Abstract
In special relativity, events that are simultaneous in one inertial reference frame (IRF) are not so in another. 75 years ago, L I Mandelstam showed that the absolute simultaneity of events in different IRFs is achieved by using infinitely fast signals instead of light to synchronize clocks. 25 years later, F R Tangherlini showed in an independent study how special coordinates and time transform in this situation from one IRF to another. Although different IRFs enter on different footing in this case (the observer's frame being the privileged one), the Tangherlini transformations are still capable of describing the known experimental special relativity tests.