Introduction

Modern physics is built upon three principal pillars, quantum mechanics, special relativity, and general relativity. Historically, these principles were developed as logically independent extensions of classical Newtonian mechanics. While each theory constitutes a logically self-consistent framework, unification of these fundamental principles encountered unprecedented difficulties. Quantum mechanics and special relativity were unified in the middle of the last century, giving birth to relativistic quantum field theory. While tremendously successful in explaining experimental data, ultraviolet infinities in the calculations hint that the theory can not be in its final form. Unification of quantum mechanics with general relativity proves to be a much more difficult task and is still the greatest unsolved problem in theoretical physics.

In view of the difficulties involved with unifying these principles, we can ask a simple but rather bold question: is it possible that the three principles are not logically independent, but rather that there is an hierarchical order in their logical dependence? In particular, we notice that both relativity principles can be formulated as statements of symmetry. When applying nonrelativistic quantum mechanics to systems with a large number of degrees of freedom, we sometimes find that symmetries can emerge in the low-energy sector, which are not present in the starting Hamiltonian.