A Stronger Twin Paradox

A well-known objection to Einstein's Theory of Relativity is the Twin Paradox. Most scientists do not take it very seriously, but here I explain why I think some of the attempted answers are unsatisfactory, and then, even though I do not believe that the original paradox was ever really resolved, I give a version of it that I believe is stronger.

                                                                                       Supplement

When I first came up with this thought experiment I used 12 million kilometers as the radius of the circle. I did so because I visualized something similar to a track that is used for race cars or horse racing except that it would be a circle instead of an oval. But I later realized that the g-forces would be much too extreme at those speeds with a circle of that size, so then I changed the radius to be 120 million kilometers. I did not calculate what the g-forces would be to come up with that number, I just figured that surely that would be big enough based upon a rough estimate of how long it would take the ship traveling at .75c to make a complete revolution around the circle. I actually thought that I was giving myself plenty of leeway that time. But I continued to wonder about it and recently I did find a formula to calculate the g-force caused by circular motion that I think applies in this case. If I am using that formula correctly (which is certainly not guaranteed, as mathematical calculations are not my strength) it looks as though 120 million kilometers is still not large enough, not even close actually.

I guess it makes sense. The speeds that we are talking about here are so much faster than anything that we are familiar with in everyday experience that it is hard to fully grasp it sometimes. If the ship going .75c covers nearly 225,000,000 meters in only one second then even a very slight deviation from a perfectly straight path during that second would create a very strong acceleration on the passengers’ bodies as the ship acted upon them to make them follow a curved path rather than a straight one. That curve would have to be extremely slight for this to be a tolerable level of acceleration for those passengers, which of course means a circle with a very large circumference.

It is embarrassing to have made a mistake like this but I cannot remove it. However I made a significantly improved version of this argument in a work titled: Special Relativity Effects are Optical Illusions. https://zenodo.org/record/4407957#.YJosLz9OnIU  You can find where it is located in the table of contents.

I also have another argument that I think is better. It does not employ the twin scenario but it addresses many of the same issues. That is called: How Two Key Tenets of Relativity Lead to a Self-Contradiction. It can be found here: https://zenodo.org/record/4511452#.YJoodj9OnIU