Basil Hiley Quantum Theory, the Implicate Order
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Arxiv:0908.1787V1 [Quant-Ph] 13 Aug 2009 Ematical Underpinning
August 13, 2009 18:17 Contemporary Physics QuantumPicturalismFinal Contemporary Physics Vol. 00, No. 00, February 2009, 1{32 RESEARCH ARTICLE Quantum picturalism Bob Coecke∗ Oxford University Computing Laboratory, Wolfson Building, Parks Road, OX1 3QD Oxford, UK (Received 01 02 2009; final version received XX YY ZZZZ) Why did it take us 50 years since the birth of the quantum mechanical formalism to discover that unknown quantum states cannot be cloned? Yet, the proof of the `no-cloning theorem' is easy, and its consequences and potential for applications are immense. Similarly, why did it take us 60 years to discover the conceptually intriguing and easily derivable physical phenomenon of `quantum teleportation'? We claim that the quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the arrays of 0s and 1s of the early days of computer programming practice. Using a technical term from computer science, the quantum mechanical formalism is `low-level'. In this review we present steps towards a diagrammatic `high-level' alternative for the Hilbert space formalism, one which appeals to our intuition. The diagrammatic language as it currently stands allows for intuitive reasoning about interacting quantum systems, and trivialises many otherwise involved and tedious computations. It clearly exposes limitations such as the no-cloning theorem, and phenomena such as quantum teleportation. As a logic, it supports `automation': it enables a (classical) computer to reason about interacting quantum systems, prove theorems, and design protocols. -
Dynamical Relaxation to Quantum Equilibrium
Dynamical relaxation to quantum equilibrium Or, an account of Mike's attempt to write an entirely new computer code that doesn't do quantum Monte Carlo for the first time in years. ESDG, 10th February 2010 Mike Towler TCM Group, Cavendish Laboratory, University of Cambridge www.tcm.phy.cam.ac.uk/∼mdt26 and www.vallico.net/tti/tti.html [email protected] { Typeset by FoilTEX { 1 What I talked about a month ago (`Exchange, antisymmetry and Pauli repulsion', ESDG Jan 13th 2010) I showed that (1) the assumption that fermions are point particles with a continuous objective existence, and (2) the equations of non-relativistic QM, allow us to deduce: • ..that a mathematically well-defined ‘fifth force', non-local in character, appears to act on the particles and causes their trajectories to differ from the classical ones. • ..that this force appears to have its origin in an objectively-existing `wave field’ mathematically represented by the usual QM wave function. • ..that indistinguishability arguments are invalid under these assumptions; rather antisymmetrization implies the introduction of forces between particles. • ..the nature of spin. • ..that the action of the force prevents two fermions from coming into close proximity when `their spins are the same', and that in general, this mechanism prevents fermions from occupying the same quantum state. This is a readily understandable causal explanation for the Exclusion principle and for its otherwise inexplicable consequences such as `degeneracy pressure' in a white dwarf star. Furthermore, if assume antisymmetry of wave field not fundamental but develops naturally over the course of time, then can see character of reason for fermionic wave functions having symmetry behaviour they do. -
Quantum Trajectories: Real Or Surreal?
entropy Article Quantum Trajectories: Real or Surreal? Basil J. Hiley * and Peter Van Reeth * Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK * Correspondence: [email protected] (B.J.H.); [email protected] (P.V.R.) Received: 8 April 2018; Accepted: 2 May 2018; Published: 8 May 2018 Abstract: The claim of Kocsis et al. to have experimentally determined “photon trajectories” calls for a re-examination of the meaning of “quantum trajectories”. We will review the arguments that have been assumed to have established that a trajectory has no meaning in the context of quantum mechanics. We show that the conclusion that the Bohm trajectories should be called “surreal” because they are at “variance with the actual observed track” of a particle is wrong as it is based on a false argument. We also present the results of a numerical investigation of a double Stern-Gerlach experiment which shows clearly the role of the spin within the Bohm formalism and discuss situations where the appearance of the quantum potential is open to direct experimental exploration. Keywords: Stern-Gerlach; trajectories; spin 1. Introduction The recent claims to have observed “photon trajectories” [1–3] calls for a re-examination of what we precisely mean by a “particle trajectory” in the quantum domain. Mahler et al. [2] applied the Bohm approach [4] based on the non-relativistic Schrödinger equation to interpret their results, claiming their empirical evidence supported this approach producing “trajectories” remarkably similar to those presented in Philippidis, Dewdney and Hiley [5]. However, the Schrödinger equation cannot be applied to photons because photons have zero rest mass and are relativistic “particles” which must be treated differently. -
The Stueckelberg Wave Equation and the Anomalous Magnetic Moment of the Electron
The Stueckelberg wave equation and the anomalous magnetic moment of the electron A. F. Bennett College of Earth, Ocean and Atmospheric Sciences Oregon State University 104 CEOAS Administration Building Corvallis, OR 97331-5503, USA E-mail: [email protected] Abstract. The parametrized relativistic quantum mechanics of Stueckelberg [Helv. Phys. Acta 15, 23 (1942)] represents time as an operator, and has been shown elsewhere to yield the recently observed phenomena of quantum interference in time, quantum diffraction in time and quantum entanglement in time. The Stueckelberg wave equation as extended to a spin–1/2 particle by Horwitz and Arshansky [J. Phys. A: Math. Gen. 15, L659 (1982)] is shown here to yield the electron g–factor g = 2(1+ α/2π), to leading order in the renormalized fine structure constant α, in agreement with the quantum electrodynamics of Schwinger [Phys. Rev., 73, 416L (1948)]. PACS numbers: 03.65.Nk, 03.65.Pm, 03.65.Sq Keywords: relativistic quantum mechanics, quantum coherence in time, anomalous magnetic moment 1. Introduction The relativistic quantum mechanics of Dirac [1, 2] represents position as an operator and time as a parameter. The Dirac wave functions can be normalized over space with respect to a Lorentz–invariant measure of volume [2, Ch 3], but cannot be meaningfully normalized over time. Thus the Dirac formalism offers no precise meaning for the expectation of time [3, 9.5], and offers no representations for the recently– § observed phenomena of quantum interference in time [4, 5], quantum diffraction in time [6, 7] and quantum entanglement in time [8]. Quantum interference patterns and diffraction patterns [9, Chs 1–3] are multi–lobed probability distribution functions for the eigenvalues of an Hermitian operator, which is typically position. -
Bohmian Mechanics Versus Madelung Quantum Hydrodynamics
Ann. Univ. Sofia, Fac. Phys. Special Edition (2012) 112-119 [arXiv 0904.0723] Bohmian mechanics versus Madelung quantum hydrodynamics Roumen Tsekov Department of Physical Chemistry, University of Sofia, 1164 Sofia, Bulgaria It is shown that the Bohmian mechanics and the Madelung quantum hy- drodynamics are different theories and the latter is a better ontological interpre- tation of quantum mechanics. A new stochastic interpretation of quantum me- chanics is proposed, which is the background of the Madelung quantum hydro- dynamics. Its relation to the complex mechanics is also explored. A new complex hydrodynamics is proposed, which eliminates completely the Bohm quantum po- tential. It describes the quantum evolution of the probability density by a con- vective diffusion with imaginary transport coefficients. The Copenhagen interpretation of quantum mechanics is guilty for the quantum mys- tery and many strange phenomena such as the Schrödinger cat, parallel quantum and classical worlds, wave-particle duality, decoherence, etc. Many scientists have tried, however, to put the quantum mechanics back on ontological foundations. For instance, Bohm [1] proposed an al- ternative interpretation of quantum mechanics, which is able to overcome some puzzles of the Copenhagen interpretation. He developed further the de Broglie pilot-wave theory and, for this reason, the Bohmian mechanics is also known as the de Broglie-Bohm theory. At the time of inception of quantum mechanics Madelung [2] has demonstrated that the Schrödinger equa- tion can be transformed in hydrodynamic form. This so-called Madelung quantum hydrodynam- ics is a less elaborated theory and usually considered as a precursor of the Bohmian mechanics. The scope of the present paper is to show that these two theories are different and the Made- lung hydrodynamics is a better interpretation of quantum mechanics than the Bohmian me- chanics. -
Infinite Potential Show Title: Generic Show Episode #101 Date: 3/17/20 Transcribed by Daily Transcription Tre
INFINITE POTENTIAL SHOW TITLE: GENERIC SHOW EPISODE #101 DATE: 3/17/20 TRANSCRIBED BY DAILY TRANSCRIPTION_TRE 00:00:28 DAVID BOHM People talked about the world, and I said, "Where does it end?" and, uh, uh... MALE And what answer did they give? DAVID BOHM Well, they-I never, uh, I don't remember. It wasn't terribly convincing I suppose. [LAUGH] DR. DAVID C. It was, uh, a night, and we were SCHRUM walking under the stars, black sky, and he looked up to the stars, and he said, "Ordinarily, when we look to the sky and look to the stars, we think of stars as objects far out and vast spaces between them." He said, "There's another way we can look at it. We can look at the vacuum at the emptiness instead as a planum, as infinitely full rather than infinitely empty. And that the material objects themselves are like little bubbles, little vacancies in this vast sea." 00:01:25 DR. DAVID C. So David Bohm, in a sense, was SCHRUM using that view to have me look at the stars and to have a sense of the night sky all of a sudden in a different way, as one whole living organism and these little bits that we call matter as sort to just little holes in it. DR. DAVID C. He often mentioned just one other SCHRUM aspect of this, that this planum, in a cubic centimeter of the planum, there's more, uh, energy matter than in the entire visible Page 2 of 62 universe. -
Pilot-Wave Theory, Bohmian Metaphysics, and the Foundations of Quantum Mechanics Lecture 8 Bohmian Metaphysics: the Implicate Order and Other Arcana
Pilot-wave theory, Bohmian metaphysics, and the foundations of quantum mechanics Lecture 8 Bohmian metaphysics: the implicate order and other arcana Mike Towler TCM Group, Cavendish Laboratory, University of Cambridge www.tcm.phy.cam.ac.uk/∼mdt26 and www.vallico.net/tti/tti.html [email protected] – Typeset by FoilTEX – 1 Acknowledgements The material in this lecture is largely derived from books and articles by David Bohm, Basil Hiley, Paavo Pylkk¨annen, F. David Peat, Marcello Guarini, Jack Sarfatti, Lee Nichol, Andrew Whitaker, and Constantine Pagonis. The text of an interview between Simeon Alev and Peat is extensively quoted. Other sources used and many other interesting papers are listed on the course web page: www.tcm.phy.cam.ac.uk/∼mdt26/pilot waves.html MDT – Typeset by FoilTEX – 2 More philosophical preliminaries Positivism: Observed phenomena are all that require discussion or scientific analysis; consideration of other questions, such as what the underlying mechanism may be, or what ‘real entities’ produce the phenomena, is dismissed as meaningless. Truth begins in sense experience, but does not end there. Positivism fails to prove that there are not abstract ideas, laws, and principles, beyond particular observable facts and relationships and necessary principles, or that we cannot know them. Nor does it prove that material and corporeal things constitute the whole order of existing beings, and that our knowledge is limited to them. Positivism ignores all humanly significant and interesting problems, citing its refusal to engage in reflection; it gives to a particular methodology an absolutist status and can do this only because it has partly forgotten, partly repressed its knowledge of the roots of this methodology in human concerns. -
Non-Locality in the Stochastic Interpretation of the Quantum Theory Annales De L’I
ANNALES DE L’I. H. P., SECTION A D. BOHM Non-locality in the stochastic interpretation of the quantum theory Annales de l’I. H. P., section A, tome 49, no 3 (1988), p. 287-296 <http://www.numdam.org/item?id=AIHPA_1988__49_3_287_0> © Gauthier-Villars, 1988, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A » implique l’accord avec les conditions générales d’utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Ann. Inst. Henri Poincare, Vol. 49, n° 3, 1988, 287 Physique theorique Non-Locality in the Stochastic Interpretation of the Quantum Theory D. BOHM Department of Physics, Birkbeck College (London University), Malet Street, London WC1E 7HX ABSTRACT. - This article reviews the stochastic interpretation of the quantum theory and shows in detail how it implies non-locality. RESUME . - Cet article presente une revue de 1’interpretation stochas- tique de la theorie quantique et montre en detail en quoi elle implique une non-localite. 1. INTRODUCTION It gives me great pleasure on the occasion of Jean-Pierre Vigier’s retire- ment to recall our long period of fruitful association and to say something about the stochastic interpretation of the quantum theory, in which we worked together in earlier days. Because of requirements of space, however, this article will be a condensation of my talk (*) which was in fact based on a much more extended article by Basil Hiley and me [1 ]. -
The Quantum Potential And''causal''trajectories For
REFERENCE IC/88/161 \ ^' I 6 AUG INTERNATIONAL CENTRE FOR / Co THEORETICAL PHYSICS THE QUANTUM POTENTIAL AND "CAUSAL" TRAJECTORIES FOR STATIONARY STATES AND FOR COHERENT STATES A.O. Barut and M. Bo2ic INTERNATIONAL ATOMIC ENERGY AGENCY UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION IC/88/161 I. Introduction International Atomic Energy Agency During the last decade Bohm's causal trajectories based on the and concept of the so called "quantum potential" /I/ have been evaluated United Nations Educational Scientific and Cultural Organization in a number of cases, the double slit /2,3/, tunnelling through the INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS barrier /4,5/, the Stern-Gerlach magnet /6/, neutron interferometer /8,9/, EPRB experiment /10/. In all these works the trajectories have been evaluated numerically for the time dependent wave packet of the Schrodinger equation. THE QUANTUM POTENTIAL AND "CAUSAL" TRAJECTORIES FOR STATIONARY STATES AND FOR COHERENT STATES * In the present paper we study explicitly the quantum potential and the associated trajectories for stationary states and for coherent states. We show how the quantum potential arises from the classical A.O. Barut ** and M. totii *** action. The classical action is a sum of two parts S ,= S^ + Sz> one International Centre for Theoretical Physics, Trieste, Italy. part Sj becomes the quantum action, the other part S2 is shifted to the quantum potential. We also show that the two definitions of causal ABSTRACT trajectories do not coincide for stationary states. We show for stationary states in a central potential that the quantum The content of our paper is as follows. Section II is devoted to action S is only a part of the classical action W and derive an expression for the "quantum potential" IL in terms of the other part. -
John Von Neumann's “Impossibility Proof” in a Historical Perspective’, Physis 32 (1995), Pp
CORE Metadata, citation and similar papers at core.ac.uk Provided by SAS-SPACE Published: Louis Caruana, ‘John von Neumann's “Impossibility Proof” in a Historical Perspective’, Physis 32 (1995), pp. 109-124. JOHN VON NEUMANN'S ‘IMPOSSIBILITY PROOF’ IN A HISTORICAL PERSPECTIVE ABSTRACT John von Neumann's proof that quantum mechanics is logically incompatible with hidden varibales has been the object of extensive study both by physicists and by historians. The latter have concentrated mainly on the way the proof was interpreted, accepted and rejected between 1932, when it was published, and 1966, when J.S. Bell published the first explicit identification of the mistake it involved. What is proposed in this paper is an investigation into the origins of the proof rather than the aftermath. In the first section, a brief overview of the his personal life and his proof is given to set the scene. There follows a discussion on the merits of using here the historical method employed elsewhere by Andrew Warwick. It will be argued that a study of the origins of von Neumann's proof shows how there is an interaction between the following factors: the broad issues within a specific culture, the learning process of the theoretical physicist concerned, and the conceptual techniques available. In our case, the ‘conceptual technology’ employed by von Neumann is identified as the method of axiomatisation. 1. INTRODUCTION A full biography of John von Neumann is not yet available. Moreover, it seems that there is a lack of extended historical work on the origin of his contributions to quantum mechanics. -
Photon Wave Mechanics: a De Broglie - Bohm Approach
PHOTON WAVE MECHANICS: A DE BROGLIE - BOHM APPROACH S. ESPOSITO Dipartimento di Scienze Fisiche, Universit`adi Napoli “Federico II” and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli Mostra d’Oltremare Pad. 20, I-80125 Napoli Italy e-mail: [email protected] Abstract. We compare the de Broglie - Bohm theory for non-relativistic, scalar matter particles with the Majorana-R¨omer theory of electrodynamics, pointing out the impressive common pecu- liarities and the role of the spin in both theories. A novel insight into photon wave mechanics is envisaged. 1. Introduction Modern Quantum Mechanics was born with the observation of Heisenberg [1] that in atomic (and subatomic) systems there are directly observable quantities, such as emission frequencies, intensities and so on, as well as non directly observable quantities such as, for example, the position coordinates of an electron in an atom at a given time instant. The later fruitful developments of the quantum formalism was then devoted to connect observable quantities between them without the use of a model, differently to what happened in the framework of old quantum mechanics where specific geometrical and mechanical models were investigated to deduce the values of the observable quantities from a substantially non observable underlying structure. We now know that quantum phenomena are completely described by a complex- valued state function ψ satisfying the Schr¨odinger equation. The probabilistic in- terpretation of it was first suggested by Born [2] and, in the light of Heisenberg uncertainty principle, is a pillar of quantum mechanics itself. All the known experiments show that the probabilistic interpretation of the wave function is indeed the correct one (see any textbook on quantum mechanics, for 2 S. -
David Bohm's Theory of the Implicate Order: Implications for Holistic Thought Processes*
ISSUES IN INTEGRATVE STUDIES No. 13, pp. 1-23 (1995) David Bohm's Theory of the Implicate Order: Implications for Holistic Thought Processes* by Irene J. Dabrowski, Ph.D. Division of Social Services, St. John's University, New York Abstract: David Bohm's theory of quantum physics, which focuses on the schism between matter and consciousness, is discussed in terms of positivist knowledge and the interdisciplinary holistic paradigm. This paper examines how scientific and educational holism, predicated on the relationship between knowledge and reality, fosters innovative approaches such as evolutionary learning, a pedagogical application of general systems theory. In pursuit of right- brain thought and a unified knowledge base, diverse modes of inquiry are presented in the context of Bohm's thesis of an implicate order. Given that holistic thought processes generate a reality-based knowledge, problem-solving styles are examined, which reveal the holistic orientation of proactive problem-solving. Interdisciplinary dialogue is identified as an essential way for moving toward holistic expressions and networks of thought. NEW VERSIONS of the sciences as well as other academic disciplines are being formulated in terms of a naturalistic mode of inquiry (Lincoln, 1989; Palm, 1979). The emergent post-positivist paradigm is directed toward a holistic conception of reality, replacing the Cartesian, mechanistic mode of conceptualization (Capra, 1982; Guba, 1981; Lincoln, 1989; Turner, 1990), In fact, characteristics of the "whole paradigm" are being identified in a variety of disciplines (Lincoln, 1989, p. 69). New dimensions include a refocusing from simple to complex realities, the movement from the mechanical to the holographic, and the emphasis from linear to mutual causality (Lincoln & Guba, 1985; Macy, 1991; Schwartz & Ogilvy, 1979).