相关论文: Quantum mechanics without spacetime - a possible c…
By considering a new form of dimensional reduction for noncommutative field theory, we show that the signature of spacetime may be changed. In particular, it is demonstrated that a temporal dimension can emerge from a purely Euclidean…
Noncommutative geometry, in its many incarnations, appears at the crossroad of various researches in theoretical and mathematical physics: from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and…
The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full spacetime covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical…
Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first…
We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional…
Time in quantum gravity is not a well-defined notion, despite its central role in the very definition of dynamics. Using the formalism of quantum geometrodynamics, we shortly review the problem and illustrate it with two proposed solutions.…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
A consistent quantum theory of gravity has remained elusive ever since the emergence of General Relativity and Quantum Field Theory. Attempts to date have not yielded a candidate that is either free from problematic theoretical…
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
The paper addresses the quantization of minisuperspace cosmological models by studying a possible solution to the problem of time and time asymmetries in quantum cosmology. Since General Relativity does not have a privileged time variable…
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model…
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…
Quantum field planes furnish a noncommutative differential algebra $\Omega$ which substitutes for the commutative algebra of functions and forms on a contractible manifold. The data required in their construction come from a quantum field…
Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are…
The concepts of space, time, and matter are of central importance in any theory of the gravitational field. Here I discuss the role that these concepts might play in quantum theories of gravity. To be concrete, I will focus on the most…
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
We give a brief account of the description of the standard model in noncommutative geometry as well as the thermal time hypothesis, questioning their relevance for quantum gravity.