# Physics Without Physics

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## Abstract

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 re-foundation 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 currently observed regime where discreteness is not visible is the so-called “relativistic regime” of small wavevectors, which holds for all energies ever tested (and even much larger), where the usual free quantum field theory is perfectly recovered. In the present quantum discrete theory Einstein relativity principle can be restated without using space-time in terms of invariance of the eigenvalue equation of the automaton/walk under change of representations. Distortions of the Poincaré group emerge at the Planck scale, whereas special relativity is perfectly recovered in the relativistic regime. Discreteness, on the other hand, has some plus compared to the continuum theory: 1) it contains it as a special regime; 2) it leads to some additional features with GR flavor: the existence of an upper bound for the particle mass (with physical interpretation as the Planck mass), and a global De Sitter invariance; 3) it provides its own physical standards for space, time, and mass within a purely mathematical adimensional context. The paper ends with the future perspectives of this project, and with an Appendix containing biographic notes about my friendship with David Finkelstein, to whom this paper is dedicated.

## Keywords

Quantum fields axiomatics Quantum automata Walks Planck scale## Notes

### Acknowledgments

The present long-term unconventional project has needed a lot of energy and determination in the steps that had to be faced within the span of more than seven years. The work done up to now would have not been possible without the immeasurable contribution of some members of my group QUit in Pavia, as it can be seen from the list of references. All of them embraced with enthusiasm the difficult problems posed by the program, at the risk of their careers, in a authentically collaborative interaction. In particular, I am mostly grateful to Paolo Perinotti, with whom I had the most intense and interesting interactions of my entire career. I’m then very grateful to my postdocs Alessandro Bisio e Alessandro Tosini for their crucial extensive contribution, and to my PhD students Marco Erba and Nicola Mosco, and my previous PhD student Franco Manessi. I am very grateful to my long-date friend Matt Brin for introducing me to some among the top mathematicians in geometric group theory, which otherwise it would have been impossible for me to meet. In particular: Benson Farb, Dennis Calegari, Cornelia Drutu, Romain Tessera, and Roberto Frigerio. I personally learnt a lot from Benson Farb in four meetings in at the Burgeois Pig café in Chicago, during my august visits at NWU in Evanston, and am grateful to Dennis Calegari for two interesting meetings at UC. With Paolo Perinotti and Marco Erba we have visited Cornelia Drutu in Oxford, Romain Tessera in Paris, and Roberto Frigerio in Pisa, and from them we could learnt fast crucial mathematical notions and theorems, which otherwise it would have taken ages for us to find in books and articles. I want then to acknowledge some friends that enthusiastically supported me in the difficult stages of the advancement of this program, in particular my mentor and friend Attilio Rigamonti, and my friends Giorgio Goggi, Catalina Curceanu, Marco Genovese, all of them experimentalists, along with the theoreticians Lee Smolin, Rafael Sorkin, Olaf Dryer, Lucien Hardy, Kalamara Fotini Markopoulou, Bob Coecke, Tony Short, Vladimir Buzek, Renato Renner, Wolfgang Schleich, Lev B. Levitin, and Andrei Khrennikov, for appreciating the value of this research since the earlier heuristic stage. For inspiring scientific discussions I like to acknowledge Seth Lloyd, Reinhard F. Werner, Norman Margolus, Giovanni Amelino-Camelia, Shahn Majid, Louis H. Kauffman, and Carlo Rovelli, whereas I wish to thank Arkady Plotnitsky and Gregg Jaeger for very exciting discussions about history and philosophy of physics. I want finally to remark again the great help that I got from David Finkelstein, of whom I have been honored to be friend, and whose enthusiasm have literally boosted the second part of this project. Financially I acknowledge the support of the John Templeton foundation, whithout which the present project could had never take off from the preliminary heuristic stage.

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