Related papers: Space-time structure may be topological and not ge…

Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the…

We study in this paper different topos-theoretical approaches to the problem of construction of General Theory of Relativity. In general case the resulting space-time theory will be non-classical, different from that of the usual Einstein…

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…

We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of intrinsic topological order with the spontaneous breaking of discrete time-translation symmetry. We show…

Any acceptable quantum gravity theory must allow us to recover the classical spacetime in the appropriate limit. Moreover, the spacetime geometrical notions should be intrinsically tied to the behavior of the matter that probes them. We…

The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…

Topological phases of matter have sparked an immense amount of activity in recent decades. Topological materials are classified by topological invariants that act as a non-local order parameter for any symmetry and condition. As a result,…

In architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on point-sets. Shapes made with points can be understood more generally as finite arrangements…

Topological defects are produced during phase transitions in the very early Universe. They arise in most unified theories of strong, weak and electromagnetic interactions. These lectures focus on the role of topological defects in…

We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…

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…

We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a…

We study the emergence of Minkowski space-time from a causal network. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from…

Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…

The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…

The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via…

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied…

The topology of the causal boundary for standard static spacetimes--spacetimes time-invariantly conformal to a metric product of the Lorentz line and a Riemannian manifold--is studied in depth. As this is given in terms of a set of…

The dimensional structure of space-time is investigated according to physical and mathematical methods. We show that ther are various empirical and theoretical restrictions on the number of independent dimensions of space-time, consequently…

There are two classes of topologies most often placed on the space of Lorentz metrics on a fixed manifold. As I interpret a complaint of R. Geroch [Relativity, 259 (1970); Gen. Rel. Grav., 2, 61 (1971)], however, neither of these standard…