The constancy of the speed of light is a fundamental principle of special relativity. In this theory, the speed of light in a vacuum, denoted by "c," is considered an invariant quantity that remains constant regardless of the motion of the source or the observer. This constancy of the speed of light is a cornerstone of our understanding of the universe.
In special relativity, space and time are intertwined in a four-dimensional framework known as spacetime. The theory postulates that the laws of physics should be the same for all observers in inertial reference frames. However, different observers in relative motion will measure different distances and time intervals between events.
To reconcile this, special relativity introduces the concept of "spacetime intervals" that are invariant. These intervals combine both the spatial and temporal components of an event and remain the same for all observers, regardless of their relative motion. The spacetime interval is given by the equation:
Δs² = c²Δt² - Δx² - Δy² - Δz²
In this equation, Δs represents the spacetime interval, Δt represents the time interval between two events as measured by one observer, and Δx, Δy, and Δz represent the spatial intervals between the same events.
The crucial insight of special relativity is that for all observers, regardless of their relative motion, the quantity (cΔt)² - Δx² - Δy² - Δz² remains constant. This means that the relative motion of observers affects the spatial and temporal components in a way that keeps the spacetime interval invariant.
As a consequence of this invariant spacetime interval, the speed of light is observed to be constant. It means that the ratio of the spatial interval to the time interval between two events (Δx/Δt) observed by one observer will be different from the ratio observed by another observer in relative motion. However, the speed of light (c) will be the same for all observers, regardless of their relative motion.
So, in special relativity, the constancy of the speed of light is a fundamental principle that emerges from the consistent interplay between space and time, resulting in an invariant spacetime interval for all observers.