Quantum-Informational Principles for Physics

Abstract

It is time to to take a pause of reflection on the general foundations of physics, for re-examining the logical solidity of the most basic principles, as the relativity and the gravity-acceleration equivalence. The validity at the Planck scale of such principles is under dispute. A constructive criticism engages us in seeking new general principles, which reduce to the old ones only in the already explored domain of energies. At the very basis of physics there are epistemological and operational rules for the same formulability of the physical law and for the computability of its theoretical predictions. Such rules give rise to new solid principles, leading us to a quantum-information theoretic formulation, that hinges on the logical identification of the experimental protocol with the quantum algorithm.

The following dissertation is a minimally updated version of the original essay presented at the FQXi Essay Contest 2012 “Questioning the foundations”. A short summary of the follow-ups and recent 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. [23]. Other results can be found in Ref. [20, 30, 31].

The main result is contained in manuscript [23], 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 the new Ref. [32].

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 the Boson as an emergent notion [33].

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.