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In Einstein's papers, he used light speed as a reference speed. What if we use a greater finite speed and do the same calculations. Won't this greater speed then be the limit.

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OP's suggestion seems equivalent to giving the photon a (rest) mass, cf. physics.stackexchange.com/q/4700/2451 –  Qmechanic Dec 30 '11 at 14:28

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The speed of light isn't the reference speed because Einstein picked it---which would imply that you could pick something else---but because the laws of physics seem to be invariant on Lorentz boosts with $c=\text{the speed of light in a vacuum}$.

When Einstein was doing the work the clearest experimental evidence came from the form of Maxwell's Equations and results of Michelson and Morley's interferometry experiments. These days we have other evidence, including direct evidence such as the behavior of very energetic particles in accelerators.

That is, the special place of the speed of light is an experimental fact.

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The light speed is invariant under constant motion, and there can only be one speed with this property. If you use a slower speed than light speed, and you chase the object in the same direction, it will slow down relative to you, until your velocity is equal to its velocity, and it stops.

If you look at an object going away from you at a greater speed than that of light (like the spot of a laser pointer on a wall, for example) , and you chase after it, the faster you go, the faster it recedes from you, until your speed reaches a certain value, at which point the object's motion is instantaneous relative to you. If you go any faster, it goes the other way relative to you (all superluminal).

Only one speed stays the same regardless of the motion of the observer, and this unique speed is the one used by Einstein in his papers. It happens to be the speed of light, but it is a geometrical thing, having nothing to do with the particular dynamics of light.

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Can you please give a link to the geometrical proof that you mention. Thank you –  nikhil bachhawat Dec 30 '11 at 13:50
    
You can start with the answer here: physics.stackexchange.com/questions/12435/… . Once you understand how the pythagorean theorem works, with a minus sign, the uniqueness of the invariant slope (i.e. speed) follows from noting that x^2-t^2=0 implies x/t=1. –  Ron Maimon Dec 30 '11 at 13:52

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