robphy-CircularLightClocks-VisualizingProperTimeInSpecialRelativity
(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.)
A circular light clock 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".)
This will be true for all inertial observers in relative motion.
Abstracting from this experiment, one can define a
"circle of simultaneous events according to a given inertial observer"
as the
intersection of "the future light cone of tick 0" and the "past light cone of tick 1",
both events on the inertial observer's worldline.
This is based on my article
"Visualizing Proper-Time in Special Relativity"
Physics Teacher (Indian Physical Society), v46 (4), pp. 132-143 (October-December 2004)
https://arxiv.org/abs/physics/0505134
Here are some related videos (using VPython):
https://www.youtube.com/watch?v=tIZeqRn7cmI ( Time Dilation)
https://www.youtube.com/watch?v=NqjAOyGR82s ( Clock Effect / Twin Paradox )
A 2-dimensional version led to my article a graphical method of calculation in special relativity using "light-clock-diamonds"
"Relativity on rotated graph paper"
American Journal of Physics 84, 344 (2016);
https://doi.org/10.1119/1.4943251
( https://arxiv.org/abs/1111.7254 old draft)
and a recent chapter
"Introducing Relativity on Rotated Graph Paper"
Ch 7 of "Teaching Einsteinian Physics in Schools
An Essential Guide for Teachers in Training and Practice" (2021)
Magdalena Kersting, David Blair eds.
( ISBN 9781760877712 )
[For a visualization of the light-clock diamonds,
see https://www.geogebra.org/m/HYD7hB9v and
https://www.framingham.edu/faculty/smabrouk/Maa/mathfest2016/tcps9/
for my presentation at MAA MathFest 2016 ]