Computer Simulation of Quantum Mechanics - Porthouse The name of this file is WPD.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. This file deals with miscellaneous questions about the problem of quantum-mechanical wave-particle duality, in an effort to clear up any misunderstandings. It is based in part upon arguments which I have met in the physics section of the CompuServe science forum. New questions can be put to me to be considered for inclusion. This subject has been graced by the contributions of David Bohm, who wasn't the sort of person to be pushed around. In seeking to follow his example, I will adopt a rather pugnacious style at times, but this file is after all conversational. You have been warned! David T.C. Porthouse CompuServe 100425,3501 Northumberland (1) What's wrong with the existing theory of quantum mechanics? Nothing, if the only experiments we ever did were ensemble-experiments. An ensemble-experiment is where we do an experiment over and over again and then take the average result in the limit as the number of trials goes to infinity. If you run WPD.BAS, which is a simulated experiment, you will see that it takes about 10,000 trials to get an idea of which way things are going to reasonable accuracy. At the discrete level, which is the level of the individual experiment, or what may be rather infelicitously called the sub-ensemble level, we have a problem. The Schroedinger theory makes predictions such as saying we will find 0.1234 of an ensemble-electron in a potential well which means that after 10,000 trials we can expect to record 1,234 occasions on which an electron is captured. Experience indicates that this type of prediction can be confirmed up to one part in 100,000,000,000 in the statistical limit, and I think that's good enough to say that the theory is exact in the statistical limit. Unfortunately, at the level of the individual experiment, we cannot have such a thing as 0.1234 of an electron. We either see one electron or none. The standard theory of quantum mechanics is false at the discrete level. This attack on the standard theory is often illustrated with the story of Schroedinger's Cat. Let's get it clear: at the ensemble level, the existing theory is perfect, and nothing is going to turn up in any future ensemble-experiment to shake this view. There are no chinks in the armour of quantum mechanics at the ensemble level. When I said nothing at the beginning of this reply, I did mean absolutely nothing. (2) Well OK, but statistical predictions are the only predictions we can have. We can have computer simulations as well. Such a computer simulation can incorporate a random number generator, as introduced by Alexandre Chorin in fluid dynamics. The question is how to inject random numbers into a number-crunching job on the Schroedinger and Maxwell equations. My ideas are given in WPD3.BAS but I am open to suggestions. Being human, I am naturally taken with my own ideas, but I would be happy to act as principal cheerleader for something better, which is an honourable attitude. In my opinion, the problem of wave-particle duality only makes sense as a problem in the context of computer simulation. Maybe that's an extreme view, but let's just get this view on the table for discussion. I have now published the modules DIRAC2.BAS, VEC4.BAS and DWAVEF.BAS which do the number-crunching. These modules taken together are a work of engineering in the absence of a random number generator. Once we start talking about including a random number generator, then we are talking physics. All the files mentioned in this reply are on this website. (3) You are ascribing reality to the wave function. Surely it's just a calculational device? This objection, and many others like it, is derived from the work of Niels Bohr, commonly called the Copenhagen Interpretation. This inter- pretation may be summed up succinctly as Disappointment to Computer Programmers In fact, that's the only thing we need to know about the Copenhagen Interpretation: it predicts failure for me, or anyone who responds to my call for ideas, and the rest of the argument, all the stuff about logical positivism and complementarity, is just an elaboration of the basic idea. Critics of the Copenhagen Interpretation would do well to remember its utter simplicity, which can be summarised in my four initials - DTCP. We shall just have to wait and see if the Copenhagen Interpretation turns out to be correct. No one has taken up the challenge in WPD1.BAS, so perhaps I am the only person left in the world who still has any regard for Niels Bohr. I am at least willing to give the devil his due. If no one can produce a convincing computer simulation of wave-particle duality within one hundred years, say, then I would be saying that Bohr was right, and we should all be positivists. (4) You are trying to visualise the inner workings of quantum mechanics without the use of photons. This is the objection which Niels Bohr himself would have raised, and it is one to take seriously. I accept that the objector is not guilty of ignoratio elenchi and that the objector is showing some "gut feeling" for quantum mechanics. Let us try doing computer simulations of wave-particle duality, and maybe after one hundred years of failure we will have to give up. In my opinion, if we do fail then it will be tragic for scientific research because we will start to run up against lots of problems that we can never solve by anything but empiricism. Such is the Curse of Bohr. (5) So you're going to take on the great Niels Bohr? Yes. I've got lots of new weapons: the Internet, virtual-time simulation, object-oriented programming, random number generators, variable algorithms and the Vernam cipher. None of these were available to Einstein when he debated with Bohr. I think that the Vernam cipher is the super-weapon which will prove to be decisive. We now have a means of tackling John Gribbin's "Schroedinger's Kittens" problem. Other people might have guessed at the operation of a natural Vernam cipher from looking at Charles Bennett's work, but there are many other problems to solve, and it happens to be me who has also published OOP.TXT which introduces object-oriented programming to physicists. Ronald Hurst is working on a lattice-based approach to the computer simulation of wave-particle duality, derived from De Broglie. I can imagine him succeeding with his aims - at least I cannot see any obvious obstacles. He may have to change his specific approach a few times, but the idea of a lattice which can hide information, particularly superluminal communications, is sound. Perhaps we will end up with two theories. (6) How will you modify the Schroedinger equation without conflicts with experiment? I won't. Once we introduce a random number generator into the picture, then we have the Vernam cipher available for free (see VERNAM.TXT). With the Vernam cipher available, we can sneak superluminal communications under the noses of a committee made up of Albert Einstein, Alan Turing, Niels Bohr, Chester Nimitz and any other clever or dangerous people. We can then talk tachyonics without fear, subject to the condition that we cannot end up with a theory that can be used for macroscopic superluminal communication between human beings. The Schroedinger equation has a tachyonic degree of freedom which is open to exploitation. In mathematical language, the Schroedinger equation is replaced by a Schroedinger condition, and Maxwell's equation by a Maxwell condition. This is described in WPD3.BAS. (7) Surely nothing can travel faster than light? This objection is based on ignorance of the way in which the result is derived. See RELAY.BAS in the physics library or on this website for a review. Briefly, the result is derived by the method of Reductio ad Absurdum, which assumes the validity of the Law of the Excluded Middle, which law is known to be false in quantum mechanics. Things can travel at superluminal speed within quantum mechanics as long as there is no possibility of macroscopic superluminal communication between entities such as human beings. Note here that I might talk about tachyonics, but my views are after all quite orthodox. Failure to understand the invalidity of the Law of the Excluded Middle is responsible for many howlers in the application of quantum mechanics. Even an experienced practitioner like Murray Gell-Mann can get it wrong. See Chapter 12 of his book "The Quark and the Jaguar" which is entitled "quantum mechanics and flapdoodle". No doubt I will make a few blunders myself, particularly if I am uploading complicated computer programs. Please don't be too "gleeful" if you spot any. Just tell me. The fact that Professor Gell-Mann has got it wrong does not mean that I have got it right - that remains to be seen. At this stage, we need imagination and we could do without doctrines which mislead or restrict our curiosity. (8) You shouldn't use the word "Things" when you say "Things can travel at superluminal speed". This is the Copenhagen Interpretation taken to the extreme of denying its opponents any language in which to state their case, as in the "Newspeak" of George Orwell's "1984". OK, I know that logical positivism began as a critique of language, but you are overdoing it. (9) What new experimental results can you predict? How does your theory differ from quantum mechanics? I remind you that I hope to do a simulation in which either one electron or none is captured in a potential well. Beyond that, we shall just have to see. No doubt my simulations, if successful, will suggest other experiments to do in due course. At the level of the ensemble of computer simulations, there should be no difference between my theory and the standard theory of quantum mechanics. This will need to be checked. Since I do not modify the Schroedinger and Maxwell equations, I am not anticipating any problems at the ensemble level. I repeat the argument that the existing theory of quantum mechanics is false at the discrete level. This type of objection usually paraphrases Karl Popper in some way. I haven't actually read any of his books, but his ideas are cited often enough for me to know the general idea. I understand that Karl Popper has had a go at interpreting quantum mechanics, but he has had nothing to say that will make the slightest difference to my computer simulations. I am afraid that I am not impressed. Popper's arguments are based upon classical logic, and we might expect some surprises in quantum mechanics. Popper's general attitude reflects a dislike of aimless arguments. The onus is on me to come up with a working EPR-complete computer simulation of quantum mechanics, which I have yet to do. There are objective criteria of success or failure. (10) Shouldn't we be doing real experiments instead of messing around with computers? At the moment, we don't know how to do computer simulations of wave- particle duality, and this is a matter worthy of our curiosity. You omit to mention the price tag on your experiments. If you want to persuade the taxpayer to spend a very large sum of money on the search for the Higgs boson, then don't you think that that taxpayer might be entitled to log on to the Internet and download a computer simulation of W and Z particles in action? How will you set about producing such a simulation? How about going along with me for the moment? (11) Isn't this talk of tachyonics far-fetched? Einstein's theory of Special Relativity was far-fetched in the days when the fastest object on Earth was a steam locomotive like the "City of Truro" which broke the 100 mph (160 kph) barrier in 1904. The experimental evidence is that at the ensemble level, Einstein-locality holds good, but quantum mechanics is nonlocal at the discrete level according to Alain Aspect. I am trying to reflect this in my theory. Are you saying that we should never make any effort to formulate a theory about Aspect's experiment? There are some people who say just that. They take the Copenhagen Interpretation and cover it up with waffle, but that is what they are saying. The Internet and computer simulation give us the ability to ensure that the Special Theory of Relativity is taught in primary schools, where once it would have been considered too difficult for undergraduates. Once relativity is perceived as an easy subject, which it is, we can move on to tachyonics. The technology developed by Charles Bennett is now being tested in the field by Hugo Zbinden and others. Round about January 1st 2001 you will be able to order goods via the Internet through normal channels, but send your credit card details using quantum cryptography. It would be embarrassing to begin the 21st Century with the engineers racing ahead with things which physicists don't understand. (12) Don't tachyonic or nonlocal theories have the defect that they sneak in the reactionary idea of a privileged frame of reference? Not necessarily. Physicists are used to describing things in terms of cause and effect, but if a certain cause is always followed by a certain effect, then the concept of cause and effect is merely a tautology, in which case cause and effect may be reversed. There exist a class of phenomena for which this argument is not mere sophistry, the formation of the Von Karman vortex street being one example, and the uncontrollable random nonlocal collective phenomena of quantum mechanics being another example. These phenomena are rare by the standards of our normal experience. Accordingly, we can have nonlocal theories of quantum mechanics where cause-and-effect in one frame of reference becomes effect-and-cause in another frame, and there need be no objection to this. It's a hard argument to swallow, and I have had to struggle to convince myself, but then we have all been brought up on cause-and-effect. This argument, as far as I know, is original to me. It has a precursor in J.S. Mill's criticism of the syllogism. I wouldn't be surprised to find philosophical criticisms of causality which echo Mill, but I don't know of anyone who has taken things as far as I have. I don't expect everyone to accept this argument all at once, and it is hardly necessary. Please become familiar with my computer simulation of the Von Karman vortex street and the argument I derive from it. That will do for the time being. (13) There are several other interpretations of quantum mechanics, and they are all much of a muchness. What's different about yours? My efforts at computer simulation can either succeed or fail. If I fail, I will just have to slink away and think of something else, perhaps random gauge transformations. The capital sins are ignoratio elenchi and windbaggery. I am not guilty of either of these, I trust, so I am not insulting your intelligence by proposing a theory which merely turns out to be wrong. If it is wrong I will admit it myself. (14) What do you think of these other interpretations? I don't bash the opposition. Let's see all these interpretations represented on the Internet. Professor Gell-Mann is entitled to argue ad rem for his "consistent histories" interpretation. In a computer simulation of consistent histories, I would expect to see a cleavage-wave moving at superluminal speed away from an observation. One might plead ignorance of computer programming. Actually any smart physicist could do well to avoid computers until object-oriented programming becomes available. Now it is available, there is no excuse. The constructs of object-oriented programming remind me of nouns, adjectives and verbs, so anyone who is good at natural languages should take to it like a duck to water (nouns=records, adjectives=unary operators, verbs=binary operators, DIRAC2.BAS is richly endowed with examples of all of these). I will show respect for honest failures where the intentions were constructive. People who talk big and act little will see a different face of me, so if you want to argue for the Copenhagen Interpretation then please comply with the request in WPD1.BAS, so I know you have at least the guts to put your reputation on the line. I have to produce a computer simulation somehow, and computer programming leaves no time for waffle. (15) The idea of a natural Vernam cipher is anthropomorphic. I suppose it is. What's the problem? (16) Your theory takes randomness for granted. Surely you should be trying to explain it? David Bohm, for example, was keen on determinism, though he did think about randomism as well. This is really an opinion rather than an objection. If I can get my computer simulation to work, then I won't rule out the future possibility of a deterministic theory being able to explain everything which I did. Such a theory risks telling us how to build a macroscopic superluminal communications device! Maybe it will turn out that such a device can be built, but it requires the entire universe as fuel in order to operate at the Planck level. That would stop us arguing. (17) I don't think much of WPD3.BAS. Tell me how to modify my theory, or tell me an alternative theory. By all means tell me where I am wrong, but don't leave me empty-handed as a computer simulator. If you want to communicate equations, fax me on + 44 1670 590650. If I think you are wrong I will be polite about it, because I respect honest effort. As a computer simulator, I cannot abide vagueness, so don't be surprised if you are told to put up or shut up. Whatever you say, the show must go on. I need something to soldier on with. (18) WPD3.BAS bypasses the peer-review system. The rules are different. In the first place, my basic unit of communication is the computer simulation rather than the written word, and obviously the Internet is the place to publish. WPD3.BAS merely represents current wisdom, and may be "vaporised" at any moment for the sake of something better. If I don't hear of anything better, then I must plod on with what I have. The modules DIRAC2.BAS, VEC4.BAS and DWAVEF.BAS represent a public facility: the world's first numerical particle-accelerator, as far as I know, with the Internet as its platform. In future, I am sure, we will have modules to deal with the electroweak and strong interactions. It is now open to anyone to suggest how to use this facility to model wave-particle duality. Success will take the form of a working computer simulation, which anyone will be able to download. I will keep the very latest version of DIRAC2.BAS uploaded all the time, so in principle, you could know that it is successful (or otherwise) before I do, if you happen to have a superfast computer. I have acquired a Cyrix M2 to run as a "stealth" computer. I will use this to study the local capture of an electron in a potential well. After this, I might upgrade to a still faster computer to do nonlocal studies. At a guess, I will be successful with local capture studies, but may have problems with nonlocal studies. If finally successful, I will submit my results to a journal in the normal way. (19) WPD3.BAS has a novel type of mathematics! No new ideas; no progress. The same can be said of Ronald Hurst's approach. A lattice may seem an unusual idea, but that's the sort of new idea we need. (20) WPD3.BAS fudges it when you talk about an eddy viscosity based on a W or Z particle. Here is an obvious piece of hand-waving. You're entitled to your point of view. Consider doing all your computer simulations using the Standard Model, and good luck to you. (21) I'll believe it when I see it. That's what any sensible person would say at the moment. It is the current "correct" interpretation of quantum mechanics. Stay with Copenhagen for the time being, until you are able to download a convincing computer simulation of something better. This may be known as the Feynman Interpretation. (22) When are we going to see it? DIRAC2.BAS hasn't changed for ages. I will shortly be able to get on with DIRAC2.BAS. You could always help me by taking over responsibility for the gravity or relativity programs. I will give you an assignment, see how you perform, and then hand over if you do well enough (as if it is for me to judge!). I am doing this as an amateur. I haven't got loads of money, but I can now afford a Cyrix M2 (I assembled it myself). This is all I need for the moment. (23) You are doing this as an amateur? I earn a living as a computer programmer (obvious?). Unlike a professional physicist, I have no deadlines to meet. I first thought of an ultraluminal oscillation driving a tachyonic Brownian motion in 1979 (at the age of 24) as the most extreme idea I could think of (under Edward DeBono's influence). I thought up the immutability of the Schroedinger equation and variable algorithm in 1986. I thought of the Vernam cipher in 1991, at about the same time as I began to program DIRAC.BAS. Over the years, I read everything I could get my hands on, and never reached a verdict until I was really sure. Now things are speeding up a bit. I have nothing new to add to the theory and it's a matter of actually getting on with computer simulations. No professional physicist could get away with working on this sort of time scale in the world of Margaret Thatcher and Newt Gingrich. A young professional physicist might also have problems questioning the dogma that nothing can travel faster than light in front of colleagues who fail to grasp the subtleties of the subject. In addition, he or she would need to learn quantum mechanics, philosophy and computer programming (if I am to be believed). This takes years, and philosophy in particular tends to require a certain degree of maturity to understand what the philosopher is getting at. At the age of 43 I may manage this. (24) Does your theory preserve the symmetry between electrons and photons? There are many experiments done with electrons which can be matched to experiments done with photons. The symmetry is broken from our point of view, as beings composed of fermions, because electron-detectors need not have moving parts, but photon-detectors must do so. It is expected that the treatment by quantum mechanics of these moving parts will preserve the symmetry between electrons and photons. At the moment, the project associated with DIRAC2.BAS is aimed at electrons, but photons will be tackled in the future. My theory is symmetric in that there are random tachyonic fluctuations in both the wave function and the electromagnetic field. It is hoped that the joint correlation of these fluctuations can carry useable information like a Vernam cipher. This remains to be seen. The moving parts of different photon-detectors are nonlocally interchangeable. The description of this by quantum mechanics opens up the matter channel, so the two-channel Vernam cipher is back in action. This is how I expect to simulate correlations between photons in the future. (25) How will you deal with many-body problems? I haven't thought about it much. I would hope to replace exponential-time algorithms with polynomial-time algorithms. Since then, I have been convinced by James Baugh that this is a false hope in principle. Maybe we can devise ad hoc polynomial- time algorithms for some problems, but in general we are shackled to the requirement for an exponential-time algorithm. I think that the prospects of a computer simulation of the Big Bang are the principal casuality of Baugh's argument. The Big Bang is the ultimate high energy event where we might expect exponential-time behaviour to be important. We still need to find the asymptotic low-energy theory which runs in polynomial-time but which gets the Chandrasekhar limit right for a neutron star. (26) I cannot run your BAS files. In Northumberland we build railways to a Standard Gauge of 4 ft. 8 1/2 ins. and all the neighbouring counties have adopted the same gauge. The equivalent in computing is I.B.M. P.C. + MicroSoft QBasic + CompuServe. What's the problem? Are you like those people who have built a railway across the Nullarbor Plain which changes gauge abruptly at the border between South and Western Australia? (This is a joke - it is actually Standard Gauge all the way) Motorola's 7 ft. gauge processor is undoubtedly better, but it just hasn't caught on and people get fed up with break-of-gauge problems. You can get an I.B.M. emulator for your M680x0 machine, but it is probably cheaper to buy a secondhand 80x86 computer and a discounted version of MSDOS 5.0. Comments from M680x0 users are welcome. A secondhand 8086 with QBasic, a 2400 baud modem, a CompuServe subscription and SYMBOL.BAS is the cheapest way to put equations on the screen of a computer in New Zealand. This is the attraction. If you have any problems running BAS files on standard equipment like this, then please let me know. I am unashamedly plugging commercial products (I am not receiving any commissions). In the past I might have recommended the products of Robert Stephenson and Company, of Forth Street, Newcastle upon Tyne, as the world standard. Many other manufacturers have since produced Stephenson-compatible products, to the point where the original home of the industrial revolution has long been eclipsed. (27) I haven't looked at your TXT files or BAS files. Do your homework and don't waste my time. (28) This subject is very argumentative. Yes, it is. We need to be clear-headed to find our way through the quantum jungle. Arguments should be fought out as rival computer simulations, which you can download and judge for yourself. This does at least make everything ad rem and takes personalities out of it. CLICK ON "BACK" OR "BACKWARD" TO RETURN TO THE PREVIOUS PAGE ______________________________________________________________________________ This author's website is http://ourworld.compuserve.com/homepages/anima/quantum.htm His e-mail address is 100425.3501@compuserve.com Fellow CompuServe subscribers may of course contact him on 100425,3501