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I'm traveling the space, and the solar system is going to be smaller and smaller. There is no way to determine who is actually moving?

  • Yup. They see you getting smaller too. Any other questions? – knzhou Aug 20 '18 at 17:06
  • @knzhou, well, so simple.. No, about this topic, no, thanks –  Aug 20 '18 at 17:07
  • What does "actually moving" even mean? Is anything ever "actually" at rest? It's all relative. – Daddy Kropotkin Aug 20 '18 at 17:09
  • @N.Steinle, yeah, I thought a lot about this. I think the only thing that is actually in rest always is we in our frames of references. But "me" is very difficult term –  Aug 20 '18 at 17:13

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So if you are moving normal to the ecliptic, the solar system will not be smaller. It's only length contracted in the direction of motion.

Now if you are moving say, along the Earth's semi-minor orbital axis at near $c$, you will see an extremely elliptical orbit, as the is length contracted in one dimension, and an ellipse is a squished circle.

Does that mean you are moving? Well if you try to understand the Earth's orbit with Newton's gravity, you will have to conclude that you are moving and the circular orbit has been length contracted, along with some time dilation.

Of course, if you decide that you are stationary and the solar system is moving, the Sun will have a stress-energy tensor that includes its motion such that the orbital solution that you compute will be what you see.

So: No, it's all relative.

JEB
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