According to the theory of relativity, when an object approaches the speed of light, space contracts along its direction of motion. This phenomenon is known as length contraction. It is not merely a perceptual effect but a physical consequence of the theory.
Length contraction occurs as a result of the interplay between space and time. As an object accelerates towards the speed of light, time dilation causes time to slow down for the moving object relative to a stationary observer. Simultaneously, length contraction occurs, causing distances in the direction of motion to appear shorter from the perspective of the stationary observer.
The combination of time dilation and length contraction ensures that the speed of light remains constant for all observers, regardless of their relative motion. It is a fundamental aspect of the theory of relativity and has been confirmed by numerous experiments and observations.
So, to answer your question, space indeed physically contracts for a light-speed traveler relative to a stationary observer. However, it's important to note that this contraction is only significant at speeds close to the speed of light and does not have observable effects in everyday life or at slower velocities.