Massimo Pauri

Università di Parma | UNIPR · Department of Physics and Earth Sciences

It is highly likely that Quantum Theory will eventually provide a substantial clarification of the neural basis of subjectivity in general (including, with various gradation, all living beings) and, consequently, at least indirectly, of Philosophy of Mind and Mind-Body relation. In this Essay it is argued, however, that the so-called quantum indete...

If the classical structure of space-time is assumed to define an a priori scenario for the formulation of quantum theory (QT), the coordinate representation of the solutions \(\psi (\vec x,t)(\psi (\vec x_1 , \ldots ,\vec x_N ,t))\) of the Schroedinger equation of a quantum system containing one (N) massive scalar particle has a preferred status. L...

A critical re-examination of the history of the concepts of space (including spacetime of general relativity and relativistic quantum field theory) reveals a basic ontological elusiveness of spatial extension, while, at the same time, highlighting the fact that its epistemic primacy seems to be unavoidably imposed on us (as stated by A.Einstein “gi...

The Hamiltonian structure of General Relativity (GR), for both metric and tetrad gravity in a definite continuous family of space-times, is fully exploited in order to show that: i) the "Hole Argument" can be bypassed by means of a specific "physical individuation" of point-events of the space-time manifold $M^4$ in terms of the "autonomous degrees...

This is the first of a couple of papers in which the problematic relation between quantum ontology and spatio-temporal representation and experience is analyzed. The first paper deals with the deep implications that the discovery of the quantum of action (Planck 1900) and the consequent formulation of quantum theory had on the notion of physical pr...

"The last remnant of physical objectivity of space-time" is disclosed in the case of a continuous family of spatially non-compact models of general relativity (GR). The {\it physical individuation} of point-events is furnished by the intrinsic degrees of freedom of the gravitational field, (viz, the {\it Dirac observables}) that represent - as it w...

The Hamiltonian structure of general relativity (GR), for both metric and tetrad gravity in a definite continuous family of space-times, is fully exploited in order to show that: (i) the Hole Argument can be bypassed by means of a specific physical individuation of point-events of the space-time manifold M 4in terms of the autonomous degrees of fre...

“The last remnant of physical objectivity of space–time” is disclosed in the case of a continuous family of spatially non-compact models of general relativity (GR). The physical individuation of point-events is furnished by the autonomous degrees of freedom of the gravitational field (viz., the Dirac observables) which represent—as it were—the onti...

The main aim of our paper is to show that interpretative issues belonging to classical General Relativity (GR) might be preliminary to a deeper understanding of conceptual problems stemming from on-going attempts at constructing a quantum theory of gravity. Among such interpretative issues, we focus on the meaning of general covariance and the rela...

This is the first of a couple of papers in which the peculiar capabilities of the Hamiltonian approach to general relativity are exploited to get both new results concerning specific technical issues, and new insights about old foundational problems of the theory. The first paper includes: (1) a critical analysis of the various concepts of symmetry...

In non-relativistic mechanics the center of mass of an isolated system is easily separated out from the relative variables. For a N-body system these latter are usually described by a set of Jacobi normal coordinates, based on the clustering of the centers of mass of sub-clusters. The Jacobi variables are then the starting point for separating {\it...

In non-relativistic mechanics the center of mass of an isolated system is easily separated out from the relative variables. For a N-body system these latter are usually described by a set of Jacobi normal coordinates, based on the clustering of the centers of mass of sub-clusters. The Jacobi variables are then the starting point for separating {\it...

"The last remnant of physical objectivity of space-time" is disclosed, beyond the Leibniz equivalence, in the case of a continuous family of spatially non-compact models of general relativity. The "physical individuation" of point-events is furnished by the intrinsic degrees of freedom of the gravitational field, (viz, the "Dirac observables") that...

(abridged)The achievements of the present work include: a) A clarification of the multiple definition given by Bergmann of the concept of {\it (Bergmann) observable. This clarification leads to the proposal of a {\it main conjecture} asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables...

1 Abstract The main aim of our paper is to show that interpretative issues belonging to classical General Relativity (GR) might be preliminary to a deeper understanding of conceptual problems stemming from on-going attempts at constructing a quantum theory of gravity. Among such interpretative issues, we focus on the meaning of general covari-ance...

Dixon's multipoles for a system of N relativistic positive-energy scalar particles are evaluated in the rest-frame instant form of dynamics. The Wigner hyper-planes (intrinsic rest frame of the isolated system) turn out to be the natural framework for describing multipole kinematics. Classical concepts like the {\it barycentric tensor of inertia} t...

The main aim of our paper is to show that interpretative issues belonging to classical General Relativity (GR) might be preliminary to a deeper understanding of conceptual problems stemming from on-going attempts at constructing a quantum theory of gravity. Among such interpretative issues, we focus on the meaning of general covariance and the rela...

(Abridged Abstract) This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called {\it Hole Argument} in general relativity. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the {\it weak} ADM energy...

This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called "Hole Argument" in general relativity. Such achievements include: 1) the analysis of the "Hole" phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravi...

For the past two decades, Einstein's Hole Argument (which deals with the apparent indeterminateness of general relativity due to the general covariance of the field equations) and its resolution in terms of Leibniz equivalence (the statement that Riemannian geometries related by active diffeomorphisms represent the same physical solution) have been...

In the Wigner-covariant rest-frame instant form of dynamics it is possible to develop a relativistic kinematics for the N-body problem. The Wigner hyperplanes define the intrinsic rest frame and realize the separation of the center-of-mass. Three notions of {\it external} relativistic center of mass can be defined only in terms of the {\it external...

In this paper we study the perturbations of the charged, dilaton black hole, described by the solution of the low energy limit of the superstring action found by Garfinkle, Horowitz and Strominger. We compute the complex frequencies of the quasi-normal modes of this black hole, and compare the results with those obtained for a Reissner-Nordström an...

After the separation of the center-of-mass motion, a new privileged class of canonical Darboux bases is proposed for the non-relativistic N-body problem by exploiting a geometrical and group theoretical approach to the definition of {\it body frame} for deformable bodies. This basis is adapted to the rotation group SO(3), whose canonical realizatio...

In special relativity, the definition of coordinate systems adapted to generic accelerated observers is a long-standing problem, which has found unequivocal solutions only for the simplest motions. We show that the Märzke-Wheeler construction, an extension of the Einstein synchronization convention, produces accelerated systems of coordinates with...

The concepts of space and time, both in regards to Newtonian space + time (non-relativistic theory) and Minkowski’s spacetime (relativistic quantum field theory), remained essentially unchanged during the development of quantum theory. There are, however, several aspects indicating their provisional status. I leave aside the attempts to construct a...

It is commonly thought that the birth of modern natural science was made possible by an intellectual shift from a mainly abstract and speculative conception of the world to a carefully elaborated image based on observations. There is some grain of truth in this claim, but this grain depends very much on what one takes observation to be. In the phil...

Observability and Scientific Realism It is commonly thought that the birth of modern natural science was made possible by an intellectual shift from a mainly abstract and specuJative conception of the world to a carefully elaborated image based on observations. There is some grain of truth in this claim, but this grain depends very much on what one...

Although the Unruh and Hawking phenomena are commonly linked to field quantization in "accelerated" coordinates or in curved spacetimes, we argue that they are deeply rooted at the classical level. We maintain in particular that these effects should be best understood by considering how the special-relativistic notion of "particle" gets blurred whe...

The possible external couplings of an extended non-relativistic classical system are characterized by gauging its maximal dynamical symmetry group at the centre-of-mass. The Galilean one-time and two-times harmonic oscillators are exploited as models. The following remarkable results are then obtained: 1), a peculiar form of interaction of the syst...

22Exx Lie groups (For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90) 70H15 Canonical and symplectic transformations 70H40 Relativistic dynamics 70H45 Constrained dynamics, Dirac's theory of constraints (See also 70F20, 70F25, 70Gxx)

There is hardly any experience that seems more immediately and constantly given to us than the unrelenting flow of time and the all pervasive coming to an end of everything around and in us. Surely, the experience of change and the related deep conviction that the past is already settled and the future is not yet decided, are among the most basic a...

In the preceding paper we developed a reformulation of Newtonian gravitation as a gauge theory of the extended Galilei group. In the present one we derive two generalizations of Newton's theory (a 10-fields and an 11-fields theory) in terms of an explicit Lagrangian realization of the absolute time dynamics of a Riemannian 3-space. They rum out to...

Many of the fundamental theories of modern physics can be considered as descriptions of dynamical systems subjected to constraints. The study of these constrained dynamical systems, in particular the problems encountered in formulating them as quantum systems, has many profound links with geometry. These links were explored in the Symposium on Geom...

The possible external couplings of an extended non-relativistic classical system are characterized by gauging its maximal symmetry group at the center-of-mass. The Galilean one-time and two-times harmonic oscillators are exploited as models.

We report synthetically about a general treatment of classical theories of gravitation as "gauge" theories of the extended Galilei group, including two generalizations of Newton's theory

Newton's standard theory of gravitation is reformulated in terms of a generally Galilei-covariant action principle as a gauge theory of the extended Galilei group. A suitable modification of Utiyama's method for gauging the projective realization of the Galilei group associated with the free mass-point, together with the connections between the con...

In a preceding paper we developed a reformulation of Newtonian gravitation as a {\it gauge} theory of the extended Galilei group. In the present one we derive two true generalizations of Newton's theory (a {\it ten-fields} and an {\it eleven-fields} theory), in terms of an explicit Lagrangian realization of the {\it absolute time} dynamics of a Rie...

The extended Galilei group is "gaugeized" à la Utiyama. The request that the action for the non-relativistic free mass point be (quasi)-invariant under the Galilei "gauge" transformations leads to the introduction of eleven "compensating" fields with suitable "gauge" transformation properties. Then, the equations of motion for these fields are obta...

In the present article we discuss whether or not ansatzes more general than those considered hitherto, for the representation in terms of plane waves of eigensolutions of the Schro¨dinger equation for a free particle in a plane convex polygonal domain, lead to the construction of a complete set for a class of domains larger than the well-known one,...

Summary An answer is given to a question asked by Loinger concerning a three-vector constant of the motion for the free Dirac electron.

A generalization of Newtonian gravitation theory is obtained by a suitable limiting procedure from the ADM action of general relativity coupled to a mass-point. Three particular theories are discussed and it is found that two of them are invariant under an extended Galilei gauge group.

Motivated by a recently advanced conjecture on the ergodic properties of Quantum Systems, the problem of solving the Schro¨dinger equation for a free particle in a plane polygonal enclosure is revisited. It will be shown that two elementary lemmas suffice to give a complete characterization of the polygons for which a solution can be found in terms...

The aim of the present contribution is twofold: 1) to argue in favour of the thesis according to which the Universe as a whole cannot be considered as a scientific object in any sense that such words have had in the historical development of physics. Although the classical dialectical arguments are not used, the conclusion will be drawn that, essen...

With reference to our previous characterization of quantum ergodicity and recent results on classical billiards, we conjecture a special form for Poisson's summation formula in the case of rational polygons. This special form allows us to give a precise formulation of an algorithm leading to the expression of the corresponding eigenvalues.

One reason for reconsidering the traditional debate about the nature of space and time at a Meeting on “probability in the sciences” is simply that present scientific knowledge in microphysics clearly suggests that probability is fundamentally related to the very concepts of space and time.

Equations of motion for point-like test masses subjected to Yang-Mills-Lorentz and gravitational forces are derived from geodesic motion in the multidimensional space of a non-Abelian Kaluza-Klein theory with vanishing cosmological constant.

We briefly review a recently proposed version of the multidimensional (generalized non-Abelian Kaluza-Klein) gauge theory. A generalized equivalence principle is discussed and used to derive the equations of motion for pointlike test masses with nonvanishing Yang-Mills charges. A curious consequence of causality is noted: these classical point char...

We show that standard nonabelian Kaluza-Klein (K-K) theories violate gauge invariance. Gauge-symmetric K-K theories are outlined; for any compact gauge group, they lead to spontaneously compactified solutions which imply the vanishing of the cosmological constant.

A complete classification is given of the two‐dimensional Hamiltonian systems (whose Hamilton–Jacobi equation separates in Cartesian or polar coordinates) which admit strictly periodic motions for open sets of initial conditions (completely degenerate systems). Any of the systems which are separable in Cartesian coordinates turn out to be canonical...

The physical meaning of the relativistic action-at-a-distance dynamics for two particles in a canonical framework is investigated on the basis of a general formalism introduced in previous works. Starting from the well-known prescription given by Bakamjian and Thomas in terms of ''center-of-mass'' (Q,P) and ''internal'' (rho,pi) canonical coordinat...

The canonical realizations of the full Poincaré group in classical mechanics are studied by means of a general formalism introduced in preceding papers. The resulting classification displays significant analogies with the quantum one. The irreducible realizations, corresponding to positive, zero, and imaginary mass particles with or without spin, a...

A rigorous formulation of the connection between nonergodicity (degeneration) of the motion of a Hamiltonian system and existence of global constants of motion (isolating integrals) is proposed. Necessary and sufficient conditions for the occurrence of a properly defined kind of complete degeneration are given. Finally, a wide‐spread opinion is cri...

Within the framework of the Dirac instant form of classical relativistic dynamics, the most general

An intrinsic quantization procedure based on higher symmetries of classical dynamical systems and utilizing the techniques of van Hove and Souriau is proposed. The procedure is intrinsically Hamiltonian but not explicitly canonical in that the Heisenberg algebra plays no fundamental role. The proposed method is applied to the n‐dimensional harmonic...