Time, Distance, Velocity, Redshift: a Personal Guided Tour

An attempt to answer the question " Can we observe galaxies that recede faster than light " led to a re-examination of the notions of time, distance, velocity and redshift as they occur in newtonian physics, special relativity, general relativity and cosmol-ogy. A number of misconceptions were uncovered. It was found that, once freed of preconceptions of special relativity the above question is easily and unequivocally answered. Over the past fifteen years or so I have been a student of cosmology. I was puzzled by the following question: according to the celebrated Hubble's Law that says velocity of recession is proportional to distance, there must come a distance so large that a galaxy located there is receding at the speed of light. What then happens to the photon the galaxy emits in our direction ? Will that photon ever reach us ? Or if it does reach us, will its redshift be infinite and hence it will make zero impact ? In that case, that distance must be marking the boundary of our observable universe; is that distance what is known as horizon ? Or has the Hubble Law broken down long before that point ? Or have we missed the point entirely and forgotten that velocity at a distant point is simply not defined in General Relativity ? I eventually worked out the answers and these were given in my (1997) paper. And it dawned on me that all the above " questions " are wrong questions, prompted by what I call the " Shadows of Special Relativity ". Once it is recognized that modern cosmology, dubbed " relativistic " , is based not on Special Relativity, but on General Relativity, and not on General Rel-ativity alone, but also on the Cosmological Principle, the answers emerge with no more than first-year college mathematics. The present essay is a systematic clearing-up of all the dead wood and misconceptions encountered on the way. I have not refrained from using non-technical language, homely analogies, formal comparisons whenever these contribute to undesratanding.