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In Einstein's relativity the assumption that infinity is the only invariant speed is dropped and replaced by a constant , therefore making the Galilean transformation a special case. Mathematically this constant can be anything from 0 to infinity.

It is generally accepted that the observer invariant speed corresponds physically to the speed of light (and is used as a postulate of special relativity). However current experimental claims have sown the seeds of doubt, even though they haven't been satisfactorily confirmed as yet. Even so, proving that anything can travel faster than the speed of light does not violate Einsteins relativity in that the key point is not that equals the speed of light but that there can be a finite observer invariant speed.

The observer invariant speed is also the main reason why no object can ever reach the speed of light, or more precisely the invariant speed itself. This arises from the fact that an object observes its own speed, or its personal speed, as always being zero since it is not in motion relative to itself. Another observer may observe the object's speed as . Since an object's personal speed can never be anything other than zero it can never coincide with the speed measured by the other observer (unless the speed is zero in which case it is a trivial example). This being the case, neither the object's personal speed or the measured speed can ever be the invariant speed, or the speed of light.