Since the first part of the twentieth century, it has been maintained that faster-than-light motion could produce time travel into the past with its accompanying causality-violating paradoxes. Part of the problem is that the Lorentz transformation (LT) presumes that time is isotropic, as does the Minkowski diagram based upon it, whereas entropy and the arrow of time govern in the real world. This paper demonstrates that time travel into the past and causality violation occur only when speeds "greater than" infinity are involved, and this absurdity is refuted by studying relativistic dynamics in certain scenarios that purportedly lead to causality violation and allowing it to instruct us in limiting the LT in certain other scenarios. Thus there is no justification for the block universe concept and the implication that the past is "back there somewhere" and can be accessed from the present, thus preventing causality paradoxes.