(This GeoGebra visualization is an extension of my earlier visualization of the spacetime diagram of the Michelson-Morley apparatus https://www.geogebra.org/m/XFXzXGTq . However, the current visualization is based on the following.)[br][br]A [b]circular light clock[/b] is a generalization of the Michelson-Morley apparatus (interpreted as a pair of spatially-orthogonal light clocks). Along the worldline of an inertial observer, a light flash signal traces out a cone (the light cone) on a spacetime diagram. When the signals strike a circular arrangement of mirrors around the observer (simultaneously in her frame), the reflections are received by the observer at a common event on her worldline--this marks the first tick of the clock. (This is sometimes called a "causal diamond".)[br]This will be true for all inertial observers in relative motion.[br][br]Abstracting from this experiment, one can define a [br][b]"circle of simultaneous events according to a given inertial observer"[/b][br] as the [br][b]intersection of "the future light cone of tick 0" and the "past light cone of tick 1",[/b] [br]both events on the inertial observer's worldline.[br][br][br]This is based on my article [br][br][b][i]"Visualizing Proper-Time in Special Relativity"[/i][/b][br]Physics Teacher (Indian Physical Society), v46 (4), pp. 132-143 (October-December 2004) [br]https://arxiv.org/abs/physics/0505134 [br][br]Here are some related videos (using VPython):[br]https://www.youtube.com/watch?v=tIZeqRn7cmI ( Time Dilation)[br]https://www.youtube.com/watch?v=NqjAOyGR82s ( Clock Effect / Twin Paradox )[br][br]A 2-dimensional version led to my article a graphical method of calculation in special relativity using "light-clock-diamonds"[br][br][b][i]"Relativity on rotated graph paper"[/i][/b][br]American Journal of Physics 84, 344 (2016); [br]https://doi.org/10.1119/1.4943251[br]( https://arxiv.org/abs/1111.7254 old draft)[br][br]and a recent chapter[br][br][b][i]"Introducing Relativity on Rotated Graph Paper"[/i][/b][br]Ch 7 of "Teaching Einsteinian Physics in Schools[br]An Essential Guide for Teachers in Training and Practice" (2021)[br]Magdalena Kersting, David Blair eds.[br]( ISBN 9781760877712 )[br][br][For a visualization of the light-clock diamonds,[br]see https://www.geogebra.org/m/HYD7hB9v and[br]https://www.framingham.edu/faculty/smabrouk/Maa/mathfest2016/tcps9/ [br]for my presentation at MAA MathFest 2016 ]