Possibly not. CompuServe subscriber James Baugh argues that at best, a computer simulation of quantum mechanics will result in an exponential-time algorithm. At worst, it is impossible. Call this Baugh's Conjecture (see Note 1).
The reader is surely aware of the standard many-body Schroedinger equation. Realising this as a computer program, whether as an eigenvalue-problem or an initial-value problem, leads to an exponential-time algorithm. Baugh is asserting this as a general principle. The standard multi-dimensional Schroedinger equation may be replaced by something else, like something in just three dimensions, but one cannot evade the exponential-time requirement nevertheless. Here is a quantity surveyor's view which is easy to understand: no matter how much theorising you do, you're always shackled to the requirement for an exponential-time algorithm when you come to do the number-crunching.
In the classical N-body problem, we have O(N*N) interactions, readily dealt with by a polynomial-time computer simulation. In the quantum N-particle problem, every assembly of particles is also a particle, so to speak, putting us in exponential-time country with
N
O (2 )
possible interactions. This is the quantifiable ontological difference between classical mechanics and quantum mechanics. Ontological arguments are common currency.
To put things another way, the formalism of quantum mechanics has to respect the possibility that all the particles will suddenly amalgamate into one large particle or several large particles, which may then disintegrate again. There may be other conservation laws which prevent such amalgamations, but these laws are unknown to the formalism. This requirement of the formalism saddles us with the exponential-time algorithm, unless perhaps we are content to stick to very low energies where amalgamations and disintegrations are unknown.
Exponential-time algorithms are practically useless. We may be able to view a computer simulation of the collapse of the wave function in a simple geometry, which will give us great intellectual satisfaction, but that is the best we can do. Beyond that, there's nothing.
The author agrees that Baugh is almost certainly correct. Note this is an agreement across the dividing line between realism and positivism. Baugh's instincts put him in the positivist camp, while the author is in the realist camp. Here is some bad news for the author, but it is accepted. Now at least, we know.
Realists have been saying for years that the existing theory of quantum mechanics is incomplete, which is obviously true when we look at the question of computer simulation. Now we have Baugh saying OK, but anything less than an exponential-time algorithm will also be incomplete. One can only say that's fair enough.
Chasing quantum mechanics has given the author plenty of stimulus to deal with computer simulation of physics in general, and this is of practical benefit, but the benefits have already been realised. Chasing a computer simulation of the collapse of the wave function is a hobby and nothing more.
This lowers the stakes. We are now dealing with an esoteric subject which is not quite finalised. If you want to dispute the author's views, there is no longer any need to get hot under the collar about it. Just the same, you ought to put your views in writing if you are predicting failure for the author's project.
We have raised the question of quantised vorticity in Brownian motion as a counter-example to the Copenhagen Interpretation. What judgements can we make now about its validity as a counter-example? The judgement is upheld that it is valid, and epistemology is for the chop. The friends of Niels Bohr may retort that there is no distinction between bosonic and fermionic vortices, and there are no known stars held up by vortex degeneracy pressure (this is a reference to neutron stars and white dwarf stars). Yes, but epistemological arguments are being replaced by ontological arguments. We repeat that ontological arguments are common currency.
Pragmatism says that we might as well stick with the Copenhagen Interpretation. This amounts to confusing ontology with epistemology, but if you want to advance some other interpretation, then to what purpose? The requirement for an exponential-time algorithm is unbeatable. Do you agree?
The real bugbear of quantum nonlocality is not the obvious one, but rather the fact that it allows nonlocal collections of particles to behave as single pseudo-particles, requiring an exponential-time algorithm for their computer simulation. We are no longer deceived.
We can see now why quantum mechanics is so difficult to understand. There are two veils, first an epistemological veil and second an ontological veil. We are probably able to get underneath the epistemological veil at some effort (we have to deal with Bell's Theorem). Immediately behind that is the ontological veil provided by Baugh's Conjecture, which cannot be lifted.
A likely casualty of Baugh's Conjecture is the computer simulation of the Big Bang, which could be bad news for militant atheists (see Note 2 below). We can take this one philosophically, but what about computer simulations of chemical reactions, like useful drugs for example? It would be nice to have an asymptotic low-energy theory which is EPR-complete but not Baugh-complete, runs in polynomial time and delivers on the Pauli exclusion principle. This is surely possible. A poor man's version of such a theory might rely on the fact that all electromagnetic particles which obey the exclusion principle also have a magnetic moment, and therefore repel each other, but this could get the Chandrasekhar limit spectacularly wrong in the computer simulation of a neutron star.
On the whole, it is believed that the Copenhagen Interpretation can be demolished by a working computer simulation, but this could be a Pyrrhic victory, achieved at great effort but with not much beyond in theoretical terms (there may be practical benefits though). High-energy many-body computer simulations will be permanently impossible due to the requirement for an exponential-time algorithm (some means of cheating on this in particular applications will doubtless be found but there will never be a general-purpose computer simulation). Here is the middle-of-the-road view on quantum mechanics. Being in the middle doesn't mean it's right, but we can be realists and not positivists, ontologists and not epistemologists, some of the time.
James Baugh's discussion with this author in November 1997 via CompuServe probably makes him the first to 'fire a shot in anger' on this question. Baugh's Conjecture stands irrespective of the issue of EPR-completeness. One could say that Baugh-completeness is required as well. This discussion did make the author change his mind on the general significance of what he is trying to do.
Further enquiry with MetaCrawler, now that we know what to look for and how to look, reveals a page by Peter Shor which suggests that Richard Feynman got there first (no surprise there). Baugh is arguing a rather more general and insistent case than Feynman, and so it is Baugh's Conjecture that we talk about.
It isn't good enough to argue like Edward Tryon that the Universe came into being as a result of a quantum fluctuation, and this is wholly in accord with the laws of physics. Let's see this realised as a Internet-available computer simulation before we make up our minds. There could be 'Hand of God' correlations to be set to make this simulation work, even if Tryon's argument is otherwise correct. The existence of such correlations needs to be disproved, and only an actual working simulation can do that. If the simulation is defeated by the requirement for an exponential-time algorithm, then it's just tough luck for anti-Creationists. By Creationism we mean the orthodox view that God created the Universe in the Big Bang some 10,000,000,000 years ago, a view such as the late Louis de Broglie might have held. We do not mean the crank-industry that exists in parts of the USA. The author's own view is similar to de Broglie's, but if anyone ever produces a computer simulation of the Big Bang without needing to invoke a God, then he may have to revise his view!
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