This chapter begins a short, two-chapter section on calculations that specifically impact the philosophy of quantum mechanics. A quantitative discussion of the famous Einstein–Podalsky–Rosen (EPR) experiment is given, as well as a mathematical discussion of problems with the many-worlds hypothesis, the Bohmian pilot-wave hypothesis, and the “transactional” hypothesis for interpreting quantum mechanics.

Given the philosophical problems of the Copenhagen interpretation, several other approaches to interpreting quantum mechanics have been proposed over the years. This chapter surveys four of these approaches, namely the many-worlds hypothesis, Bohmian “pilot waves,” positivist approaches, and spontaneous collapse of the quantum wave function. Problems with each of these approaches are discussed.

This chapter guides the reader through three related enigmas of modern physics. The first is a mystery of quantum mechanics. Important aspects of quantum mechanics are still not truly understood, although competing theories have been proposed, including the Many-Worlds approach. The second enigma is the emergence of spacetime, and especially the way it interacts with gravity. Rather than following the traditional methodology of ‘quantising’ classical theories, the author proposes an alternative approach and instead seeks gravity within quantum mechanics. The chapter concludes with a discussion of the mystery of the arrow of time: what distinguishes the past from the future. Together, these three mysteries of modern physics serve as an important reminder of the endurance of enigmas in the very foundations of scholarly fields. Re-examining founding principles can provide a constructive alternative means of investigating mysteries, not only in modern science but also across other disciplines.