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But if they measure the order of events differently, they may both be correct. That is because light is always perceived as being the same speed regardless of the observer.
And yet, causality is preserved, and there is a clear specific mathematical relationship between the two frames of reference.
So you will measure differently, but as soon as you do the math to account for your different frames of reference, you will again have the same measurements. Of course, we know there is an objective mathematical relationship between the two frames of reference, because the speed of light is constant.