Introduction to General Relativity

Abstract

The formulations of the theories of special and general relativity and of the theory of quantum mechanics in the first decades of the twentieth century are a fundamental milestone in science, not only for their profound implications in physics but also for the research methodology. In the same way, the courses of special and general relativity and of quantum mechanics represent an important milestone for every student of physics. These courses introduce a different approach to investigate physical phenomena, and students need some time to digest such a radical change. In Newtonian mechanics and in Maxwell’s theory of electrodynamics, the approach is quite empirical and natural. First, we infer a few fundamental laws from observations (e.g., Newton’s Laws) and then we construct the whole theory (e.g., Newtonian mechanics). In modern physics, starting from special and general relativity and quantum mechanics, this approach may not be always possible. Observations and formulation of the theory may change order. This is because we may not have direct access to the basic laws governing a certain physical phenomenon. In such a case, we can formulate a number of theories, or we can introduce a number of ansatzes to explain a specific physical phenomenon within a certain theory if we already have the theory, and then we compare the predictions of the different solutions to check which one, if any, is consistent with observations. For example, Newton’s First, Second, and Third Laws can be directly inferred from experiments. Einstein’s equations are instead obtained by imposing some “reasonable” requirements and they are then confirmed by comparing their predictions with the results of experiments. In modern physics, it is common that theorists develop theoretical models on the basis of “guesses” (motivated by theoretical arguments but without any experimental support), with the hope that it is possible to find predictions that can later be tested by experiments.