Spacetime and particle dynamics in Energetic Causal Sets.
PT-CERN Call 2022/2
FCUL (Universidade de Lisboa)
IA - Instituto de Astrofísica e Ciências do Espaço
We devote this project to fundamental issues of Physics inspired by progress in Quantum Gravity. Exploiting Sorkin’s causal sets approach [1; 2] and its award-winning development as Energetic Causal Sets by project supervisor Cortês and Smolin , I will study the structure of spacetime and its connection to time irreversibility, the emergence of Lorentzian manifolds and QFT dynamics on these spaces, cosmological signatures, and the nature of entropy. I will extend and enhance the simulations in [3; 4] to a more realistic 3+1D model, including Lorentz covariance and a cross-section for causal links. Supervisors Cortês and Liddle have already worked on the 2+1D case with encouraging results. These simulations will clarify the mechanism of transition from micro to macro causal structures and between reversible and irreversible regimes. The micro and macro causal structures need not agree in the causal sets approach. This dissonance is called disordered causality, and inspires us to quantise the causal structure using the Two Vector State Formalism [5; 6; 7]. Lorentzian manifolds can emerge from causal structures [8; 9; 10; 11]. We will exploit this possibility to retrieve the time-asymmetric extension of GR proposed by Cortês et al. [12; 13] by means of Cartan’s tetrad formulation of GR which allows to match the emergent flat spacetime to a curved manifold. Gravitational wave propagation is a promising observational test of this setup. Causal structures and entropy are profoundly connected [2; 14; 15]. We analyze this relation and work out astrophysical and cosmological scenarios. In particular, we will examine black hole entropy and the Bekenstein formula, and reinterpret the information and firewall paradoxes. Finally, the dynamics of vector and spinor fields in causal sets are yet to be determined. I will investigate them building the action for the electromagnetic field and coupling it to complex scalar and spinor fields.