Albert Einstein was right when he proposed the constancy of the speed of light regardless of motion of the source and motion of the observer. The constancy of the speed of light follows directly from the non-existence of the ether. However, Einstein's principle of relativity of space and time, which was derived from the light postulate and the principle of relativity, was wrong because: 1. it led to many paradoxes, and 2. absolute motion has been detected in other experiments. Special relativity was therefore a wrong interpretation of the light postulate. This paper provides a new insight that reveals the deep mystery underlying the many mutually contradicting light speed experiments. The new theory, known as Apparent Source Theory, states that the speed of light is constant and absolute motion exists at the same time. The speed of light is fundamentally constant relative to the observer but appears to be variable when measured. At the heart of Apparent Source Theory is the (one-way and two-way ) constancy of the speed of light regardless of motion of the source, motion of the observer, motion of the mirror, for uniform velocity or acceleration.