Showing papers on "Hole argument published in 2006"

The hole argument for covariant theories

Abstract: The hole argument was developed by Einstein in 1913 while he was searching for a relativistic theory of gravitation. Einstein used the language of coordinate systems and coordinate invariance, rather than the language of manifolds and diffeomorphism invariance. He formulated the hole argument against covariant field equations and later found a way to avoid it using coordinate language. In this paper we shall use the invariant language of categories, manifolds and natural objects to give a coordinate-free description of the hole argument and a way of avoiding it. Finally we shall point out some important implications of further extensions of the hole argument to sets and relations for the problem of quantum gravity.

Physical theory and its interpretation : essays in honor of Jeffrey Bub

Abstract: Preface A new modal interpretation of quantum mechanics in terms of relational properties Joseph Berkovitz and Meir Hemmo Why special relativity should not be a template for a reformulation of quantum mechanics Harvey Brown and Chris Timpson On symmetries and conserved quantities in classical mechanics Jeremy Butterfield On the notion of a physical theory of an incompletely knowable domain William Demopoulos Markov properties and quantum experiments Clark Glymour Quantum entropy Stan Gudder Symmetry and the scope of scientific realism Richard Healey Is it true or is it false or somewhere in between? The logic of quantum mechanics C.J. Isham Einstein's hole argument and Weyl's field-body relationalism Herbert Korte Quantum mechanics as a theory of probability Itamar Pitowsky John von Neumann on quantum correlations Miklos Redei Kriske, Tupman and quantum logic: The quantum logician's conundrum Allen Stairs Bibliography of the publications of Jeffrey Bub to 2006 Index

Explaining Leibniz equivalence as difference of non-inertial appearances: Dis-solution of the Hole Argument and physical individuation of point-events

Abstract: ”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 ontic part of the metric field. The physical role of the epistemic part (viz. the gauge variables) is likewise clarified as embodying the unavoidable non-inertial aspects of GR. At the end the philosophical import of the Hole Argument is substantially weakened and in fact the Argument itself dis-solved, while a specific four-dimensional holistic and structuralist view of space-time (called oint-structuralism) emerges, including elements common to the tradition of both substantivalism and relationism. The observables of our models undergo real temporal change: this gives new evidence to the fact that statements like the frozen-time character of evolution, as other ontological claims about GR, are model dependent.

Explaining Leibniz-equivalence as difference of non-inertial appearances: dis-solution of the Hole Argument and physical individuation of point-events

Abstract: "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 were - the {\it ontic} part of the metric field. The physical role of the {\it epistemic} part (viz. the {\it gauge} variables) is likewise clarified as emboding the unavoidable non-inertial aspects of GR. At the end the philosophical import of the {\it Hole Argument} is substantially weakened and in fact the Argument itself dis-solved, while a specific four-dimensional {\it holistic and structuralist} view of space-time, (called {\it point-structuralism}), emerges, including elements common to the tradition of both {\it substantivalism} and {\it relationism}. The observables of our models undergo real {\it temporal change}: this gives new evidence to the fact that statements like the {\it frozen-time} character of evolution, as other ontological claims about GR, are {\it model dependent}. \medskip Forthcoming in Studies in History and Philosophy of Modern Physics

A hole revolution, or are we back where we started?

Abstract: Doubts are raised concerning Rickles' claim that ``an exact analog of the hole argument can be constructed in the loop representation of quantum gravity'' (Rickles, `A new spin on the hole argument', Studies in History and Philosophy of Modern Physics 36 (2005) 415–434).

The Hole Argument. Physical Events and the Superspace

Abstract: The 'hole argument'(the English translation of German 'Lochbetrachtung') was formulated by Albert Einstein in 1913 in his search for a relativistic theory of gravitation. The hole argument was deemed to be based on a trivial error of Einstein, until 1980 when John Stachel (Talk on Einsteins Search for General Covariance, 1912-1915 at the GRG meeting in Jena 1980) recognized its highly non-trivial character. Since then the argument has been intensively discussed by many physicists and philosophers of science. (See e.g., Earman & Norton (1987), Gaul & Rovelli (1999), Stachel & Iftime(2005}, and Iftime & Stachel(2006).) I shall provide here a coordinate-free formulation of the argument using the language of categories and bundles, and generalize the argument for arbitrary covariant and permutable theories (see Iftime & Stachel(2006). In conclusion I shall point out a way of avoiding the hole argument, by looking at the structure of the space of solutions of Einstein's equations on a space-time manifold. This superspace Q(M) is defined as the orbit space of space-time solutions on M under the action of the diffeomorphisms of M, and it plays an important role in the study of the gravitational field and attempts to find a theory of quantum gravity (QG).

Bringing the hole argument back in the loop: A response to Pooley

Abstract: Against Pooley [(2006a). A hole revolution, or are we back where we started? Studies in History and Philosophy of Modern Physics, 37(2) (this issue)], I stand firm on my claim that a hole argument can be constructed in the framework of loop quantum gravity. In this brief response, I shall attempt to make it clearer why this is so, and try to pinpoint and diagnose the main points of disagreement between us.

Gauge and the Hole Argument

Abstract: In this paper I shall extend the formulation of the hole argument to permutable theories. As covariant theories provides a general mathematical framework for classical physics, permutable theories provide the language for quantum physics. This analogy is deeply founded: as covariant theories are defined functorially on the category of manifolds and local diffeomorphisms with values into the category of fibered manifolds and fiber-preserving morphisms, and some rule of selecting sections([5]), permutable theories are functorially defined on the category of sets and permutations with values into the category of fibered sets and fiber-preserving automorphisms, and rules of selecting sections. One of the main features of covariant theories, in particular general relativity, is that the field equation possesses gauge freedom associated with global diffeomorphisms of the underlying manifold. I shall explain here how the hole argument is a reflection of this gauge freedom. Finally I shall point out some implications of the hole argument to individuation problem of basic objects in physics.

Explaining Leibniz-equivalence away: Dis-solution of the Hole Argument and physical individuation of point-events

Abstract: "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 were - the {\it ontic} part of the metric field The physical role of the {\it epistemic} part (viz the {\it gauge} variables) is likewise clarified as emboding the unavoidable non-inertial aspects of GR At the end the philosophical import of the {\it Hole Argument} is substantially weakened and in fact the Argument itself dis-solved, while a specific four-dimensional {\it holistic and structuralist} view of space-time, (called {\it point-structuralism}), emerges, including elements common to the tradition of both {\it substantivalism} and {\it relationism} The observables of our models undergo real {\it temporal change}: this gives new evidence to the fact that statements like the {\it frozen-time} character of evolution, as other ontological claims about GR, are {\it model dependent} \medskip Forthcoming in Studies in History and Philosophy of Modern Physics

The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics

Abstract: A modern re-visitation of the consequences of the lack of an intrinsic notion of instantaneous 3-space in relativistic theories leads to a reformulation of their kinematical basis emphasizing the role of non-inertial frames centered on an arbitrary accelerated observer. In special relativity the exigence of predictability implies the adoption of the 3+1 point of view, which leads to a well posed initial value problem for field equations in a framework where the change of the convention of synchronization of distant clocks is realized by means of a gauge transformation. This point of view is also at the heart of the canonical approach to metric and tetrad gravity in globally hyperbolic asymptotically flat space-times, where the use of Shanmugadhasan canonical transformations allows the separation of the physical degrees of freedom of the gravitational field (the tidal effects) from the arbitrary gauge variables. Since a global vision of the equivalence principle implies that only global non-inertial frames can exist in general relativity, the gauge variables are naturally interpreted as generalized relativistic inertial effects, which have to be fixed to get a deterministic evolution in a given non-inertial frame. As a consequence, in each Einstein's space-time in this class the whole chrono-geometrical structure, including also the clock synchronization convention, is dynamically determined and a new approach to the Hole Argument leads to the conclusion that "gravitational field" and "space-time" are two faces of the same entity. This view allows to get a classical scenario for the unification of the four interactions in a scheme suited to the description of the solar system or our galaxy with a deperametrization to special relativity and the subsequent possibility to take the non-relativistic limit.

Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity

Abstract: 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 of freedom" of the vacuum gravitational field ("Dirac observables"), while the "Leibniz equivalence" is reduced to differences in the "non-inertial appearances" (connected to "gauge" variables) of the same phenomena. ii) the chrono-geometric structure of a solution of Einstein equations for given, gauge-fixed, initial data (a "3-geometry" satisfying the relevant constraints on the Cauchy surface), can be interpreted as an "unfolding" in mathematical global time of a sequence of "achronal 3-spaces" characterized by "dynamically determined conventions" about distant simultaneity. This result stands out as an important "conceptual difference" with respect to the standard chrono-geometrical view of Special Relativity (SR) and allows, in a specific sense, for an "endurantist" interpretations of ordinary "physical objects" in GR.

Gauge and General Relativity

Abstract: One of the main features of covariant theories, in particular general relativity, is that the field equation possesses gauge freedom associated with global diffeomorphisms of the underlying manifold. I shall explain here how the hole argument is a reflection of this gauge freedom. Finally I shall point out some implications of the hole argument and extend the hole argument to the case of permutable theories. As covariant theories provides a general mathematical framework for classical physics, permutable theories provide the language for quantum physics. Permutable theories are defined functorially on the category of sets and permutations with values into the category of fibered sets and fiber-preserving automorphisms, and rules of selecting sections. The hole argument for permutable theories is intimately related with the individuation problem of the base elements (e.g., elementary particles). This is a consequence of the fact that the automorphisms of the base space provides the gauge freedom of the fields.

Clock Synchronization, Dirac Observables and Gauge Variables in Canonical Gravity and the Objectivity of Spacetime.

Abstract: This is a review of the chrono-geometrical structure of special and general relativity with a special emphasis on the role of non-inertial frames and of the conventions for the synchronization of distant clocks. ADM canonical metric and tetrad gravity are analyzed in a class of space-times suitable to incorporate particle physics by using Dirac theory of constraints, which allows to arrive at a separation of the genuine degrees of freedom of the gravitational field, the Dirac observables describing generalized tidal effects, from its gauge variables, describing generalized inertial effects. A background-independent formulation (the rest-frame instant form of tetrad gravity) emerges, since the chosen boundary conditions at spatial infinity imply the existence of an asymptotic flat metric. By switching off the Newton constant in presence of matter this description deparametrizes to the rest-frame instant form for such matter in the framework of parametrized Minkowski theories. The problem of the objectivity of the spacetime point-events, implied by Einstein's Hole Argument, is analyzed.

Relational Spacetime Ontology

Abstract: In the aftermath of the rediscovery of Einstein’s hole argument by Earman and Norton (1987), we hear that the ontological relational/substantival debate over the status of spacetime seems to have reached stable grounds. Despite Einstein’s early intention to cast GR’s spacetime as a relational entity a la Leibniz-Mach, most philosophers of science feel comfortable with the now standard sophisticated substantivalist (SS) account of spacetime. Furthermore, most philosophers share the impression that although relational accounts of certain highly restricted models of GR are viable, at a deep down level, they require substantival spacetime structures. SS claims that although manifold spacetime points do not enjoy the sort of robust existence provided by primitive identity, it is still natural to be realistic about the existence of spacetime as an independent entity in its own right. It is argued that since the bare manifold lacks the basic spacetime structures –such as geometry and inertia- one should count as an independent spacetime the couple manifold +metric (M, g). The metric tensor field of GR encodes inertial and metrical structure so, in a way, it plays the explanatory role that Newtonian absolute space played in classical dynamics. In a nutshell, according to the SS account of spacetime, one should view the metric field of GR as the modern version of a realistically constructed spacetime since it has the properties –or contains the structures- that Newtonian space had. I will try to dismantle the widespread impression that a relational account of full GR is implausible. To do so, I will start by highlighting that when turning back to the original Leibniz-Newton dispute one sees that substantivalism turns out prima facie triumphant since Newton was able to successfully formulate dynamics. However, to give relationalism a fair chance, one can also put forward the following hypothetical questions: What if Leibniz –or some leibnizian- had had a good relational theory? What role would geometry play in this type of theory? Would it be natural to view geometry and inertia as intrinsic properties of substantival space –if not spacetime? Would it still seem natural to interpret the metric field of GR along substantival lines regardless of the fact that it also encodes important material properties such as energy-momentum? After bringing these questions out into the light I will cast some important doubts on the substantival (SS) interpretation of the metric field. Perhaps the metric turns out to be viewed as a relational matter field. Finally, to strengthen the relational account of spacetime I expect to remove the possible remaining interpretative tension by briefly discussing the relevance of two important facts: i) Dynamical variables are usually linked to material objects in physical theories. The metric field of GR is a dynamical object so, I claim, it should be viewed as a matter field. ii) Barbour and Bertotti (BB2, 1982) have provided and alternative formulation of classical dynamics. They provide a “genuinely relational interpretation of dynamics” (Pooley & Brown 2001). Geometry and inertia become –contra SS- relational structures in BB2.

Chapter 15: Introduction

Abstract: Publisher Summary The nature of space and time is a traditional philosophical subject. Whether space is an independently existing substance and whether time is a measure of change in material processes or something that exists and flows even if there are no material processes going on are questions that go back to the very beginning of natural philosophy. Despite this longevity, no consensus has been reached, and these issues are still exercising the minds of both scientists and philosophers. The past few decades have even seen an upsurge of interest. This is because of a number of factors. Among these figures, the revival of the substantivalism versus relationalism debate as a consequence of the foundational studies of general relativity, especially the renewed attention for Einstein's notorious hole argument. The diffeomorphism invariance of the equations of general relativity appears to indicate that prima facie different models of the theory that are related to each other by diffeomorphisms actually represent the same physical situation. The only difference between any two such models is in the manifold points where events take place. If the verdict of physical sameness is accepted, the implication is that only physical objects and fields and their coincidence relations are relevant for the specification of the state of the universe. The identity of the spacetime points at which events take place plays no role. This suggests that it may be unnecessary to accept these points as independent parts of the ontological furniture of the world.