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If I would stand on a space ship traveling with a speed of 0,99c I would be moving 7 times slower from Earth's perspective. But if I would look back on Earth I would see everything moving 7 times faster then from my perspective. Right?

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Absolutely not. Both you and the people on Earth would see each other moving $7$ times slower. To repeat myself: you would see them going $7$ times slower and they would see you going $7$ times slower.

This is because of the main principle of special relativity. As long as neither of you is accelerating there is nothing to choose between your frame of reference and the Earth's frame of reference. Just as the people on Earth are free to describe themselves as stationary and you as moving at $0.99c$ you are free to describe yourself as stationary and them moving in the opposite direction at $0.99c$. Neither point of view has a more valid claim to being "stationary" than the other so both must see the other as being slowed down.

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