Computer Simulation of Quantum Mechanics - Porthouse The name of this file is BOOKS.TXT (C) 1996 David T.C. Porthouse. Copies of this text file may be made for bona fide non-profit purposes of education or research. These copies may be made either Internet to client computer, or subsequently from one client computer to another. All other rights are reserved. David Porthouse asserts the moral right to be identified as the author of this work, and of any quotation from it. This work is not produced with the intention of making profits for the author, but if anyone else ("the user") uses it for a profitable purpose, then 50% royalties are due on gross profit, and the expense of providing an Account of Profits under English Law will be borne by the user as an expense against gross profits. The user will bear the expenses, including travel and subsistence, of any solicitor, barrister or chartered accountant employed by the author and engaged in the pursuit of the author's rights. ISBN numbers have been added to this list where known. That usually means that the reviewer has a copy of the book in-house. John Gribbin, Schroedinger's Kittens / and the search for reality, Weidenfeld & Nicolson, London 1995, ISBN 0-297-81519-9. This book is right up to date, with material on Charles Bennett and John Cramer. Dr. Gribbin has tended to opt for Cramer while hedging his bets. There is some justification for this. We need a nonlocal system of communications so that "Schroedinger's Kittens" are able to exchange messages, and Cramer's proposal was the best on offer at the time the book was written. Since then, this reviewer has proposed a natural Vernam cipher on CompuServe. That gives us two information-flow theories. Cramer's theory proposes that information flows by a zigzag path, sometimes backwards in time. The Vernam cipher takes a direct line, but the question of the relativity of simultaneity has to be watched. One view in this book is wrong, namely that we can pick and choose our interpretation of quantum mechanics to suit the problem. There can be no peaceful coexistence between this reviewer and the Copenhagen Interpretation. Either one day we will have a computer simulation of wave-particle duality or we won't. Between this reviewer and Niels Bohr, someone has to be wrong. One would like to know the name of the person who argued that George Zweig was a 'charlatan' (page 193). No one is reticent about naming those English astronomers who failed to discover Neptune (Airy and Challoner), and physics is about putting one's head on the block. Zweig took a big risk, and anyone who slighted him ought to take the same risk with their reputation. David Bohm and Basil Hiley, The Undivided Universe / An ontological interpretation of quantum theory, Routledge, London 1993, ISBN 0-415-06588-7 (hardback) and ISBN 0-415-12185-X (paperback). This is not a book for the beginner. It assumes that the reader is familiar with the subject matter at least to the extent of knowing topics like Aspect's experiment and Schroedinger's cat. Something like Jim Baggott's book (next entry) would make a suitable introduction. This reviewer is too close to the subject matter to give a fair review. This book is essential reading for anyone directly involved. There are computer programs featured in this book. Could we please see them on the Internet? No publication = no science. Given the caveat concerning this reviewer, it may be commented that Bohm and Hiley do not see the need for any collapse of the wave function. If the reviewer can get his own ideas working as a computer simulation, then there will probably be experiments we can do which will show that someone's theory is wrong. These experiments will have the character of Marlan Scully's "quantum eraser". This book has a Library of Congress catalogue number, a matter which can only be regarded with cynicism given the facts of Bohm's life. Jim Baggott, The Meaning of Quantum Theory, Oxford University Press, Oxford 1992, ISBN 0-19-855575-X. Up to date for 1992, comprehensive, and a good complement to textbooks which treat quantum mechanics in the usual way, which emphasises the mathematics but not the interpretation. The conclusion is false: either one day we will have a working computer simulation of wave-particle duality (victory for the realists = David Bohm, Basil Hiley, this reviewer) or we won't (victory for the positivists = Niels Bohr, Eugene Wigner, John Wheeler). This is one feature of quantum mechanics that is strictly governed by classical logic, of the kind which so far has been followed by the Nobel Awards Committee. The realist school subdivides into a determinist school (David Bohm, Basil Hiley) and a randomist school of which this reviewer is the only declared member, but this subdivision is not of the same fundamental significance since David Bohm has thought about randomism from time to time. Euan Squires, Conscious Mind in the Physical World, Adam Hilger, Bristol 1990, ISBN 0-7503-0045-0 (hardback) and 0-7503-0046-9 (paperback). A considerable part of this book is concerned with the interpretation of quantum mechanics. The parts that are not make interesting reading in order to "round out" one's knowledge. The material on Goedel's theorem is interesting. It means frustration for mathematical empire-builders. The alternative is to regard mathematics as a experimental or playtime activity, as this reviewer does when he proposes variable algorithm in WPD3.BAS. This reviewer disagrees with section 11.3, where the prospects for a modified Schroedinger equation are discussed. Modifying the Schroedinger equation leads to false predictions at the ensemble level (this problem ain't easy). One alternative is to look for a new degree of freedom in the Schroedinger equation. This reviewer proposes a tachyonic DOF. Ronald Hurst proposes a lattice-based DOF, where he has to deliver the solution of the Schroedinger equation on a space-time lattice, but off the lattice he can do as he wishes. Abner Shimony, Conceptual Foundations of Quantum Mechanics, Chapter 13 in "The New Physics", edited and introduced by Paul C.W. Davies, Cambridge University Press, Cambridge 1989, ISBN 0-521-30420-2 (hardback) and 0-521-43831-4 (paperback). Excellent review article. A lot in a short space. Looking at the rest of the book, there are plenty of things which this reviewer finds almost impossible to understand. Let's see some computer simulations, downloadable via the Internet, to make things clearer! Alastair Rae, Quantum Physics: Illusion or Reality?, Cambridge University Press, Cambridge 1986, ISBN 0-521-26023-X (hardback) and 0-521-27802-3 (paperback). Short value-for-money introductory text. Rae has recently written a standard introduction to quantum mechanics with a last chapter on the subject of interpretation, which is timely when we should shortly be able to use the technology of quantum crytography developed by Charles Bennett to send credit card information in a manner which BOTH uses the Vernam cipher AND detects eavesdroppers. Paul C.W. Davies & J.R. Brown, editors, The Ghost in the Atom / A discussion of the mysteries of quantum physics, Cambridge University Press, Cambridge 1986, ISBN 0-521-30790-2 (hardback) and 0-521-31316-3 (paperback). Transcripts of interviews for BBC Radio, broadcast in 1984. The interesting view is John Taylor's view, which can be summed up as saying that the problem doesn't exist. If you have a computer simulation of the Schroedinger equation, it's a waste of time talking about how to add a random number generator however much Alexandre Chorin might have inspired you and however much you might see randomness in quantum mechanical experiments. J.C. Polkinghorne, The Quantum World, Longman, London 1985, ISBN 0-14-022653-2. Short value-for-money introductory text, still on sale. The point of the title is that according to Niels Bohr, there is no "Quantum World"; all we have is a collection of mathematical recipes for making certain types of prediction. People like Einstein and Bohm said that the Quantum World does exist, and this reviewer wants to bring it within the scope of computer simulation, which forces him to do some hard thinking. John Gribbin, In Search of Schroedinger's Cat / Quantum physics and reality, Corgi, London 1984, Black Swan edition ISBN 0-552-12555-5. The prequel to Schroedinger's Kittens (see above). Popular, equation-free introduction. Ilya Prigogine and Isabelle Stengers, Order out of Chaos, Heinemann, London 1984. Flamingo edition ISBN 0-00-654115-1. Ilya Prigogine, From Being to Becoming, Freeman, San Francisco 1980. These books are not for the beginner and are best regarded as source- books of ideas. As such, they have influenced this reviewer. A "particle" is not a miniature billiard ball, but rather the fundamental agent of entropy production. Thermodynamics is not a superstructure which sits on top of dynamics, but rather a fundamental subject in its own right. These ideas look difficult to deal with. This reviewer's interpretation of "thermodynamics" may be summed up as "reach for the random number generator" when doing computer simulations. Without the RNG, any computer simulation of a Hamiltonian system or its quantum-mechanical equivalent is bound to be isentropic (this is the old Loschmidt-Zermelo argument). The combination of RNG and chaotic dynamics results in entropy production. Prigogine tends to argue that chaotic dynamics alone can lead to entropy production (private communication). For the moment, let's just call a truce and say that the Heisenberg Uncertainty Principle may be represented in classical dynamics by means of ordinary Brownian motion on the scale of Planck's constant, after the style of Alexandre Chorin. Surely no one will dispute that! Peter T. Landsberg, editor, The Enigma of Time, Adam Hilger, Bristol 1982, ISBN 0-85274-547-8. The subject matter of this book is the arrow of time, which overlaps strongly with the interpretation of quantum mechanics according to this reviewer. Any large-scale computer simulation has a Landsberg's Demon problem: we know all about the system in every detail and the fine-grained entropy is demonstrably constant. We need to fetch in a random number generator to get entropy production. We can then use the RNG to set up a Vernam cipher in order to send communications at superluminal speed when we want to simulate quantum mechanics. If the reviewer can get the Vernam cipher working in his computer program, then he expects people to agree with his views on the arrow of time problem. Otherwise, reserve your judgement. Heinz Pagels, The Cosmic Code / quantum physics as the language of nature, Michael Joseph, London 1982, re-printed in Pelican Books, ISBN 0-14-022547-1. This book comes tantalisingly close to the reviewer's idea of a natural Vernam cipher, hence a (biassed) commendation. Excellent for the date it was written. David Bohm, Wholeness and the Implicate Order, Routledge, London 1980, re-issued 1995, ISBN 0-415-11966-9. This is a book which this reviewer read many years ago, and which has just been re-issued. The reviewer has bought and re-read the re-issue recently. It is suggested that the reader begin directly at Chapter 4, read through to the end, and re-commence at Chapter 1. This book is best regarded as a source-book of ideas, not just of the quantum potential, but also tachyonic Brownian motion. As such, it has had a tremendous influence upon this reviewer. Paul C.W. Davies, The Physics of Time Asymmetry, Surrey University Press, Guildford 1974. The "official" view of entropy production is given here, namely that it is an illusion of large numbers. This reviewer's alternative view is that quantum randomness is the agent of entropy production. Much of the time in computer simulation, quantum randomness can be modelled as ordinary or classical Brownian motion. Richard Feynman, Robert Leighton & Matthew Sands, The Feynman Lectures on Physics, Volume III, Addison Wesley, Boston (Massachusetts) 1965. The inspiration for WPD.BAS. The Feynman Interpretation of quantum mechanics is still correct: we just don't know the answer. This reviewer thinks he does, but is still working on DIRAC2.BAS. Titus Lucretius Carus, De Natura Rerum, posthumous private publication (?), Rome c. 55 B.C.. English translation: Lucretius, On the Nature of the Universe, Penguin Classics, Harmondsworth, Middlesex 1951, translated by Ronald Latham. Lucretius suggested that atoms can swerve on their path, and this is the origin of free will. Perhaps the atoms swerve under the influence of a random magnetic field, a view to take seriously. We cannot get into an argument here about free will, but for "free will" try reading "entropy production". This reviewer's first guess at wave-particle duality (see WPD3.BAS) is directly influenced by Lucretius. 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