It from Qubit

Abstract

In this essay I will embark on the venture of changing the realist reader’s mind about the informational viewpoint for physics: “It from Bit”. I will try to convince him of the amazing theoretical power of such paradigm. Contrarily to the common belief, the whole history of physics is indeed a winding road making the notion of “physical object”—the “It”—fade away. Such primary concept, on which the structure of contemporary theoretical physics is still grounded, is no longer logically tenable. The thesis I advocate here is that the “It” is emergent from pure information, an information of special kind: quantum. The paradigm then becomes: “It from Qubit”. Quantum fields, particles, space-time and relativity simply emerge from countably infinitely many quantum systems in interaction. Don’t think that, however, we can cheat by suitably programming a “simulation” of what we see. On the contrary: the quantum software is constrained by very strict rules of topological nature, which minimize the algorithmic complexity. The rules are: locality, unitarity, homogeneity, and isotropy of the processing, in addition to minimality of the quantum dimension. What is amazing is that from just such simple rules, and without using relativity, we obtain the Dirac field dynamics as emergent.

The following dissertation is a minimally updated version of the original essay presented at the FQXi Essay Contest 2013 “It From Bit or Bit From It”. A short summary of the follow-ups and main research results is given in the Postscriptum.

Postscriptum

All predictions contained in this Essay has been later derived, and are now available in technical papers. The reader should look at Ref. [7] and the new Refs. [23, 25, 26]. The main result is contained in manuscript [7], entitled “Derivation of the Dirac equation from informational principles”. There it is proved the remarkable result that from the only general assumptions of locality, homogeneity, isotropy, linearity and unitarity of the interaction network, only two quantum cellular automata follow that have minimum dimension two, corresponding to a Fermi field. The two automata are connected by CPT, manifesting the breaking of Lorentz covariance. Both automata converge to the Weyl equation in the relativistic limit of small wave- vectors, where Lorentz covariance is restored. Instead, in the ultra- relativistic limit of large wave-vectors (i.e. at the Planck scale), in addition to the speed of light one has extra invariants in terms of energy, momentum, and length scales. The resulting distorted Lorentz covariance belongs to the class of the Doubly Special Relativity of Amelino-Camelia/Smolin/Magueijo. Such theory predicts the phenomenon of relative locality, namely that also coincidence in space, not only in time, depends on the reference frame. In terms of energy and momentum covariance is given by the group of transformations that leave the automaton dispersion relations unchanged. Via Fourier transform one recovers a space-time of quantum nature, with points in superposition. All the above results about distorted Lorentz covariance are derived in Ref. [13].

The Weyl QCA is the elementary building block for both the Dirac and the Maxwell field. The latter is recovered in the form of the de Broglie neutrino theory of the photon. The Fermionic fundamental nature of light follows from the minimality of the field dimension, which leads to theory Boson as an emergent notion [26].

The discrete framework of the theory allows to avoid all problems that plague quantum field theory arising from the continuum, including the outstanding problem of localization. Most relevant, the theory is quantum ab initio, with no need of quantization rules.