In the theory of relativity, specifically special relativity, the concept of "relativity of simultaneity" and "length contraction" explains how two observers moving relative to each other can come up with the same result for certain measurements, such as length.
According to special relativity, space and time are not absolute, but rather depend on the relative motion between observers. When two observers are in relative motion, their measurements of time and space can be different due to a phenomenon called time dilation and length contraction.
Time dilation refers to the phenomenon where time appears to pass more slowly for a moving object as observed by a stationary observer. Similarly, length contraction refers to the phenomenon where the length of a moving object appears shorter along its direction of motion as observed by a stationary observer.
Let's consider an example of two observers, A and B, moving relative to each other. Observer A is at rest relative to an object, while observer B is moving at a high speed relative to the object. From observer A's perspective, the length of the object will be its "proper length," which is the length as measured when the object is at rest relative to observer A.
From observer B's perspective, due to length contraction, the length of the object will appear shorter along the direction of motion relative to observer B. However, this apparent contraction in length is exactly compensated by the time dilation effects experienced by observer B. As a result, both observers, A and B, will measure the same value for the length of the object.
This phenomenon ensures that the laws of physics remain consistent for all observers, regardless of their relative motion. It's important to note that the principle of relativity does not mean that all measurements will be the same for all observers, but rather that certain physical quantities and relationships, such as the speed of light, are invariant and consistent for all observers.