Related papers: Quantum state reduction, and Newtonian twistor the…
The implementation of Einstein's principle of equivalence in Koopman-von Neumann (KvN) mechanics is discussed. The implementation is very similar to the implementation of this principle in quantum mechanics. This is not surprising, because…
Models for deterministic quantum mechanics of Cartan-Randers type are introduced, together with the fundamental notions of the concentration of measure theory. We explain how the application of the concentration of measure to Cartan-Randers…
We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
We discuss an alternative version of non- relativistic Newtonian mechanics in terms of a real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme correspondent with the standard formulation.…
In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time…
The concept of twisted Poincar\'e symmetry, as well as some implications, are reviewed. The spin-statistics relation and the nonlocality of NC QFT are discussed in the light of this quantum symmetry. The possibility of a twisted symmetry…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
Using the quantum Hamilton-Jacobi equation within the framework of the equivalence postulate, we construct a Lagrangian of a quantum system in one dimension and derive a third order equation of motion representing a first integral of the…
We investigate the interaction of the gravitational field with a quantum particle. First, we give the proof of the equality of the inertial and the gravitational mass for the nonrelativistic quantum particle, independently of the…
With an eye on developing a quantum theory of gravity, many physicists have recently searched for quantum challenges to the equivalence principle of general relativity. However, as historians and philosophers of science are well aware, the…
The argument is re-examined that the program of deriving the rule of state reduction from the Schroedinger equation holding for the object-apparatus composite system falls into a vicious circle or an infinite regress called the von Neumann…
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
By applying Schwinger's variational principle to the Einstein$-$Cartan action for the gravitational field, we derive quantum commutation relations between the metric and torsion tensors.
These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…
I give a brief introduction to the relation between loop quantum gravity and twistor theory, and comment on some perspectives on the problem of time.
We review a possible framework for (non)linear quantum theories, into which linear quantum mechanics fits as well, and discuss the notion of ``equivalence'' in this setting. Finally, we draw the attention to persisting severe problems of…
The Einstein-Cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. The former is an extension of general relativity and refers to four-dimensional space-time, while we introduce…