A Local Causal Model of Spacetime Dynamics

Abstract

The model of spacetime dynamics proposed here specifies how spacetime emerges, how changes of spacetime propagate, and how changes in spacetime arising from multiple sources accumulate. The overall goal of the model was to achieve maximum compatibility with general relativity and with Einstein's equation; this goal appears to be achievable except at very small scales, where the discreteness of the units of space matters. The elementary structure of space(-time) that is assumed in this model is a derivative of causal dynamical triangulation. At the elementary level, space consists of a (discrete) number of interconnected space points, each of which is connected to a small number of neighbouring space points. The curvature of spacetime is expressed by the density of these space points and by the arrangement of the connections between them. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Based on the model of the dynamics of curved discrete spacetime, a model of quantum field theory in curved discrete spacetime is described. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out space point connections. Compatibility with standard quantum field theory requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to 3 n > in/out connections.

The Generation of Quantum Objects by Quantum Loops

“…The process of space state progression consists of the repeated application of Spread-out/Bundle operations to all space points that are identified by gravitation dynamic ≠ 0 (see Definition 4). Further details on the subject of Section 4 can be found in [7] and [4].…”

“…Sources of space change dynamics. In [7] and [4], the sources of space change dynamics are described as quantum objects. In the present article, the model of spacetime dynamics is also applied to the dynamics of quantum objects and quantum fields.…”

“…The local causal model of spacetime dynamics described in [7] and [4] and summarized in Section 4 has been developed with the goal of providing a basis for a local causal model of QT/QFT. The application of the model to quantum theory and quantum field theory is described in the following: Open Access Library Journal In Definition 4, the gravitational field ψ G is represented by the gravitationspec attribute.…”

“…The loop behaviour described above applies to fermionic and bosonic field types. In addition to these field types, in Section 6.1 the gravitational field G ψ and Schrödinger field Open Access Library Journal namics described in [7] and [4] and in Section 4.3, quantum objects are treated as the sources of spacetime dynamics, that is, sources of the gravitational field.…”

“…Thus, a causal model of the dynamics of spacetime has been developed with these major goals: 1) as much as possible, be compatible with general relativity theory (GRT) and 2) should match the main features of the evolving model of QT/QFT. The causal model of spacetime dynamics is described in [4]. Because the model of spacetime dynamics is a major prerequisite of the work described in the present paper, a short description is also given in Section 4.…”