Computer Simulation of Quantum Mechanics - Porthouse

The name of this file is BOHR.HTM



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The Copenhagen Interpretation

says in a nutshell that this website is a waste of time and resources. The type of computer simulation that is being sought is impossible in principle. To see a thing you have to use photons, and unfortunately at the level of quantum mechanics, these photons kick around the thing you are trying to observe. A computer simulation would allow you to see what was happening without using photons, using some sort of 'light of second sight'.

The Copenhagen Interpretation says that the 'light of second sight' doesn't exist. That's all. It is much easier to understand and more informative than any other interpretation of quantum mechanics. For that reason, it is still the official interpretation as of April 1998 (this date is regularly changed).

The Copenhagen Interpretation should really be called the Bohr Theory, since it is a proper theory and not just an interpretation. If you want to oppose this theory, then the onus is on you to produce a computer simulation which is 'EPR-complete'. This is a challenge which the author is willing to accept. Here it is taken for granted that nothing but a computer simulation can deliver the goods, but then non-simulators have been kicking the problem around for years, and have got nowhere.

The expression 'light of second sight' is taken from Irish Gaelic mythology. By denying its existence in the epistemological sense used here, the Copenhagen Interpretation may be classed as a super-realist view of quantum mechanics. Claims that you will find elsewhere which imply that Niels Bohr was trying to hoodwink us are just rubbish. Bohr was simply advocating what he thought was right, and the view down in Ockham is that indeed he was right, and still is. As of now, there is no hard evidence that Bohr got it wrong.

We have a nice irony here. Bohr's principal opponent today is apparently this author, but this author may well turn out to be Bohr's principal champion in spite of himself. We shall see.

Bohr's argument rests on an epistemological proposition about the 'light of second sight'. Other objections which may have been raised by the Copenhagen school, such as the indivisibility of the quantum of action or anything relating to Bell's Theorem, will probably turn out to be false.

One odd feature of the Copenhagen Interpretation is that it is impossible to find anyone who will sign their name to it, despite it being still the official interpretation. The author will sign his name to the proposition that perpetual motion machines are impossible, so what's the problem? From time to time, there are physicists who pose as the successor to Niels Bohr, but when a signature is asked for, it is not forthcoming. If anyone claims to be a follower of Niels Bohr, then they ought to sign up for the assertion that a computer simulation of wave-particle duality is impossible for all time to come, without which what they say is vacuous. We can all be 'um er' physicists, but sometimes we have to put our head on the block.

Can we think of a counter-example to the Copenhagen Interpretation as described here? Consider a cloud of two-dimensional point vortices where all the vortices have the same strength. They are also in Brownian motion as proposed by Alexandre Chorin. The viscosity is equal to the quantum of vorticity. Well, quantisation of vorticity is a wavelike phenomenon, while Brownian motion of vorticity is a particle-like phenomenon, so here we have a possible computer simulation of wave-particle duality. You can argue about this one if you like, but there is no escaping the standard conclusion that further research needs to be done.

For this author there may be one cloud on the horizon. CompuServe subscriber James Baugh has proposed what we will call Baugh's Conjecture in relation to many-body problems:

A computer simulation of the quantum many-body problem must use an exponential-time algorithm, or essential correlations will be lost.

The reader is presumably aware that the standard multi-dimensional wave-function treatment of the quantum many-body problem leads in computational terms to an exponential-time algorithm, and such algorithms are hated by computer programmers. Baugh's Conjecture says that the search for an alternative general polynomial-time algorithm is futile. Often we will be able to cheat on the Conjecture and use polynomial-time algorithms anyway, but there will be some computer simulations (The Big Bang? The human brain?) where we cannot.

Baugh's Conjecture looks like a product of the Copenhagen school, but it isn't. Off-hand, let us guess that the Copenhagen Interpretation will turn out to be false, but Baugh's Conjecture will turn out to be true. The Copenhagen Interpretation is too severe, but Baugh's Conjecture draws the line where we may feel it should be drawn. A project for the computer simulation of the Big Bang would be a modern Tower of Babel and a monument to human pride, and there surely ought to be some reason why it would fail. On the other hand, denying us the ability to do computer simulations of even the simplest quantum mechanical systems is too obscurantist.

The author can get on with the attack on simple systems, and probably will not have to deal with Baugh's Conjecture in his lifetime.


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