Tuesday, 6 December 2005

Quantum Limitations

Quantum Foam

As I already said in another post, quantum mechanics is a wide confirmed and one of the most successful theories about nature we (humans) ever created. The agreement of predictions with experiments is amazing and there are no known experiments that contradict the theory.

However, this is not the end of the story. QM is successful for its mathematics describes nature with tantalizing precision, but the math was tailored from experiments to fit them. This means that QM, unlike Relativity, is not derived from some fundamental principle. The lack of this principle is what is behind the great numbers of alternative interpretations apart from the ortodox one, which leads to strange situations like the Schroedinger Cat.

The lack of a first principles derivation still is responsible for the existence of alternative theories that try to explain qunatum phenomena, like Bohmian Mechanics, where David Bohm tries to explain quantum behavior by a misterious quantum field that permeates spacetime, and Stochastic Electrodynamics, pioneered by Timothy Boyer, which uses classical mechanics plus a random background field of electric particles and is able to find a lot of good results. But no theory yet has been proven to be exactly equal or superior to QM.

When I talk about the success of QM, I´m not talking yet about quantum field theory (QFT). QFT arises from the merging of QM with special relativity. It has a lot of success, but the way these results are extracted from the body of the theory is very trick and most of scientists have the feeling that this should not be the final answer. Although when supplied with some experimental measurements QFT can give results that agree with experiments by one part in a billion (in QED, for example), the calculations come from infinite series expansions that do not converge. The expansions are truncated and a lot of work on renormalizing (take the infinites away) the theory must be made.

The point is that even giving the correct values for several quantities, QFT begins with a very questionable (in my view) procedure: you simply transform equations from classical physics in equations for fields, solve by expanding in Fourier series and then impose quantum commutation relations between the fields and the canonical conjugate momenta. It is a recipe. We don´t know exactly what we are doing, but we borrow the procedure of imposing these relations from plain QM and go on. Another thing: the conjugate momenta comes from a lagrangean density that is constructed in such a way that it gives the correct equations of motion, again without any fuindamental principle. This procedure works with some tricks for Electrodynamics and for Weak and Strong Forces (giving rise to electroweak theory and to QCD), but fails miserably with gravity.

In my view (and my only view, what means that it is not the current view of scientific community), without a clear understanding of what we are really doing, we can´t even be sure if we should quantize gravity. Critics of string theory say that after so much time without success, maybe string theory is a wrong way, but the endeavour of quantizing gravity is much older and we could not do it till this day. I´m not saying that quantum gravity is not worth pursuing, I´m just saying that maybe there is a tiny possibility that nature did not choose this path. However, today the probability that QG exists probably is higher than that it do not. We have to wait more theoretical results or experiments.

Just to cite a tentative for deriving QM from first principles, it is worth looking at the papers of Ariel Caticha, he is trying to show that QM can be obtained by applying principles of information theory and bayesian inference to physics. The main theory is in Insufficient reason and entropy in quantum theory (quant-ph/9810074). He is also trying to show that general relativity can be obtained from the same principles: The Information Geometry of Space and Time (gr-qc/0508108).

Picture: Quantum Foam - taken from http://www.journal-kempten.de/

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