Related papers: An algebraic approach to gravitational quantum mec…
Gravitation, according to General Relativity, is an attribute of space-time's geometry and hence not a force in the Newtonian sense. This is a consequence of Einstein's equivalence principle, which so far passed all experimental tests with…
In Einstein's gedankenexperiment for measuring space and time, an ensemble of clocks moving through curved spacetime measures geometry by sending signals back and forth, as in the global positioning system (GPS). Combining well-known…
The existence of minimal length scale has motivated the proposal of generalized uncertainty principle, which provides a potential routine to probe quantum gravitational effects in low-energy quantum mechanics experiment. Hitherto, the…
A free scalar field minimally coupled to gravity model is quantized and the Wheeler-DeWitt equation in minisuperspace is solved analytically, exhibiting positive and negative frequency modes. The analysis is performed for positive, negative…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
We consider the scenario of a fluctuating spacetime due to a deformed commutation relation with a fluctuating deformation parameter, or to a fluctuating metric tensor. By computing the resulting dynamics and averaging over these…
An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt…
This paper elaborates on an intrinsically quantum approach to gravity, which begins with a general framework for quantum mechanics and then seeks to identify additional mathematical structure on Hilbert space that is responsible for gravity…
Loop Quantum Gravity is a formalism for describing the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity. The most important result of LQG is that geometric quantities such as area and…
Many theories that attempt to formulate a quantum description of gravity suggest the existence of a fundamental minimum length scale. A popular method for incorporating this minimum length is through a modification of the Heisenberg…
It is shown that introducing the quantum effects using deBroglie--Bohm theory in the canonical formulation of gravity would change the constraints algebra. The new algebra is derived and shown that it is the clear projection of general…
A satisfactory theory of quantum gravity may necessitate a drastic modification of our perception of space-time, by giving it a foamy structure at distances comparable to the Planck length. It is argued in this essay that the experimental…
The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under…
Relational formulations of classical mechanics and gravity have been developed by Julian Barbour and collaborators. Crucial to these formulations is the notion of shape space. We indicate here that the metric structure of shape space allows…
Although the deformation of the Heisenberg algebra by a minimal length has become a central tool in quantum gravity phenomenology, it has never been rigorously obtained and is often derived using heuristic reasoning. In this study, we move…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to so-called Generalized…
We derive the quantum Einstein equations (which are the quantum generalisation of the Einstein equations of classical gravity) from Bohmian quantum gravity. Bohmian quantum gravity is a non-classical geometrodynamics (in the ADM formalism)…
Assuming a minimum value for area measurement, the emergence of quantum mechanics can be easily motivated from naive consideration of gravitational force. Here we provide some pedagogical examples and extensions. At the same time, the role…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…