Replacing the Notion of Spacetime Distance by the Notion of Correlation

Abstract

Spacetime is conventionally viewed as a stage on which actors, in the form of massive and massless matter, move. In this study, we explore what may lie beyond this picture. The starting point is the observation that quantum field fluctuations are the more strongly correlated the shorter their spacetime distance. The notion of spacetime distance can, therefore, be replaced by the notion of correlation strength. This suggests a new picture in which the abstract 2-point and multi-point correlations are the primary structure, a picture which is essentially information-theoretic. In the low energy regime, the secondary notions of spacetime and of matter would then emerge as approximate representations of the abstract correlators, namely, in the form of Feynman rules on curved spacetime.

Quantum signatures of black hole mass superpositions

“…al. and Kempf [56,57]. Recall that in general relativity, spacetime is described by the pair (M, σ) where M is a differentiable manifold and σ(x, x ) is the Synge world function (or the geodesic distance) for two points (x, x ) [58][59][60][61].…”

“…Since the quantum correlations of a field decay with the magnitude of the distance between spacetime points, these studies replaced the notion of proper distance with that of an appropriate measure of such correlations. In [57], the Feynman propagator is used, but other objects like the Wightman function (most relevant to this work) are also suitable. Using the Wightman function, the spacetime metric can be expressed as (22) where Υ(D) = −(1/2)(Γ(D/2 − 1)/(4π D/2 )) 2 D−2 and D > 2 is the spacetime dimension 5 .…”

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

“…While this approach has also been applied to stochastic models, it addresses neither the determinism of initial conditions in such models, nor more subtle questions of nonlocality and the structure of space-time with corresponding frameworks used for it. The latter is the topic of discussions, new proposals, and continuous debates that are seen often in the domain of quantum mechanics [98][99][100][101][102][103][104].…”

Spacetime curvature from ultra rapid measurements of quantum fields

“…Although this approach does not provide a full theory of quantum gravity, it gives important results, such as the Unruh and Hawking effects [1][2][3][4] and the model of inflation [5], which describes the universe fractions of seconds after its creation. A more recent application of this semiclassical theory is to rephrase classical notions of space and time intervals in terms of properties of quantum fields [6][7][8][9]. As argued in [8,9], this rephrasing might lead to a quantum theory of spacetime, which could redefine the notions of distance and time close to the Planck scale.…”

“…A more recent application of this semiclassical theory is to rephrase classical notions of space and time intervals in terms of properties of quantum fields [6][7][8][9]. As argued in [8,9], this rephrasing might lead to a quantum theory of spacetime, which could redefine the notions of distance and time close to the Planck scale.…”