Can metatheoretical misconceptions be ultimately responsible for the lack of breakthroughs in fundamental physics in recent decades? The answer outlined in the essay is yes. First I discuss such a misconception - that mathematics in physics is merely a description and therefore even fundamental mathematical entities (such as a manifold) do not represent counterparts in the physical world. Then I examine an instance of this misconception - that the four-dimensional manifold in relativity is only “an abstract four-dimensional mathematical continuum” - and summarize Minkowski's arguments that this four-dimensional manifold does represent a real four-dimensional world (spacetime). Finally, I discuss several negative implications of this misconception for the advancement of fundamental physics, including one which makes it impossible even to identify a radical (but not inconceivable) reason for the unsuccessful attempts to create a theory of quantum gravity.
Vesselin Petkov