Conceptual unification of elementary particles, black holes and the primordial states of the universe

The unification of black holes and elementary particles is at the center of theoretical physics today and astroparticle physics. It has long been searched, but never successfully accomplished. For the first time, this unification is proposed in a conceptual way, by a researcher in Paris Observatory, and includes the primordial states of the universe: the states describing inflation (whose existence is supported by the recent cosmic microwave background observations) and the states describing an earlier (more microscopic or more quantum) phase for which is predicted a discrete spectrum and a new phase transition. This phase transition would be the quantum gravity counterpart of the (non linear) Jeans instability with cosmological constant and with a more complex and richer structure.
The classical-quantum (de Broglie) duality at the basis of quantum mechanics is here extended to the quantum gravity or string regime (that is, wave-particle-string duality). Remarkably, this classical-semiclassical-quantum gravity duality precisely describes the whole history of black hole evaporation and the universe evolution.

Macroscopic black holes arise through the gravitational collapse of stellar bodies. Microscopic black holes could arise from high density concentrations (of the order of the Planck energy scale) in the early universe, as well as from the collisions of particles at such energy scales. Microscopic black holes are necessarily quantum and their properties governed by quantum or semiclassical gravity, evaporation through Hawking radiation is a typical effect of these black holes. Microscopic black holes share in some respects analogies with elementary particles, and on the other hand, show many important differences. A theory of quantum gravity, or "theory of everything" such as string theory, should account for an unified and consistent description of both black holes and elementary particles, and the physics of the early universe as well.

Hawking radiation from a black hole:
a pair "particle" (P, red) and "anti-particle" (A, green) is created, and while the anti-particle is attracted and annihilated in the black hole, the particle escape. The black hole has lost mass.
Basic open string     Basic close string (loop)
In string theory, the elementary particles are considered as excitation modes of elementary strings. Since they are built for a theory of quantum gravity, the size of the strings are supposed of the order of the Planck length, which is about 10-33 centimeters
(illustrations from

de Sitter states are relevant since they describe the inflation era of the early universe and most probably, the acceleration of the present universe; they correspond to a positive cosmological constant. Anti de Sitter states correspond to a negative cosmological constant, they appear in particle unification models and allow interesting comparison between the positive and negative cosmological constant effects.

A conceptual unification of the quantum properties of black holes, elementary particles, de Sitter and Anti de Sitter states has been recently provided by Norma G. Sanchez (see article hep-th/0312018). The conducting line of argument is the classical-quantum (de Broglie, Compton) duality, at the basis of quantum mechanics, here extended to the quantum gravity (string) regime (that is, wave-particle-string duality). The semiclassical and quantum (string) gravity regimes are thus respectively characterized and related: sizes, masses, accelerations and temperatures.

The Hawking temperature, elementary particle and string temperatures are shown to be the same concept in different energy regimes and turn out to be the precise classical-quantum duals of each other. Similarly, this result holds for the black hole decay rate, heavy particle and string decay rates; black hole evaporation ends as quantum string decay into pure (non mixed) non thermal radiation.

Microscopic density of states and entropies in the two (semiclassical and quantum) gravity regimes are derived and related, an unifying formula for black holes, de Sitter and anti-de Sitter states is provided in the two regimes. Interestingly enough, a phase transition towards the de Sitter string temperature (which is shown to be the precise quantum dual of the semiclassical (Hawking-Gibbons) de Sitter temperature) is found and characterized, and the quantum discrete mass spectrum of black holes, de Sitter and anti de Sitter radii or cosmological constant obtained.

This is not an assumed or conjectured duality: the results of quantum fields and strings in black holes, de Sitter, Anti-de Sitter and conformal string backgrounds remarkably show these relations. And, as the wave-particle duality, this semiclassical-quantum gravity duality does not relate to the number of dimensions, nor to a particular symmetry. Cosmological evolution goes from a quantum string phase to a semiclassical phase (inflation) and then to the classical (standard Friedman-Robertson-Walker) phase. Remarkably, the wave-particle-string duality precisely manifests in this evolution, and can be viewed as a mapping between asymptotic states and so as a scattering -matrix description.

These findings do not make use of conjectures, proposals, principles, (CPP's) formulated in the last years in connection with string theory. String dynamics in curved backgrounds started well before CPP's, many results for strings in curved backgrounds addressed nowadays (strings on Anti-de Sitter, on plane waves, semiclassical and canonical string quantization, rotating strings, null strings, integrable string equations, time dependent string backgrounds) can be found in the references below and refs therein.

N. G. Sanchez
Conceptual unification of elementary particles, black holes, quantum de Sitter and Anti de Sitter string states hep-th/0312018

Norma Sanchez (Observatoire de Paris, LERMA)