On the Quantum Measurement Problem

In this paper, I attempt a personal account of my understanding of the measurement problem in quantum mechanics, which has been largely in the tradition of the Copenhagen interpretation. I assume that (i) the quantum state is a representation of knowledge of a (real or hypothetical) observer relative to her experimental capabilities; (ii) measurements have definite outcomes in the sense that only one outcome occurs; (iii) quantum theory is universal and the irreversibility of the measurement process is only “for all practical purposes”. These assumptions are analyzed within quantum theory and their consistency is tested in Deutsch’s version of the Wigner’s friend gedanken experiment, where the friend reveals to Wigner whether she observes a definite outcome without revealing which outcome she observes. The view that holds the coexistence of the “facts of the world” common both for Wigner and his friend runs into the problem of the hidden variable program. The solution lies in understanding that “facts” can only exist relative to the observer.

[1]  이진형,et al.  Quantum Theory : Concepts and Methods by Asher Peres (Kluwer Academic Publishers, 1995) , 2010 .

[2]  Niels Bohr,et al.  Discussion with Einstein on Epistemological Problems in Atomic Physics , 1996 .

[3]  A. Peres.  Recurrence Phenomena in Quantum Dynamics , 1982 .

[4]  Markus P. Mueller,et al.  A derivation of quantum theory from physical requirements , 2010, 1004.1483.

[5]  T. Maudlin.  Three measurement problems , 1995 .

[6]  Borivoje Dakic,et al.  The classical limit of a physical theory and the dimensionality of space , 2013, 1307.3984.

[7]  I. Pitowsky,et al.  Two Dogmas About Quantum Mechanics , 2007, 0712.4258.

[8]  L. Hardy.  Quantum Theory From Five Reasonable Axioms , 2001, quant-ph/0101012.

[9]  Asher Peres,et al.  Quantum Theory: Concepts and Methods , 1994 .

[10]  Lluis Masanes,et al.  Three-dimensionality of space and the quantum bit: an information-theoretic approach , 2012, 1206.0630.

[11]  O. Freire,et al.  The Origin of the Everettian Heresy , 2009 .

[12]  W. Pauli.  Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg , 2005 .

[13]  G. Yocky,et al.  Decoherence , 2018, Principles of Quantum Computation and Information.

[14]  Weber,et al.  Unified dynamics for microscopic and macroscopic systems. , 1986, Physical review. D, Particles and fields.

[15]  A. Peres.  When Is a Quantum Measurement? a , 1986 .

[16]  J. Bell,et al.  Speakable and Unspeakable in Quatum Mechanics , 1988 .

[17]  Shimon Malin,et al.  What Are Quantum States? , 2006, Quantum Inf. Process..

[18]  P. Heelan.  Heisenberg and radical theoretic change , 1975 .

[19]  G. Choppin.  Symmetries and reflections (Wigner, Eugene P.) , 1968 .

[20]  C. Rovelli,et al.  Relational Quantum Mechanics , 2006 .

[21]  W. Zurek.  Decoherence, einselection, and the quantum origins of the classical , 2001, quant-ph/0105127.

[22]  Roger Colbeck,et al.  No extension of quantum theory can have improved predictive power , 2010, Nature communications.

[23]  R. Penrose.  On Gravity's role in Quantum State Reduction , 1996 .

[24]  David Deutsch,et al.  Quantum theory as a universal physical theory , 1985 .

[25]  Caslav Brukner,et al.  Classical world arising out of quantum physics under the restriction of coarse-grained measurements. , 2007, Physical review letters.

[26]  O. Freire,et al.  The origin of the Everettian heresy $ , 2009 .

[27]  Simon Saunders,et al.  What is the Problem of Measurement , 1994 .

[28]  Ph Jacquod,et al.  Decay of the Loschmidt echo for quantum states with sub-planck-scale structures. , 2002, Physical review letters.

[29]  Ruediger Schack,et al.  Quantum-Bayesian Coherence , 2009, 1301.3274.

[30]  Č. Brukner,et al.  Quantum Theory and Beyond: Is Entanglement Special? , 2009, 0911.0695.

[31]  N. David Mermin,et al.  Boojums All The Way Through , 1990 .

[32]  N. Bohr,et al.  On the notions of causality and complementarity. , 1950, Science.

[33]  J. Bell,et al.  Speakable and Unspeakable in Quantum Mechanics: Preface to the first edition , 2004 .

[34]  Mandel,et al.  Observation of quantum interference effects in the frequency domain. , 1992, Physical review letters.

[35]  G. D’Ariano,et al.  Informational derivation of quantum theory , 2010, 1011.6451.

[36]  Diósi,et al.  Models for universal reduction of macroscopic quantum fluctuations. , 1989, Physical review. A, General physics.

[37]  Caslav Brukner,et al.  Information and Fundamental Elements of the Structure of Quantum Theory , 2002, quant-ph/0212084.

[38]  Itamar Pitowsky.  Quantum Mechanics as a Theory of Probability , 2006 .

[39]  A. Zeilinger,et al.  Speakable and Unspeakable in Quantum Mechanics , 1989 .

[40]  H. Stöckmann,et al.  Quantum Chaos: An Introduction , 1999 .

[41]  Robert W. Spekkens,et al.  Einstein, Incompleteness, and the Epistemic View of Quantum States , 2007, 0706.2661.

[42]  Alexia Auffèves,et al.  Contexts, Systems and Modalities: A New Ontology for Quantum Mechanics , 2014, 1409.2120.

[43]  M. Schlosshauer,et al.  Niels Bohr as Philosopher of Experiment: Does Decoherence Theory Challenge Bohr's Doctrine of Classical Concepts? , 2015, 1502.06547.

[44]  Asher Peres,et al.  Stability of quantum motion in chaotic and regular systems , 1984 .

[45]  Aage Petersen,et al.  The Philosophy of Niels Bohr , 1963 .

[46]  E. Wigner.  Remarks on the Mind-Body Question , 1995 .

[47]  Ruediger Schack,et al.  QBism and the Greeks: why a quantum state does not represent an element of physical reality , 2014, 1412.4211.

[48]  Armen E. Allahverdyan,et al.  Understanding quantum measurement from the solution of dynamical models , 2011, 1107.2138.

[49]  Niels Bohr,et al.  ON THE NOTIONS OF CAUSALITY AND COMPLEMENTARITY1 , 1948 .

[50]  Caslav Brukner,et al.  Conditions for quantum violation of macroscopic realism. , 2007, Physical review letters.

[51]  Marek Zukowski,et al.  Quantum non-locality—it ainʼt necessarily so... , 2014, 1501.04618.

[52]  Hans Halvorson,et al.  Deep beauty : understanding the quantum world through mathematical innovation , 2011 .