Related papers: Classical Spacetime Structure
As repeatedly emphasized by Einstein our knowledge of the structure of space and time is based entirely on inferences from observations of physical objects and processes. At the most fundamental level these objects and processes are…
We develop a so-called theory of ensembles in phase space and use it to investigate the construction of a quantum-classical hybrid theory. We use Galilei covariance and the Lie algebra of the Galilei group as a guide to constructing the…
This work is essentially a review of a new spacetime model with closed causal curves, recently presented in another paper (Class. Quantum Grav. \textbf{35}(16) (2018), 165003). The spacetime at issue is topologically trivial, free of…
GR and other theories have been obtained from 3-space rather than spacetime principles. I explore consequences of this as regards the Problem of Time.
In this essay based on 0907.2939, we argue that the emergence of classically connected spacetimes is intimately related to the quantum entanglement of degrees of freedom in a non-perturbative description of quantum gravity. Disentangling…
Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate…
Quantum mechanics can seem like a departure from everyday experience of the physical world, but constructivist theories assert that learners build new ideas from their existing ones. To explore how students can navigate this tension, we…
From antiquity the conceptual perception of space changed painfully and at a relatively slow pace. It went through mythological descriptions, religious beliefs, metaphysical worldviews and cosmological models with a mechanistic structure,…
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…
The equations of Hamiltonian gravity are often considered ugly cousins of the elegant and manifestly covariant versions found in the Lagrangian theory. However, both formulations are fundamental in their own rights because they make…
This paper provides a thorough introduction to the causal set hypothesis aimed at students, and other interested persons, with some knowledge of general relativity and nonrelativistic quantum mechanics. I elucidate the arguments for why the…
The properties of the stable distance over stable spacetimes are used as a reference to propose a simplified, abstract notion of spacetime. The discussion shows that spacetime, with its topology, causal order and (upper semi-continuous)…
Quantum-classical correspondence in conservative chaotic Hamiltonian systems is examined using a uniform structure measure for quantal and classical phase space distribution functions. The similarities and differences between quantum and…
Classical mechanics unfolds within absolute time and Euclidean space, yet our knowledge of where events occur, when they occur, and how motion evolves is inherently uncertain. The special Galilean group provides a natural setting for…
Our assumption that spacetime is a continuum leads to many challenges in mathematical physics. Singularities, divergent integrals and the like threaten many of our favorite theories, from Newtonian gravity to classical electrodynamics,…
We briefly review some results concerning the problem of classical singularities in general relativity, obtained with the help of the theory of differential spaces. In this theory one studies a given space in terms of functional algebras…
Between the microscopic domain ruled by quantum gravity, and the macroscopic scales described by general relativity, there might be an intermediate, "mesoscopic" regime, where spacetime can still be approximately treated as a differentiable…
The advantages to consider the ordinary space-time as the symplectic rather than pseudo-orthogonal one are indicated, and the consequences of extending this view to extra space/time dimensions are discussed.
Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive…
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…