The elements of General Relativity

This chapter is a survey of central ideas and equations in general relativity. The basic equations are written down with a view to seeing where we are heading in the book, and in order to present both the field theory and the geometric interpretation of gravity. The central role of the metric is introduced, and the equivalence principle is discussed. It is emphasized that spacetime interval is both a mathematical and a physical idea. It is explained how gravity works “behind the scenes” by modifying equations which otherwise look like familiar equations of electromagnetism. The sense in which acceleration is in some respects a relative and in some respects an absolute concept is explained. It is shown why the motion of matter, not just its mass, must influence gravitation. The stress-energy tensor is introduced and defined.

GRAVITATIONAL DRIVING: GEODESICS WARPED BY SOLITONS OF ACCELERATION

<p>Abstract. This article discusses the basic science to be considered as the background for a speculative technology of gravitational propulsion. Generalized functions are applied to the formalism of general relativity to introduce finite dynamic intervals of spacetime to be warped by acceleration solitons, the latter being interpreted as causing geodesic bends in the spacetime continuum.</p><p><strong>Key words</strong>: soliton, propultion, gravitational tail, warp-drive spacetime, spacetime interval.</p><p>=============================================================================</p><p>Dieser Artikel beschreibt die Grundlagenforschung, die als Hintergrund einer spekulativen Technologie des Gravitationsantriebs betrachtet werden soll. Verallgemeinerte Funktionen werden auf den Formalismus der allgemeinen Relativitätstheorie angewendet, um die richtigen Abstände als dynamische Raumzeitintervalle zu definieren. Einsame Beschleunigungswellen werden so interpretiert, dass sie die geodätischen Abweichungen im Raumzeitkontinuum verursachen.</p><p><strong>Schlüsselwörter</strong>: Soliton, Antrieb, Gravitationsschwanz, Warp-Drive-Raumzeit, Raumzeitintervall.</p>

Discrete Hilbert space, the Born Rule, and quantum gravity

Quantum gravitational effects suggest a minimal length, or spacetime interval, of order of the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is that quantum states with norm below some very small threshold do not exist. The exclusion of what Everett referred to as maverick branches is necessary for the emergence of the Born Rule in no collapse quantum mechanics. We discuss this in the context of quantum gravity, showing that discrete models (such as simplicial or lattice quantum gravity) indeed suggest a discrete Hilbert space with minimum norm. These considerations are related to the ultimate level of fine-graining found in decoherent histories (of spacetime geometry plus matter fields) produced by quantum gravity.