Related papers: The Way from Rota to Quantum Mechanics
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…
This Festschrift in honour of J. A. de Azcarraga gives an introduction to the concept of duality, i.e., to the relativity of the notion of a quantum, in the context of the quantum mechanics of a finite number of degrees of freedom. Although…
Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of…
Quantum mechanics emerged as the result of a successful resolution of stringent empirical and profound conceptual conflicts within the development of atomic physics at the beginning of the last century. At first glance, it seems to be…
The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space C, but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
For the first time it is shown that the logic of quantum mechanics can be derived from Classical Physics. An orthomodular lattice of propositions, characteristic of quantum logic, is constructed for manifolds in Einstein's theory of general…
It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of…
By means of the examples of classical and Bohmian quantum mechanics, we illustrate the well-known ideas of Boltzmann as to how one gets from laws defined for the universe as a whole to dynamical relations describing the evolution of…
At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would…
Logical probability theory was developed as a quantitative measure based on Boole's logic of subsets. But information theory was developed into a mature theory by Claude Shannon with no such connection to logic. A recent development in…
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…
We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous…
A generalized view of Duality is offered as a bridge between physical sciences and the more abstract philosophical dimensions bordering on mysticism. To that end several examples of duality are first cited from from conventional physics…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
By investigating the Feynman Path Integral we prove that elementary quantum particle dynamics are directly associated to single compact (cyclic) world-line parameters, playing the role of the particles' internal clock, implicit in ordinary…
Since its inception, many physicists have seen in quantum mechanics the possibility, if not the necessity, of bringing cognitive aspects into the play, which were instead absent, or unnoticed, in the previous classical theories. In this…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…