X-Message-Number: 14106 From: Date: Sun, 16 Jul 2000 07:29:55 EDT Subject: beyond nanotech, a taste of quantum world I have said before why the first quantification is the logical next step beyond nanotech, the technological limit of classical mechanics. Today, QM (quantum mechanics) remains a mysterious subject outside specialized circles. Here I'll give a taste of its many forms, the objective be to bring it into the domain we think we can grasp in a practical way (going from science to technology, with a look at cryonics) Everybody know (or must!) about newtonian dynamics based on the equation : Force = Mass x Acceleration. Unfortunately, that formalism becomes very cumbersome and intractable when there are more than 2 or 3 moving parts in a system. Lagrange, in its sejourns on the border of the Bourget lake in South-East France was the first to give an alternative description based on the difference between kinetic and potential energy. In his honnor, that difference is called the Lagrangian. Richard Feynmann (the inventor of nanotechnology) has pushed that formalism into the so called path integral representation. After Lagrange and its sentimental problems, came Hamilton, its physics representation was baser on the sum of the kinetic and potential energy, a quantity now called the hamiltonian H. An even more general and complex formalism was produced by Jacobi. Poisson has produced a full set of formalisms based on its brackets (the Poisson's brackets define the amount of torsion or Lie's derivative in a system). At the end of 19th century, it was realized that Hamilton's formalism was in fact four infinite classes of formalisms. Today physics users when looking at a problem, choose their own hamilton derived formalism best suited to the question at hand. Other formalisms, don't have that adaptability or are too complicated (Jacobi). Whatever the choice we may make, the result is the same in a linear space. To go from these expressions of classical physics to the quantum domain, we need only to add the constrain of an elementary unit of action (the product of energy by time). Schrodinger, who was both a greath mathematician and a nazi, has selected the hardest way: the Jacobi formalism, so he could put the then new domain of QM on the most general setting and demonstrate its kindship to the superior race. Today users throw in the h constant of action in the H hamiltonian and don't bother. This is the thing to do when working at the function *or* operator level with a single time parameter. The limit is the "or". When it turns to *and*, with a time intervention at both, function and operator level, this last one is no more in the linear domain and different representations give different answers. They no more describe the same reality. That must comes as no surprise: The tensor forms of QM are known too (and mostly) as squeezed states and there are many of them for a given tensor rank. Well, if you get until here, you have now a fairly good look at the frame of basic theoretical physics. Now you know that, outside relativity, the 20th century revolution in physics summarized simply into adding h to H :-) Yvan Bozzonetti. Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=14106