Related papers: Classical and Quantum Limits in Bohmian Quantum Co…
The Planck scale is usually believed to be an unpassable wall. Putting a cutoff there and thinking of it as a quantized spacetime entity shows that. However, this is exactly the cause of many problems in quantum gravity. The cosmological…
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…
An analysis is made of the relation between quantum theory and classical mechanics, in the context of the limit $\hbar \to 0$. Several ways in which this limit may be performed are considered. It is shown that Schr\"odinger's equation for a…
Many quantum systems may have the same classical limit. We argue that in the classical limit their traces do not necessarily converge one to another. The trace formula allows to express quantum traces by means of classical quantities as…
In this article, we investigate Bohm's view of quantum theory, especially Bohm's quantum potential, from a new perspective. We develop a quasi-Newtonian approach to Bohmian mechanics. We show that to arrive at Bohmian formulation of quantum…
Bohmian mechanics can be generalized to a relativistic theory without preferred foliation, with a price of introducing a puzzling concept of spacetime probability conserved in a scalar time. We explain how analogous concept appears…
We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton-Jacobi equation. While in the classically forbidden regions these quantum quantities directly tend to the…
We obtain two-sided bounds on kinetic and potential energies of a bound state of a quantum particle in the semiclassical limit, as the Planck constant $\hbar\ri 0$. Proofs of these results rely on the generalized virial theorem obtained in…
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, these extraordinarily small effects may in fact have a real and significant influence on our world. A calculation suggests that the minute…
It is well known that, due to the uncertainty principle, the Planck constant sets a resolution boundary in phase space and the resulting trade-off in resolution between incompatible measurements has been thoroughly investigated. It is also…
Quantum speed limits set an upper bound to the rate at which a quantum system can evolve. Adopting a phase-space approach we explore quantum speed limits across the quantum to classical transition and identify equivalent bounds in the…
We consider the problem of constraining a particle to a submanifold Sigma of configuration space using a sequence of increasing potentials. We compare the classical and quantum versions of this procedure. This leads to new results in both…
The old cosmological-constant (CC) problem indicates an inconsistency of the usual formulation of semiclassical gravity. The usual formulation of semiclassical gravity also seems to be inconsistent with the conventional interpretation of…
We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…
Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the…
Among the many perplexing results of quantum mechanics is one that contradicts a result from introductory physics: the possibility of finding a quantum particle in a region that would be forbidden classically by energy conservation. An…
I give a review of the conceptual issues that arise in theories of quantum cosmology. I start by emphasising some features of ordinary quantum theory that also play a crucial role in understanding quantum cosmology. I then give motivations…
We consider classical and quantum dynamics on potentials that are asymptotically unbounded from below. By explicit construction we find that quantum bound states can exist in certain bottomless potentials. The classical dynamics in these…
We study the Newtonian cosmology taking into account the leading classical and quantum corrections of order $\mathcal{O}(G^{2})$ in the Newtonian potential. We first derive the modified Friedmann equations starting from the non-relativistic…
In this paper we discuss the quantum potential approach of Bohm in the context of quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe to a set of equations describing the time evolution of…