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Over the last decade a growing number of quantum-gravity researchers has been looking for opportunities for the first ever experimental evidence of a Planck-length quantum property of spacetime. These studies are usually based on the…
We review the possibility that quantum fluctuations in the structure of space-time at the Planck scale might be subject to experimental probes. We study the effects of space-time foam in an approach inspired by string theory, in which…
This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given space-like…
We propose measurement-based quantum computation (MBQC) as a quantum mechanical toy model for spacetime. Within this framework, we discuss the constraints on possible temporal orders enforced by certain symmetries present in every MBQC. We…
Probabilistic Spacetime is a simple generalization of the classical model of spacetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
Nowadays, quantum simulation schemes come in two flavours. Either they are continuous-time discrete-space models (a.k.a Hamiltonian-based), pertaining to non-relativistic quantum mechanics. Or they are discrete-spacetime models (a.k.a…
Astrophysical observations provide a picture of the universe as a 4-dim homogeneous and isotropic flat space-time dominated by an unknown form of dark energy. To achieve such a cosmology one has to consider in the early universe an…
This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often…
This paper is generally concerned with understanding how the uncertainty principle arises in formulations of quantum mechanics, such as the decoherent histories approach, whose central goal is the assignment of probabilities to histories.…
In quantum mechanical experiments one distinguishes between the state of an experimental system and an observable measured in it. Heuristically, the distinction between states and observables is also suggested in scattering theory or when…
Simple models of a classical spacetime foam are considered, which consist of identical static defects embedded in Minkowski spacetime. Plane-wave solutions of the vacuum Maxwell equations with appropriate boundary conditions at the defect…
A century after the advent of Quantum Mechanics and General Relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable,…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
It is found that the existence of spacetime foam leads to a situation in which the number of fundamental quantum bosonic fields is a variable quantity. The general aspects of an exact theory that allows for a variable number of fields are…
A lattice quantum gravity model in 4 dimensional Riemannian spacetime is constructed based on the SU(2) Ashtekar formulation of general relativity. This model can be understood as one of the family of models sometimes called ``spin foam…
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…
We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum…
In generic models of cosmological inflation, quantum fluctuations strongly influence the spacetime metric and produce infinitely many regions where the end of inflation (reheating) is delayed until arbitrarily late times. The geometry of…
Fluctuation terms and higher moments of a quantum state imply corrections to the classical equations of motion that may have implications in early-universe cosmology, for instance in the state-dependent form of effective potentials. In…