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As someone who knows very little special-relativity (and none of the math) I understood that if you take a car moving down the road (at constant velocity) and approaching an observer, there is no preferred or fundamental reference frame. So both statements below are true:

From the car's reference frame the observer and the road are moving towards it.

From the observer's reference frame the car is moving towards them.

both things are true and there is no way to show that it is really the car that's moving and not the observer and the road. From what I learned this was the motivation behind the theory of special relativity that all constant velocity motion is relative (and light moves at the same speed in all frames of reference).

However can we not tell that the car is really moving (if the car was moving at a constant speed close to the speed of light) because it would experience time dilation and we would see that an atomic clock on the car ticks slower that one with the observer. Doesn't this just bring back the problem that special relativity was trying to solve. Because it would seem that from the car's reference frame the road and the observer are moving towards it at close to light speed and the observer should experience time dilation?

How does the twins paradox work if from's the reference frame of the twin on the spaceship it is the earth and the other twin that moves away at near light speed?

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Motion is still relative because both observers conclude that the other observer is time dilated by the same amount.

This is actually the paradox in "the twin paradox". Not that one twin ends up younger than the other (that is true and has been experimentally validated), but that each twin concludes that the other was time dilated ends up younger.

The resolution of the paradox is that the twins are not symmetric because only one (the twin in the spaceship) has changed frames - when he turned his spaceship around.

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