From Kerr to Heisenberg

Abstract

In this paper, we consider the space-time of a charged mass endowed with an angular momentum. The geometry is described by the exact Kerr–Newman solution of the Einstein equations. The peculiar symmetry, though exact, is usually described in terms of the gravito-magnetic field originated by the angular momentum of the source. A typical product of this geometry is represented by the generalized Sagnac effect. We write down the explicit form for the right/left asymmetry of the times of flight of two counter-rotating light beams along a circular trajectory. Letting the circle shrink to the origin the asymmetry stays finite. Furthermore it becomes independent both from the charge of the source (then its electromagnetic field) and from Newton’s constant: it is then associated only to the symmetry produced by the gravitomagnetic field. When introducing, for the source, the spin of a Fermion, the lowest limit of the Heisenberg uncertainty formula for energy and time appears.

A tale of analogies: a review on gravitomagnetic effects, rotating sources, observers and all that

“…Consequently, a gravitoelectromagnetic analogy naturally emerges in full GR when we are dealing with a non time-orthogonal metric like (42). However, the great majority of experimental studies on GR is done in weakfield conditions, i.e.…”

“…The above metric is quite general in its form and, in particular, it said to be non time-orthogonal, because g 0i ≠ 0. We focus on the asymmetry in the propagation times of two signals in the spacetime described by the line-element (42); this asymmetry is the socalled Sagnac time delay, which we describe here with extensive reference to the papers by Rizzi and Ruggiero [40], Rizzi and Ruggiero [36], Ruggiero and Tartaglia [41], Tartaglia and Ruggiero [42].…”