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In special relativity, a rocket traveling at .5c will take .86 years (in the astronauts frame) to travel 1 light year (in a stationary observer frame). There are two possible ways to look at this

  1. The astronaut could say that he saw length contraction so he did not in fact travel 1 light year in his frame.
  2. The astronaut could say that in his frame he travelled at faster than $c$.

I understand that it is a basic premise of SR that the laws of physics are the same in all frames of reference and that nothing can travel faster than c in any frame.

So what is the reasoning that we chose length contraction rather than faster than $c$ travel to explain this conundrum? If we imagine that our astronaut had never heard of Einstein and these basic postulates, which option would he choose as the explanation, and why?

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    $\begingroup$ ...faster than $c$ travel well this kinda violates the postulate that nothing travels faster than the speed of light. So is your question really, "Why is this maximum limit taken as a postulate?" $\endgroup$
    – Kyle Kanos
    Commented Jun 19 at 18:34
  • $\begingroup$ @KyleKanos yes, you could say that. If you look at it as an outsider, either one of the postulates is as strange as the other. I'm wondering why we chose length contraction as the correct answer. $\endgroup$
    – foolishmuse
    Commented Jun 19 at 18:36
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    $\begingroup$ What would the astronaut measure light speed to be in his own reference frame? $\endgroup$
    – Marius Ladegård Meyer
    Commented Jun 19 at 18:54
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    $\begingroup$ @foolishmuse, a measurement is independent of what theory you use to frame the interpretation of that measurement. And as far as we can tell based on experimental evidence, he would measure it to be $c$. So of course he cannot be travelling faster than that; as WillO pointed out, according to him he is not moving at all. $\endgroup$
    – Marius Ladegård Meyer
    Commented Jun 19 at 18:58
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    $\begingroup$ @foolishmuse "The astronaut could say that in his frame he travelled at faster than c" This is nonsense. The astronaut did not travel faster than light because the length is contracted in his frame. It is a fundamental postulate of relativity that if A moves with velocity $v$ relative to B, B will move at velocity $-v$ relative to A. $\endgroup$
    – Vincent Thacker
    Commented Jun 19 at 19:51

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The basic principle is that if you are holding a ruler and a stopwatch, and you measure the speed of some object with your ruler and your stopwatch at your location, then you will never measure a velocity faster than $c$.

And indeed if you use your ruler and your stopwatch to measure the speed of light (or any massless particle) at your location then you will always get the result $c$.

And this is true in both special and general relativity.

The physical significance of $c$ measured in this way is that it is a constant related to the geometry of spacetime. Everyone will measure the same value of $c$ because everyone is living in the same spacetime.

In your suggested experiment the astronaut is not measuring distances with their own ruler. You are suggesting they measure time with the own clock, but distance with the ruler of the guy stuck on Earth. You can do this, and you'll get a number, but since you are mixing up different units your result won't have any fundamental significance.

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