Theoretical physics is a speculative branch of Physics that, starting from the assumption of basic hypotheses, develops them using the mathematical language to arrive at the enunciation of physical laws in the form of equations, thus representing, together with experimental physics, one of the two essential moments of scientific investigation in physics: the greater the universality of the laws, i.e. the larger is their domain of validity, the more important will be the corresponding theory. In other words, theoretical physics is that branch of physics that uses mathematical models and, more recently, numerical tools, in an attempt to rationalize, explain and predict natural phenomena.
The roots of theoretical physics go back to Greek philosophy, where the concepts of matter, energy, space, time, and causality slowly began to acquire the form we know today, along with the belief that nature can be described through mathematical symbolism. But the era of modern theoretical physics began several centuries later, in the early 1600s, with the Copernican paradigm shift in astronomy, followed closely by the discovery of the mathematical expression of planetary orbits by Kepler, who put to good use the meticulous observations of Tycho Brahe.
Simultaneously, the great physical insights of Galileo Galilei and the analytical geometry of Descartes were incorporated into the classical mechanics of Isaac Newton, extended in the eighteenth century by Joseph-Louis Lagrange, Leonhard Euler and William Rowan Hamilton, with whom the fruitful dialogue between mathematics and physics inaugurated two millennia earlier by Pythagoras had its final triumph.
The nineteenth century saw the consolidation of the idea of energy through the inclusion of heat, and then electricity, magnetism, light and finally mass. In this context the laws of thermodynamics, and in particular the introduction of the concept of entropy, began to offer a macroscopic explanation for the properties of matter, whose theoretical framework was instead provided by the statistical mechanics of Boltzmann and Gibbs, which relates the microscopic properties of individual atoms and molecules with the macroscopic properties of the materials we observe in everyday life, thus justifying thermodynamics as the natural result of the statistical and mechanical laws of the microscopic level.
But the pillars of modern theoretical physics, and perhaps the most revolutionary theories in the history of physics, were built at the beginning of the twentieth century: on the one hand, Newtonian mechanics was generalized by Einstein’s special relativity, which with general relativity also provided a kinematic explanation of Newton’s gravity; on the other hand, quantum mechanics led to an explanation of black body radiation and anomalies in the specific heat of solids, allowing a greater understanding of the internal structure of atoms and molecules.
Nowadays theoretical physicists are working to unify the main theories in an attempt to understand definitively the functioning of the Universe, from the cosmological scale to that of elementary particles (see for example the inflationary cosmology, the Standard Model, quantum field theory, QCD, superfluidity, quantum information, and so on), passing through the mesoscopic level represented by the physics of the solid state (see mechanics of solids, fluid dynamics, electronic structure of materials, chaos and complexity theories, theory of complex networks, etc.. ), up to the most recent applications of physical models to apparently distant fields such as biology, economics, sociology and so on (see biophysics, ecophysics, sociophysics, etc.). All these research fields are active within the Department of Physics and Astronomy of Catania with several groups of theoretical physicists engaged in these directions and international collaborations with other universities and research centers in the world.