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Teaching quantum mechanics


Do we need a fundamental generalization of quantum mechanics?
Murray Gell-Mann Scientist
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Quantum mechanics is protean, in the sense that you can keep changing the representation, in fact at every time you can change the representation, and the representation has a huge freedom in change of representation, in change of basis. Besides that, even if you're given the basis at every single time, there's a huge freedom of coarse-graining. So the number of possible realms is gigantic, and yet we seem to use almost always a realm that can be called hydrodynamic. It’s described by ranges of values of operators, which are integrals of conserved or almost conserved densities over small volumes of space, and spaced at small intervals of time. And the volumes of space are chosen to be large enough for some kind of internal equilibrium to occur, but small enough to, well, to allow the realm to be maximal; that would be one way to say it.

Now, what properties this usual quasi-classical realm has, so that everything we know about uses it, is one thing we've tried to understand. Quasi, by quasi-classical we mean that these variables very crudely obey classical equations over considerable intervals of time, interrupted constantly by small fluctuations and occasionally by big branchings, big probabilistic branchings. So we are concerned with what makes a realm quasi-classical; why this particular quasi-classical realm seems to play an important role; is there perhaps some fundamental restriction on the representation of quantum mechanics, or ithe transformation theory is really only approximate? One great virtue of our method is that it allows treating, as Hartle has shown in some papers, it allows treating the general relativistic situation, that is a situation in which gravitation as well as all other fields is… is quantized and there are huge quantum variations in the metric. Under those conditions it's very difficult to define a sequence of time slices so that the usual Schrödinger approach to quantum mechanics can be implemented. But this approach, this sum over histories approach, where the history's coarse-grained enough… coarse-grained enough to be strongly decoherent—that works. And the other one may be impossible actually, may not be possible to formulate quantum mechanics any other way. This may be a slight generalization of quantum mechanics. When I wrote an article for the Feynman memorial issue of Physics Today I mentioned that, that Richard was always upset because he felt he had done mostly mathematical work on theories that had been proposed by other people and he wanted to do a fundamental theory of his own. And maybe it will turn out that the sum over histories work actually is a fundamental generalization of quantum mechanics that's necessary, rather than simply a reformulation of quantum mechanics. And our… our work may tend in that direction.

New York-born physicist Murray Gell-Mann (1929-2019) was known for his creation of the eightfold way, an ordering system for subatomic particles, comparable to the periodic table. His discovery of the omega-minus particle filled a gap in the system, brought the theory wide acceptance and led to Gell-Mann's winning the Nobel Prize in Physics in 1969.

Listeners: Geoffrey West

Geoffrey West is a Staff Member, Fellow, and Program Manager for High Energy Physics at Los Alamos National Laboratory. He is also a member of The Santa Fe Institute. He is a native of England and was educated at Cambridge University (B.A. 1961). He received his Ph.D. from Stanford University in 1966 followed by post-doctoral appointments at Cornell and Harvard Universities. He returned to Stanford as a faculty member in 1970. He left to build and lead the Theoretical High Energy Physics Group at Los Alamos. He has numerous scientific publications including the editing of three books. His primary interest has been in fundamental questions in Physics, especially those concerning the elementary particles and their interactions. His long-term fascination in general scaling phenomena grew out of his work on scaling in quantum chromodynamics and the unification of all forces of nature. In 1996 this evolved into the highly productive collaboration with James Brown and Brian Enquist on the origin of allometric scaling laws in biology and the development of realistic quantitative models that analyse the influence of size on the structural and functional design of organisms.

Tags: Physics Today, Jim Hartle, Richard Feynman

Duration: 3 minutes, 55 seconds

Date story recorded: October 1997

Date story went live: 29 September 2010