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.