The Universe of Codes

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Andrea Gregori

A work in progress, the progress of works

My research about quantization of gravity and unification of Relativity and Quantum Mechanics took explicitly the direction that would have later led me to the formulation in terms of "universe of codes" in 2001. Here I list only the papers that concern this particular development. This list therefore does not consider my former research work, although a big part of this work was a necessary premise, and many arguments used in later works are based on previous results. These are however properly cited in the bibliography contained in the papers listed here. The turning point in my research has been a thorough investigation of string-string duality for Z2 orbifold compactifications to four dimensions:

String-String triality for d=4, Z2 orbifolds, JHEP 0206:041,2002, arXiv:hep-th/0110201v2

Through this analysis I first got the idea that the natural environment in which to investigate the physical properties of non-perturbative string theory is that of a fully compactified target space. In this space the difference between what have to be considered "internal" coordinates and what the physical space-time is not that the first ones are compactified whereas the other ones are infinitely extended, but lies in the fact that the first ones are twisted, whereas the other ones not, and are therefore "expandable" in their size. This led me to the idea of an expanding but always of finite size universe, and to the very first paper of the project:

Entropy, String Theory and our World, arXiv:hep-th/0207195v3

Many topics and statements there contained are expressed in a very preliminary and immmature way, therefore I suggest the reading only if one really wants to follow the idea from the very beginning of its development. One of the main ideas introduced there, is to impose to a theory describing the physics of the world we observe to be self-contained within the space of the universe, extended only up to the (expanding) horizon of observation (i.e. limited to the causal region we live-in). This leads in a natural way (i.e. without special cancellation mechanisms) to the correct value of the cosmological constant and to time-dependent masses and couplings. In particular, the consequences for the couplings have been first discussed in:

On the Time Dependence of Fundamental Constants, arXiv:hep-ph/0209296v2

and, for the cosmological term, in:

Naturally Time Dependent Cosmological Constant, arXiv:hep-th/0402126v1

In these papers it is also discussed how the assumption of working in a horizon-bounded universe implies that a non-vanishing cosmological term can be viewed as a Casimir term, the ground energy of a quantum scenario in a bounded space, thereby suggesting the existence of a subtle relation between classical and quantum theory.

All these ideas have been re-elaborated and presented in a more advanced form in:

An Entropy-Weighted Sum over Non-Perturbative Vacua, arXiv:0705.1130v2

After that, I realized that the time-dependence of masses, couplings, and therefore also of molecular binding energy levels, very mild on a daily scale, but no more negligible on a cosmologic scale, has potential deep consequences on the natural evolution of biological species: it leads to a set of phases of different but relatively long duration, during which the evolution seems to "rest", separated by much shorter phases of rapid evolution, corresponding to the resonance peak of energy absorption by biological molecules, scaling at a different speed as compared to the cosmic energy radiation. I discussed how surprisingly well this model fits with the paleontological data in:

A note on the phases of natural evolution, arXiv:0712.0074v1

The first paper in which the idea of obtaining the physical universe through the weighted sum over geometries consisting of distributions along a discrete target space of an occupation number corresponding to what has to be interpreted as "energy" is first presented in:

About combinatorics, and observables, arXiv:0712.0471v2

Working with a discrete space had been suggested to me by the property possessed by string theory of having a minimal length. After thorough investigation, this setup proved to lead not only to a universe with the properties of quantum mechanics, but also, in a large-scale limit, to imply special relativity, as later observed in:

Relativity as classical limit in a combinatorial scenario, arXiv:0911.0518v1

Having at hand a physical scenario that includes both quantum mechanics and special and general relativity, realizing therefore a "unification" of these two aspects of the physical world within a framework in which it is possible to compute physical quantities, allowed me to look from a new perspective at "classical" topics such as black holes. In this theoretical scenario the Schwarzschild singularity, a singularity of the classical solution of the Einstein's equation, is removed when considering quantum gravity effects (I stress, not just the usual flat geometry quantum effects, but the very quantization of space). Indeed, in such a universe the only object that shows the typical properties of a black hole is the entire universe itself, as argued in:

Is the Universe the only existing Black Hole?, arXiv:1006.5826v1

The consequences of the quantization of the geometry of space can be observed not only on the large. cosmological scale of the universe, but also on the small scale of microscopical quantum systems with a non-trivial geometry of energy (and matter) distribution, such as the superconductors. Since the critical temperature of superconduction is in turn related to the amount of quantum delocalization, and in this scenario the amount of quantum uncertainty depends on the geometry, one obtains a relation between cristalline structure of a material and critical temperature quite in good agreement with the experimental observations. This allows us to view high-temperature superconductivity as a special case of the very same phenomenon of low-temperature superconductivity:

On the critical temperatures of superconductors: a quantum gravity approach, arXiv:1007.3731v1

Knowing the relation between geometry and critical temperature is potentially interesting for applied physics of materials and engineering. Quantum geometry effects are arguably at work also in gravity screening phenomena related to superconductors, especially in accelerated systems, as discussed in:

A note on the gravity screening in quantum systems, arXiv:1105.4997v1

In the same year I posted the revised and updated version of the theoretical setup, from its definition in terms of discrete distributions, and the physical interpretation in terms of a quantum-relativistic universe, to the calculation of physical quantities such as the masses of the elementary particles and couplings through the passage to a string theory limit on the continuum:

Combinatorics, observables, and String Theory, arXiv:1103.4000v1


Combinatorics, observables, and String Theory: part II, arXiv:1103.3998v1

All the arguments concerning the construction of the theoretical scenario have been then further developed, revised and corrected, and are now presented in their most updated form in three papers. Although structured for an independent reading, from a logical point of view these are three chapters of a unique work:

A physical universe from the universe of codes, arXiv:1206.0596v1

The superstring representation of the universe of codes, arXiv:1206.3443v1

The spectrum of the universe of codes, viXra:1301.0102

One of the topics considered in the former versions of this research, namely, the issue of the violation of CP, has been extended and moved to a separate paper:

CP Violation: Beyond Field Theory? viXra:1206.0093

CP violation seems today to be a less attractive topic than the (supposed) discovery of the Higgs boson. Indeed, in my opinion it is not correct to separate phenomena concerning elementary particles, and forget that a theory, or a model, adjusted in order to explain one of them, must also be able to explain the other ones. The Standard Model fails in predicting the amount of CP violation in the D-meson system by one entire order of magnitude. In the case of π-mesons it seems to give a correct prediction, but as a matter of fact this is not a true prediction, because it is rather a matter of fitting one experiment with one parameter, the phase of the CKM matrix. So, the experimental data serve to fix a value for this parameter. The proof of the model would be to test it with a second, independent experiment. This is precisely given by the D-system, where however the Standard Model fails. So should we go on and trust anyway the theory up to forcing the interpretation of the newly observed resonance at 125 GeV at Cern as an undoubtable Higgs signal? Only because the model, which anyway proves to give wrong predictions somewhere else, predicts at a non-specified energy the existence of such a boson? In "CP violation: Beyond field theory?" I argue that, since the entire explanation of the CP phenomenon is based on a representation of the mass matrix, and masses are only correctly dealt with within a quantum gravity theory, a correct explanation of CP violation can only be looked for in a quantum gravity theory. The same holds for the resonance supposed to be due to a Higgs field, as I discuss in "The Spectrum of the Universe of Codes". Indeed, both CP violation and the 125 GeV resonance find an explanation within the theoretical framework of the "universe of codes", where they are correctly predicted.

Prime numbers and the structures of the universe of codes, viXra:1401.0116

It is here argued that prime numbers may play for the set of combinatoric weights of the theory a role of building blocks, somehow similar in importance to the one of the free states in quantum mechanics. The topics of this paper are introduced in the paragraph "the role of prime numbers" of the short introduction.

Selected papers

A physical universe from the universe of codes (2012)

The superstring representation of the universe of codes (2012)

The spectrum of the universe of codes (2012)

CP violation: beyond field theory? (2012)

On the critical temperatures of superconductors: a quantum gravity approach (2010)

A note on the phases of natural evolution (2007)

Prime numbers and the structures of the universe of codes (2014)