Looking Beyond Classical Mechanics

P. Enders

This chapter introduces the paradigm ‘quantization as selection problem’ by means of few historical remarks. They include Einstein’s 1907 reasoning, Schrödinger’s 1926 derivation of his wave equation, and Gödel’s theorem and Munchhausen’s trilemma. The latter ones concern questions, which can be posed, but not be answered within CM. Such questions transcendent CM. This book poses the question, how the mechanics of oscillators without turning points looks like. (“oscillators without turning points” means oscillators, which may assume configurations beyond the classical turning points.)

G.C. Stey

David B. Cook

Orientation and Outlook Probabilities: Simple Probabilities A More Careful Look at Probabilities Classical Mechanics: The Hamilton-Jacobi Equation Angular Momentum Schrodinger's Mechanics: Prelude: Particle Diffraction The Genesis of Schrodinger's Mechanics The Schrodinger Equation Identities: Momenta and Dynamical Variables Abstracting the Structure Interpretation from Applications: The Quantum Kepler Problem The Harmonic Oscillator and Fields Perturbation Theory and Epicycles Formalisms and Hidden Variables Disputes and Paradoxes: Measurement at the Microscopic Level Paradoxes Beyond Schrodinger's Mechanics?

Dugald R. Murdoch

Bohr's general thesis of complementarity conveys the idea that we can, and perhaps must, make use of the classical physical concepts in quantum physics, notwithstanding the inadequacies of these concepts; but we can use them only within the limits circumscribed by the quantum of action – beyond these limits the classical concepts cease to be well defined. This idea originated in his thesis that the conceptual structure of the quantum theory is in a sense a generalisation of the conceptual scheme of classical mechanics; and this thesis was a corollary of the correspondence principle. During the first months of 1927 Bohr regarded quantum mechanics as the quantum-theoretical generalisation of classical mechanics to which he had been looking forward. He came also to think that quantum mechanics required in a sense the generalisation of the two classical models of particle and wave. In classical physics these two models generally pertain to different theories, the particle model to the mechanical theory of matter, the wave model to the electromagnetic theory of radiation. In quantum physics, however, the two models pertain to one theory, quantum mechanics, and each is applicable to matter and radiation. Where discontinuity obtains, the standard classical models of matter and radiation cease to be well defined, and the alternative, non-standard models may be used. There is no logical inconsistency in this dual use of the models since each is appropriately applicable only in different empirical circumstances.