Feynman propagators are obtained, and explicit expressions for charge and four-momentum operators are derived which exhibit a remarkable formal resemblance to their local counterparts. It is shown that the essential results of the LSZ formalism for interacting fields also have their counterpart in SQFT, and that the same holds true (...) of Wightman's reconstruction theorem. Fields on quantum space-time do not obey the local (anti)-commutativity postulate, but we argue that due to the uncertainty principle this postulate cannot be operationally justified as an expression of microcausality despite the customary identification of the two notions. An operationally consistent microcausality condition is proposed instead. (shrink)

This paper shows how different axiomatic and constructive approaches within quantum field theory can be understood in terms of the so-called ,picture theory' of Heinrich Hertz. Each approach will count as a different picture due to the different status of the various concepts (symbols) they are employing, like observables, gauge invariance, confinement or the space-time continuum. An important difference with the original Hertzian approach is the fact that the different approaches in quantum (...) class='Hi'>field theory have partially overlapping, partially supplementing domains of application. This also marks some of the parallels and differences with contemporary debates on structural realism and model-theoretic approaches in the philosophy of physics. The objection that the talk about different pictures just relies on the fact that quantum field theory is unfinished will be countered. Finally, the Hertzian approach will be briefly elaborated and embedded into its philosophical successor projects of Cassirer and Goodman. German Dieser Aufsatz zeigt, wie verschiedene axiomatische und konstruktive Ansätze in der Quantenfeldtheorie mit Hilfe der sogenannten ,,Bildtheorie“ von Heinrich Hertz verstanden werden können. Aufgrund der unterschiedlichen Stellungen der verschiedenen Konzepte (Symbole), die diese Ansätze benutzen - wie etwa Observable, Eichinvarianz, Confinement oder Raum-Zeit-Kontinuum - wird jeder als ein eigenes Bild zu betrachten sein. Ein wichtiger Unterschied zu Hertz' ursprünglicher Fassung der Bildtheorie sind dabei die unterschiedlichen Anwendungsbereiche der Ansätze in der Quantenfeldtheorie. Diese überschneiden sich zum Teil, zum Teil ergänzen sie einander. Dadurch ergeben sich für die bildtheoretische Interpretation wichtige Parallelen und Unterschiede zu anderen Positionen in der Philosophie der Physik, insbesondere zum Strukturrealismus und zur Modell-Theorie. Neben diesen diskutiere ich den Einwand, dass die Redeweise von verschiedenen Bildern in der Quantenfeldtheorie nur deshalb möglich sei, weil die Theorie noch nicht abgeschlossen ist. Schließlich erweitere ich die Hertzsche Bildtheorie und setze sie dabei in Beziehung zu ihren philosophischen Nachfolgeprojekten bei Cassirer und Goodman. (shrink)

The Schrödinger equation for a particle of rest mass $m$ and electrical charge $ne$ interacting with a four-vector potential $A_i$ can be derived as the non-relativistic limit of the Klein–Gordon equation $\left( \Box '+m^2\right) \varPsi =0$ for the wave function $\varPsi $ , where $\Box '=\eta ^{jk}\partial '_j\partial '_k$ and $\partial '_j=\partial _j -\mathrm {i}n e A_j$ , or equivalently from the one-dimensional action $S_1=-\int m ds +\int neA_i dx^i$ for the corresponding point particle in the semi-classical approximation $\varPsi \sim (...) \exp {(\mathrm {i}S_1)}$ , both methods yielding the equation $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2m}\eta ^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + m + n e\phi \right) \varPsi $ in Minkowski space–time , where $\alpha ,\beta =1,2,3$ and $\phi =-A_0$ . We show that these two methods generally yield equations that differ in a curved background space–time $g_{ij}$ , although they coincide when $g_{0\alpha }=0$ if $m$ is replaced by the effective mass $\mathcal{M}\equiv \sqrt{m^2-\xi R}$ in both the Klein–Gordon action $S$ and $S_1$ , allowing for non-minimal coupling to the gravitational field, where $R$ is the Ricci scalar and $\xi $ is a constant. In this case $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2\mathcal{M}'} g^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + \mathcal{M}\phi ^{(\mathrm g)} + n e\phi \right) \varPsi $ , where $\phi ^{(\mathrm g)} =\sqrt{g_{00}}$ and $\mathcal{M}'=\mathcal{M}/\phi ^{(\mathrm g)} $ , the correctness of the gravitational contribution to the potential having been verified to linear order $m\phi ^{(\mathrm g)} $ in the thermal-neutron beam interferometry experiment due to Colella et al. Setting $n=2$ and regarding $\varPsi $ as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space–time. Conservation of probability and electrical current requires both electromagnetic gauge and space–time coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div ${{\varvec{A}}}=\hbox {div}{{\varvec{A}}}^{(\mathrm g)}=0$ , where ${{\varvec{A}}}^{\alpha }=-A^{\alpha }$ and ${{\varvec{A}}}^{(\mathrm g)\alpha }=-\phi ^{(\mathrm g)}g^{0\alpha }$ . The quantum-cosmological Schrödinger (Wheeler–DeWitt) equation is also discussed in the $\mathcal{D}$ -dimensional mini-superspace idealization, with particular regard to the vacuum potential $\mathcal V$ and the characteristics of the ground state, assuming a gravitational Lagrangian $L_\mathcal{D}$ which contains higher-derivative terms up to order $\mathcal{R}^4$ . For the heterotic superstring theory , $L_\mathcal{D}$ consists of an infinite series in $\alpha '\mathcal{R}$ , where $\alpha '$ is the Regge slope parameter, and in the perturbative approximation $\alpha '|\mathcal{R}| \ll 1$ , $\mathcal V$ is positive semi-definite for $\mathcal{D} \ge 4$ . The maximally symmetric ground state satisfying the field equations is Minkowski space for $3\le {\mathcal {D}}\le 7$ and anti-de Sitter space for $8 \le \mathcal {D} \le 10$. (shrink)

It is argued that in his critique of standard nonrelativistic quantum mechanics Einstein formulated three requirements as necessary for a physical theory to be compatible with the field-theorectical paradigm, and it is shown that local, relativistic, algebraic quantum field theory typically satisfies those criteria-although, there are still open questions concerning the status of operational separability of quantum systems localized in space like separated space-time regions. It is concluded that local algebraic (...) quantum field theory can be viewed as a research program that Einstein suggested informally in 1948 and that was realized only later in mathematical physics. (shrink)

Already in 1835 Lobachevski entertained the possibility of multiple geometries of the same type playing a role. This idea of rival geometries has reappeared from time to time but had yet to become a key idea in space-time philosophy prior to Brown's _Physical Relativity_. Such ideas are emphasized towards the end of Brown's book, which I suggest as the interpretive key. A crucial difference between Brown's constructivist approach to space-time theory and orthodox " (...) class='Hi'>space-time realism" pertains to modal scope. Constructivism takes a broad modal scope in applying to all local classical field theories---modal cosmopolitanism, one might say, including theories with multiple geometries. By contrast the orthodox view is modally provincial in assuming that there exists a _unique_ geometry, as the familiar theories have. These theories serve as the "canon" for the orthodox view. Their historical roles also suggest a Whiggish story of inevitable progress. Physics literature after c. 1920 is relevant to orthodoxy primarily as commentary on the canon, which closed in the 1910s. The orthodox view explains the spatio-temporal behavior of matter in terms of the manifestation of the real geometry of space-time, an explanation works fairly well within the canon. The orthodox view, Whiggish history, and the canon have a symbiotic relationship. If one happens to philosophize about a theory outside the canon, space-time realism sheds little light on the spatio-temporal behavior of matter. Worse, it gives the _wrong_ answer when applied to an example arguably _within_ the canon, a sector of Special Relativity, namely, _massive_ scalar gravity with universal coupling. Which is the true geometry---the flat metric from the Poincare' symmetry group, the conformally flat metric exhibited by material rods and clocks, or both---or is the question faulty? How does space-time realism explain the fact that all matter fields see the same curved geometry, when so many ways to mix and match exist? Constructivist attention to dynamical details is vindicated; geometrical shortcuts can disappoint. The more exhaustive exploration of relativistic field theories in particle physics, especially massive theories, is a largely untapped resource for space-time philosophy. (shrink)

We examine the time discontinuity in rotating space–times for which the topology of time is S1. A kinematic restriction is enforced that requires the discontinuity to be an integral number of the periodicity of time. Quantized radii emerge for which the associated tangential velocities are less than the speed of light. Using the de Broglie relationship, we show that quantum theory may determine the periodicity of time. A rotating Kerr–Newman black hole and a (...) rigidly rotating disk of dust are also considered; we find that the quantized radii do not lie in the regions that possess CTCs. (shrink)

The vision of quantum physics developed by David Bohm, and especially the idea of the implicit order, can be considered the true epistemological foundation of quantum field theory and the idea of a quantum vacuum that underlies the observable forms of matter, energy and space-time. Assuming the non-locality as the crucial visiting card of quantum processes, it is thus possible to arrive directly to the transactional interpretation and to the idea of a (...) non-local quantum vacuum in which the behaviour of a subatomic particle constitutes the manifestation of more elementary creation/annihilation processes of quanta. (shrink)

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard (...) for space-time measurements. In the considered flat-space case, the fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis. (shrink)

The history of the theory of general relativity presents unique features. After its discovery, the theory was immediately confirmed and rapidly changed established notions of space and time. The further implications of general relativity, however, remained largely unexplored until the mid 1950s, when it came into focus as a physical theory and gradually returned to the mainstream of physics. This essay presents a historiographical framework for assessing the history of general relativity by taking into account (...) in an integrated narrative intellectual developments, epistemological problems, and technological advances; the characteristics of post–World War II and Cold War science; and newly emerging institutional settings. It argues that such a framework can help us understand this renaissance of general relativity as a result of two main factors: the recognition of the untapped potential of general relativity and an explicit effort at community building, which allowed this formerly disparate and dispersed field to benefit from the postwar changes in the scientific landscape. (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 derive the first analytical formula for the density of "Dark Matter" (DM) at all length scales, thus also for the rotation curves of stars in galaxies, for the baryonic Tully–Fisher relation and for planetary systems, from Einstein's equations (EE) and classical approximations, in agreement with observations. DM is defined in Part I as the energy of the coherent gravitational field of the universe, represented by the additional equivalent ordinary matter (OM), needed at all length scales, to explain classically, (...) with inclusion of the OM, the _observed coherent_ gravitational field. Our derivation uses both EE and the Newtonian approximation of EE in Part I, to describe semi-classically in Part II the advection of DM, created at the level of the universe, into galaxies and clusters thereof. This advection happens proportional with their own classically generated gravitational field g, due to self-interaction of the gravitational field. It is based on the universal formula ρ D = λgg′ 2 for the density ρ D of DM advected into medium and lower scale structures of the observable universe, where λ is a universal constant fixed by the Tully–Fisher relations. Here g′ is the gravitational field of the universe; g′ is in main part its own source, as implied in Part I from EE. We start from a simple electromagnetic analogy that helps to make the paper generally accessible. This paper allows for the first time the exact calculation of DM in galactic halos and at all levels in the universe, based on EE and Newtonian approximations, in agreement with observations. (shrink)

Physical time plays a different role in general relativity than in quantum mechanics and the particle physics based on it. The first section of this chapter provides a brief survey of the main approaches to quantum gravity and then proceeds to consider the lessons that can be drawn from two distinct strategies for discovering a theory of quantum gravity. In the next section, the chapter first explicates the fate of time in approaches to (...) class='Hi'>quantum gravity that start with general relativity (GR) and attempt to quantize it. Second, it investigates approaches to quantum gravity that start from quantum particle physics. The third and fourth sections respectively offer an assessment of time as understood in string theory and 'non‐commutative' field theory. One of the important possibilities for time in quantum gravity is that it might fail to commute with space. (shrink)

Substantivalists claim that spacetime enjoys an existence analogous to that of material bodies, while relationalists seek to reduce spacetime to sets of possible spatiotemporal relations. The resulting debate has been central to the philosophy of space and time since the Scientific Revolution. Recently, many philosophers of physics have turned away from the debate, claiming that it is no longer of any relevance to physics. At the same time, there has been renewed interest in the debate among physicists (...) working on quantum gravity, who claim that the conceptual problems which they face are intimately related to interpretative questions concerning general relativity . My goal is to show that the physicists are correct--there is a close relationship between the interpretative issues of classical and quantum gravity. ;In the first part of the dissertation I challenge the received view that substantivalism has a commanding advantage over relationalism on grounds internal to GR. I argue that this view is based on a misconception of the relationships between realism and substantivalism, and between empiricism and relationalism. This has led to a narrow conception of relationalism. Once this is relinquished it can be seen that none of the standard arguments in favor of substantivalism are cogent. ;In the second part of the dissertation, I consider the way in which considerations arising out of quantum gravity bear upon the substantival-relational debate. I develop a framework in which to discuss the interpretative problems of gauge theories and place GR in this context. From this perspective, I provide a taxonomy of interpretative options, and show how the hole argument arises naturally as a consequence of gauge freedom. This means that certain substantivalist interpretations of GR render the theory indeterministic. In the final chapter, I argue that, far from being a drawback, this presents an opportunity for substantivalists. Examples from quantum mechanics, quantum field theory, and quantum gravity, are used to demonstrate that the ambiguities inherent in quantization can lead to an interpretative interplay between theories. In the case of quantum gravity, this means that substantivalism and relationalism suggest, and are suggested by, distinct approaches to quantizing GR. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer (...) is not Turing machine – Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

In quantum relativistic Hamiltonian dynamics, the time evolution of interacting particles is described by the Hamiltonian with an interaction-dependent term (potential energy). Boost operators are responsible for (Lorentz) transformations of observables between different moving inertial frames of reference. Relativistic invariance requires that interaction-dependent terms (potential boosts) are present also in the boost operators and therefore Lorentz transformations depend on the interaction acting in the system. This fact is ignored in special relativity, which postulates the universality of Lorentz transformations (...) and their independence of interactions. Taking into account potential boosts in Lorentz transformations allows us to resolve the “no-interaction” paradox formulated by Currie, Jordan, and Sudarshan [Rev. Mod. Phys. 35, 350 (1963)] and to predict a number of potentially observable effects contradicting special relativity. In particular, we demonstrate that the longitudinal electric field (Coulomb potential) of a moving charge propagates instantaneously. We show that this effect as well as superluminal spreading of localized particle states is in full agreement with causality in all inertial frames of reference. Formulas relating time and position of events in interacting systems reduce to the usual Lorentz transformations only in the classical limit (ħ→0) and for weak interactions. Therefore, the concept of Minkowski space-time is just an approximation which should be avoided in rigorous theoretical constructions. (shrink)

In connection with the "Philosophy of Science" research program conducted by the Deutsche Forschungsgemeinschaft a colloquium was held in Munich from 18th to 20th May 1919. This covered basic structures of physical theories, the main emphasis being on the interrelation of space, time and mechanics. The present volume contains contributions and the results of the discussions. The papers are given here in the same order of presentation as at the meeting. The development of these "basic structures of physical (...) theories" involved diverging trends arising from different starting points in philosophy and physics. In order to obtain a clear comparison between these schools of thought, it was appropriate to concentrate discussion on geometry and chronology as the common foundation of classical and quantum mechanics. As a rather simple and "Tell prepared field of study, geochronometry seemed suited to analysing these mutually exclusive positions. vii D. Mayr and G. Sussmann (eds.), Space, Time, and Mechanics, vii. Copyright © 1983 by D. Reidel Publishing Company. ACKNOWLEDGEMENT The editors gratefully appreciate the sponsorship of the Deutsche Forschungsgemeinschaft and the cooperation of the authors and publisher. It is also a pleasure to thank Frau M.-L. Grohmann and Frau I. Thies for their organisational and especially Frau B. Grund for typing and clerical work. D. MAYR G. SUSSMANN 1982 University of Munich viii INTRODUCTION The distinct positions present at the symposium may be roughly divided into three schools that differ in their philosophical interpretation of physics and their meta-... ~. (shrink)

Ghost Dirac’s fermions are a manifestation of virtual particles. One fermion is the particle whose companion is the antiparticle. An ensemble of these fermions coupled in pairs represents the Bose-Einstein condensate. This condensate forms the superfluid ether. Due to the Meissner effect inherent in a superfluid medium, the paired fermions are inaccessible for instrument observation. For that reason, the ghost particles can pose the dark matter that, together with the dark energy, can be the fundamental basis of physical reality. In (...) the article, we consider this item through the prism of the Dirac equation stemming from the superfluid quantum ether. The latter is the inherent ubiquitous parent of fermion particle-antiparticle pairs. (shrink)

Schwinger's action principle is formulated for the quantum system which corresponds to the classical system described by the LagrangianL c( $\dot x$ , x)=(M/2)gij(x) $\dot x$ i $\dot x$ j−v(x). It is sufficient for the purpose of deriving the laws of quantum mechanics to consider onlyc-number variations of coordinates and time. The Euler-Lagrange equation, the canonical commutation relations, and the canonical equations of motion are derived from this principle in a consistent manner. Further, it is shown that (...) an arbitrary point transformation leaves the forms of the fundamental equations invariant. The judicious choice of the quantal Lagrangian is essential in our formulation. A quantum mechanical analog of Noether's theorem, which relates the invariance of the quantal action with a conservation law, is established. The ambiguities in the quantal Lagrangian are also discussed and it is pointed out that the requirement of invariance is not sufficient to determine uniquely the quantal Lagrangian and the Hamiltonian. (shrink)

Textbooks present classical particle and field physics as theories of physical systems situated in Newtonian absolute space. This absolute space has an influence on the evolution of physical processes, and can therefore be seen as a physical system itself; it is substantival. It turns out to be possible, however, to interpret the classical theories in another way. According to this rival interpretation, spatiotemporal position is a property of physical systems, and there is no substantival spacetime. The traditional (...) objection that such a relationist view could not cope with the existence of inertial effects and other manifestations of the causal efficacy of spacetime can be answered successfully. According to the new point of view, the spacetime manifold of classical physics is a purely representational device. It represents possible locations of physical objects or events; but these locations are physical properties inherent in the physical objects or events themselves and having no existence independently of them. In relativistic quantum field theory the physical meaning of the spacetime manifold becomes even less tangible. Not only does the manifold lose its status as a substantival container, but also its function as a representation of spacetime properties possessed by physical systems becomes problematic. 'Space and time' become ordering parameters in the web of properties of physical systems. They seem to regain their traditional meaning only in the non-relativistic limit in which the classical particle concept becomes approximately applicable. (shrink)

We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang’s quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, λ and R, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of (...) the latter fact, we find a certain kind of kinematical holographic relation in YSTA, which may be regarded as a primordial form of the holographic principle suggested so far in the framework of the present quantum theory that appears now in the contraction limit of YSTA, λ→0 and R→∞. (shrink)

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In (...) the second part, we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology. (shrink)

The quantum mechanical description of the evolution of an unstable system defined initially as a state in a Hilbert space at a given time does not provide a semigroup (exponential) decay, law. The Wigner–Weisskopf survival amplitude, describing reversible quantum transitions, may be dominated by exponential type decay in pole approximation at times not too short or too long, but, in the two channel case, for example, the pole residues are not orthogonal, and the evolution does riot (...) correspond to a semigroup (experiments on the decay of the neutral K-meson system strongly support the semigroup evolution postulated, by Lee, Oehme and Yang, and Yang and Wu). The scattering theory of Lax and Phillips, originally developed for classical wave equations, has been recently extended to the description of the evolution of resonant states in the framework of quantum theory. The resulting evolution law of the unstable system is that of a semigroup, and the resonant state is a well-defined function in the Lax–Phillips Hilbert space. In this paper we apply this theory to a relativistically covariant quantum field theoretical form of the (soluble) Lee model. We construct the translation representations with the help of the wave operators, and show that the resulting Lax–Phillips S-matrix is an inner function (the Lax–Phillips theory is essentially a theory of translation invariant subspaces). In the special case that the S-matrix is a rational inner function, we obtain the resonant state explicitly and analyze its particle (V, N, θ) content. If there is an exponential bound, the general case differs only by a so-called trivial inner factor, which does not change the complex spectrum, but may affect the wave function of the resonant state. (shrink)

A survey is presented of the essential principles for formulating relativistic wave equations in curved spacetime. The approach is relatively simple and avoids much of the philosophical debate about covariance principles, which is also indicated. Hypercomplex numbers provide a natural language for covariance symmetry and the two important kinds of covariant derivative.

It is taken for granted that the explanation of the Universe’s space-time dimension belongs to the host of the arguments that exhibit the superiority of modern (inflationary) cosmology over the standard model. In the present paper some doubts are expressed . They are based upon the fact superstring theory is too formal to represent genuine unification of general relativity and quantum field theory. Neveretheless, the fact cannot exclude the opportunity that in future the superstring (...) theory can become more physical. Hence this paper does not aim to query neither string cosmology, nor superstring theory; it asks for “tolerance in the matters cosmological”. It advices the researchers not to dwell on the common way of unification and to take into consideration the other ways as well. (shrink)

The geometro-stochastic quantization of a gauge theory for extended objects based on the (4, 1)-de Sitter group is used for the description of quantized matter in interaction with gravitation. In this context a Hilbert bundle ℋ over curved space-time B is introduced, possessing the standard fiber ℋ $_{\bar \eta }^{(\rho )} $ , being a resolution kernel Hilbert space (with resolution generator $\tilde \eta $ and generalized coherent state basis) carrying a spin-zero phase space (...) representation of G=SO(4, 1) belonging to the principal series of unitary irreducible representations determined by the parameter ρ. The bundle ℋ, associated to the de Sitter frame bundle P(B, G), provides a geometric arena with built-in fundamental length parameter R (taken to be of the order of 10−13 cm characterizing hadron physics) yielding, in the presence of gravitation, a quantum kinematical framework for the geometro-stochastic description of spinless matter described in terms of generalized quantum mechanical wave functions, Ψ x ρ (ξ, ζ), defined on #x210B;. By going over to a nonlinear realization of the de Sitter group with the help of a section ξ(x) on the soldered bundle E, associated to P, with homogeneous fiber V′4⋍G/H, one is able to recover gravitation in a de Sitter gauge invariant manner as a gauge theory related to the Lorentz subgroup H of G. ξ(x) plays the dual role of a symmetry-reducing and an extension field. After introducing covariant bilinear source currents in the fields Ψ x ρ (ξ, ζ) and their adjoints determined by G-invariant integration over the local fibers in ℋ, a quantum fiber dynamical (QFD) framework is set up for the dynamics at small distances in B determining the geometric quantities beyond the classical metric of Einstein's theory through a set of current-curvature field equations representing the source equations for axial vector torsion and the de Sitter boost contributions to the bundle connection (the latter defining the soldering forms of the Cartan connection in P(B, G) in the nonlinear gauge). The presented bundle framework yields a theory for quantized material objects in interaction with gravitation, the long-range metrical part of which remains classical. (shrink)

Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of lightcnot being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constanthrequires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature (...) evolving continuously “in time”, has to be replaced by an infinite manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics:To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values ofh, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action. (shrink)

We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle–wave characteristics of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources. The final world model treated here contains only gravonons and a scalar matter (...) field. The gravonons are localized in the environment of the massive particles which generate them. The solution of the Schrödinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: There is a chooser mechanism for the selection of the localization site. The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which at present cannot be controlled experimentally and therefore let the choice appear statistical. The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. The times at which telegraph like jumps occur depend on subtleties of the gravonon structure which at present cannot be controlled experimentally and therefore let the telegraph-like jumps appear statistical. The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of CQM is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave function in configuration space according to Schrödinger’s equation without the need of introducing a probabilistic interpretation. (shrink)

In this compendium of essays, some of the world's leading thinkers discuss their conceptions of space and time, as viewed through the lens of their own discipline. With an epilogue on the limits of human understanding, this volume hosts contributions from six or more diverse fields. It presumes only rudimentary background knowledge on the part of the reader. Time and again, through the prism of intellect, humans have tried to diffract reality into various distinct, yet seamless, atomic, (...) yet holistic, independent, yet interrelated disciplines and have attempted to study it contextually. Philosophers debate the paradoxes, or engage in meditations, dialogues and reflections on the content and nature of space and time. Physicists, too, have been trying to mold space and time to fit their notions concerning micro- and macro-worlds. Mathematicians focus on the abstract aspects of space, time and measurement. While cognitive scientists ponder over the perceptual and experiential facets of our consciousness of space and time, computer scientists theoretically and practically try to optimize the space-time complexities in storing and retrieving data/information. The list is never-ending. Linguists, logicians, artists, evolutionary biologists, geographers et cetera, all are trying to weave a web of understanding around the same duo. However, our endeavour into a world of such endless imagination is restrained by intellectual dilemmas such as: Can humans comprehend everything? Are there any limits? Can finite thought fathom infinity? We have sought far and wide among the best minds to furnish articles that provide an overview of the above topics. We hope that, through this journey, a symphony of patterns and tapestry of intuitions will emerge, providing the reader with insights into the questions: What is Space? What is Time? Chapter [15] of this book is available open access under a CC BY 4.0 license. (shrink)

This introduction to one of the liveliest and most popular fields in philosophy is written specifically for a beginning readership with no background in philosophy or science. Step-by-step analyses of the key arguments are provided and the philosophical heart of the issues is revealed without recourse to jargon, maths, or logical formulas. The book introduces Einstein's revolutionary ideas in a clear and simple way, along with the concepts and arguments of philosophers, both ancient and modern that have proved of lasting (...) value. Specifically, the theories of the ancient Greek philosophers, Zeno, Euclid and Parmenides are considered alongside the ideas of Newton, Leibniz and Kant as well as the giants of twentieth-century physics, Einstein and Lorentz. The problems at the heart of the philosophy of space and time, such as change, motion, infinity, shape, and inflation, are examined and the seismic impact made by relativity theory and quantum theory is assessed in the light of the latest research. The writing is lucid and entertaining, allowing a beginning readership to grasp some difficult concepts while offering the more experienced reader a succinct and illuminating presentation of the state of the debate. "Space, Time and Einstein" shows the reader the excitement of scientific discovery and the beauty of theory in the search for answers to these fundamental questions. (shrink)

We show that the special relativistic dynamics when combined with quantum mechanics and the concept of superstatistics can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy scales. This interpretation leads to Feynman amplitudes that are in the Euclidean regime identical to transition probability of a Brownian particle propagating through a granular space. Some kind of spacetime granularity could be therefore held responsible for the emergence at larger scales of various symmetries. For (...) illustration we consider also the dynamics and the propagator of a spinless relativistic particle. Implications for doubly special relativity, quantum field theory, quantum gravity and cosmology are discussed. (shrink)

The availability of unitarily inequivalent representations of the canonical commutation relations constituting a quantization of a classical field theory raises questions about how to formulate and pursue quantum field theory. In a minimally technical way, I explain how these questions arise and how advocates of the Hilbert space and of the algebraic approaches to quantum theory might answer them. Where these answers differ, I sketch considerations for and against each approach, as well (...) as considerations which might temper their apparent rivalry. (shrink)

We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to quantum field theory. By means of the Dirac sea model—exemplified in the electron sector of the standard model neglecting radiation—we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the (...) level of wave functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem, and explains the appearance of creation and annihilation events. 1Bohmian Mechanics from Quantum Mechanics to Quantum Field Theory2The Dirac Sea Model3Equilibrium States and the Vacuum4Excitations of the Vacuum and the Fock Space Formalism5The Appearance of Particle Creations and Annihilations6The Merits of the Bohmian Approach. (shrink)