The idea that the speed of light is not additive to its source is a fundamental concept in physics, as described by Einstein's theory of special relativity. According to this theory, the speed of light in a vacuum, denoted by "c," is a constant value that is independent of the motion of its source or the observer.
In classical physics, the addition of velocities is straightforward. If an object moves with a velocity of 10 feet per second (10 ft/s) in one direction and a beam of light is emitted in the same direction, one might intuitively expect that the velocity of light would be the sum of the object's velocity and the speed of light, resulting in a velocity greater than c. However, experimental evidence and the theory of special relativity demonstrate that this is not the case.
The Michelson-Morley experiment you mentioned was conducted in the late 19th century and aimed to detect the hypothetical "ether" medium through which light was believed to propagate. The experiment's null result, meaning it did not detect any significant change in the speed of light based on the Earth's motion through space, challenged the prevailing notion of an absolute frame of reference.
Einstein's special theory of relativity, developed in 1905, provided an explanation for the Michelson-Morley experiment and reconciled the results with the constancy of the speed of light. According to this theory, the speed of light is the same for all observers, regardless of their relative motion. Instead of adding velocities linearly, special relativity introduces a concept called velocity addition formula, which takes into account the relativistic effects of time dilation and length contraction.
In the case you described, if you were moving at a velocity of 10 ft/s to the north and you shined a laser in the same direction, the measured speed of light by an observer at rest relative to you would still be c, not 10 ft/s + c. This is because the velocity addition formula of special relativity accounts for the relativistic effects, ensuring that the speed of light remains constant for all observers.
Experimental evidence from various sources, such as particle accelerators and astronomical observations, consistently confirms the constancy of the speed of light and validates the predictions of special relativity. These findings support the notion that the speed of light is not additive to its source but remains constant regardless of the motion of the source or the observer.