About a year ago I provided a rough outline of what what I thought (based mainly on the book "Relativity Visualized" by L. Epstein) would happen during the twins paradox scenario and sought confirmation that I had it about right:
Seemingly, the consensus was that I did have it about right. In light of that, would it not be a good idea to make a computer animation showing what I described, and even better, to make it precise by using relativity to calculate the actual values that I estimated?
Edit: the animation should show what happens and/or you see in real time. This would be a huge improvement. So the distance traveled by the ship can't be a matter of light years, but instead should be a few light seconds, or light minutes, at most (or whatever the user of the animation/game can stand). So instead of traveling to a star, the ship should make a return journey from the Earth to an asteroid, space probe/telescope or planet in the solar system, or perhaps to the sun and back. The traveling twin won't age noticeably, but this doesn't matter, as we can consider the time as measured by the ship clock instead. It's harder to imagine a ship with so much acceleration that it reaches nearly light speed in second or minutes, but that doesn't matter. This way you see what happens in each frame of reference or what images you'd see in with your telescope (not what really happens in your frame of reference) at the actual rate. Time flows at the normal rate.End of edit.
But seemingly no one has ever done this. At least, I have never seen such a video, and I have looked at a lot of relativity animations. I could be wrong about this I suppose.
This seems really weird. Nearly everyone has heard of the twins paradox, but no one has seen an accurate and complete (by which I mean including a clock at each important location) animation of it, it seems. I wouldn't have thought it would be all that difficult, either, as what each clock shows at each time could be calculated by the same computer that is used to make the animation. And I learned recently (on Physics SE) that you only need special relativity for the twins paradox, because there in no action by gravity.
Google offered https://youtu.be/uh6bHORgC-Y when I searched for "relativity animation showing desynchronization".
So my question is how could one make an accurate and complete computer animation of the twins paradox of special relativity?
In light of the comments and the first answer I see I wasn't clear enough about what I mean by "an animation". I mean a sort of computer-generated cartoon, showing the earth, a distant star (edit: or rather, something a few light minutes away at most), and a rocket flying to the star and back to earth. I'm not talking about having explanations, nor of graphs. I don't envision anything abstract. Everything would be in plain view. Clocks would indicate time in the normal way. Time dilation would be indicated by slow running of one or more clocks. Time desychronization would be seen plainly in the desynchronization of the clocks. There would in a sense be no need to understand anything. It's just what happens. The one complication would be how everything is different for the ship and the twin on it, but that could be easily dealt with by having three versions of the story, one for the earth, one for the ship, and one for star. It is a case of showing rather telling, although probably a matter of showing three stories, as seen at each of the three objects (earth, star, and ship).
It's not as abstract as some might imagine (as shown by comments: "It would have to communicate the ideas of spacetime as a mathematical space, and of a simultaneity hyperplane as a slice through it." and "A candidate for that is the animated gif available on wikipedia, titled Lorentz transform of worldline. The geometrical counterpart of Lorentz transformation is a scissor-like motion of the coordinate axes with respect to each other." and "The twin that accelerated, you would have to explain why you are trying to isolate the accelerating part from the non-accelerating contribution to time dilation."
I hope it's more clear now that the viewer wouldn't see anything totally unfamiliar, or anything that needed explaining (although explanation could be good). It's like when you explain conservation of angular momentum by an animation or movie of an ice skater. You don't need to show anything except ice, person, and ice skates. You see them moving. There is no positive need for any vectors showing forces, velocities, angles, or angular accelerations and so on. All that is optional, or can come later.
Also, if you look at the linked to question from eight or nine months ago, it doesn't say anything about any optical illusions or any other effects due signal delay, blue or red shifting, or any other tricks of the light, so to speak, caused by moving at close the speed of the light. On the other hand, it doesn't make clear, that unlike most, I am not talking about anything involving light-caused illusions.
Maybe I should edit that other question to make that clear, but for now I'll just make the point here that everything I've said in both that question and this is based on the idea of the framework of clocks and rods. See my answer here for a layman-level explanation of what that means: https://physics.stackexchange.com/a/718723/295887. This means that I am at all times talking, like L.Epstein (whose book I highly recommend), about what is actually happening, before any effects due to signal delay add a second layer of changes, and obfuscate everything.
Finally, I'm not talking about even showing space and time, or anything abstract, and certainly not explaining such things, but rather a rocket making a journey through space that has some (very large) clocks placed in it. A physical scene containing objects a child can recognize and understand.
And everything happening at the actual speed.
If something is moving in a frame of reference, it kind of doesn't have a color or a brightness itself, although a Doppler shifted (illusory) image of it can be seen in a telescope together with an illusory brightness. So it would need to be represented by some sort of monochrome shade of some color, e.g. gray, allowing one to see the Lorentz contraction, time dilation, and time desynchronization that is really happening, and its actual velocity. Maybe superposed onto that (or that you can toggle back and forth from) could be what you'd see, i.e. the brightened/dimmed and blue/red shifted, rotated, crazy-speeding (e.g. faster than light), and crazy-fast running clocks (faster than at rest, sometimes) illusory versions of the real objects.
If you could see objects that are behind other objects, for example they are made of netting, would that also be good, especially if you are going to superpose what you see onto what happens in each frame of reference?
