In Einstein's example of the relativity of simultaneity, he introduced the concept of the constancy of the speed of light, which is a fundamental principle of his theory of special relativity.
In this example, Einstein considered two observers, A and B, who are in relative motion to each other. Suppose there is a flash of light emitted at the midpoint between the two observers. According to classical Newtonian physics, one might expect that the observer closest to the flash would perceive the light reaching them first, while the other observer would perceive a delay before seeing the light.
However, Einstein's theory of special relativity states that the speed of light in a vacuum is constant for all observers, regardless of their relative motion. This means that both observer A and observer B will measure the speed of light to be the same value, regardless of their velocities or positions.
To reconcile this constancy of the speed of light, Einstein proposed that space and time are not absolute, but rather are interconnected in a four-dimensional framework called spacetime. In this framework, the observations of simultaneity for events happening at different locations are relative and depend on the observer's motion.
According to special relativity, when observers are in relative motion, their perceptions of simultaneity can differ. The ordering of events and the synchronization of clocks can be relative and depend on the observer's frame of reference. This implies that two events considered simultaneous by one observer may not be simultaneous for another observer in relative motion.
By postulating the constancy of the speed of light, Einstein revolutionized our understanding of space, time, and the behavior of objects at high speeds. It led to the discovery of time dilation, length contraction, and other phenomena that are fundamental to the theory of special relativity.