The experience in Quantum Information has led the community to look at foundations of Quantum Theory under a completely new angle, regarding the theory as a “theory of information”, and leading to an axiomatization of Quantum Theory in information-theoretic terms. The need of addressing also the “Mechanics” side of the “Quantum” shifts now the focus toward the much wider landscape of Quantum Field Theory (QFT), corresponding to adding new principles that rule the information-processing achieving the “flow” of information. The exploration of the theoretical power of the new informational paradigm is now in business over the complete physical landscape.
In the talk it will be shown how the Dirac equation in three space-dimensions can be derived, without assuming Special Relativity, from principles of pure information-theoretic nature: unitarity, locality, homogeneity, and isotropy of the interactions, along with the requirement of minimal-dimension of the quantum field. Such principles all together can be synthesized by the only requirement of minimal algorithmic complexity of the information processing. The new informational principles are equivalent to a description of the field evolution in terms of a Quantum Cellular Automaton (QCA).
Differently from the lattice-gas theories, where QFT is recovered in the continuum limit, the automaton should be thought as the discrete Planck scale description of the field, regarding the QCA theory as a candidate for an extension of QFT that describes in a unified way all scales ranging from Planck to Fermi. From the informational principles one derives indeed two possible QCAs that are connected each other by the CPT symmetry. The Dirac equation is recovered from both QCAs in the relativistic limit of small momenta, whereas Lorentz covariance holds as an approximate symmetry, and the general covariance valid also in the ultra-relativistic regime is a Doubly-Special Relativity of the kind precognized by Amelino-Camelia, Smolin, and Magueijo.
The QCA theory has a list of good features that QFT lacks, and making the QCA an ideal framework for a quantum theory of gravity: the QCA framework is quantum ab-initio, is computable, has no divergences, avoids all problems arising from the continuum such as the localization and the causality issues. In addition, relativistic covariance is emergent and not assumed a priori. A simple asymptotic approach allows to derive a general dispersive Schroedinger equation that holds in all regimes for narrow-band states describing quantum particles. Such equation allows us to make predictions for possible experimental evidences or falsifications of the theory.