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We prove definitive results on the global stability of the flat space among solutions of the Einstein-Klein-Gordon system. Our main theorems in this monograph include: (1) A proof of global regularity (in wave coordinates) of solutions of…
An orbiting `photon clock' is proposed to test directly the relativity of simultaneity of special relativity. This is done by comparison of the arrival times at a ground station of three microwave signals transmitted by two satellites…
The notion that the metric field in general relativity can be understood as a property of space-time rests on a feature of the theory sometimes called universal coupling -- the claim that rods and clocks "measure" the metric in a way that…
One of the characteristic features of categorical systems theory is that the behavior of systems can be characterized by certain morphisms into them. In other words, behaviors form a representable covariant functor to Set. And more…
A possible solution to the problem of providing a spacetime description of the transmission of signals for quantum entangled states is obtained by using a bimetric spacetime structure, in which quantum entanglement measurements alter the…
Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space…
In earlier papers we showed unpredictability beyond quantum uncertainty in atomic clocks, ensuing from a proven gap between given evidence and explanations of that evidence. Here we reconceive a clock, not as an isolated entity, but as…
Continuing from a companion article: 'Random walks and contracting elements I: Deviation inequality and limit laws', we study random walks on metric spaces with contracting elements. We prove that random subgroups of the isometry group of a…
We elaborate on a geometric characterization of the electromagnetic properties of matter. A fundamental complex quantity, z_{L}, is introduced to study the localization properties of extended quantum systems. z_L, which allows us to…
Two important classes of quantum structures, namely orthomodular posets and orthomodular lattices, can be characterized in a classical context, using notions like partial information and points of view. Using the formalism of representation…
Time is a parameter playing a central role in our most fundamental modeling of natural laws. Relativity theory shows that the comparison of times measured by different clocks depends on their relative motions and on the strength of the…
In the article we present explicit expressions for quantum fluctuations of spacetime in the case of $(4+n)$-dimensional spacetimes, and consider their holographic properties and some implications for clocks, black holes and computation. We…
We argue that special and general theories of relativity implicitly assume spacetime events correspond to quantum measurement outcomes. This leads to a change in how one should view the equivalence of spacetime and gravity. We describe a…
Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an ad hoc fashion. Here, instead, we start from the…
We show that there exists a divergent correlation length in 2d quantum gravity for the matter fields close to the critical point provided one uses the invariant geodesic distance as the measure of distance. The corresponding…
We study the scattering of photons from periodically modulated quantum-optical systems. For excitation-number conserving quantum optical systems, we connect the analytic structure of the frequency-domain N-photon scattering matrix of the…
Sorting quantum fields into different modes according to their Fock-space quantum numbers is a highly desirable quantum operation. In this Letter, we show that a pair of two-level emitters, chirally coupled to a waveguide, may scatter…
We introduce the concept of monodromy coordinates for representing solutions to large polynomial systems. Representing solutions this way provides a time-memory trade-off in a monodromy solving algorithm. We describe an algorithm, which…
The localization tensor is a measure of distinguishability between insulators and metals. This tensor is related to the quantum metric tensor associated with the occupied bands in momentum space. In two dimensions and in the thermodynamic…
We describe the geomety of a set of scalar fields coupled to gravity. We consider the formalism of a differential Z_2-graded algebra of $2\times 2$ matrices whose elements are differential forms on space-time. The connection and the…