Is Einstein's metric theory of gravitation to be quantized to yield a complete and logically consistent picture of the geometry of the real world in the presence of quantized material sources? To answer this question, we give arguments that there is a consistent way to extend general relativity to small distances by incorporating further geometric quantities at the level of the connection into the theory and introducing corresponding field equations for their determination, allowing thereby the metric and the Levi-Civita (...) connection to remain classical quantities. The dualism between matter and geometry is extended to quantized fields with the help of a Hibert bundle ℋ raised over a Riemann-Cartan spacetime. Quantized subnuclear matter fields (generalized quantum mechanical wave functions) are sections on ℋ which determine generalized bilinear currents acting as sourc currents for the bundle geometry at small distances. The established dualism between matter and the underlying bundle geometry contains general relativity as a classical part. (shrink)

The paper explains why the de Broglie–Bohm theory reduces to Newtonian mechanics in the macroscopic classical limit. The quantum-to-classical transition is based on three steps: (i) interaction with the environment produces effectively factorized states, leading to the formation of _effective wave functions_ and hence _decoherence_; (ii) the effective wave functions selected by the environment—the pointer states of decoherence theory—will be well-localized wave packets, typically Gaussian states; (iii) the quantum potential of a Gaussian state becomes negligible under (...) standard classicality conditions; therefore, the effective wave function will move according to Newtonian mechanics in the correct classical limit. As a result, a Bohmian system in interaction with the environment will be described by an effective Gaussian state and—when the system is macroscopic—it will move according to Newtonian mechanics. (shrink)

This thesis introduces a new theoretical tool to explore the notion of time and temporal order in quantum mechanics: the relativistic quantum "clock" framework. It proposes novel thought experiments showing that proper time can display quantum features, e.g. when a "clock" runs different proper times in superposition. The resulting new physical effects can be tested in near-future laboratory experiments (with atoms, molecules and photons as "clocks"). The notion of time holds the key to the regime where (...) class='Hi'>quantum theory and general relativity overlap, which has not been directly tested yet and remains largely unexplored by the theory. The framework also applies to scenarios in which causal relations between events become non-classical and which were previously considered impossible to address without refuting quantum theory. The relativistic quantum "clock" framework offers new insights into the foundations of quantum theory and general relativity. (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)

A number of arguments purport to show that quantum field theory cannot be given an interpretation in terms of localizable particles. We show, in light of such arguments, that the classical ħ→0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbar \rightarrow 0$$\end{document} limit can aid our understanding of the particle content of quantum field theories. In particular, we demonstrate that for the massive Klein–Gordon field, the classical limits of number operators can be understood to encode (...) local information about particles in the corresponding classical field theory. (shrink)

We revisit the nonrelativistic problem of a bound, charged particle subject to the random zero-point radiation field, with the purpose of revealing the mechanism that takes it from the initially classical description to the final quantum-mechanical one. The combined effect of the zpf and the radiation reaction force results, after a characteristic time lapse, in the loss of the initial conditions and the concomitant irreversible transition of the dynamics to a stationary regime controlled by the field. In this (...) regime, the canonical variables x, p become expressed in terms of the dipolar response functions to a set of field modes. A proper ordering of the response coefficients leads to the matrix representation of quantum mechanics, as was proposed in the early days of the theory, and to the basic commutator x^,p^=iħ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left[ {\hat{x}},{\hat{p}}\right] =i\hbar $$\end{document}. Further, the connection with the corresponding Fokker–Planck equation valid in the Markov approximation, allows one to obtain the radiative corrections of qed. These results reaffirm the essentially electrodynamic and stochastic nature of the quantum phenomenon, as proposed by stochastic electrodynamics. (shrink)

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution (...) of a given probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise. (shrink)

In this article, we explore the heuristic power of the theoretical distinction between framework and interaction theories applied to the case of General Relativity. According to the distinction, theories and theoretical elements can be classified into two different groups, each with clear ontological, epistemic and functional content. Being so, to identify the group to which a theory belongs would suffice to know a priori its prospects and limitations in these areas without going into a detailed technical analysis. We make (...) the exercise here with General Relativity, anticipate its ontological, epistemic and functional content and show afterwords that such expectations are justified in this case, being consistent with formal issues of General Relativity. With this, we attempt to make a case for the use of the distinction as a powerful tool for scientific and philosophical analysis. (shrink)

In early April 1911 Albert Einstein arrived in Prague to become full professor of theoretical physics at the German part of Charles University. It was there, for the first time, that he concentrated primarily on the problem of gravitation. Before he left Prague in July 1912 he had submitted the paper "Relativität und Gravitation: Erwiderung auf eine Bemerkung von M. Abraham" in which he remarkably anticipated what a future theory of gravity should look like. At the occasion of the Einstein-in-Prague (...) centenary an international meeting was organized under a title inspired by Einstein's last paper from the Prague period: "Relativity and Gravitation, 100 Years after Einstein in Prague". The main topics of the conference included: classical relativity, numerical relativity, relativistic astrophysics and cosmology, quantum gravity, experimental aspects of gravitation, and conceptual and historical issues. The conference attracted over 200 scientists from 31 countries, among them a number of leading experts in the field of general relativity and its applications. This volume includes abstracts of the plenary talks and full texts of contributed talks and articles based on the posters presented at the conference. These describe primarily original results of the authors. Full texts of the plenary talks are included in the volume "General Relativity, Cosmology and Astrophysics--Perspectives 100 Years after Einstein in Prague", editions. J. Bičák and T. Ledvinka, published also by Springer Verlag. (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 analyze the interrelation of quantum and classical entanglement. The latter notion is widely used in classical optic simulation of some quantum-like features of light. We criticize the common interpretation that “quantum nonlocality” is the basic factor differing quantum and classical realizations of entanglement. Instead, we point to the breakthrough Grangier et al. experiment on coincidence detection which was done in 1986 and played the crucial role in rejection of classical field models (...) in favor of quantum mechanics. Classical entanglement sources produce light beams with the coefficient of second order coherence \} \ge 1.\) This feature of classical entanglement is obscured by using intensities of signals in different channels, instead of counting clicks of photo-detectors. The interplay between intensity and clicks counting is not just a technicality. We elevate this issue to the high foundational level. (shrink)

Experiments witnessing the entanglement between two particles interacting only via the gravitational field have been proposed as a test whether gravity must be quantized. In the language of quantum information, a non-quantum gravitational force would be modeled by local operations with classical communication, which cannot generate entanglement in an initially unentangled state. This idea is criticized as too constraining on possible alternatives to quantum gravity. We present a parametrized model for the gravitational interaction of quantum (...) matter on a classical spacetime, inspired by the de Broglie–Bohm formulation of quantum mechanics, which results in entanglement and thereby provides an explicit counterexample to the claim that only a quantized gravitational field possesses this capability. (shrink)

The present essay provides a new metaphysical interpretation of Relational Quantum Mechanics (RQM) in terms of mereological bundle theory. The essential idea is to claim that a physical system in RQM can be defined as a mereological fusion of properties whose values may vary for different observers. Abandoning the Aristotelian tradition centered on the notion of substance, I claim that RQM embraces an ontology of properties that finds its roots in the heritage of David Hume. To this regard, defining (...) what kind of concrete physical objects populate the world according to RQM, I argue that this theoretical framework can be made compatible with (i) a property-oriented ontology, in which the notion of object can be easily defined, and (ii) moderate structural realism, a philosophical position where relations and relata are both fundamental. Finally, I conclude that under this reading relational quantum mechanics should be included among the full-fledged realist interpretations of quantum theory. (shrink)

This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is (...) required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon entertaining background independence in classical (rather than quantum) physics. By this development, and interpreting shape theory as modelling background independence, this book further establishes background independence as a field of study. Background independent mechanics, as well as minisuperspace (spatially homogeneous) models of GR and perturbations thereabout are used to illustrate these points. As hitherto formulated, the different facets of the Problem of Time greatly interfere with each others' attempted resolutions. This book explains how, none the less, a local resolution of the Problem of Time can be arrived at after various reconceptualizations of the facets and reformulations of their mathematical implementation. Self-contained appendices on mathematical methods for basic and foundational quantum gravity are included. Finally, this book outlines how supergravity is refreshingly different from GR as a realization of background independence, and what background independence entails at the topological level and beyond. (shrink)

We give a partial answer to the question whether the Schrödinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one dimensional harmonic oscillator subject to a random force can be described by the Schrödinger equation for a period of time depending on the frequency and the energy of the oscillator. We achieve this by deriving the postulates of (...) Nelson’s stochastic formulation of quantum mechanics for a random force depending on a small parameter. We show that the same result applies to small potential perturbations around the harmonic oscillator. We also show that the noise spectrum can be chosen to obtain the result for all oscillator frequencies for fixed mass. We discuss heuristics to generalize the result for a particle in one dimension in a potential where the motion can be described using action-angle variables. The main motivation of this paper is to provide a step for constructing a Newtonian theory which would approximately reproduce quantum mechanics both in unitary evolution and measurement regimes. (shrink)

We argue, in light of Collapse Model interpretation of quantum theory, that the fundamental division between the quantum and classical behaviors might be analogous to the division of thermodynamic phases. A specific relationship between the collapse parameter $$(\lambda )$$ and the collapse length scale ( $$r_C$$ ) plays the role of the coexistence curve in usual thermodynamic phase diagrams. We further claim that our functional relationship between $$\lambda$$ and $$r_C$$ is strongly supported by the existing International Germanium (...) Experiment (IGEX) collaboration data. This result is preceded by a brief discussion of quantum measurement theory and the Ghirardi–Rimini–Weber (GRW) model applied to the free wavepacket dynamics. (shrink)

Arguments by Sorkin (Impossible measurements on quantum fields. In: Directions in general relativity: proceedings of the 1993 International Symposium, Maryland, vol 2, pp 293–305, 1993) and Borsten et al. (Phys Rev D 104(2), 2021. https://doi.org/10.1103/PhysRevD.104.025012 ) establish that a natural extension of quantum measurement theory from non-relativistic quantum mechanics to relativistic quantum theory leads to the unacceptable consequence that expectation values in one region depend on which unitary operation is performed in a spacelike separated region. (...) Sorkin [ 1 ] labels such scenarios ‘impossible measurements’. We explicitly present these arguments as a no-go result with the logical form of a reductio argument and investigate the consequences for measurement in quantum field theory (QFT). Sorkin-type impossible measurement scenarios clearly illustrate the moral that Microcausality is not by itself sufficient to rule out superluminal signalling in relativistic quantum theories that use Lüders’ rule. We review three different approaches to formulating an account of measurement for QFT and analyze their responses to the ‘impossible measurements’ problem. Two of the approaches are: a measurement theory based on detector models proposed in Polo-Gómez et al. (Phys Rev D, 2022. https://doi.org/10.1103/physrevd.105.065003 ) and a measurement framework for algebraic QFT proposed in Fewster and Verch (Commun Math Phys 378(2):851–889, 2020). Of particular interest for foundations of QFT is that they share common features that may hold general morals about how to represent measurement in QFT. These morals are about the role that dynamics plays in eliminating ‘impossible measurements’, the abandonment of the operational interpretation of local algebras \({\mathcal {A}}(O)\) as representing possible operations carried out in region _O_, and the interpretation of state update rules. Finally, we examine the form that the ‘impossible measurements’ problem takes in histories-based approaches and we discuss the remaining challenges. (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)

We discuss the possibility of “fifth forces” in relativistic gravitation theories of fourth order. The fifth force may be an analog to the “weak forces” in the theories of electroweak interactions.

We introduce nebit, a classical bit with a signed probability distribution. We study its properties and basic transformations that can be applied to it. Then, we introduce a simple dynamical model – a classical random walk supplemented with nebits. We show that such a model exhibits some counterintuitive non-classical properties and that it can achieve or even exceed the speedup of Grover’s quantum search algorithm. The proposed classical dynamics never reveals negativity of nebits and thus (...) we do not need any operational interpretation of negative probabilities. We argue that nebits can be useful as a measure of non-classicality as well as a tool to find new quantum algorithms. (shrink)

A new formulation of what may be called the “fundamental theorem of the theory of relativity” is presented and proved in -space-time, based on the full classification of special transformations and the corresponding velocity addition laws. A system of axioms is introduced and discussed leading to the result, and a study is made of several variants of that system. In particular the status of the group axiom is investigated with respect to the condition of the two-way isotropy of light. (...) Several issues which are ignored or misunderstood in the literature are emphasized. (shrink)

The principal results of Schrödinger's paper are reviewed and a possible extension of his formalism for diffusion processes to general quantum mechanical processes is given. The formalism is not in accord with the general theory of transformation of quantum mechanics and violates the basic assumption of the unpredictable change of a system due to a measurement. Nevertheless, the formalism leads to a density operator which is constructed according to accepted quantum mechanical rules.

We describe the picture of physical processes suggested by Edward Nelson’s stochastic mechanics when generalized to quantum field theory regularized on a lattice, after an introductory review of his theory applied to the hydrogen atom. By performing numerical simulations of the relevant stochastic processes, we observe that Nelson’s theory provides a means of generating typical field configurations for any given quantum state. In particular, an intuitive picture is given of the field “beable”—to use a phrase of John Stewart (...) Bell—corresponding to the Fock vacuum, and an explanation is suggested for how particle-like features can be exhibited by excited states. We then argue that the picture looks qualitatively similar when generalized to interacting scalar field theory. Lastly, we compare the Nelsonian framework to various other proposed ontologies for QFT, and remark upon their relative merits in light of the effective field theory paradigm. Links to animations of the corresponding beables are provided throughout. (shrink)

We discuss the solution proposed by Fermi to the so called “4/3 problem” in the classical theory of the electron, a problem which puzzled the physics community for many decades before and after his contribution. Unfortunately his early resolution of the problem in 1922–1923 published in three versions in Italian and German journals (after three preliminary articles on the topic) went largely unnoticed. Even more recent texts devoted to classical electron theory still do not present his argument or (...) acknowledge the actual content of those articles. The calculations initiated by Fermi at the time are completed here by formulating and discussing the conservation of the total 4-momentum of the accelerated electron as seen from the instantaneous rest frame in which it is momentarily at rest. (shrink)

Previous work has shown that spontaneous collapse of Fock states of identical fermions can be modeled as arising from random Rabi oscillations between two states. In this paper, a mathematical formalism is presented to incorporate this into many-body quantum field theory. This formalism allows for nonlocal collapse in the context of a relativistic system. While there is no absolute time-ordering of events, this approach allows for a coherent narrative of the collapse process.

This paper elaborates on an intrinsically quantum approach to gravity, which begins with a general framework for quantum mechanics and then seeks to identify additional mathematical structure on Hilbert space that is responsible for gravity and other phenomena. A key principle in this approach is that of correspondence: this structure should reproduce spacetime, general relativity, and quantum field theory in a limit of weak gravitational fields. A central question is that of “Einstein separability,” and asks how (...) to define mutually independent subsystems, e.g. through localization. Familiar definitions involving tensor products or operator subalgebras do not clearly accomplish this in gravity, as is seen in the correspondence limit. Instead, gravitational behavior, particularly gauge invariance, suggests a network of Hilbert subspaces related via inclusion maps, contrasting with other approaches based on tensor-factorized Hilbert spaces. Any such localization structure is also expected to place strong constraints on evolution, which are also supplemented by the constraint of unitarity. (shrink)

General relativity and quantum mechanics have both revealed the relativity of certain notions that were previously thought to be absolute. I clarify the precise sense in which these theories are relational, and I argue that the various aspects of relationality pertain to the same movement in the progress of physical theories.

In the iconic measurements of atomic spin-1/2 or photon polarization, one employs two separate noninteracting detectors. Each detector is binary, registering the presence or absence of the atom or the photon. For measurements on a d-state particle, we recast the standard von Neumann measurement formalism by replacing the familiar pointer variable with an array of such detectors, one for each of the d possible outcomes. We show that the unitary dynamics of the pre-measurement process restricts the detector outputs to the (...) subspace of single outcomes, so that the pointer emerges from the apparatus. We propose a physical extension of this apparatus which replaces each detector with an ancilla qubit coupled to a readout device. This explicitly separates the pointer into distinct quantum and (effectively) classical parts, and delays the quantum to classical transition. As a result, one not only recovers the collapse scenario of an ordinary apparatus, but one can also observe a superposition of the quantum pointer states. (shrink)

We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. Thisintrinsic timeis associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, (...) properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in its companion work (Gradenigo, Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant, 2021). (shrink)

This paper reviews the origin of inertia according to Mach's principle and Weber's law of gravitation. The resulting theory is based on simultaneous nonlocal gravitational interactions between particles in the solar system and others in the remote universe beyond the Milky Way galaxy. It explains the precession of the perihelion of Mercury. A most important implication of the Mach-Weber theory of the force of inertia is the necessity for a large amount of uniformly distributed matter in the galactic universe. This (...) matter could be the source of the cosmic background radiation. Nonlocal inertia forces are compatible with a static universe and also with an expanding universe but the latter would demand slow changes in the mass of particles and the gravitational constant. (shrink)

After a brief survey of arguments for a unitary particle theory of matter, offered by the writer in previous publications, the following new items are discussed. (1) The wave part of the dual aspect of matter, resting on the translation formula λ=h/p, is not covariant in the nonrelativistic domain. And relativistically, it is untenable not only on methodological grounds, but because it leads to obvious contradictions to elementary experience, e.g., in the equilibrium between a material oscillator and radiation. (2) The (...) photon story as usually presented is rectified historically and factually. (3) The previous derivation by the writer of quantum mechanical theory from a nonquantal background is supplemented, in order to be conclusive, by the postulate that the general probability relation is to become the ordinary addition law in the average. (4) Quotations from the writings of prominant dualists, intended by the latter to support their ideology, disclose a fantastic disarray of pseudophilosophical standpoints which can be cleared up only by repudiating the alleged dual nature of matter and of light and by ceasing to constantly mix up the contrast between particles and fields with that between particles and waves, and by returning to a strictly unitary aspect. (shrink)

We have recently developed a new understanding of probability in quantum gravity. In this paper we provide an overview of this new approach and its implications. Adopting the de Broglie–Bohm pilot-wave formulation of quantum physics, we argue that there is no Born rule at the fundamental level of quantum gravity with a non-normalisable Wheeler–DeWitt wave functional \(\Psi\). Instead the universe is in a perpetual state of quantum nonequilibrium with a probability density \(P\ne \left| \Psi \right| ^{2}\). (...) Dynamical relaxation to the Born rule can occur only after the early universe has emerged into a semiclassical or Schrödinger approximation, with a time-dependent and normalisable wave functional \(\psi\), for non-gravitational systems on a classical spacetime background. In that regime the probability density \(\rho\) can relax towards \(\left| \psi \right| ^{2}\) (on a coarse-grained level). Thus the pilot-wave theory of gravitation supports the hypothesis of primordial quantum nonequilibrium, with relaxation to the Born rule taking place soon after the big bang. We also show that quantum-gravitational corrections to the Schrödinger approximation allow quantum nonequilibrium \(\rho \ne \left| \psi \right| ^{2}\) to be created from a prior equilibrium ( \(\rho =\left| \psi \right| ^{2}\) ) state. Such effects are very tiny and difficult to observe in practice. (shrink)

One of the foremost goals of research in physics is to find the most basic and universal theories that describe our universe. Many theories assume the presence of absolute space and time in which the physical objects are located and physical processes take place. However, it is more fundamental to understand time as relative to the motion of another object, e.g., the number of swings of a pendulum, and the position of an object primarily relative to other objects. This paper (...) aims to explain how using the principle of relationalism, classical mechanics can be formulated on a most elementary space, which is freed from absolute entities: shape space. In shape space, only the relative orientation and length of subsystems are taken into account. A sufficient requirement for the validity of the principle of relationalism is that by changing a system’s scale variable, all the theory’s parameters that depend on the length, get changed accordingly. In particular, a direct implementation of the principle of relationalism introduces a proper transformation of the coupling constants of the interaction potentials in classical physics. This change leads consequently to a transformation in Planck’s measuring units, which enables us to derive a metric on shape space in a unique way. In order to find out the classical equations of motion on shape space, the method of “symplectic reduction of Hamiltonian systems” is extended to include scale transformations. In particular, we will give the derivation of the reduced Hamiltonian and symplectic form on shape space, and in this way, the reduction of a classical system with respect to the entire similarity group is achieved. (shrink)

In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly generates gauge transformations. By construing change as essential time dependence, one can find change locally in vacuum GR in the Hamiltonian formulation just where it should be. But what if spinors are present? This paper is motivated by the tendency in space-time philosophy tends (...) to slight fermionic/spinorial matter, the tendency in Hamiltonian GR to misplace changes of time coordinate, and the tendency in treatments of the Einstein-Dirac equation to include a gratuitous local Lorentz gauge symmetry along with the physically significant coordinate freedom. Spatial dependence is dropped in most of the paper, both restricting the physical situation and largely fixing the spatial coordinates. In the interest of including all and only the coordinate freedom, the Einstein-Dirac equation is investigated using the Schwinger time gauge and Kibble-Deser symmetric triad condition are employed as a \ version of the DeWitt-Ogievetsky-Polubarinov nonlinear group realization formalism that dispenses with a tetrad and local Lorentz gauge freedom. Change is the lack of a time-like stronger-than-Killing field for which the Lie derivative of the metric-spinor complex vanishes. An appropriate \-friendly form of the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first class-constraints, is shown to change the canonical Lagrangian by a total derivative, implying the preservation of Hamilton’s equations. Given the essential presence of second-class constraints with spinors and their lack of resemblance to a gauge theory, it is useful to have an explicit physically interesting example. This gauge generator implements changes of time coordinate for solutions of the equations of motion, showing that the gauge generator makes sense even with spinors. (shrink)

Quantum probability is used to provide a new organization of basic quantum theory in a logical, axiomatic way. The principal thesis is that there is one fundamental time evolution equation in quantum theory, and this is given by a new version of Born’s Rule, which now includes both consecutive and conditional probability as it must, since science is based on correlations. A major modification of one of the standard axioms of quantum theory allows the implementation of (...) various mathematically distinct models (commonly called ‘pictures’) of them. A natural definition of isomorphism of models is presented next. For a given Hamiltonian the standard ‘pictures’ of quantum theory (e.g., Schrödinger, Heisenberg, interaction) are isomorphic models, whose probabilities are nonetheless model independent. The Schrödinger equation remains valid in one model of the axioms, even though it is no longer the fundamental equation of time evolution. All the usual calculations of standard, textbook quantum theory remain valid, but they are put in a new light. For example, the ‘collapse’ of the state is now viewed in the Schrödinger model as _one_ step in a _two_ step algorithm for calculating _one_ conditional probability. In the isomorphic Heisenberg model, where states are constant in time, one has the same conditional probability given by the same formula. Also, entanglement is defined in a new, more general model independent way as an aspect of quantum probability without using ‘collapse’ or tensor products. (shrink)

The Aharonov–Bohm phase shift in a particle interference pattern when electrons pass a long solenoid is identical in form with the optical interference pattern shift when a piece of retarding glass is introduced into one path of a two-beam optical interference pattern. The particle interference-pattern deflection is a relativistic effect of order $$1/c^{2}$$, though this relativity aspect is rarely mentioned in the literature. Here we give a thorough analysis of the classical electromagnetic aspects of the interaction between a (...) solenoid or toroid and a charged particle. We point out the magnetic Lorentz force which the solenoid or toroid experiences due to a passing charge. Although analysis in the rest frame of the solenoid or toroid will involve back Faraday fields on the charge, the analysis in the inertial frame in which the charge is initially at rest involves forces due to only electric fields where forces are equal in magnitude and opposite in direction. The classical analysis is made using the Darwin Lagrangian. We point out that the classical analysis suggests an angular deflection independent of Planck’s constant $$\hbar $$, where the deflection magnitude is identical with that given by the traditional quantum analysis, but where the deflection direction is unambiguous. (shrink)

One of the basic observations of the classical world is that physical entities are real and can be distinguished from each other. However, within quantum theory, the idea of physical realism is not well established. A framework to analyse how observations in experiments can be described using some physical states of reality was recently developed, known as ontological models framework. Different principles when imposed on the ontological level give rise to different theories, the validity of which can be (...) tested based on the statistics generated by these theories. Using the ontological models framework, we formulate a novel notion of classicality termed ontic-distinguishability, which is based upon the physical principles that in classical theories extremal states are physical states of reality and every sharp measurement observes the state of the system perfectly. We construct a communication task in which the success probability is bounded from above for ontological models satisfying the notion of ontic-distinguishability. Contrary to previous notions of classicality which either required systems of dimension strictly greater than two or atleast three preparations, a violation of ontic-distinguishability can be observed using just a pair of qubits and a pair of incompatible measurements. We further show that violation of previously known notions of classicality such as preparation non-contextuality and Bell’s local causality is a violation of ontic-distinguishability. (shrink)

Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories—a framework in which quantum theory is a special case. We list desiderata which the definition should meet. For 3-dimensional systems, we provide a fully-defined recipe which satisfies these desiderata. We discuss the higher dimensional case where some freedom of choice is left remaining. We apply the definition (...) to example toy theories, and discuss how the quantum notion of time evolution as a phase between energy eigenstates generalises to other theories. (shrink)

In this paper we describe a novel approach to defining an ontologically fundamental notion of co-presentness that does not go against the tenets of relativity theory. We survey the possible reactions to the problem of the present in relativity theory, introducing a terminological distinction between a static role of the present, which is served by the relation of simultaneity, and a dynamic role of the present, with the corresponding relation of co-presentness. We argue that both of these relations (...) need to be equivalence relations, but they need not coincide. Simultaneity, the sharing of a temporal coordinate, need not have fundamental ontological import, so that a relativizing strategy with respect to simultaneity seems promising. The notion of co-presentness, on the other hand, does have ontological import, and can therefore not be relativized to an observer or to an arbitrarily chosen frame. We argue that a formal representation of indeterminism can provide the structure needed to anchor the relation of co-presentness, and that this addition is in fact congenial to the notion of dynamic time as requiring real change. The resulting picture is one of an extended dynamic present, implying a formal distinction between static simultaneity and dynamic co-presentness. After working out the basics of our approach in the simpler framework of branching time, we provide our full analysis in the framework of branching space-times, which allows for a formal definition of modal correlations. The spatial extension of the dynamic present can reach as far as the modal correlations do. In the limit, the dynamic present could extend across a maximal space-like hypersurface. (shrink)

In this book, leading theorists present new contributions and reviews addressing longstanding challenges and ongoing progress in spacetime physics. In the anniversary year of Einstein's General Theory of Relativity, developed 100 years ago, this collection reflects the subsequent and continuing fruitful development of spacetime theories. The volume is published in honour of Carl Brans on the occasion of his 80th birthday. Carl H. Brans, who also contributes personally, is a creative and independent researcher and one of the founders of (...) the scalar-tensor theory, also known as Jordan-Brans-Dicke theory. In the present book, much space is devoted to scalar-tensor theories. Since the beginning of the 1990s, Brans has worked on new models of spacetime, collectively known as exotic smoothness, a field largely established by him. In this Festschrift, one finds an outstanding and unique collection of articles about exotic smoothness. Also featured are Bell's inequality and Mach's principle. Personal memories and historical aspects round off the collection. (shrink)

In the traditional frame of classical electrodynamics, a hydrogen atom would emit electromagnetic waves and thus constantly lose energy, resulting in the fall of the electron on the proton over a finite period of time. The corresponding results were derived under the assumption of the instantaneous interaction between the proton and the electron. In 2004, Raju published a paper where he removed the assumption of the instantaneous interaction and studied the role of a time delay in the classical (...) hydrogen atom. He introduced a model of this effect that can be solved analytically. He calculated the radius rsel of a selected orbit, for which this effect and the radiation reaction force would cancel each other with respect to the tangential acceleration. It turned out that rsel is by an order of magnitude smaller than the Bohr radius. In the present paper we use Raju’s model for the corresponding gravitational situation. In frames of Newton’s gravity, we calculate analytically the radius and the energy Esel of a selected orbit, for which the retardation effect and the radiation reaction force would cancel each other out with respect to the tangential acceleration. Then we compare our outcome with some results of Kaplan’s solution for the two-body gravitational problem based on the Schwarzschild’s field. We show that Esel is very close to the minimum energy of bound states obtained by Kaplan in Einstein’s gravity. We emphasize that the selected orbit from the present paper represents the second only physical situation where the radiation reaction force is zero, but the radiation-caused energy loss is not zero. (shrink)

A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis for developing (...) the Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations. (shrink)

The Hole Argument is primarily about the meaning of general covariance in general relativity. As such it raises many deep issues about identity in mathematics and physics, the ontology of space–time, and how scientific representation works. This paper is about the application of a new foundational programme in mathematics, namely homotopy type theory, to the Hole Argument. It is argued that the framework of HoTT provides a natural resolution of the Hole Argument. The role of the Univalence Axiom in (...) the treatment of the Hole Argument in HoTT is clarified. (shrink)

Recent work on the hole argument in general relativity by Weatherall has drawn attention to the neglected concept of models’ representational capacities. I argue for several theses about the structure of these capacities, including that they should be understood not as many-to-one relations from models to the world, but in general as many-to-many relations constrained by the models’ isomorphisms. I then compare these ideas with a recent argument by Belot for the claim that some isometries “generate new possibilities” in (...) general relativity. Philosophical orthodoxy, by contrast, denies this. Properly understanding the role of representational capacities, I argue, reveals how Belot’s rejection of orthodoxy does not go far enough, and makes better sense of our practices in theorizing about spacetime. (shrink)

These proceedings collect the selected contributions of participants of the First Karl Schwarzschild Meeting on Gravitational Physics, held in Frankfurt, Germany to celebrate the 140th anniversary of Schwarzschild's birth. They are grouped into 4 main themes: I. The Life and Work of Karl Schwarzschild; II. Black Holes in Classical General Relativity, Numerical Relativity, Astrophysics, Cosmology, and Alternative Theories of Gravity; III. Black Holes in Quantum Gravity and String Theory; IV. Other Topics in Contemporary Gravitation. Inspired by (...) the foundational principle ``By acknowledging the past, we open a route to the future", the week-long meeting, envisioned as a forum for exchange between scientists from all locations and levels of education, drew participants from 15 countries across 4 continents. In addition to plenary talks from leading researchers, a special focus on young talent was provided, a feature underlined by the Springer Prize for the best student and junior presentations. (shrink)

This survey article is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative simultaneity relation in the context of Minkowski spacetime; (ii) the ``geometrized" version of Newtonian gravitation theory (also known as Newton-Cartan theory); and (iii) the possibility of recovering the global geometric structure of spacetime from its ``causal structure".

The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have presented the possibility of studying the classical limit in terms of the decoherence of relevant observables of the system. On the basis of this approach, in this paper we introduce the classical limit from a logical perspective, by studying the (...) way in which the logical structure of quantum properties corresponding to relevant observables acquires Boolean characteristics. (shrink)

The reduction from Einstein's to Newton's gravitation theories (and intermediate steps) is used to exemplify reduction in physical theories. Both dimensionless and dimensional reduction are presented, and the advantages and disadvantages of each are pointed out. It is concluded that neither a completely reductionist nor a completely antireductionist view can be maintained. Only the mathematical structure is strictly reducible. The interpretation (the model, the central concepts) of the superseded theory T′ can at best only partially be derived directly from the (...) superseding theory T; it is severely constrained by the mathematical structure, and it can involve qualitatively different central terms that cannot be logically related between T and T′. (shrink)

A generalized Schrödinger equation containing correction terms to classical kinetic energy, has been derived in the complex vector space by considering an extended particle structure in stochastic electrodynamics with spin. The correction terms are obtained by considering the internal complex structure of the particle which is a consequence of stochastic average of particle oscillations in the zeropoint field. Hence, the generalised Schrödinger equation may be called stochastic Schrödinger equation. It is found that the second order correction terms are similar (...) to corresponding relativistic corrections. When higher order correction terms are neglected, the stochastic Schrödinger equation reduces to normal Schrödinger equation. It is found that the Schrödinger equation contains an internal structure in disguise and that can be revealed in the form of internal kinetic energy. The internal kinetic energy is found to be equal to the quantum potential obtained in the Madelung fluid theory or Bohm statistical theory. In the rest frame of the particle, the stochastic Schrödinger equation reduces to a Dirac type equation and its Lorentz boost gives the Dirac equation. Finally, the relativistic Klein–Gordon equation is derived by squaring the stochastic Schrödinger equation. The theory elucidates a logical understanding of classical approach to quantum mechanical foundations. (shrink)