Abstract The study of the classical theory of optical fluctuations and coherence is an important preliminary to the development of the corresponding quantum-mechanical theory. The classical theory is useful for a physical understanding of the various effects and many of the classical concepts carry over into the quantum theory. In addition, a knowledge of the classical theory is useful for identification of the nature of the specifically quantum properties that some light beams may exhibit. Thus it is shown in Chapter 5 that the classical and quantum theories yield the ame predictions for chaotic light, but that there exist other kinds of light that elude any satisfactory classical description. The nature of such ‘nonclassical’ light i5, of course, more sharply appreciated by contrast with the limitations on the possible kinds of light inherent in the classical theory.
One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance." These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? One important feature of quantum theory is that it has a classical limit, recovering classical theory through the process of decoherence. We show that any theory with a classical limit must contain entangled states, thus establishing entanglement as an inevitable feature of any theory superseding classical theory.
We consider the description of classical oscillatory motion in ZM theory, and explore the relationship of ZM theory to semi-classical Bohr-Sommerfeld quantization. The treatment illustrates some features of ZM theory, especially the inadequacies of classical and semi-classical treatments due to non-analyticity of the mapping of classical trajectories onto the ZM clock field. While the more complete ZM formalism is not developed here, the non-analyticities in the classical treatment resemble issues in the comparison of classical and quantum formalisms. We also show that semi-classical quantization is valid for a periodic manifold in ZM theory, though the quantum number
n=0 is allowed, as it would be in quantum mechanics for a periodic manifold. Still, this suggests a connection to the first-order success of Bohr theory in describing the phenomenology of atomic quantum states. The approximate nature of the semi-classical treatment of three dimensional atomic orbits is, however, also apparent in relation to ZM theory. These observations are preliminary to a discussion of ZM theory in relation to quantum mechanics and quantum field theory in subsequent papers.