The Law of Causality and Its Limits Vienna Circle Collection
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Introduction to Dynamical Triangulations
Introduction to Dynamical Triangulations Andrzej G¨orlich Niels Bohr Institute, University of Copenhagen Naxos, September 12th, 2011 Andrzej G¨orlich Causal Dynamical Triangulation Outline 1 Path integral for quantum gravity 2 Causal Dynamical Triangulations 3 Numerical setup 4 Phase diagram 5 Background geometry 6 Quantum fluctuations Andrzej G¨orlich Causal Dynamical Triangulation Path integral formulation of quantum mechanics A classical particle follows a unique trajectory. Quantum mechanics can be described by Path Integrals: All possible trajectories contribute to the transition amplitude. To define the functional integral, we discretize the time coordinate and approximate each path by linear pieces. space classical trajectory t1 time t2 Andrzej G¨orlich Causal Dynamical Triangulation Path integral formulation of quantum mechanics A classical particle follows a unique trajectory. Quantum mechanics can be described by Path Integrals: All possible trajectories contribute to the transition amplitude. To define the functional integral, we discretize the time coordinate and approximate each path by linear pieces. quantum trajectory space classical trajectory t1 time t2 Andrzej G¨orlich Causal Dynamical Triangulation Path integral formulation of quantum mechanics A classical particle follows a unique trajectory. Quantum mechanics can be described by Path Integrals: All possible trajectories contribute to the transition amplitude. To define the functional integral, we discretize the time coordinate and approximate each path by linear pieces. quantum trajectory space classical trajectory t1 time t2 Andrzej G¨orlich Causal Dynamical Triangulation Path integral formulation of quantum gravity General Relativity: gravity is encoded in space-time geometry. The role of a trajectory plays now the geometry of four-dimensional space-time. All space-time histories contribute to the transition amplitude. -
Causality and Determinism: Tension, Or Outright Conflict?
1 Causality and Determinism: Tension, or Outright Conflict? Carl Hoefer ICREA and Universidad Autònoma de Barcelona Draft October 2004 Abstract: In the philosophical tradition, the notions of determinism and causality are strongly linked: it is assumed that in a world of deterministic laws, causality may be said to reign supreme; and in any world where the causality is strong enough, determinism must hold. I will show that these alleged linkages are based on mistakes, and in fact get things almost completely wrong. In a deterministic world that is anything like ours, there is no room for genuine causation. Though there may be stable enough macro-level regularities to serve the purposes of human agents, the sense of “causality” that can be maintained is one that will at best satisfy Humeans and pragmatists, not causal fundamentalists. Introduction. There has been a strong tendency in the philosophical literature to conflate determinism and causality, or at the very least, to see the former as a particularly strong form of the latter. The tendency persists even today. When the editors of the Stanford Encyclopedia of Philosophy asked me to write the entry on determinism, I found that the title was to be “Causal determinism”.1 I therefore felt obliged to point out in the opening paragraph that determinism actually has little or nothing to do with causation; for the philosophical tradition has it all wrong. What I hope to show in this paper is that, in fact, in a complex world such as the one we inhabit, determinism and genuine causality are probably incompatible with each other. -
Causality in Quantum Field Theory with Classical Sources
Causality in Quantum Field Theory with Classical Sources Bo-Sture K. Skagerstam1;a), Karl-Erik Eriksson2;b), Per K. Rekdal3;c) a)Department of Physics, NTNU, Norwegian University of Science and Technology, N-7491 Trondheim, Norway b) Department of Space, Earth and Environment, Chalmers University of Technology, SE-412 96 G¨oteborg, Sweden c)Molde University College, P.O. Box 2110, N-6402 Molde, Norway Abstract In an exact quantum-mechanical framework we show that space-time expectation values of the second-quantized electromagnetic fields in the Coulomb gauge, in the presence of a classical source, automatically lead to causal and properly retarded elec- tromagnetic field strengths. The classical ~-independent and gauge invariant Maxwell's equations then naturally emerge and are therefore also consistent with the classical spe- cial theory of relativity. The fundamental difference between interference phenomena due to the linear nature of the classical Maxwell theory as considered in, e.g., classical optics, and interference effects of quantum states is clarified. In addition to these is- sues, the framework outlined also provides for a simple approach to invariance under time-reversal, some spontaneous photon emission and/or absorption processes as well as an approach to Vavilov-Cherenkovˇ radiation. The inherent and necessary quan- tum uncertainty, limiting a precise space-time knowledge of expectation values of the quantum fields considered, is, finally, recalled. arXiv:1801.09947v2 [quant-ph] 30 Mar 2019 1Corresponding author. Email address: [email protected] 2Email address: [email protected] 3Email address: [email protected] 1. Introduction The roles of causality and retardation in classical and quantum-mechanical versions of electrodynamics are issues that one encounters in various contexts (for recent discussions see, e.g., Refs.[1]-[14]). -
Time and Causality in General Relativity
Time and Causality in General Relativity Ettore Minguzzi Universit`aDegli Studi Di Firenze FQXi International Conference. Ponta Delgada, July 10, 2009 FQXi Conference 2009, Ponta Delgada Time and Causality in General Relativity 1/8 Light cone A tangent vector v 2 TM is timelike, lightlike, causal or spacelike if g(v; v) <; =; ≤; > 0 respectively. Time orientation and spacetime At every point there are two cones of timelike vectors. The Lorentzian manifold is time orientable if a continuous choice of one of the cones, termed future, can be made. If such a choice has been made the Lorentzian manifold is time oriented and is also called spacetime. Lorentzian manifolds and light cones Lorentzian manifolds A Lorentzian manifold is a Hausdorff manifold M, of dimension n ≥ 2, endowed with a Lorentzian metric, that is a section g of T ∗M ⊗ T ∗M with signature (−; +;:::; +). FQXi Conference 2009, Ponta Delgada Time and Causality in General Relativity 2/8 Time orientation and spacetime At every point there are two cones of timelike vectors. The Lorentzian manifold is time orientable if a continuous choice of one of the cones, termed future, can be made. If such a choice has been made the Lorentzian manifold is time oriented and is also called spacetime. Lorentzian manifolds and light cones Lorentzian manifolds A Lorentzian manifold is a Hausdorff manifold M, of dimension n ≥ 2, endowed with a Lorentzian metric, that is a section g of T ∗M ⊗ T ∗M with signature (−; +;:::; +). Light cone A tangent vector v 2 TM is timelike, lightlike, causal or spacelike if g(v; v) <; =; ≤; > 0 respectively. -
Studies on Causal Explanation in Naturalistic Philosophy of Mind
tn tn+1 s s* r1 r2 r1* r2* Interactions and Exclusions: Studies on Causal Explanation in Naturalistic Philosophy of Mind Tuomas K. Pernu Department of Biosciences Faculty of Biological and Environmental Sciences & Department of Philosophy, History, Culture and Art Studies Faculty of Arts ACADEMIC DISSERTATION To be publicly discussed, by due permission of the Faculty of Arts at the University of Helsinki, in lecture room 5 of the University of Helsinki Main Building, on the 30th of November, 2013, at 12 o’clock noon. © 2013 Tuomas Pernu (cover figure and introductory essay) © 2008 Springer Science+Business Media (article I) © 2011 Walter de Gruyter (article II) © 2013 Springer Science+Business Media (article III) © 2013 Taylor & Francis (article IV) © 2013 Open Society Foundation (article V) Layout and technical assistance by Aleksi Salokannel | SI SIN Cover layout by Anita Tienhaara Author’s address: Department of Biosciences Division of Physiology and Neuroscience P.O. Box 65 FI-00014 UNIVERSITY OF HELSINKI e-mail [email protected] ISBN 978-952-10-9439-2 (paperback) ISBN 978-952-10-9440-8 (PDF) ISSN 1799-7372 Nord Print Helsinki 2013 If it isn’t literally true that my wanting is causally responsible for my reaching, and my itching is causally responsible for my scratching, and my believing is causally responsible for my saying … , if none of that is literally true, then practically everything I believe about anything is false and it’s the end of the world. Jerry Fodor “Making mind matter more” (1989) Supervised by Docent Markus -
Philosophy of Science -----Paulk
PHILOSOPHY OF SCIENCE -----PAULK. FEYERABEND----- However, it has also a quite decisive role in building the new science and in defending new theories against their well-entrenched predecessors. For example, this philosophy plays a most important part in the arguments about the Copernican system, in the development of optics, and in the Philosophy ofScience: A Subject with construction of a new and non-Aristotelian dynamics. Almost every work of Galileo is a mixture of philosophical, mathematical, and physical prin~ a Great Past ciples which collaborate intimately without giving the impression of in coherence. This is the heroic time of the scientific philosophy. The new philosophy is not content just to mirror a science that develops independ ently of it; nor is it so distant as to deal just with alternative philosophies. It plays an essential role in building up the new science that was to replace 1. While it should be possible, in a free society, to introduce, to ex the earlier doctrines.1 pound, to make propaganda for any subject, however absurd and however 3. Now it is interesting to see how this active and critical philosophy is immoral, to publish books and articles, to give lectures on any topic, it gradually replaced by a more conservative creed, how the new creed gener must also be possible to examine what is being expounded by reference, ates technical problems of its own which are in no way related to specific not to the internal standards of the subject (which may be but the method scientific problems (Hurne), and how there arises a special subject that according to which a particular madness is being pursued), but to stan codifies science without acting back on it (Kant). -
Causation As Folk Science
1. Introduction Each of the individual sciences seeks to comprehend the processes of the natural world in some narrow do- main—chemistry, the chemical processes; biology, living processes; and so on. It is widely held, however, that all the sciences are unified at a deeper level in that natural processes are governed, at least in significant measure, by cause and effect. Their presence is routinely asserted in a law of causa- tion or principle of causality—roughly, that every effect is produced through lawful necessity by a cause—and our ac- counts of the natural world are expected to conform to it.1 My purpose in this paper is to take issue with this view of causation as the underlying principle of all natural processes. Causation I have a negative and a positive thesis. In the negative thesis I urge that the concepts of cause as Folk Science and effect are not the fundamental concepts of our science and that science is not governed by a law or principle of cau- sality. This is not to say that causal talk is meaningless or useless—far from it. Such talk remains a most helpful way of conceiving the world, and I will shortly try to explain how John D. Norton that is possible. What I do deny is that the task of science is to find the particular expressions of some fundamental causal principle in the domain of each of the sciences. My argument will be that centuries of failed attempts to formu- late a principle of causality, robustly true under the introduc- 1Some versions are: Kant (1933, p.218) "All alterations take place in con- formity with the law of the connection of cause and effect"; "Everything that happens, that is, begins to be, presupposes something upon which it follows ac- cording to a rule." Mill (1872, Bk. -
Popper, Objectification and the Problem of the Public Sphere
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by The Australian National University Popper, Objectification and the Problem of the Public Sphere Jeremy Shearmur1 1. Introduction: World 3 Popper’s approach to philosophy was anti-psychologistic, at least since he wrote The Two Fundamental Problems of the Theory of Knowledge (cf. Popper 2009 [1979; 1930-3]). In his work, anti-psychologism meant not an opposition to the recognition of psychological activity and its significance (in correspondence with Hayek in the 1950s he identified himself as a dualist interactionist), but, rather, an opposition to the reduction of knowledge to psychology. He stressed – in ways that are familiar from Frege and the early Husserl – the non-psychologistic status of logic. And in The Open Society (Popper 1945), with reference to Marx, he stressed his opposition to attempts to offer psychologistic explanations in the social sciences. His own interpretation of ‘methodological individualism’ viewed human action as taking place in social situations. His short papers on the mind-body problem in the 1950s (included in Popper 1963) developed an argument that the descriptive and argumentative functions of language posed a problem for reductionistic accounts of the mind-body relation. While in his ‘Of Clouds and Clocks’ (in Popper 1972), issues concerning what he was subsequently to call ‘world 3’ played an important role in his more systematic treatment of the mind-body problem. As David Miller suggested, Popper called world 3 in to redress the balance of world 1 and world 2 (see Popper 1976b, note 302). -
Einstein and the Development of Twentieth-Century Philosophy of Science
Einstein and the Development of Twentieth-Century Philosophy of Science Don Howard University of Notre Dame Introduction What is Albert Einstein’s place in the history of twentieth-century philosophy of science? Were one to consult the histories produced at mid-century from within the Vienna Circle and allied movements (e.g., von Mises 1938, 1939, Kraft 1950, Reichenbach 1951), then one would find, for the most part, two points of emphasis. First, Einstein was rightly remembered as the developer of the special and general theories of relativity, theories which, through their challenge to both scientific and philosophical orthodoxy made vivid the need for a new kind of empiricism (Schlick 1921) whereby one could defend the empirical integrity of the theory of relativity against challenges coming mainly from the defenders of Kant.1 Second, the special and general theories of relativity were wrongly cited as straightforwardly validating central tenets of the logical empiricist program, such as verificationism, and Einstein was wrongly represented as having, himself, explicitly endorsed those same philosophical principles. As we now know, logical empiricism was not the monolithic philosophical movement it was once taken to have been. Those associated with the movement disagreed deeply about fundamental issues concerning the structure and interpretation of scientific theories, as in the protocol sentence debate, and about the overall aims of the movement, as in the debate between the left and right wings of the Vienna Circle over the role of politics in science and philosophy.2 Along with such differences went subtle differences in the assessment of Einstein’s legacy to logical empiricism. -
Philipp Frank at Harvard University: His Work and His Influence
Philipp Frank at Harvard University: His Work and His Influence The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Holton, Gerald. 2006. Phillip Frank at Harvard: His Work and his Influence. Synthese 153 (2): 297-311. doi.org/10.1007/ s11229-005-5471-3 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:37837879 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA 10/12/04 Lecture at Philipp Frank Conferences in Prague & Vienna, Sept-Oct. ‘04 Philipp Frank at Harvard: His Work and his Influence by Gerald Holton My pleasant task today is to bring to life Philipp Frank’s work and influence during his last three decades, when he found a refuge and a position in America. In what follows, I hope I may call him Philipp--having been first a graduate student in one of his courses at Harvard, then his teaching assistant sharing his offices, then for many years his colleague and friend in the same Physics Department, and finally, doing research on his archival holdings kept at Harvard. I also should not hide my large personal debt to him, for without his recommendation in the 1950s to the Albert Einstein Estate, I would not have received its warm welcome and its permission, as the first one to do historical research in the treasure trove of unpublished letters and manuscripts, thus starting me on a major part of my career in the history of science. -
Sacred Rhetorical Invention in the String Theory Movement
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Communication Studies Theses, Dissertations, and Student Research Communication Studies, Department of Spring 4-12-2011 Secular Salvation: Sacred Rhetorical Invention in the String Theory Movement Brent Yergensen University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/commstuddiss Part of the Speech and Rhetorical Studies Commons Yergensen, Brent, "Secular Salvation: Sacred Rhetorical Invention in the String Theory Movement" (2011). Communication Studies Theses, Dissertations, and Student Research. 6. https://digitalcommons.unl.edu/commstuddiss/6 This Article is brought to you for free and open access by the Communication Studies, Department of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Communication Studies Theses, Dissertations, and Student Research by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. SECULAR SALVATION: SACRED RHETORICAL INVENTION IN THE STRING THEORY MOVEMENT by Brent Yergensen A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy Major: Communication Studies Under the Supervision of Dr. Ronald Lee Lincoln, Nebraska April, 2011 ii SECULAR SALVATION: SACRED RHETORICAL INVENTION IN THE STRING THEORY MOVEMENT Brent Yergensen, Ph.D. University of Nebraska, 2011 Advisor: Ronald Lee String theory is argued by its proponents to be the Theory of Everything. It achieves this status in physics because it provides unification for contradictory laws of physics, namely quantum mechanics and general relativity. While based on advanced theoretical mathematics, its public discourse is growing in prevalence and its rhetorical power is leading to a scientific revolution, even among the public. -
What Scientific Theories Could Not Be Author(S): Hans Halvorson Reviewed Work(S): Source: Philosophy of Science, Vol
What Scientific Theories Could Not Be Author(s): Hans Halvorson Reviewed work(s): Source: Philosophy of Science, Vol. 79, No. 2 (April 2012), pp. 183-206 Published by: The University of Chicago Press on behalf of the Philosophy of Science Association Stable URL: http://www.jstor.org/stable/10.1086/664745 . Accessed: 03/12/2012 10:32 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press and Philosophy of Science Association are collaborating with JSTOR to digitize, preserve and extend access to Philosophy of Science. http://www.jstor.org This content downloaded by the authorized user from 192.168.52.67 on Mon, 3 Dec 2012 10:32:52 AM All use subject to JSTOR Terms and Conditions What Scientific Theories Could Not Be* Hans Halvorson†‡ According to the semantic view of scientific theories, theories are classes of models. I show that this view—if taken literally—leads to absurdities. In particular, this view equates theories that are distinct, and it distinguishes theories that are equivalent. Furthermore, the semantic view lacks the resources to explicate interesting theoretical relations, such as embeddability of one theory into another.