Time-dilation in a General Departure and Rejoin Scenario

Time dilation due to motion was initially theorized by the Lorentz transformation and Einstein's theory of special relativity. To date, experimental data has meticulously confirmed these theoretical predictions with high precision. The majority of experimental setups designed to validate these predictions often involve scenarios of departure and reunion. However, understanding the traveler's perspective in such scenarios, as exemplified by the twin paradox, is rarely straightforward. This paper introduces a novel graphical tool called the velocity-time diagram, specifically tailored for general departure and return scenarios while excluding the expansion of the universe. Grounded in a re-organized axiomatic system, this tool facilitates intuitive and straightforward quantitative analysis. Crucially, the proposed approach aligns seamlessly with all existing experimental data, offering a simpler and more intuitive explanation for time dilation. Moreover, it fosters a deeper comprehension of the nature of time.