Thursday, October 06, 2005

Large hbar limit and macroscopic limit of quantum theory

The necessity of large hbar phases has been actually highly suggestive since the first days of quantum mechanics. The classical looking behavior of macroscopic quantum systems remains still a poorly understood problem and large hbar phases provide a natural solution of the problem.

In TGD framework quantum coherence regions correspond to space-time sheets. Since their sizes are arbitrarily large the conclusion is that macroscopic and macrotemporal quantum coherence are possible in all scales. Standard quantum theory definitely fails to predict this and the conclusion is that large hbar phases for which quantum length and time scales are proportional to hbar and long are needed.

Somewhat paradoxically, large hbar phases explain the effective classical behavior in long length and time scales. Quantum perturbation theory is an expansion in terms of gauge coupling strengths inversely proportional to hbar and thus at the limit of large hbar classical approximation becomes exact! Also the Coulombic contribution to the binding energies of atoms vanishes at this limit. The fact that we experience world as a classical only tells that large hbar phase is essential for our sensory perception. Of course, this is not the whole story and the full explanation requires a detailed anatomy of quantum jump.

For more details see the chapter Was von Neumann Right After All? of TGD.

Matti Pitkänen


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