David Finkelstein was very fond of the new information-theoretic paradigm of physics advocated by John Archibald Wheeler and Richard Feynman. Only recently, however, the paradigm has concretely shown its full power, with the derivation of quantum theory (Chiribella et al., Phys. Rev. A 84:012311, 2011; D'Ariano et al., 2017) and of free quantum field theory (D'Ariano and Perinotti, Phys. Rev. A 90:062106, 2014; Bisio et al., Phys. Rev. A 88:032301, 2013; Bisio et al., Ann. Phys. 354:244, 2015; Bisio et al., Ann. Phys. 368:177, 2016) from informational principles. The paradigm has opened for the first time the possibility of avoiding physical primitives in the axioms of the physical theory, allowing a refoundation of the whole physics over logically solid grounds. In addition to such methodological value, the new information-theoretic derivation of quantum field theory is particularly interesting for establishing a theoretical framework for quantum gravity, with the idea of obtaining gravity itself as emergent from the quantum information processing, as also suggested by the role played by information in the holographic principle (Susskind, J. Math. Phys. 36:6377, 1995; Bousso, Rev. Mod. Phys. 74:825, 2002). In this paper I review how free quantum field theory is derived without using mechanical primitives, including space-time, special relativity, Hamiltonians, and quantization rules. The theory is simply provided by the simplest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the three following simple principles: homogeneity, locality, and isotropy. The inherent discrete nature of the informational derivation leads to an extension of quantum field theory in terms of a quantum cellular automata and quantum walks. A simple heuristic argument sets the scale to the Planck one, and the observed regime is that of small wavevectors ...

34 pages, 8 figures. Paper for in memoriam of David Finkelstein