Rafael Angel Araya-Gochez

(nearly-)indistinghishable Fermi-Dirac occupation states of the TAPIR:

a.k.a. [0-1]

"...because the warrior, having chosen a path, has but one goal: to traverse its full length."

from "The Teachings of Don Juan" by Carlos Castaneda.


Welcome to Rafael 's web page. I was a visitor at Caltech's Theoretical Astrophysics group (a.k.a. TAPIR) from about 2000 to 2005, working on various Magnetohydrodynamic and General Relativity problems in Astrophysics. More recently, I moved to mathematical physics driven primarily by a desire to understand "the dark mysteries of the Universe"; namely, Dark Matter and the cosmological constant problem (a.k.a. Dark Energy). In a nut-shell, for roughly the last ten years I have aimed to make sense of the mathematical structure of gravity in the modern language of symmetries. This exercise led me to formulate a theory of gravity at low energies that incorporates the most fundamental symmetries of spacetime in a geometrically intrinsic manner; literally building Universal space from its core foundational constituents. The first paper in a series of papers that expound this program is entitled ''On the Algebraic Structure of Spacetime and 3rd Quantization". In it, I conclude that a thoroughly organic

"quantization of spacetime"

endows it with matter content upon incorporation of the symmetries of the Standard Model of particle physics; in particular, a coupling to the Higgs Vacuum Expectation Value (see the comments from Annals of Physics below). The framework then naturally leads to a clear prediction for a Dark Matter particle in the form of a non--super-symmetric Majorana spinor..

Unfortunately, this research has been entirely unfunded and unsponsored (PLEASE e-mail me if interested in either).

In hindsight, given the fundamental building blocks of the standard model–and those of the electro-weak sector in particular–advancing this particular flavor of spinor as a dark matter candidate seems quite natural. All I did was:

Split the electron in half, mirror the side that talks to the Higgs (left), dispose of the side that doesn't (right), put it back together and VOILA: a massive, spin 1/2 particle with identical electro-weak quantum numbers as the Higgs boson: (T3, Y) = (1/2, -1/2). As the electromagnetic charge: Q = T3 + Y, is the sum of isospin and weak hyper-charge, this results in a fermion with zero electric charge...

Notably, throughout our work, the notion arose in top-down fashion from deeming spacetime as a single algebraic structure under the fundamental premise of building integrable geometric structures over the field of real numbers. Perhaps more curious is the fact that Albert Einstein himself, along with collaborator Walther Mayer, sought a similar unification scheme through the use of so-called semi-vectors. These are no more than pairs of left handed or right handed, complex, 2-component Weyl spinors (Ref. pg. 124 of "Einstein's Unification"). However, their efforts failed precisely because they sought electrically charged Dirac spinors as opposed to the more symmetric, electrically neutral Majorana spinors that emerge by considering spacetime as a real integrable structure. Evidently, none suspected the existence of dark matter back then. (Disclaimer: I just became aware of this remarkable connection on 09/15/2018.)

The early years: 2000-2005

Nascent black holes are conjectured to occur at the cores of very massive stars to yield Gamma-ray Bursts. As I set out to understand the magnetic nature of accretion flows onto black holes, I was first to carry out a fully general relativistic analysis of the problem (in the Cowling approximation). In a subsequent paper, I make the prediction that the black hole may be driven into a strongly vibrating mode by heavy clumps of material falling in through the "event horizon" in unison with the hole's natural oscillating tempo. The energy of such vibrations would radiate away in a very uniform pattern of Gravitational Waves that may someday be observed by LIGO. Remarkably, the 2017 Nobel Prize in Physics was rightfully awarded to the LIGO collaboration for the monumental first detection of gravitational waves; this time from a very powerful collision black holes. The signal I proposed is much weaker than this first detection but would be very characteristic of the quasi-ringing modes in a hyper-accreting stellar mass black hole.

More recently: 2008-2017

After a rendezvous with mathematical finance and game theory, I was drawn back to the realm of theoretical physics by the cosmological constant problem. Standard fare in modern physics posits that empty space is endowed with quantum energy. Although quantum physics and general relativity are fundamentally inconsistent with each other, the mathematical framework invoked by Albert Einstein to construct the General Theory of Relativity admits an extra term--a.k.a. the cosmological term--that accounts for the "virtual" energy of the vacuum. Taken at face value, such conjecture leads to an outlandish dynamical effect: a "speeding up" in the expansion of the fabric of space-time associated with the growth of vacuum in the Universe. Astonishingly, today we know that the expansion of the Universe has indeed been accelerating for well over half of the time the Universe's been around! However, this effect is much too weak to fit into the standard model of particle physics; in particular, it seems to point towards our clear misunderstanding of the physical vacuum!

I am chiefly concerned with fundamentally geometric constructions of [quantum] gravity where a non-vanishing cosmological constant could arise naturally as a by product of interpreting gravity as a ``gauge theory" of an underlying symmetry principle; e.g., gauging the deSitter group in a quasi--Yang-Mills form. Yet, gravity as a gauge theory has a far richer mathematical structure than a standard Yang-Mills gauge theory. In particular, the gauge fields of gravity must account for the frames of general relativity in a very peculiar way. I have taken the faithful representation of the Lorentz group--more technically, its simply connected component--to constitute the core foundational symmetry of spacetime and combine this with some fancy math to accommodate for gravity's significantly more complex mathematical structure: algebraic, geometric and topological. This is the physical content of graviforms as postulated in my first paper. Rather amusingly, I start with general relativity and end up with a curious variant of a quantum field theory without explicit coordinate referents! More technically, my thesis sustains that the use of quotient algebras facilitates the most transparent interpretation of spin structure as a manifestly quantum phenomenon. The formal machinery goes by the name of quantum ring theory and it facilitates a transparent interpretation of spacetime as a quantized derivation algebra with a dual character. The generalized frames of general relativity then encompass spin structure in the form of "singular geometric points" and this leads to the prediction for a Dark Matter particle at the electro-weak scale; i.e., with a mass within a factor of 2 from the mass of the Higgs particle.

Status: this paper was submitted to Annals of Physics on December 8th, 2017. This is an abridged version of the anonymous reviwer's comments received on January 13th, 2018:

This manuscript discusses issues on (or possibly beyond) the boundary of recognized physics. The notion of spacetime is not the standard one and the notion of quantum theory for spacetime does not appear to be the standard one. Research in this area may well need novel ideas but, in order for those to be of interest to other scientists, clarity of ideas it of utmost importance...

Unfortunately, he/she concluded that that version of the paper did not meet such a criterium. Reflecting upon this perception led me to realize that indeed the proposed notion of spacetime is highly non-standard: Roughly speaking, instead of coordinates: (t, x, y, z), the fundamental ingredient is a hybrid notion of "volume" as a geometrical structure that can be integrated to yield either 4-volume in its standard guise or a Majorana fermion mass corresponding to the mass of the proposed dark matter particle.

Quantization of spacetime then corresponds to viewing 4-volume as a two state system: a ground state or "normal vacuum" and an excited state corresponding to a dark matter particle.

I completed the formal mathematical implementation of such phenomenology during the month of July, 2018.

On Friday August 24th, revised manuscripts addressing critical peer criticism by Roman Buniy ( Institute for Quantum Studies at Chapman University) were submitted to the Physical Review D ; however, due to the novel algebraic setup (mostly ring theory), on September 2 the editor communicated that (the papers) "would be more suitable for a more mathematically oriented journal than for Physical Review D." To be fair, in this iteration of the fundamental paper I had to develop what could be construed as a notion of "calculus on an algebraic manifold". This concoction lies in between the mathematician's algebraic variety and the physicist's notion of (point set) manifold. Subsequently, the papers were submitted to the Journal of Mathematical Physics on September 5th, 2018.

Atonement: I am a man driven to search for Truth through mathematics. In my humble opinion, ring theory may be the most suitable toolset to understand spacetime as a "simple substance" for a thoroughly organic theory of everything. However, I am not so seduced by the beauty of mathematics as to loose sight of the truth in physics. Still, I reckon that the dual nature of spacetime as belabor in my research program is very real indeed. Mathematically, this duality follows from a deep algebraic fact developed in the first Appendix of my fundamental paper. From a physical perspective, it is obvious that spacetime is not a Lie algebra; however, the exterior product of two copies of the cotangent space does takes its values on a Lie algebra. The duality of spacetime is nothing more than the institution of the two algebras associated with the vector and spinor representations of the Lorentz group on such a product. Furthermore, causal structure is instilled upon the abstract space by the inclusion of singular geometric points thus leading to a local foliation of the space. This notion of spacetime is thus causal and spin at SGP's. This is the physical content of quantum ring theory as I am formulating it..

This page was last updated on October 27, 2018.