Sir Martin Reese’s second model of 1978 was another Population III (pre-galactic stellar) explanation but with the motivation of deriving the photon-to-baryon ratio from known astrophysical processes. As the chapter explains, this motivation was interconnected with concerns about fine-tuning physical constants and cosmological parameters to enable a habitable universe. The non-primordial origin of the CMB Reese worked out with Bernard J. Carr was driven by adherence to the simplicity of a hypothesis. He expressed sympathy with Paul Dirac’s hypothesis of large number of coincidences that established relations between the age of the universe and atomic units, the gravitational constant and cosmic time, and the number of nucleons and cosmic time in terms of large dimensionless numbers. Dirac turned his initial hypothesis into a full-fledged but unusual and intriguing variant of the Big Bang model. The chapter presents some discussions of the model with respect to the precision of the measurements of the CMB.

The purpose of this chapter is to clearly define the mathematical objects that describe particles of various kinds: bosons (spin-0 and spin-1) or spin-1/2 fermions. Starting from the Schrödinger equation, the Klein–Gordon equation, the Dirac equation and the Maxwell equations are detailed, leading to the description of the associated quantised field – a well-adapted framework to treat states composed of many particles that can be created or annihilated when they interact. The notion of 4-current is introduced, and the quantisation of the various fields is presented. With the Dirac equation, the spinor’s properties are described extensively. The interpretation of the solutions of the Dirac equation in terms of antiparticles and spin or helicity degrees of freedom is then detailed. Helicity and chirality are also treated carefully. Finally, the Maxwell field and the Proca field are described, highlighting their specificities in terms of polarisation degrees of freedom.

This chapter examines Cassirer's view on contemporary science. It revisits Cassirer's lesser-known work Determinism and Indeterminism in Modern Physics and argues that it harbors a significantly new stage of his philosophy of physical science. On the one hand, this work presents the quantum formalism as a limiting pole of the Bedeutungsfunktion, the highest mode of symbolic formation according to Cassirer’s “phenomenology of cognition.” Inspired by Paul Dirac, Cassirer understands quantum mechanics as a symbolic calculus for deriving probabilistic predictions of measurement outcomes without regard to underlying wave or particle “images” – or, as an exemplar of abstract symbolic thought. On the other hand, Cassirer recognizes the philosophical significance of the use of group theory in quantum mechanics as advancing a purely structural concept of object in physics. Hence, Ryckman reveals that Cassirer drew epistemological consequences from the symbolic character of contemporary physical theory that retain relevance for philosophy of science today.