Related papers: Spacetime could be simultaneously continuous and d…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
The spacetime structure of the spatially uniformly expanding universe is described in terms of a kind of global space and global time instead of the space and time we usually recognize. The global space at some instant is a space in which…
A holistic view of the cosmological appearance and development of space is obtained by studying space as a spherically closed surface of a 4-sphere in a zero energy balance between motion and gravitation. Such an approach re-establishes…
Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape…
We assume that space-time at the Planck scale is discrete, quantised in Planck units and "qubitsed" (each pixel of Planck area encodes one qubit), that is, quantum space-time can be viewed as a quantum computer. Within this model, one finds…
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 problem of classifying boundary points of space-time, for example singularities, regular points and points at infinity, is an unexpectedly subtle one. Due to the fact that whether or not two boundary points are identified or even…
Although we lack complete understanding of quantum aspects of gravitation, it is usually agreed, using general arguments, that a final quantum gravity theory will endow space and time with some (fundamental or effective) notion of…
This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts are developed in a totally combinatorial flavor. Some issues…
A novel definition of the stimulus-specific information is presented, which is particularly useful when the stimuli constitute a continuous and metric set, as for example, position in space. The approach allows one to build the spatial…
The complete set of solutions of two dimensional classical string theory are constructed for any curved spacetime. They describe folded strings moving in curved spacetime. Surprizing stringy behavior becomes evident at singularities such as…
The classical spacetime is usually described by a differentiable manifold with infinitely many degrees of freedom. Occasionally though, it is useful to consider an approximation whose number of degrees of freedom is finite. There are…
Nerd abstract: Observational constraints on spacetime are reviewed, focusing on how the underlying physics (dark matter, dark energy, gravity) can be tested rather than assumed. Popular abstract: Space is not a boring static stage on which…
A model of discrete space-time is presented which is, in a sense, both Lorentz invariant and has no restriction on the relative velocity between particles (except v < c). The space-time has an inbuilt indeterminacy. Published originally as…
A set of data supposed to give possible axioms for spacetimes. It is hoped that such a proposal can serve to become a testing ground on the way to a general formulation. At the moment, the axioms are known to be sufficient for cases with a…
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…
We apply the ``consistent discretization'' approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism…
I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of…
We focus on the question: "Is space fundamentally discrete or continuous?" in the context of current quantum gravity research. In particular, we paint a scenario based on the idea that 'quantum space' is a sort of peculiar condensed matter…
In this two-part paper we propose an extension of Connes' notion of even spectral triple to the Lorentzian setting. This extension, which we call a spectral spacetime, is discussed in part II where several natural examples are given which…