KERR'S GRAVITY AS A QUANTUM GRAVITY ON THE COMPTON LEVEL

Abstract

The Dirac theory of electron and QED neglect gravitational field, while the corresponding to electron Kerr-Newman gravitational field has very strong influence on the Compton distances. It polarizes space-time, deforms the Coulomb field and changes topology. We argue that the Kerr geometry may be hidden beyond the Quantum Theory, representing a complimentary space-time description. 1.Introduction. The Kerr-Newman solution displays many relationships to the quantum world. It is the anomalous gyromagnetic ratio g = 2, stringy structures and other features allowing one to construct a semiclassical model of the extended electron 1–4 which has the Compton size and possesses the wave properties. Meanwhile, the quantum theory neglects the gravitation at all. The attempts to take into account gravity are undertaken by superstring theory which is based on the space-time description of the extended stringy elementary states: Points ! Extended Strings, and also, on the unification of the Quantum Theory with Gravity on Planckian level of masses Mpl, which correspond to the distances of order 10 33 cm. Note, that spin of quantum particles is very high with respect to the masses. In particular, for electron S = 1/2, while m � 10 22 (in the units G = ~ = c = 1). So, to estimate gravitational field of spinning particle, one has to use the Kerr, or Kerr-Newman solutions, 5 contrary to the ordinary estimates based on spherical symmetric solutions. Performing such estimation, we obtain a striking contradiction with the above scale of Quantum Gravity ! Indeed, for the Kerr and Kerr-Newman solutions we have the basic relation between angular momentum J, mass m and radius of the Kerr singular ring a : J = ma. Therefore, Kerr’s gravitational field of a spinning particle is extended together with the Kerr singular ring up to the distances a = J/m = ~/2m � 10 22 which are of the order of the Compton length of electron 10 11 cm., forming a singular closed string a . Since a >> m, this string is naked (no event horizon of black hole). In the Kerr geometry, in analogy with string theory the ‘point-like’ Schwarzschild singularity turns into an extended string of the Compton size. Note, that the Kerr string is not only analogy. It was shown that the Kerr singular ring is indeed the string, 8 and, in the analog of the Kerr solution to low energy string theory, 9 the field around the Kerr string is similar to the field around a heterotic string. 10 It is an Alice topological string, 2,4 and the Kerr space exhibits