If there was something like a Lorentz transformation for v=c, it wouldn't be one-to-one, so it wouldn't be mathematically compatible with the structure of relativity. So although general relativity is far more permissive than Newtonian mechanics about changes of coordinates, there is a restriction that they should be smooth, one-to-one functions. The arrow either hit the bull's-eye or it didn't. Either the particles collided or they didn't. In relativity, we expect that even if different observers disagree about many things, they agree about intersections of world-lines. One of the most basic geometrical ideas is intersection. Since arguments from positivism can often kill off perfectly interesting and reasonable concepts, we might ask whether there are other reasons not to allow such frames. It would take an infinite amount of energy to accelerate Einstein and his motorcycle to the speed of light. If we accept this philosophical stance (which is by no means compatible with every concept we ever discuss in physics), then we need to be able to physically realize this frame in terms of an observer and measuring devices.
#Speed of light how to
The most straightforward argument is based on the positivist idea that concepts only mean something if you can define how to measure them operationally. But we now know, thanks to Einstein himself, that it really doesn't make sense to talk about such observers. As a young student, Einstein tried to imagine what an electromagnetic wave would look like from the point of view of a motorcyclist riding alongside it.
This kind of question has a long and honorable history.
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