Sounding the Universe with a relativistic solar sailboat or Einstein-Dirac fermions
The Universe exerts a curiosity on man that is both undeniable and fundamental. To unravel the mysteries of the Cosmos, man is driven to develop two major investigative strategies: direct exploration by sending space probes, and indirect exploration by observing cosmic electromagnetic fields, gravitational waves or particles such as fermions.
Following these two strategies, in this thesis we develop, in the first approach (consisting of sending a space probe), a relativistic kinematic and dynamical model of photonic sails (light sails) with arbitrary reflectivity and absorbance, moving in a non-rectilinear manner with the aim of exploring interstellar space. The problem is to determine the sail's trajectory in a Minkowski spacetime, a four-dimensional variety. From detailed calculations, we obtain the sail's universe line in the laser reference frame as a function of the sail's proper time.
The second approach applies the Two-State Vector Formalism and weak measurements to a homogeneous, isotropic cosmological framework. By coupling Dirac spinners to classical gravity, we calculate weak values of the energy-impulse tensor, the Z component of spin and pure states. Extending the work of Finster and Hainzl on Einstein-Dirac cosmology, we show that the accelerated expansion of the Universe can be interpreted as a consequence of post-selection. We also demonstrate that weak measurements can amplify signals using simpler equipment, thanks to judicious selection of the initial and final state vectors. In addition, this procedure highlights certain geometric properties of the Cosmos' three-dimensional space, offering a new way of exploring the structure of the Universe.
We also examine the mathematical structure on which the Dirac equation rests beyond the usual dimension and signature. This reveals a rich internal symmetry and gives rise to a particularly aesthetic diagrammatic representation.
