The Cellular Automaton Interpretation of Quantum Mechanics

When investigating theories at the tiniest conceivable scales in nature, almost all researchers today revert to the quantum language, accepting the verdict from the Copenhagen doctrine that the only way to describe what is going on will always involve states in Hilbert space, controlled by operator equations. Returning to classical, that is, non quantum mechanical, descriptions will be forever impossible, unless one accepts some extremely contrived theoretical constructions that may or may not reproduce the quantum mechanical phenomena observed in experiments. Dissatisfied, this author investigated how one can look at things differently. This book is an overview of older material, but also contains many new observations and calculations. Quantum mechanics is looked upon as a tool, not as a theory. Examples are displayed of models that are classical in essence, but can be analysed by the use of quantum techniques, and we argue that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analyse a system that could be classical at its core. We explain how such thoughts can conceivably be reconciled with Bell's theorem, and how the usual objections voiced against the notion of `superdeterminism' can be overcome, at least in principle. Our proposal would eradicate the collapse problem and the measurement problem. Even the existence of an "arrow of time" can perhaps be explained in a more elegant way than usual. Discussions added in v3: the role of the gravitational force, a mathematical physics definition of free will, and an unconventional view on the arrow of time, amongst others.

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

[2]  P. Libby The Scientific American , 1881, Nature.

[3]  G. Hooft Relating the quantum mechanics of discrete systems to standard canonical quantum mechanics , 2012, 1204.4926.

[4]  D. Bohm A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II , 1952 .

[5]  Daniel B. Miller,et al.  Two-state, reversible, universal cellular automata in three dimensions , 2005, CF '05.

[6]  S. Coleman There are no Goldstone bosons in two dimensions , 1973 .

[7]  L. Susskind,et al.  Continuum strings from discrete field theories , 1988 .

[8]  G. Hooft On the Quantum Structure of a Black Hole , 1985 .

[9]  J. Smith,et al.  Field theory in particle physics , 1986 .

[10]  G. ’t Hooft QUANTIZATION OF POINT PARTICLES IN 2+1 DIMENSIONAL GRAVITY AND SPACE-TIME DISCRETENESS , 1996 .

[11]  田中 正,et al.  SUPERSTRING THEORY , 1989, The Lancet.

[12]  Duality Between a Deterministic Cellular Automaton and a Bosonic Quantum Field Theory in 1+1 Dimensions , 2012, 1205.4107.

[13]  Bryce S. DeWitt,et al.  The Many-Universes Interpretation of Quantum Mechanics , 2015 .

[14]  M. Seevinck Parts and Wholes. An Inquiry into Quantum and Classical Correlations , 2008, 0811.1027.

[15]  J. Polchinski Superstring theory and beyond , 1998 .

[16]  G. Hooft,et al.  Three-dimensional Einstein gravity: Dynamics of flat space , 1984 .

[17]  E. Schrödinger Die gegenwärtige Situation in der Quantenmechanik , 1935, Naturwissenschaften.

[18]  H. Zeh On the interpretation of measurement in quantum theory , 1970 .

[19]  G. Hooft Classical N-particle cosmology in 2+1 dimensions , 1993 .

[20]  P. Mannheim Making the Case for Conformal Gravity , 2011, 1101.2186.

[21]  R M Sweet Introduction to crystallography. , 1985, Methods in enzymology.

[22]  THE BLACK HOLE HORIZON AS A DYNAMICAL SYSTEM , 2006, gr-qc/0606026.

[23]  Simon Kochen,et al.  The Strong Free Will Theorem , 2008, 0807.3286.

[24]  J. G. Russo Discrete strings and deterministic cellular strings , 1993 .

[25]  Classical cellular automata and quantum field theory , 2010 .

[26]  S. Carlip Exact quantum scattering in 2 + 1 dimensional gravity , 1989 .

[27]  A Generalized Shannon Sampling Theorem, Fields at the Planck Scale as Bandlimited Signals , 1999, hep-th/9905114.

[28]  G. Hooft Cosmology in 2+1 dimensions , 1993 .

[29]  M. Schlosshauer Decoherence, the measurement problem, and interpretations of quantum mechanics , 2003, quant-ph/0312059.

[30]  P. Pearle Reduction of the state vector by a nonlinear Schrödinger equation , 1976 .

[31]  Gerard 't Hooft,et al.  Quantum field theoretic behavior of a deterministic cellular automaton , 1992 .

[32]  J. Wheeler Information, physics, quantum: the search for links , 1999 .

[33]  R. Glauber Coherent and incoherent states of the radiation field , 1963 .

[34]  H. Everett "Relative State" Formulation of Quantum Mechanics , 1957 .

[35]  Abraham Paiz,et al.  Niels Bohr’s Times, in Physics, Philosophy, and Polity , 1992 .

[36]  G. Hooft Quantum gravity as a dissipative deterministic system , 1999, gr-qc/9903084.

[37]  Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer in the transition from quantum to classical , 2007, quant-ph/0703160.

[38]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[39]  L. Susskind The world as a hologram , 1994, hep-th/9409089.

[40]  R. Walde,et al.  Introduction to Lie groups and Lie algebras , 1973 .

[41]  Sabine Hossenfelder,et al.  Testing superdeterministic conspiracy , 2014, 1401.0286.

[42]  S. Hawking Particle creation by black holes , 1975 .

[43]  G. Hooft A Class of Elementary Particle Models Without Any Adjustable Real Parameters , 2011, 1104.4543.

[44]  J. Polchinski An introduction to the bosonic string , 1998 .

[45]  Nina Byers E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws , 1998 .

[46]  Gerard 't Hooft,et al.  Entangled quantum states in a local deterministic theory , 2009, 0908.3408.

[47]  J. Bell On the impossible pilot wave , 1982 .

[48]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[49]  W. Zurek The Environment, Decoherence and the Transition from Quantum to Classical , 1991 .

[50]  THE SCATTERING MATRIX APPROACH FOR THE QUANTUM BLACK HOLE: AN OVERVIEW , 1996, gr-qc/9607022.

[51]  B. Kaufman Crystal Statistics: II. Partition Function Evaluated by Spinor Analysis. III. Short-Range Order in a Binary Ising Lattice. , 1949 .

[52]  F. Wilczek Quantum Field Theory , 1998, hep-th/9803075.

[53]  L. Ryder,et al.  Quantum Field Theory , 2001, Foundations of Modern Physics.

[54]  G. Hooft Quantization of Discrete Deterministic Theories by Hilbert Space Extension , 1990 .

[55]  P. Grangier,et al.  Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment : A New Violation of Bell's Inequalities , 1982 .

[56]  Gerard 't Hooft,et al.  Equivalence relations between deterministic and quantum mechanical systems , 1988 .

[57]  Rupert Ursin,et al.  Violation of local realism with freedom of choice , 2008, Proceedings of the National Academy of Sciences.

[58]  Max Jammer,et al.  The conceptual development of quantum mechanics , 1966 .

[59]  G. Hooft The Conformal Constraint in Canonical Quantum Gravity , 2010, 1011.0061.

[60]  G. Hooft Quantization of point particles in (2+1)-dimensional gravity and spacetime discreteness , 1996, gr-qc/9601014.

[61]  K. Symanzik,et al.  Small distance behaviour in field theory and power counting , 1970 .

[62]  J. Goldstone,et al.  Field theories with « Superconductor » solutions , 1961 .

[63]  David Wallace Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation , 2003 .

[64]  A. Gleason Measures on the Closed Subspaces of a Hilbert Space , 1957 .

[65]  Jason Gallicchio,et al.  Testing Bell's inequality with cosmic photons: closing the setting-independence loophole. , 2013, Physical review letters.

[66]  G. Hooft The conceptual basis of Quantum Field Theory , 2002 .

[67]  Hamiltonian formalism for integer-valued variables and integer time steps and a possible application in quantum physics , 2013, 1312.1229.

[68]  E. Wigner,et al.  Über das Paulische Äquivalenzverbot , 1928 .

[69]  S. Adler Quantum Theory as an Emergent Phenomenon: Foundations and Phenomenology , 2012 .

[70]  C. Torrence,et al.  A Practical Guide to Wavelet Analysis. , 1998 .

[71]  Louis Vervoort,et al.  Bell’s Theorem: Two Neglected Solutions , 2012, Foundations of Physics.

[72]  Kris McDaniel,et al.  Parts and Wholes , 2010 .

[73]  J. Bell On the Einstein-Podolsky-Rosen paradox , 1964 .