Based on a general formulation for discrete-time quantum mechanics, introduced in 1], symmetries in discrete-time quantum mechanics are investigated. It is shown that any classical continuous symmetry leads to a conserved quantity in classical mechanics, as well as quantum mechanics. The transformed wave function, however, has the correct evolution if and only if the symmetry is nonanomalous.

Classical mechanics, the father of physics and perhaps of scientific thought, was initially developed in the 1600s by the famous natural philosophers (the codename for ’physicists’) of the 17th century such as Isaac Newton building on the data and observations of astronomers including Tycho Brahe, Galileo, and Johannes Kepler. Classical mechanics concerns itself with the mathematical descriptio...

In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which both quantum and classical mechanics emerge as limiting cases of a new mechanics we call ‘mesomechanics’. PACS no. 03.65.Bz

Marcos D. Caballero, Leanne Doughty, Anna M. Turnbull, Rachel E. Pepper, and Steven J. Pollock Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA Department of Physics and Centre for Computing in Science Education, University of Oslo, N-0316 Oslo, Norway School of Education and Human Development, University of Colorado Denver, Denver, Colorado 8020...

The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter sources. Thus it could be said that the currently known formulation of quantum mechanics pre-assumes the presence of classical matter fields. A more fundamental for...

In contrast to the Copenhagen interpretation we consider quantum mechanics as universally valid and query whether classical physics is really intuitive and plausible.-We discuss these problems within the quantum logic approach to quantum mechanics where the classical ontology is relaxed by reducing metaphysical hypotheses. On the basis of this weak ontology a formal logic of quantum physics can...

We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all. While the equiva...

In contrast to the Copenhagen interpretation we consider quantum mechanics as universally valid and query whether classical physics is really intuitive and plausible.-We discuss these problems within the quantum logic approach to quantum mechanics where the classical ontology is relaxed by reducing metaphysical hypotheses. On the basis of this weak ontology a formal logic of quantum physics can...

For three particles P,Q,R travelling on a straight line, let vPQ be the (relative) velocity of P as measured by Q, and define vQR, vPR similarly. According to classical mechanics, the velocity v of a particle moving on a line can be any real number, and relative velocities add by the simple formula vPR = vPQ + vQR. On the other hand, the special theory of relativity says velocities are restrict...