Related papers: 'Topological parallel world' constructed by modifi…
``One could imagine that as a result of enormously extended astronomical experience, the entire universe consists of countless identical copies of our Milky Way, that the infinite space can be partitioned into cubes each containing an…
I survey physics theories involving parallel universes, arguing that they form a natural four-level hierarchy of multiverses allowing progressively greater diversity. Level I: A generic prediction of inflation is an infinite ergodic…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
The many-worlds interpretation of quantum mechanics predicts the formation of distinct parallel worlds as a result of a quantum mechanical measurement. Communication among these parallel worlds would experimentally rule out alternatives to…
We introduce "anamorphic" cosmology, an approach for explaining the smoothness and flatness of the universe on large scales and the generation of a nearly scale-invariant spectrum of adiabatic density perturbations. The defining feature is…
Temporal sampling does more than add another axis to the vector of observables. Instead, under the recognition that how objects change (and move) in time speaks directly to the physics underlying astronomical phenomena, next-generation…
In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the…
We consider manifolds whose transition maps are restrictions of polynomial mappings $\mathbb{R}^n\to\mathbb{R}^n$, and use them to give an equivalent statement of the Jacobian conjecture over the real field.
We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized…
An analogy is developed between the bubble universe model and the Young-Laplace equation obtaining an analogic equation and commenting some numerical results produced by its application. The results, even if based on a simple analogy,…
We present the foundations of a new emerging interpretation of quantum theory bearing wide-range implications. Physical basis of the interpretation is non-questionable yet relatively new--it relies on the different structures…
A review is given of recent work aimed at constructing a quantum theory of cosmology in which all observables refer to information measurable by observers inside the universe. At the classical level the algebra of observables should be…
We construct relational observables in group field theory (GFT) in terms of covariant positive operator-valued measures (POVMs), using techniques developed in the context of quantum reference frames. We focus on matter quantum reference…
We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers.…
We review and relate two recent complementary constructions of linear local gauge-invariant observables for cosmological perturbations in generic spatially flat single-field inflationary cosmologies. After briefly discussing their physical…
It is congruous with the quantum nature of the world to view the space-time geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the space-time manifold as a purely…
Quantum set theory (QST) and topos quantum theory (TQT) are two long running projects in the mathematical foundations of quantum mechanics that share a great deal of conceptual and technical affinity. Most pertinently, both approaches…
We propose and develop a measurement scheme for quantum field theory (QFT) in curved spacetimes, in which the QFT of interest, the "system", is dynamically coupled to another, the "probe", in a compact spacetime region. Measurements of…
Hamiltonian gravity, relying on arbitrary choices of "space," can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between "spatial" and "temporal" variables.…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…