Wonders of the Quantum World

Aczel, A. D. (2001). Entanglement The Greatest Mystery in Physics, Four Walls Eight Windows, New York. A popular account of recent developments on the wonders of the quantum world. 

J. C. Polkinghome, The Quantum World (Princeton University Press, Princeton, NJ, 1989) has a wonderful treatment of the philosophical consequences of quantum mechanics. 

Chaos provides an excellent illustration of this dichotomy of worldviews (A. Peres, 1993). Without question, chaos exists, can be experimentally probed, and is well-described by classical mechanics. But the classical picture does not simply translate to the quantum view attempts to find chaos in the Schrodinger equation for the wave function, or, more generally, the quantum Liouville equation for the density matrix, have all failed. This failure is due not only to the linearity of the equations, but also the Hilbert space structure of quantum mechanics which, via the uncertainty principle, forbids the formation of fine-scale structure in phase space, and thus precludes chaos in the sense of classical trajectories. Consequently, some people have even wondered if quantum mechanics fundamentally cannot describe the (macroscopic) real world. 

Tunneling is a real, detectable phenomenon. It is not predicted by classical mechanics (and would be forbidden by it), but it arises naturally out of quantum mechanics. Its existence is the first real-life example given here of the strange and wonderful world of quantum theory. 

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