Foundations of quantum theory : a study in continuity and symmetry

Joe Rosen

Joe Rosen

The previously developed 'continuous temporal development and Noether's theorem' approach to the association of symmetries and conservations of the laws of nature, part of the foundation of any (classical or quantum) Lagrangian theory, is generalised significantly. Within this framework a strong result is obtained for the inverse Noether's theorem, associating symmetries with given conservations. A general symmetry-conservation formalism is proposed, into which both the previously developed 'linear temporal development and conserved eigenheit' approach, part of the foundation of any quantum theory and also applicable to certain classical ones, and the 'continuous temporal...' approach, as different as they are, fit nicely.

M. Guenin

A formalism is developed on an axiomatic basis and is shown to contain as special cases classical mechanics, the usual quantum mechanics, as well as the quantum theory of systems with continuous superselection rules. The structure of the symmetries of a general physical theory is studied and a classification of observables is exhibited.

Felix M. Lev

Sabine Hossenfelder argues in her blog [1] that the present situation in foundation of physics should be called not crisis but stagnation. I argue that the main reason of the stagnation is that quantum theory inherited from classical one several notions which should not be present in quantum theory. In particular , quantum theory should not involve the notion of space-time background and, since nature is discrete and even finite, quantum theory should not be based on classical mathematics involving the notions of infinitely small/large and continuity. I discuss uncertainty relations, paradox with observation of stars, symmetry on quantum level, cosmological acceleration, gravity and particle theory. My main conclusion is that the most general quantum theory should be based on finite mathematics and, as a consequence: Mathematics describing nature at the most fundamental level involves only a finite number of numbers while the notions of limit and infinitely small/large and the notions constructed from them (e.g. continuity, derivative and integral) are needed only in calculations describing nature approximately.