Enrique Martinez Viladesau Escuela Técnica Superior de Ingenieros Industriales de Barcelona (ETSIUB), Spain emviladesau@gmail.com International Journal of Fundamental Physical Sciences (IJFPS) 8 3 87-91 September, 2018 2231-8186 https://doi.org/10.14331/ijfps.2018.330118 This paper explores the operation of Lorentz transformations and the fallacy of time dilation. It analyzes the structure and interpretation of the transformation formulas, clarifying the roles of reference systems, spatial extension, and time variables. The author argues that the perceived dilation of time is due to visual interpretation from a moving reference system (MRS), rather than actual physical elongation. Using illustrative graphs and equations, the article explains how the Lorentz factor connects time variables in different frames, and suggests that observational delay is mistaken for real-time transformation. Relativity, Time dilatation, Lorentz transformation https://creativecommons.org/licenses/by-nc/4.0/