I am trying to figure out a solution for some mind-boggling, modified case of a famous twin paradox. I don’t have a physics background and I think I am missing something here which doesn’t allow me to solve that problem. But let’s get to the point.

Let’s assume we have twins each in his own spaceship. Around them there is nothing but utter void; no planets, stars etc. - nothing which they could refer to. They are completely isolated from anything, so there are no other frames of reference.

To makes things a little bit simpler let’s assume that in the past those twins abandoned their biological bodies and moved (their consciousnesses) to artificial ones made from exceptionally strong material (diamond/carbon nanotubes/adamantium/etc.) and therefore they (and also their spaceships, made from the same material) can withstand enormous G-forces and are able to accelerate at many thousands of g without turning into jelly.

The spaceships are at rest relatively to each other and their onboard clocks are synchronized. Next, the spaceship B starts accelerating in a spiral trajectory at many thousands g until it reaches 0.99c; now it is circling the spaceships A with that velocity. It is doing that for 10 years according to a clock on the spaceship A and then it is decelerating at many thousands g and comes to a complete stop nearby the spaceship A. The twins meet. If it comes to my understanding of the Einstein’s theory the twin B would be much younger now than twin A due to a time dilation resulting from moving at subliminal velocities (or maybe resulting from being under very high accelerations? Or maybe both as acceleration is a derivative of velocity?). But why is that? Isn’t velocity relative? If spaceship B is moving away at a given velocity from spaceship A it also means exactly the opposite, isn’t it? That the spaceship A is also moving away with relation to the spaceship B. So having that in mind why one twin ends up being younger than his brother? Or maybe I am terribly wrong here and they would still be at the same age, and their onboard clocks would still be synced?

Please kindly help me solve that conundrum, I am feeling I might go crazy if I think any more about it…

  • $\begingroup$ Two problems with your question: 1. What is keeping the one space ship in its circular trajectory around the other one? There needs to be some sort of force to keep it in circular motion 2. What you have described is exactly the genius of the twin paradox because only one of the twins is forced to accelerate. Think about those two things and it might answer your question. $\endgroup$ – Jaywalker May 4 '17 at 22:30

Velocity is relative. Acceleration is not. The fact that Twin B is accelerating means that we should not expect relativistic effects to be completely symmetrical. In the non-juiced version of the twins paradox, it is the acceleration of the spacefaring twin when she turns around that allows us to conclude that she will be younger than her twin. The same goes for your scenario. The accelerating twin will be younger.

  • $\begingroup$ So is it correct to say that it is an acceleration that causes time dilation and not velocity, even though they are tightly connected to each other? $\endgroup$ – infector May 4 '17 at 22:32
  • $\begingroup$ It is velocity that causes time dilation and other effects, but acceleration causes severity of these effects to be different. @WillO's answer is a good one on this aspect. $\endgroup$ – Mark H May 4 '17 at 22:43

In spaceship $A$'s frame, spaceship $B$'s clocks run slow.

Symmetrically, at any given instant, in spaceship $B$'s (instantaneous) frame, spaceship $A$'s clocks run slow. By exactly the same factor.

But unlike $A$, $B$ keeps changing frames. So you can think of $B$ as always seeing $A$'s clocks running slowly, but also constantly changing his mind about how long $A$'s clocks have been running.

From those considerations alone, it's not obvious who will have aged more when the twins come back together. Fortunately, there are other considerations that do make it obvious. The proper time along $B$'s path is shorter than the proper time along $A$'s path. Therefore on the day of their reunion, $B$ is younger.


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