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Interesting video! When studying special relativity it was easy for me to have some intuition about time contraction and how would it feel to experience it, but I always struggled with time dilation. This video helped me to develop some intuition in that regard.

Otoh around 2:50 the time seems to move faster in our system of reference, which afaik it's not what should happen. Did I miss something?

I think the use of rotation to visualize the relative speed of clocks was a good design choice both functionally and aesthetically.

That being said, as a hobbyist physicist I can't be too immediately sure about the accuracy eg. @ ~2:50, tho it does appear that the cubes further away are rotating faster which is consistent with the concept of "time ticking slower for the thing moving faster."