DOCSLIB.ORG

Lecture Notes on Foundations of Quantum Mechanics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Lecture Notes on Foundations of Quantum Mechanics Lecture Notes on Foundations of Quantum Mechanics Roderich Tumulka∗ Winter semester 2019/20 These notes will be updated as the course proceeds. Date of this update: March 4, 2020 ∗Department of Mathematics, Eberhard Karls University, Auf der Morgenstelle 10, 72076 T¨ubingen, Germany. Email: [email protected] 1 1 Course Overview Learning goals of this course: To understand the rules of quantum mechanics; to understand several important views of how the quantum world works; to understand what is controversial about the orthodox interpretation and why; to be familiar with the surprising phenomena and paradoxes of quantum mechanics. Quantum mechanics is the field of physics concerned with (or the post-1900 theory of) the motion of electrons, photons, quarks, and other elementary particles, inside atoms or otherwise. It is distinct from classical mechanics, the pre-1900 theory of the motion of physical objects. Quantum mechanics forms the basis of modern physics and covers most of the physics under the conditions on Earth (i.e., not-too-high temperatures or speeds, not-too-strong gravitational fields). \Foundations of quantum mechanics" is the topic concerned with what exactly quantum mechanics means and how to explain the phenomena described by quantum mechanics. It is a controversial topic. Here are some voices critical of the traditional, orthodox view: \With very few exceptions (such as Einstein and Laue) [...] I was the only sane person left [in theoretical physics]." (E. Schr¨odingerin a 1959 letter) \I think I can safely say that nobody understands quantum mechanics." (R. Feynman, 1965) \I think that conventional formulations of quantum theory [...] are un- professionally vague and ambiguous." (J. Bell, 1986) In this course we will be concerned with what kinds of reasons people have for criticizing the orthodox understanding of quantum mechanics, what the alternatives are, and which kinds of arguments have been put forward for or against important views. We will also discuss the rules of quantum mechanics for making empirical predictions; they are uncontroversial. The aspects of quantum mechanics that we discuss also apply to other fields of quantum physics, in particular to quantum field theory. Topics of this course: • The Schr¨odingerequation • The Born rule • Self-adjoint matrices, axioms of the quantum formalism, collapse of the wave func- tion, decoherence • The double-slit experiment and variants thereof, interference and superposition 2 • Spin, the Stern-Gerlach experiment, the Pauli equation, representations of the rotation group • The Einstein-Podolsky-Rosen argument, entanglement, non-locality, and Bell's theorem • The paradox of Schr¨odinger'scat and the quantum measurement problem • Heisenberg's uncertainty relation • Interpretations of quantum mechanics (Copenhagen, Bohm's trajectories, Ev- erett's many worlds, spontaneous collapse theories, quantum logic, perhaps others) • Views of Bohr and Einstein • POVMs and density matrices • No-hidden-variables theorems • Identical particles and the non-trivial topology of their configuration space, bosons and fermions Mathematical tools that will be needed in this course: • Complex numbers • Vectors in n dimensions, inner product • Matrices, their eigenvalues and eigenvectors • Multivariable calculus • Probability; continuous random variables, the Gaussian (normal) distribution The course will involve advanced mathematics, as appropriate for a serious discussion of quantum mechanics, but will not focus on technical methods of problem-solving (such as methods for calculating the ground state energy of the hydrogen atom). Mathematical topics we will discuss in this course: • Differential operators (such as the Laplace operator) and their analogy to matrices • Eigenvalues and eigenvectors of differential (and other) operators • The Hilbert space of square-integrable functions, norm and inner product • Projection operators • Fourier transform of a function • Positive operators and positive-operator-valued measures (POVMs) 3 • Tensor product of vector spaces • Trace of a matrix or an operator, partial trace • Special ordinary and partial differential equations, particularly the Schr¨odinger equation • Exponential random variables and the Poisson process Philosophical questions that will come up in this course: • Is the world deterministic, or stochastic, or neither? • Can and should logic be revised in response to empirical findings? • Are there in principle limitations to what we can know about the world (its laws, its state)? • Which theories are meaningful as fundamental physical theories? In particular: • If a statement cannot be tested empirically, can it be meaningful? (Positivism versus realism) • Does a fundamental physical theory have to provide a coherent story of what happens? • Does that story have to contain elements representing matter in 3-dimensional space in order to be meaningful? Physicists usually take math classes but not philosophy classes. That doesn't mean, though, that one doesn't use philosophy in physics. It rather means that physicists learn the philosophy they need in physics classes. Philosophy classes are not among the prerequisites of this course, but we will sometimes make connections with philosophy. 4 2 The Schr¨odingerEquation One of the fundamental laws of quantum mechanics is the Schr¨odingerequation N @ X 2 i = − ~ r2 + V : (2.1) ~ @t 2m i i=1 i It governs the time evolution of the wave function = t = (t; x1; x2;:::; xN ). (It can be expected to be valid only in the non-relativistic regime, i.e., when the speeds of all particles are small compared to the speed of light. In the general case (the relativistic case) it needs to be replaced by other equations, such as the Klein{Gordon equation and the Dirac equation.) We focus first on spinless particles and discuss the phenomenon of spin later. I use boldface symbols such as x for 3-dimensional (3d) vectors. Eq. (2.1) applies to a system of N particles in R3. The word \particle" is traditionally used for electrons, photons, quarks, etc.. Opinions diverge whether electrons actually are particles in the literal sense (i.e., point-shaped objects, or little grains). A system is a subset of the set of all particles in the world. A configuration of N particles is a list of their positions; configuration space is thus, for our purposes, the Cartesian product of N copies of physical space, or R3N . The wave function of quantum mechanics, at any fixed time, is a function on configuration space, either complex-valued or spinor-valued (as we will explain later); for spinless particles, it is complex-valued, so 3N : Rt × Rq ! C: (2.2) The subscript indicates the variable:pt for time, q = (x1;:::; xN ) for the configuration. Note that i in (2.1) either denotes −1 or labels the particles, i = 1;:::;N; mi are positive constants, called the masses of the particles; ~ = h=2π is a constant of nature, h is called Planck's quantum of action or Planck's constant, h = 6:63 × 10−34 kg m2s−1; @ @ @ ri = ; ; (2.3) @xi @yi @zi 2 is the derivative operator with respect to the variable xi, ri the corresponding Laplace operator 2 2 2 2 @ @ @ ri = 2 + 2 + 2 : (2.4) @xi @yi @zi V is a given real-valued function on configuration space, called the potential energy or just potential. Fundamentally, the potential in non-relativistic physics is X eiej=4π"0 X Gmimj V (x1;:::; xN ) = − ; (2.5) jxi − xjj jxi − xjj 1≤i<j≤N 1≤i<j≤N where p jxj = x2 + y2 + z2 for x = (x; y; z) (2.6) 5 3 denotes the Euclidean norm in R , ei are constants called the electric charges of the particles (which can be positive, negative, or zero); the first term is called the Coulomb potential, the second term is called the Newtonian gravity potential, "0 and G are con- stants of nature called the electric constant and Newton's constant of gravity ("0 = −12 −1 −3 4 2 −11 −1 3 −2 8:85 · 10 kg m s A and G = 6:67 × 10 kg m s ), and mi are again the masses. However, when the Schr¨odingerequation is regarded as an effective equation rather than as a fundamental law of nature then the potential V may contain terms aris- ing from particles outside the system interacting with particles belonging to the system. That is why the Schr¨odingerequation is often considered for rather arbitrary functions V , also time-dependent ones. The operator N X 2 H = − ~ r2 + V (2.7) 2m i i=1 i is called the Hamiltonian operator, so the Schr¨odingerequation can be summarized in the form @ i = H : (2.8) ~ @t The Schr¨odingerequation is a partial differential equation (PDE). It determines the 3N time evolution of t in that for a given initial wave function 0 = (t = 0) : R ! C it uniquely fixes t for any t 2 R. The initial time could also be taken to be any t0 2 R instead of 0. So far I have not said anything about what this new physical object has to do with the particles. One such connection is Born's rule. If we measure the system's configuration at time t then the outcome is random with probability density 2 ρ(q) = t(q) : (2.9) This rule refers to the concept of probability density, which means the following. The probability that the random outcome X 2 R3N is any particular point x 2 R3N is zero. However, the probability that X lies in a set B ⊆ R3N is given by Z 3N P(X 2 B) = ρ(q) d q (2.10) B (a 3N-dimensional volume integral). Instead of d3N q, we will often just write dq.A density function ρ must be non-negative and normalized, Z ρ(x) ≥ 0 ; ρ(q) dq = 1 : (2.11) R3N A famous density function in 1 dimension is the Gaussian density 2 1 − (x−µ) ρ(x) = p e 2σ2 : (2.12) 2πσ 6 A random variable with Gaussian density is also called a normal (or normally dis- tributed) random variable.
Load more

Recommended publications
  • Modified Two-Slit Experiments and Complementarity
    Journal of Quantum Information Science, 2012, 2, 35-40 http://dx.doi.org/10.4236/jqis.2012.22007 Published Online June 2012 (http://www.SciRP.org/journal/jqis) Modified Two-Slit Experiments and Complementarity Tabish Qureshi Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi, India Email: [email protected] Received March 17, 2012; revised April 25, 2012; accepted May 5, 2012 ABSTRACT Some modified two-slit interference experiments claim to demonstrate a violation of Bohr’s complementarity principle. A typical such experiment is theoretically analyzed using wave-packet dynamics. The flaw in the analysis of such ex- periments is pointed out and it is demonstrated that they do not violate complementarity. In addition, it is quite gener- ally proved that if the state of a particle is such that the modulus square of the wave-function yields an interference pat- tern, then it necessarily loses which-path information. Keywords: Complementarity; Wave-Particle Duality; Two-Slit Experiment 1. Introduction pattern, one cannot get the which-way information. The authors have a clever scheme for establishing the exis- It is generally accepted that the wave and particle aspects tence of the interference pattern without actually observ- of quantum systems are mutually exclusive. Niels Bohr ing it. First, the exact locations of the dark fringes are elevated this concept, which is probably born out of the determined by observing the interference pattern. Then, uncertainty principle, to the status of a separate principle, thin wires are placed in the exact locations of the dark the principle of complementarity [1]. fringes. The argument is that if the interference pattern Since then, the complementarity principle has been exists, sliding in wires through the dark fringes will not demonstrated in various experiments, the most common affect the intensity of light on the two detectors.
    [Show full text]
  • H074 Front Rabbits
    Colin Bruce Joseph Henry Press Washington, DC Joseph Henry Press • 500 Fifth Street, N.W. • Washington, D.C. 20001 The Joseph Henry Press, an imprint of the National Academies Press, was created with the goal of making books on science, technology, and health more widely available to professionals and the public. Joseph Henry was one of the founders of the National Academy of Sciences and a leader in early American science. Library of Congress Cataloging-in-Publication Data Bruce, Colin. Schrödinger’s rabbits : the many worlds of quantum / Colin Bruce. p. cm. ISBN 0-309-09051-2 (case) 1. Quantum theory—Popular works. I. Title. QC174.12.B78 2004 530.12—dc22 2004021021 Any opinions, findings, conclusions, or recommendations expressed in this volume are those of the author and do not necessarily reflect the views of the National Academy of Sciences or its affiliated institutions. Cover design by Michele de la Menardiere. Copyright 2004 by Colin Bruce. All rights reserved. Hand-drawn illustrations by Laura Dawes from sketches by Colin Bruce. Printed in the United States of America Dedicated to Paul Dirac physicist extraordinary who believed we must seek visualizable processes and Jim Cushing philosopher of science who believed we must find local stories PREFACE oes the weirdness of quantum indicate that there is a deep problem with the theory? Some of the greatest minds in phys- Dics, including Einstein, have felt that it does. Others prefer to believe that any conceptual difficulties can be ignored or finessed away. I would put the choice differently. The flip side of a problem is an opportunity, and the problems with the old interpretations of quan- tum present us with valuable opportunities.
    [Show full text]
  • Afshar's Experiment Does Not Show a Violation of Complementarity
    Found Phys DOI 10.1007/s10701-007-9153-5 Afshar’s Experiment Does Not Show a Violation of Complementarity Ole Steuernagel Received: 1 February 2007 / Accepted: 15 June 2007 © Springer Science+Business Media, LLC 2007 Abstract A recent experiment performed by S. Afshar [first reported by M. Chown, New Sci. 183:30, 2004] is analyzed. It was claimed that this experiment could be interpreted as a demonstration of a violation of the principle of complementarity in quantum mechanics. Instead, it is shown here that it can be understood in terms of classical wave optics and the standard interpretation of quantum mechanics. Its per- formance is quantified and it is concluded that the experiment is suboptimal in the sense that it does not fully exhaust the limits imposed by quantum mechanics. 1 Introduction Bohr’s principle of complementarity of quantum mechanics characterizes the nature of a quantum system as being dualistic and mutually exclusive in its particle and wave aspects [1]. In the famous debates between Einstein and Bohr in the late 1920’s [1] complementarity was contested but finally the argument has settled in its favor [1, 2]. Some forty years later Feynman stated in his 1963 lectures quite categorically that “No one has ever found (or even thought of) a way around the uncertainty princi- ple”[3]. Some recent discussions centered on the question of whether the principle of com- plementarity is founded on the uncertainty principle [4–12]. Irrespective of whether one does [6–8, 10, 13, 14] or does not [4, 9, 12] subscribe to Feynman’s point of view that complementarity and uncertainty are essentially the same thing [13, 14], there is agreement that the principle of complementarity is at the core of quantum mechanics.
    [Show full text]
  • Paradox in Wave-Particle Duality *
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Paradox in Wave-Particle Duality * Shahriar S. Afshar, Eduardo Flores, Keith F. McDonald, and Ernst Knoesel Department of Physics & Astronomy, Rowan University, Glassboro, NJ 08028; [email protected] “All these fifty years of conscious brooding have brought me no nearer to the answer to the question, ‘What are light quanta?’ Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken.” (Albert Einstein, 1951) We report on the simultaneous determination of complementary wave and particle aspects of light in a double-slit type welcher-weg experiment beyond the limitations set by Bohr's Principle of Complementarity. Applying classical logic, we verify the presence of sharp interference in the single photon regime, while reliably maintaining the information about the particular pinhole through which each individual photon had passed. This experiment poses interesting questions on the validity of Complementarity in cases where measurements techniques that avoid Heisenberg’s uncertainty principle and quantum entanglement are employed. We further argue that the application of classical concepts of waves and particles as embodied in Complementarity leads to a logical inconsistency in the interpretation of this experiment. KEY WORDS : principle of complementarity; wave-particle duality; non-perturbative measurements; double-slit experiment; Afshar experiment. * A Preliminary version of this paper was presented by S.S.A. at a Seminar titled “Waving Copenhagen Good-bye: Were the Founders of Quantum Mechanics Wrong?,” Department of Physics, Harvard University, Cambridge, MA 02138, 23 March, 2004. 1 1.
    [Show full text]
  • The Wave-Particle Duality—Does the Concept of Particle Make Sense in Quantum Mechanics? Should We Ask the Second Quantization?
    Journal of Quantum Information Science, 2019, 9, 155-170 https://www.scirp.org/journal/jqis ISSN Online: 2162-576X ISSN Print: 2162-5751 The Wave-Particle Duality—Does the Concept of Particle Make Sense in Quantum Mechanics? Should We Ask the Second Quantization? Sofia D. Wechsler Kiryat Motzkin, Israel How to cite this paper: Wechsler, S.D. Abstract (2019) The Wave-Particle Duality—Does the Concept of Particle Make Sense in The quantum object is in general considered as displaying both wave and Quantum Mechanics? Should We Ask the particle nature. By particle is understood an item localized in a very small vo- Second Quantization?. Journal of Quantum lume of the space, and which cannot be simultaneously in two disjoint re- Information Science, 9, 155-170. https://doi.org/10.4236/jqis.2019.93008 gions of the space. By wave, to the contrary, is understood a distributed item, occupying in some cases two or more disjoint regions of the space. The Received: June 12, 2019 quantum formalism did not explain until today the so-called “collapse” of the Accepted: September 27, 2019 Published: September 30, 2019 wave-function, i.e. the shrinking of the wave-function to one small region of the space, when a macroscopic object is encountered. This seems to happen Copyright © 2019 by author(s) and in “which-way” experiments. A very appealing explanation for this behavior Scientific Research Publishing Inc. is the idea of a particle, localized in some limited part of the wave-function. This work is licensed under the Creative Commons Attribution International The present article challenges the concept of particle.
    [Show full text]
  • Quantum Theory and Paradoxes
    International Journal of Scientific & Engineering Research, Volume 5, Issue 3, March-2014 1269 ISSN 2229-5518 Quantum theory and Paradoxes K. Salehi, Suzan M. H. Shamdeen, Esraa A. M. Saed [email protected] Moscow State University, Max-Plank Institute for Physics, University of Zakho Abstract: We want to review the Paradoxes in quantum mechanics and show that despite the large number of interpretations and ideas in Quantum Mechanics, Quantum Three variant Loic (QTL) solves the quantum well-known paradoxes. Index Terms (Keywords) — Paradox, The EPR paradox, The Schrödinger's Cat paradox, The Wheeler's delayed choice paradox, Wigner's friend paradox, The Afshar paradox, Popper's paradox, Quantum Three variant Loic (QTL). 1. Introduction paradox is a proposition that can not be described by mathematical logic because it is “true and false”. A physical paradox A is an apparent contradiction in physical descriptions of the universe. While many physical paradoxes have accepted resolutions, others defy resolution and may indicate flaws in theory. In physics as in all of science, contradictions and paradoxes are generally assumed to be artifacts of error and incompleteness because reality is assumed to be completely consistent, although this is itself a philosophical assumption. When, as in fields such as quantum physics and relativity theory, existing assumptions about reality have been shown to break down, this has usually been dealt with by changing our understanding of reality to a new one which remains self-consistent in the presence of the new evidence. A significant set of physical paradoxes are associated with the privileged position of the observer in quantum mechanics.
    [Show full text]
  • Towards Simultaneous Observation of Path and Interference of a Single Photon in a Modified Mach–Zehnder Interferometer
    622 Vol. 8, No. 4 / April 2020 / Photonics Research Research Article Towards simultaneous observation of path and interference of a single photon in a modified Mach–Zehnder interferometer 1,† 1,† 1 1,4 2,3 FENGHUA QI, ZHIYUAN WANG, WEIWANG XU, XUE-WEN CHEN, AND ZHI-YUAN LI 1School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China 2College of Physics and Optoelectronics, South China University of Technology, Guangzhou 510641, China 3e-mail: [email protected] 4e-mail: [email protected] Received 27 December 2019; revised 10 February 2020; accepted 11 February 2020; posted 13 February 2020 (Doc. ID 386774); published 1 April 2020 Classical wisdom of wave–particle duality regulates that a quantum object shows either the particle or wave nature but never both. Consequently, it would be impossible to observe simultaneously the complete wave and particle nature of the quantum object. Mathematically the principle requests that the interference visibility V and which- path distinguishability D satisfy an orthodox limit of V 2 D2 ≤ 1. The present work reports a new wave– particle duality test experiment using single photons in a modified Mach–Zehnder interferometer to demonstrate the possibility of breaking the limit. The key element of the interferometer is a weakly scattering total internal reflection prism surface, which exhibits a pronounced single-photon interference with a visibility of up to 0.97 and simultaneously provides a path distinguishability of 0.83. Apparently, the result of V 2 D2 ≈ 1.63 exceeds the orthodox limit set by the classical principle of wave–particle duality for single photons.
    [Show full text]
  • Wave Particle Duality and the Afshar Experiment
    January, 2011 PROGRESS IN PHYSICS Volume 1 Wave Particle Duality and the Afshar Experiment Aurelien´ Drezet Institut Neel, 25 rue des Martyrs 38042, Grenoble, France. E-mail: [email protected] We analyze the experiment realized in 2003-2004 by S. Afshar et al. [1] in order to refute the principle of complementarity. We discuss the general meaning of this principle and show that contrarily to the claim of the authors Bohr’s complementarity is not in danger in this experiment. 1 Introduction necessarily different photons for their recording. It is in that sense that each experiment excludes and completes recipro- In an interesting series of articles published few years ago cally the other. In the case considered before the photon is Afshar and coworkers [1,2] reported an optical experiment in absorbed during the first detection (this clearly precludes any which they claimed to refute the well known N. Bohr prin- other detection). However even a non-destructive solution for ciple of complementarity [3, 4]. Obviously this result, if jus- detection implying entanglement with other quantum systems tified, would constitute a serious attack against the orthodox has a radical effect of the same nature: the complementarity interpretation of quantum mechanics (known as the Copen- principle is still valid. For example, during their debate Bohr hagen interpretation). This work stirred much debate in dif- and Einstein [3] discussed an ideal which-way experiment in ferent journals (see for examples references [5–12]). which the recoil of the slits is correlated to the motion of the We think however that there are still some important misun- photon.
    [Show full text]
  • Why Kastner Analysis Does Not Apply to a Modified Afshar Experiment
    Why Kastner analysis does not apply to a modified Afshar experiment Eduardo Flores and Ernst Knoesel Department of Physics & Astronomy, Rowan University, Glassboro, NJ 08028 In an analysis of the Afshar experiment R.E. Kastner points out that the selection system used in this experiment randomly separates the photons that go to the detectors, and therefore no which-way information is obtained. In this paper we present a modified but equivalent version of the Afshar experiment that does not contain a selection device. The double-slit is replaced by two separate coherent laser beams that overlap under a small angle. At the intersection of the beams an interference pattern can be inferred in a non-perturbative manner, which confirms the existence of a superposition state. In the far field the beams separate without the use of a lens system. Momentum conservation warranties that which-way information is preserved. We also propose an alternative sequence of Stern-Gerlach devices that represents a close analogue to the Afshar experimental set up. Keywords: complementarity; wave-particle duality; double-slit experiment; Afshar experiment 1 1. INTRODUCTION The Afshar experiment is a version of a double slit experiment first suggested and carried out by Afshar.1 Recently Afshar et al.2 reported on a more detailed experiment that claims to have simultaneously determined complementary wave and particle aspects of light beyond the limitations set by Bohr's Principle of Complementarity. Researchers aware of the important implications of Afshar’s claims have analyzed the experiment and have either come forth or against it.3,4 A particularly important paper against Afshar’s claims was written by R.E.
    [Show full text]
  • Reply to Comments of Steuernagel on the Afshar's Experiment
    Reply to Comments of Steuernagel on the Afshar’s Experiment Eduardo V. Flores Dept. of Physics and Astronomy, Rowan University, Glassboro, NJ Abstract We respond to criticism of our paper “Paradox in Wave-Particle Duality for Non- Perturbative Measurements”. We disagree with Steuernagel's derivation of the visibility of the Afshar experiment. To calculate the fringe visibility, Steuernagel utilizes two different experimental situations, i.e. the wire grid in the pattern minima and in the pattern maxima. In our assessment, this procedure cannot lead to the correct result for the complementarity properties of a wave-particle in one particular experimental set-up. 1 Introduction We reply to the recent comments on our paper [1] by Steuernagel [2] and thank them for helping us explain our experiment more clearly. We briefly summarize what we consider their most relevant criticism and our response to it. Steuernagel questions our analysis of the experimental results of the Afshar experiment and states that their correct analysis does not pose a paradox to Bohr’s Principle of Complementarity. We want to show errors in their analysis and point out that the paradox we propose [1] remains unsolved. In summary, Steuernagel separates photons into two mutually exclusive subensembles to which the complementarity principle must therefore be applied separately. One ensemble is made of those photons that cross a wire grid and the other one is made of those that do not cross the wire grid. We argue that their claim that the two ensembles are mutually exclusive for the purpose of determination of the complementarity principle is unsupported.
    [Show full text]
  • Many-Worlds Interpretation of Quantum Mechanics: a Paradoxical Picture
    [math-ph] Many-Worlds Interpretation of Quantum Mechanics: A Paradoxical Picture Amir Abbass Varshovi∗ Faculty of Mathematics and Statistics, Department of Applied Mathematics and Computer Science, University of Isfahan, Isfahan, IRAN. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, IRAN. Abstract: The many-worlds interpretation (MWI) of quantum mechanics is studied from an unprecedented ontological perspective based on the reality of (semi-) deterministic parallel worlds in the interpretation. It is demonstrated that with thanks to the uncertainty principle there would be no consistent way to specify the correct ontology of the Universe, hence the MWI is subject to an inherent contradiction which claims that the world where we live in is unreal. Keywords: Many-Worlds Interpretation of Quantum Mechanics, (Semi-) Deterministic World, Fiducial World, Inclusive Consciousness. I. INTRODUCTION About a century after its inception, quantum mechanics is still in a perplexity to provide a precise comprehensive interpretation of its peculiar features. Even though, the orthodox interpretation of quantum theory, the so called Copenhagen interpretation, soon gained a worldwide acceptance for describing the quantum behaviors of the objective world around us, this quandary is still felt in the basics of quantum mechanics [1]. The most profound consideration to this dilemma dates back to 1930s when the Einstein-Podolsky-Rosen criticism of the Copenhagen interpretation of the theory, the EPR paradox [2], revealed an unexpected aspect of quantum physics which violates the main principle arXiv:2011.13928v1 [quant-ph] 27 Nov 2020 of special relativity allowing information to be transmitted faster than light. This phenomenon that was the most serious objection to the interpretation until then, was referred to as the entanglement effect by Schrodinger [3].
    [Show full text]
  • Particle Duality Paradox
    A model that solves to the wave-particle duality paradox Eduardo V. Flores1 Abstract Bohmian mechanics solves the wave-particle duality paradox by introducing the concept of a physical particle that is always point-like and a separate wavefunction with some sort of physical reality. However, this model has not been satisfactorily extended to relativistic levels. Here we introduce a model of permanent point-like particles that works at any energy level. Our model seems to have the benefits of Bohmian mechanics without its shortcomings. We propose an experiment for which the standard interpretation of quantum mechanics and our model make different predictions. Keywords: wave-particle duality paradox, interpretations of quantum mechanics, Bohmian mechanics 1. Introduction Quantum physics numerical predictions are outstanding at all the available energy levels. However, the same is not true about the interpretation of quantum physics [1-5]. Standard quantum theory contains a paradox known as the wave-particle duality paradox, that is, how the same object could sometimes be extended so as to produce wave interference and instantaneously it could become point-like such as a detected particle on a screen. This paradox might be symptomatic of a theory with intrinsic problems or a theory with an incorrect interpretation of its results. The mathematical success of quantum mechanics points to a problem with the interpretation of the theory. A model known as Bohmian mechanics originally proposed by Louis De Broglie and then expanded by David Bohm has no wave-particle duality paradox while the numerical results are similar to the standard quantum theory at least at the non-relativistic level.
    [Show full text]