On the Geometric Constraints of the Light Clock Model

In modern physics teaching, the optical clock model is often used to derive the relativistic time dilation formula. With the help of the Pythagorean theorem, the model derives the mathematical form of time dilation in Euclidean geometry. However, this method has certain limitations in that it ignores the problem of angular dependence when the optical signal propagates in different inertial frames. Therefore, the optical clock model can only be a heuristic model and cannot be used as a derivation basis for time dilation.