Lightcones

Figure 1. An ultrashort light pulse is emitted at A, which is the apex of a Minkowski lightcone. In our coordinate system x-y represent two axes of our ordinary world, while the third axis ct represents time. The widening of the cone upward represents the radius of the sphere of light as it increases with time. An ultrashort observation is later made at B, the apex of an inverted cone. The only way for light to be transmitted from A to B is by scattering objects placed where the two cones intersect. If the observer s velocity (v) is high, this intersection will be an ellipse that is inclined in relation to our stationary world.

Ellis et al. [30] discussed the quantum fluctuations about the mean-field solution that would correspond in field theory to quantum fluctuations in the lightcone and could be induced by higher-genus effects in the string approach. Such effects would result in stochastic fluctuations in the velocity of light as of the order of... 

Yu and Ford [32] studied the effects of compactified extra dimensions on the propagation of speed of light in the uncompactihed dimensions. There are nontrivial effects that arise from quantum fluctuations of the gravitational held, induced by the compactification. These effects take the form of lightcone fluctuations, variations in the flight times of pulses between a source and a detector. 

Z2,Z3,..., z )- Now one can study the effect of lightcone fluctuations due to gravitons in the bulk by looking at a light ray traveling parallel to one of the boundaries, say, in x axis, but separated from it by a distance z lp. This indicates the effect of quantum fluctuations in the position of the brane. 

In the field-theoretic case, they have estimated At as At fh In L, where L is the distance between the source and the detector. For astrophysical sources such as gamma-ray bursters (GRBs), the order of the effect is about 10-12 s, which falls below the sensitivity of observations. Here, At is considered as the scale of lightcone broadening. It should be noted that the sensitivity of gravity wave interferometer experiments is much better, and for these experiments one can get lightcone broadening of the order of 10 25 s, which may lie within their sensitivity. 

---