The revolution in physics : a non-mathematical survey of quanta

Anil Rajimwale

The quantum revolution in physics of the 20th century has completely transformed the nature not only of physics and science in general, but also of philosophy and our worldview. Quantum revolution began in the early 19th century with the discovery of ‘quantum’ (plural ‘quanta’) principally by Max Planck, and with theories and discoveries in the field of relativity, linked inseparably with the name of Albert Einstein. Max Planck came across the quanta when he was studying what is known as the ‘blackbody radiation’. In classical physics in particular and the classical world in general, there was no serious problems with objects, objectivity and ontology. In classical physics, particles and fields have an existence independent of the observer. In broader view, everything, the world, exists independent of the observer and of the consciousness. The first quantum-mechanical theories on electron in mid-1920s did not take into account the effect of velocity of light, and were therefore non-relativistic.

Hermann Haken, Hans Christoph Wolf

Gershon Kurizki, Goren Gordon

Henry has successfully tested the Split button of his quantum suit that enables a quantum object to be in several places at the same time. This bizarre phenomenon is explained by the superposition principle, which reflects Henry’s wavelike properties. Yet Henry remains a single entity as he splits into two superposed versions. In order to understand such behavior, the emergence of the relevant concepts, from classical wave theory, through the quanta hypothesis and the subsequent development of QM, are reviewed. The possibility of such momentous changes in human thinking as the QM scientific revolution is disconcerting if one seeks the truth of the world through physics. A retrospective of the views on the rapport of physics with reality and its roots in mythical or symbolic pictures of the world suggests that the QM revolution eludes straightforward explanation. The QM superposition principle is mathematically formulated in the appendix to this chapter.

Hermann Haken, Hans Christoph Wolf

Ivan T. Todorov

Expository notes which combine a historical survey of the development of quantum physics with a review of selected mathematical topics in quantization theory (addressed to students that are not complete novices in quantum mechanics). After recalling in the introduction the early stages of the quantum revolution, and recapitulating in Sect. 2.1 some basic notions of symplectic geometry, we survey in Sect. 2.2 the so called prequantization thus preparing the ground for an outline of geometric quantization (Sect. 2.3). In Sect. 3 we apply the general theory to the study of basic examples of quantization of Kaehler manifolds. In Sect. 4 we review the Weyl and Wigner maps and the work of Groenewold and Moyal that laid the foundations of quantum mechanics in phase space, ending with a brief survey of the modern development of deformation quantization. Sect. 5 provides a review of second quantization and its mathematical interpretation. We point out that the treatment of (nonrelativistic) bound states requires going beyond the neat mathematical formalization of the concept of second quantization. An appendix is devoted to Pascual Jordan, the least known among the creators of quantum mechanics and the chief architect of the "theory of quantized matter waves".

Hermann Haken, Hans Christoph Wolf, William Dean Brewer