Related papers: Emergence of Time
It is shown that the differential geometry of space-time, can be expressed in terms of the algebra of operators on a bundle of Hilbert spaces. The price for this is that the algebra of smooth functions on space-time has to be made…
Emergent gravity is based on the Darboux theorem or the Moser lemma in symplectic geometry stating that the electromagnetic force can always be eliminated by a local coordinate transformation as far as U(1) gauge theory is defined on a…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.
A central open problem in quantum gravity is to understand how continuum spacetime emerges from quantum-geometric degrees of freedom in a background-independent setting. A many-body perspective suggests that spacetime emerges as a…
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a…
A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides…
We present a relational framework in which temporal structure is not fundamental but emerges from correlations within a globally stationary quantum state. Each subsystem includes an internal clock, and conditional states evolve effectively…
In previous works, we showed that both time and space can emerge from entanglement within a globally constrained quantum Universe, with no background coordinates. By extending the Page and Wootters quantum time formalism to include both…
Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding…
In this paper, I emphasize those features of the extended phase space approach to quantization of gravity that distinguish it among other approaches. First of all, it is the conjecture about non-trivial topology of the Universe which was…
A monistic framework is set up where energy is the only fundamental substance. Different states of energy are ordered by a set of scalar qunatum-phase-fields. The dual elements of matter, mass and space, are described as volume- and…
By quantising the gravitational dynamics, space and time are usually forced to play fundamentally different roles. This raises the question whether physically relevent configurations could also exist which would not admit…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
A version of foliated spacetime is constructed in which the spatial geometry is described as a time dependent noncommutative geometry. The ADM version of the gravitational action is expressed in terms of these variables. It is shown that…
The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise…
A cosmological time variable is emerged from the hamiltonian formulation of unimodular theory of gravity to measure the evolution of dynamical observables in the theory. A set of constants of motion has been identified for the theory on the…
In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have proposed a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry was developed in terms of a noncommutative algebra…
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…