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Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…
In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define an fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction.…
In a recent paper Griffiths [38] has argued, based on the consistent histories interpretation, that Hilbert space quantum mechanics (QM) is noncontextual. According to Griffiths the problem of contextuality disappears if the apparatus is…
We explore the symmetry reduced form of a non-perturbative solution to the constraints of quantum gravity corresponding to quantum de Sitter space. The system has a remarkably precise analogy with the non-relativistic formulation of a…
It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion…
The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter…
We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
Relationships between objects constitute our notion of space. When these relationships change we interpret this as the passage of time. Observer interpretations are essential to the way we understand these relationships. Hence observer…
Violation of unitarity for noncommutative field theory on compact space-times is considered. Although such theories are free of ultraviolet divergences, they still violate unitarity while in a usual field theory such a violation occurs when…
We introduce a special class of bimetric theories of quantized fields with preserved classical energy conditions. More precisely, we describe the missing anti-particles in our visible universe as being trapped in a spacetime patch with…
Modern physics, via the standard model with Higgs mechanism and string theory for example, has supplied ether-like models and emergent general relativity scenarios that substantially weaken the usual defense of orthodox relativity and…
The non perturbative construction of quantum field models with nontrivial scattering in arbitrary dimension $d$ of the underlying Minkowski space-time is much more simple in the framework of quantum field theory with indefinite metric than…
We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular…
In this talk I briefly review recent developments in quantum field theories on a noncommutative Euclidean space, with Heisenberg-like commutation relations between coordinates. I will be concentrated on new physics learned from this…
Contemporary research programs in fundamental physics appear to suggest that there could be two (physical) times---or none at all. This essay articulates these possibilities in the context of quantum gravity, and in particular of…
In this paper, we outline a new approach to quantum gravity; describing states for a bounded region of spacetime as eigenstates for two classes of physically plausible gedanken experiments. We end up with two complementary descriptions in…
We put forward a model of discrete physical space that can account for the structure of space- time, give an interpretation to the postulates of quantum mechanics and provide a possible explanation to the organization of the standard model…
The "problem of time" in canonical quantum gravity refers to the difficulties involved in defining a Hilbert space structure on states -- and local observables on this Hilbert space -- for a theory in which the spacetime metric is treated…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…