Time dilation and length contraction are indeed symmetrical effects in the theory of relativity. However, it is important to consider the frame of reference when measuring these effects because different observers in different frames of reference will perceive and measure time dilation and length contraction differently. This is due to the principle of relativity, which states that the laws of physics should appear the same for all observers in inertial frames of reference.
The key idea behind the relativity of simultaneity and time dilation is that the perception of time is relative to the observer's motion relative to the observed event or object. Similarly, length contraction is relative to the observer's motion relative to the measured object.
Let's take an example to illustrate this. Imagine there are two observers, A and B, in relative motion to each other. Observer A is stationary, while Observer B is moving at a high velocity. They both have their own clocks and measuring devices.
From Observer A's perspective, they would measure their own time and lengths according to their frame of reference. Similarly, Observer B, while moving at high velocity relative to Observer A, would measure their own time and lengths according to their frame of reference. The measured values of time and length would be different for both observers due to the effects of time dilation and length contraction.
So, while time dilation and length contraction are symmetrical effects in terms of their mathematical descriptions, their actual values depend on the frame of reference of the observer making the measurements. This is a fundamental consequence of the theory of relativity and the relativity of simultaneity.