Related papers: Quantum Mechanics at Planck's scale and Density Ma…
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…
It was argued in a number of papers that the gravitational potential calculated by using the modified QFT that follows from the Planck-length deformed uncertainty relation implies the existence of black-hole remnants of the order of the…
Quantum Mechanics (QM) is a quantum probability theory based on the density matrix. The possibility of applying classical probability theory, which is based on the probability distribution function(PDF), to describe quantum systems is…
Quantum Mechanics of photons leads to a theory of Quantum Gravity that nicely matches the experimental results of varying fine structure constant,obtained from many-multiplet Quaser absorption systems and atomic clocks.The variation of that…
The cosmological constant (vacuum energy) problem is analyzed within the scope of quantum theories with UV-cut-off or fundamental length. Various cases associated with the appearance of the latter are considered both using the Generalized…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Using a particular Hilbert space representation of minimum-length deformed quantum mechanics, we show that the resolution of the wave-function singularities for strongly attractive potentials, as well as cosmological singularity in the…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
In this work we show the quaternionic quantum descriptions of physical processes from the Planck to macro scale. The results presented here are based on the concepts of the Cauchy continuum and the elementary cell at the Planck scale. The…
Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be…
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
The objective of this series of three papers is to axiomatically derive quantum mechanics from classical mechanics and two other basic axioms. In this first paper, Schreodinger's equation for the density matrix is fist obtained and from it…
In this paper, the quantization and generalized uncertainty relation for some quantum deformed algebras are investigated. For several deformed algebras, the commutation relation between the position and the momentum operator is shown to be…
Theories based on General Relativity or Quantum Mechanics have taken a leading position in macroscopic and microscopic Physics, but fail when used in the other extremity. Thus, we try to establish a new structure of united theory based on…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
Theories with Planck-scale deformed symmetries exhibit quantum time evolution in which purity of the density matrix is not preserved. In particular we show that the non-trivial structure of momentum space of these models is reflected in a…
We study the thermodynamics of various physical systems in the framework of the Generalized Uncertainty Principle that implies a minimal length uncertainty proportional to the Planck length. We present a general scheme to analytically…
In this paper, the deformed Special Relativity, which leads to an essentially new theoretical context of quantum mechanics, is presented. The formulation of the theory arises from a straightforward analogy with the Special Relativity, but…