### Abstract:

In this thesis we shall present a collection of research results about phenomena that lie at the interface between quantum physics and general relativity. The motivation behind our research work is to find alternative ways to tackle the problem of a quantum theory of/for gravitation.
In the general introduction, we shall briefly recall some of the characteristics of the well-established approaches to this problem that have been developed since the beginning of the middle of the last century. Afterward we shall illustrate why one would like to engage in alternative paths to better understand the problem of a quantum theory of/for gravitation, and the extent to which they will be able to shed some light into this problem.
In the first part of the thesis, we shall focus on formulating physics without Lorentz invariance. In the introduction to this part we shall describe the motivations that are behind such a possible choice, such as the possibility that the physics at energies near Planck regime may violate Lorentz symmetry. In the following part we shall first consider a minimalist way of breaking Lorentz invariance by renouncing the relativity principle, that corresponds to the introduction of a preferred frame, the aether frame. In this case we shall look at the transformations between a generic inertial frame and the aether frame still requiring the transformations to be linear. The second step is to establish the transformations for the energy and momentum in order to define some dynamics and design possible experiments to test such assumptions. As an application we shall present two compelling models that minimally break Lorentz invariance, the first one only in the energy-momentum sector, the second one in the transformation between inertial frames. Following along the line of physics without Lorentz invariance, we shall next explore some threshold theorems in both scattering and decay processes by considering only the existence of some energy momentum relation E(p), without making any further assumption. We shall see that quite a lot can be said and that 3-momenta can behave in a complicated and counter-intuitive manner.
In the second part of the thesis we shall address the thermodynamics of space-time and the important role played by entropy. In the introduction we shall outline the idea of induced gravity, which is the motivation behind this possible interpretation of general relativity as a mean field theory of some underlying microscopic degrees of freedom. In the next chapter we shall partially review Jacobson's thermodynamic derivation of the Einstein equations and generalise it to a generic birfucate null surface. The interesting result we shall see is that, given the construction of the thermodynamic system via some virtual constantly accelerating observers, we can assign a "virtual" definition of Clausius entropy to essentially arbitrary causal horizons. To conclude this part we shall present some of the mathematical properties of entropy. In particular we shall focus on the simpler case of single-channel Shannon entropy and study under which conditions it is infinite, even though the probability distribution is normalisable.
In the last part, we shall describe a proposal for a space-base experiment to test the effects of acceleration and gravity of quantum physics. In principle, the results of such an experiment could shed some light on fundamental questions about the overlap of quantum theory and general relativity; at the same time, they may enable experimentalists interested to implement quantum communication into space based technology, to correct adverse gravitational effects.
We conclude with a brief discussion of lessons learned from these different approaches.