Local speed of light

Graded profiles tend to equalize the transit times of different rays. There is a simple explanation for this. As a ray propagates further from the axis, (x) decreases, thus increasing the local speed of light c/n(x). This increase in speed compensates, in part, for the extra distance travelled by the ray off axis. For the hyperbolic secant profile this equalization is exact, as we show in Section 1-12. 

The local speed of light is c/n(x, y), and thus the transit time over distance z along the fiber is given by the path integral... 

In addition to the localized SP modes, metal/dielectric interfaces support surface plasmon polaritons (SPP), which propagate according to the dielectric properties of the interface at the local speed of light. The complex dispersion relationship for SPP propagation at a metal/dielectric interface is given by ... 

Locally, the speed of light is not a constant over all frequencies. 

Further analysis by Bell and others shows that the results of these experiments and the predictions of quantum mechanics are incompatible with a view of the world in which both realism and locality hold. Realism (also called objectivity) is the doctrine that external reality exists and has definite properties independent of whether or not we observe this reality. Locality excludes instantaneous action-at-a-distance and asserts that any influence from one system to another must travel at a speed that does not exceed the speed of light. Clauser and Shimony stated that quantum mechanics leads to the philosophically startling conclusion that we must either totally abandon the realistic philosophy of most working scientists, or dramatically revise our concept of space-time to permit some kind of action-at-a-distance [J. F. Clauser and A. Shimony, Rep. Prog. Phys., 41,1881 (1978) see also B. d Espagnat, Scientific American, Nov. 1979, p. 158 A. Aspect, Nature, 446, 866 (2007) S. GrOblacher et al.. Nature, 446,871 (2007)]. 

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