Quantum Mechanics and the Nature of Continuous Physical Quantities

Hans Halvorson

Hans Halvorson

Within the traditional Hilbert space formalism of quantum me-chanics, it is not possible to describe a particle as possessing, simul-taneously, a sharp position value and a sharp momentum value. Is it possible, though, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller [21], have thought that the answer to this question is No — that the status of individual continuous quantities is very different in quantum mechanics than in classical mechanics. On the contrary, I shall show that the same subtle issues arise with respect to contin-uous quantities in classical and quantum mechanics; and that it is, after all, possible to describe a particle as possessing a sharp position value without altering the standard formalism of quantum mechanics. 1

Alexander H Klotz

Martin Leckey

This paper presents a new modified quantum mechanics, Critical Complexity Quantum Mechanics, which includes a new account of wavefunction collapse. This modified quantum mechanics is shown to arise naturally from a fully discrete physics, where all physical quantities are discrete rather than continuous. I compare this theory with the spontaneous collapse theories of Ghirardi, Rimini, Weber and Pearle and discuss some implications of the theory for a realist view of the quantum realm.

Martin J. Leckey, Adrian P. Flitney

A modified form of quantum mechanics which includes a new mechanism for wavefunction collapse is proposed. The collapse provides a solution to the quantum measurement problem. This modified quantum mechanics is shown to arise naturally from a fully discrete physics, where all physical quantities are discrete rather than continuous. We compare the theory to the spontaneous collapse theories of Ghirardi, Rimini, Weber and Pearle, and argue that the new theory lends itself well to a realist interpretation of the wavefunction.