The new theory of (Special) Relativity of Electromagnetic Fields proposed earlier is based on the assumption that the observer and the source are in uniform relative speed and is based on the ‘postulate’ of absolute constancy of the speed of light. It was disappointing at first when I discovered that the theory implied a variation of the speed of light with the acceleration of an observer relative to the source. Later I found out that this variation to be vitally important as it might explain the results of the well known ‘time delay’ experiments claimed as evidences supporting Einstein’s relativity! Perhaps the variation of the speed of light with source-observer relative acceleration might explain ‘GPS correction’, Ives-Stilwell experiment and Hafele and Keating Experiment! There is a common factor in all these experiments: acceleration. However, the new theory of General Relativity of EM waves should be completed quantitatively to know its real significance. The purpose of this paper is only to announce the new theory by presenting a briefly and preliminarily; the details and more accurate quantitative analysis will be presented in future versions of this paper.