Invariant speed

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The invariant speed, or, more precisely, the observer invariant speed, is the speed that is independent of the observer.

[edit] Explanation

The concept of an observer invariant speed arises from Newtonian relativity. If a stationary person observes an object traveling at a speed v, then a non-stationary person traveling at a speed u will observe the same object traveling at a speed w where w = vu. This is the Galilean transformation. The only observer invariant speed possible in Netwonian relativity is infinite.

Einstein's theory of relativity drops the assumption that the invariant speed must be infinite and denotes the speed with the constant c. The Galilean transformation becomes a special case. Mathematically, this constant can have any value.

It is generally accepted that the observer invariant speed c corresponds physically to the speed of light, and this is a postulate of special relativity, where the speed of light is invariant in all inertial reference frames. It should be noted that proving that anything can travel faster than the speed of light does not violate Einstein's relativity since the key point is not that c equals the speed of light but that there can be a finite observer invariant speed and it is this invariant speed that's inviolable.

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 v. 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 v is zero in which case it is a trivial example). This being the case, neither the object's personal speed or the measured speed v can ever be the invariant speed, or the speed of light.

A way to visualize this is the Red Queen's race. In the Red Queen's race the Queen remains in the same spot no matter how much she runs (akin to running on a treadmill). Similarly, an accelerating object always accelerates into an inertial reference frame in which its speed v is always zero and the invariant speed is always c.