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 n ＞3 in/out connections.
Turyshev, S.G., Toth, V.T., Kinsella, G., Lee, S.-C., Lok, S.M. and Ellis, J. (2012) Support for the Thermal Origin of the Pioneer Anomaly. Physical Review Letters, 108, Article ID: 241101. https://doi.org/10.1103/PhysRevLett.108.241101