Related papers: Analogue of Null Geodesic in Quantum Spacetime
We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature $K$ are…
Using coordinate-free basic operators on toy Fock spaces \cite{AP}, quantum random walks are defined following the ideas in \cite{LP,AP}. Strong convergence of quantum random walks associated with bounded structure maps is proved under…
All gauge theories need ``something fixed'' even as ``something changes.'' Underlying the implementation of these ideas all major physical theories make indispensable use of an elaborately designed spacetime model as the ``something…
Black holes are one of the most fascinating predictions of general relativity. They are the natural product of the complete gravitational collapse of matter and today we have a body of observational evidence supporting the existence of…
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies…
Singularity theorems demonstrate the inevitable breakdown of the concept of continuous, classical spacetime under highly general conditions. Quantum gravity is expected to intervene to avoid singularities and models so far hint towards…
Searches for transient astrophysical pulses could open an exciting new window into the fundamental physics of quantum gravity. In particular, an evaporating primordial black hole in the presence of an extra dimension can produce a…
In quantum theory the vacuum is defined as a state of minimum energy that is devoid of particles but still not completely empty. It is perhaps more surprising that its definition depends on the geometry of the system and on the trajectory…
We consider how causality and micro-causality are realised in QED in curved spacetime. The photon propagator is found to exhibit novel non-analytic behaviour due to vacuum polarization, which invalidates the Kramers-Kronig dispersion…
According to quantum field theory, empty space -- the ground state of the theory with all real excitations removed -- is not empty at all, but filled with quantum-vacuum fluctuations. Their presence can manifest itself through a series of…
It is shown that there are static spacetimes with timelike curvature singularities which appear completely nonsingular when probed with quantum test particles. Examples include extreme dilatonic black holes and the fundamental string…
Starting with the Hamiltonian formulation for spacetimes with two commuting spacelike Killing vectors, we construct a midisuperspace model for linearly polarized plane waves in vacuum gravity. This model has no constraints and its degrees…
Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a…
A `quantum inequality' (a conjectured relation between the energy density of a free quantum field and the time during which this density is observed) has recently been used to rule out some of the macroscopic wormholes and warp drives. I…
We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation…
Space-time--time is a natural hybrid of Kaluza's five-dimensional geometry and Weyl's conformal space-time geometry. Translations along the secondary time dimension produce the electromagnetic gauge transformations of Kaluza--Klein theory…
The vacuum is the lowest energy state of a field in a certain region of space. This definition implies that no particles can be present in the vacuum state. In classical physics, the only features of vacuum are those of its geometry. For…
Atoms and the planets acquire their stability from the quantum mechanical incompatibility of the position and momentum measurements. This incompatibility is expressed by the fundamental commutator [x, p_x]=i hbar, or equivalently, via the…
We apply a recent formalism of quantum geodesics to the well-known bicrossproduct model $\lambda$-Minkowski quantum spacetime $[x^i,t]=\imath\lambda_p x^i$ with its flat quantum metric as a model of quantum gravity effects, with $\lambda_p$…
In this paper a theorem is derived in order to provide a wide sufficient condition for an orthogonally transitive cylindrical spacetime to be singularity-free. The applicability of the theorem is tested on examples provided by the…