Full discussion of the twin paradox by Lorentz transformations

Abstract The twin paradox is a wonderful example in special relativity which continues to cause conceptual difficulties for students. In this paper I propose a very direct method to resolve the paradox, using Lorentz Transformations to model the jumps of the astronaut between reference frames during acceleration. Such calculations often raise doubts in students and teachers about whether they have posed the problem correctly. Interesting results for the distant clocks and doubly applied time dilation are provided and interpreted, allowing an extended understanding of the space-time structure, and greater confidence in the applications of the theory of special relativity.