Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the (...) subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time. (shrink)
Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role at all. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must “forget time”, and how this can be done in the classical and in the quantum theory. The idea is to (...) develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time. (shrink)
Contrary to claims about the irrelevance of philosophy for science, I argue that philosophy has had, and still has, far more influence on physics than is commonly assumed. I maintain that the current anti-philosophical ideology has had damaging effects on the fertility of science. I also suggest that recent important empirical results, such as the detection of the Higgs particle and gravitational waves, and the failure to detect supersymmetry where many expected to find it, question the validity of certain philosophical (...) assumptions common among theoretical physicists, inviting us to engage in a clearer philosophical reflection on scientific method. (shrink)
The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe “handles” though which systems couple: they represent real relational structures to which the experimentalist has access in measurement by supplying one of the relata in the measurement procedure itself. This observation leads to a physical interpretation for the ubiquity of gauge: it (...) is a consequence of a relational structure of physical quantities. (shrink)
We study the EPR-type correlations from the perspective of the relational interpretation of quantum mechanics. We argue that these correlations do not entail any form of “non-locality”, when viewed in the context of this interpretation. The abandonment of strict Einstein realism implied by the relational stance permits to reconcile quantum mechanics, completeness, (operationally defined) separability, and locality.
Testable predictions of quantum mechanics are invariant under time reversal. But the evolution of the quantum state in time is not so, neither in the collapse nor in the no-collapse interpretations of the theory. This is a fact that challenges any realistic interpretation of the quantum state. On the other hand, this fact raises no difficulty if we interpret the quantum state as a mere calculation device, bookkeeping past real quantum events.
Quantum mechanics is not about 'quantum states': it is about values of physical variables. I give a short fresh presentation and update on the *relational* perspective on the theory, and a comment on its philosophical implications.
Is reality three-dimensional and becoming real, or is reality four-dimensional and becoming illusory? Both options raise difficulties. I argue that we do not need to be trapped by this dilemma. There is a third possibility: reality has a more complex temporal structure than either of these two naive options. Fundamental becoming is real, but local and unoriented. A notion of present is well defined, but only locally and in the context of approximations.
This is a contribution to a book on quantum gravity and philosophy. I discuss nature and origin of the problem of quantum gravity. I examine the knowledge that may guide us in addressing this problem, and the reliability of such knowledge. In particular, I discuss the subtle modification of the notions of space and time engendered by general relativity, and how these might merge into quantum theory. I also present some reflections on methodological questions, and on some general issues in (...) philosophy of science which are are raised by, or a relevant for, the research on quantum gravity. (shrink)
Following the invitation of the editors of Foundations of Physics, I give here a personal assessment of string theory, from the point of view of an outsider, and I compare it with the theory, methods, and expectations of my own field.
The sixth century -- Anaximander's contributions -- Atmospheric phenomena -- Earth floats in space, suspended in the void -- Invisible entities and natural laws -- Rebellion becomes virtue -- Writing, democracy, and cultural crossbreeding -- What is science? -- Between cultural relativism and absolute thought -- Can we understand the world without Gods? -- Prescientific thought.
Notions like meaning, signal, intentionality, are difficult to relate to a physical word. I study a purely physical definition of "meaningful information", from which these notions can be derived. It is inspired by a model recently illustrated by Kolchinsky and Wolpert, and improves on Dretske classic work on the relation between knowledge and information. I discuss what makes a physical process into a signal.
Without addressing the measurement problem (i. e., what causes the wave function to “collapse,” or to ”branch,” or a history to become realized, or a property to actualize), I discuss the problem of the timing of the quantum measurement: Assuming that in an appropriate sense a measurement happens, when precisely does it happen? This question can be posed within most interpretations of quantum mechanics. By introducing the operator M, which measures whether or not the quantum measurement has happened, I suggest (...) that, contrary to what is often claimed, quantum mechanics does provide a precise answer to this question, although a somewhat surprising one. (shrink)
I am a theoretical physicist, and, following Aristotles' injunction (Aristotle, Physics III, 202b 34), I do consider it my responsibility to discuss the problem of the notion of infinity in the world--in particular, to "inquire whether there is such a thing or not." I will do so here by illustrating some aspects of the notion of infinity in the natural sciences.
We observe entropy decrease towards the past. Does this imply that in the past the world was in a non-generic microstate? I point out an alternative. The subsystem to which we belong interacts with the universe via a relatively small number of quantities, which define a coarse graining. Entropy happens to depends on coarse-graining. Therefore the entropy we ascribe to the universe depends on the peculiar coupling between us and the rest of the universe. Low past entropy may be due (...) to the fact that this coupling is non-generic. I argue that for any generic microstate of a sufficiently rich system there are always special subsystems defining a coarse graining for which the entropy of the rest is low in one time direction. These are the subsystems allowing creatures that “live in time” —such as those in the biosphere— to exist. I reply to some objections raised to an earlier presentation of this idea, in particular by Bob Wald, David Albert and Jim Hartle. (shrink)
All human civilizations have thought that the world was made of sky above and the Earth below. All except one. For the Greeks, the Earth was a rock floating in space, and under the earth there was no ground, no turtles, nor the gigantic columns of which the Bible speaks. How did the Greeks understand that the Earth is suspended in nothingness? Who understood this and how? It is this unique "scientific revolution" of Anaximander of which the author speaks, which (...) Karl Popper called "one of the most daring ideas, revolutionary and portentous in the entire history of human thought" The concern is with the conflict that was opened, still burning, with the nature of scientific thought, its critical and rebellious character, the force with which it subverts the order of things and our image of the world of scientific knowledge, and the highly effective "error" at the same time --as we teach physics in the twentieth century. Speaking of Anaximander, the author invites us to reflect on what his ideas mean to the scientific revolution opened by Einstein. (shrink)
Shannon's notion of relative information between two physical systems can function as foundation for statistical mechanics and quantum mechanics, without referring to subjectivism or idealism. It can also represent a key missing element in the foundation of the naturalistic picture of the world, providing the conceptual tool for dealing with its apparent limitations. I comment on the relation between these ideas and Democritus.
ABSTRACT ABSTRACT: I show that Aristotelian physics is a correct and nonintuitive approximation of Newtonian physics in the suitable domain in the same technical sense in which Newton’s theory is an approximation of Einstein’s theory. Aristotelian physics lasted long not because it became dogma, but because it is a very good, empirically grounded theory. This observation suggests some general considerations on intertheoretical relationships.
Rohrlich claims that “the problem of the arrow of time in classical dynamics has been solved”. The solution he proposes is based on the equations governing the motion of extended particles. Rohrlich claims that these equations, which must take self-interaction into account, are not invariant under time reversal. I dispute this claim, on several grounds.
I show that Aristotelian physics is a correct approximation of Newtonian physics in its appropriate domain, in the same precise sense in which Newton theory is an approximation of Einstein's theory. Aristotelian physics lasted long not because it became dogma, but because it is a very good theory.
Rohrlich claims that ``the problem of the arrow of time in classical dynamics has been solved". The solution he proposes is based on the equations governing the motion of extended particles. Rohrlich claims that these equations, which must take self-interaction into account, are are not invariant under time reversal. I dispute this claim, on several grounds.
If there is a ‘platonic world’ \ of mathematical facts, what does \ contain precisely? I observe that if \ is too large, it is uninteresting, because the value is in the selection, not in the totality; if it is smaller and interesting, it is not independent of us. Both alternatives challenge mathematical platonism. I suggest that the universality of our mathematics may be a prejudice and illustrate contingent aspects of classical geometry, arithmetic and linear algebra, making the case that (...) what we call “mathematics” is always contingent. (shrink)
We sharpen a recent observation by Tim Maudlin: differential calculus is a natural language for physics only if additional structure, like the definition of a Hodge dual or a metric, is given; but the discrete version of this calculus provides this additional structure for free.
Review of the book “Anaximander, a re-assessment”, by Andrew Gregory, submitted to the "Revue des Etudes Anciennes". I take this opportunity also t present some general considerations on the relation between science, history and philosophy.
Facts happen at every interaction, but they are not absolute: they are relative to the systems involved in the interaction. Stable facts are those whose relativity can effectively be ignored. In this work, we describe how stable facts emerge in a world of relative facts and discuss their respective roles in connecting quantum theory and the world. The distinction between relative and stable facts resolves the difficulties pointed out by the no-go theorem of Frauchiger and Renner, and is consistent with (...) the experimental violation of the Local Friendliness inequalities of Bong et al.. Basing the ontology of the theory on relative facts clarifies the role of decoherence in bringing about the classical world and solves the apparent incompatibility between the ‘linear evolution’ and ‘projection’ postulates. (shrink)
A solution to the issue of time in quantum gravity is proposed. The hypothesis that time is not defined at the fundamental level (at the Planck scale) is considered. A natural extension of canonical Heisenberg-picture quantum mechanics is defined. It is shown that this extension is well defined and can be used to describe the "non-Schrödinger regime," in which a fundamental time variable is not defined. This conclusion rests on a detailed analysis of which quantities are the physical observables of (...) the theory; a main technical result of the paper is the identification of a class of gauge-invariant observables that can describe the (observable) evolution in the absence of a fundamental definition of time. The choice of the scalar product and the interpretation of the wave function are carefully discussed. The physical interpretation of the extreme "no time" quantum gravitational physics is considered. (shrink)