In the theory of relativity, time dilation is indeed symmetrical, meaning that both observers in relative motion to each other will perceive the other's time as slower. This may seem counterintuitive, but it arises from the fundamental principles of relativity.
To understand this, let's consider a simplified scenario with two observers, A and B, moving relative to each other. From observer A's perspective, they are at rest, and observer B is in motion. Likewise, from observer B's perspective, they are at rest, and observer A is in motion.
When two observers are in relative motion, they measure the passage of time using their own clocks. According to the theory of relativity, each observer will see the other's clock ticking slower than their own. This is because, in the frame of reference of each observer, it is the other observer who is moving and experiencing time dilation.
The key idea here is that there is no absolute reference frame to determine the "true" passage of time. Time is a relative concept that depends on the observer's motion and reference frame. Both observers can be correct in perceiving the other's time as slower because time dilation is a consequence of the geometry of spacetime and the relative motion between observers.
This apparent contradiction is resolved when considering that both observers experience changes in other physical quantities, such as length contraction or different spatial measurements, in a consistent manner. The symmetrical nature of time dilation is a fundamental feature of relativity that has been confirmed through numerous experimental observations and is a cornerstone of modern physics.