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If I have an object A that is 1 light year away in front of me and another B that is 1 light year behind me and initially we're not moving relative to each other and I accelerate to 0.9$c$ towards A, the length between myself and A will contract to around 0.44 light years (according to my calculation).

What happens to the length between myself and B? does it also contract to 0.44 light years? Does it expand to (1/0.44) light years?

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Lengths ahead and behind you contract by the same amount.

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  • $\begingroup$ Are you sure? It would mean that I could just accelerate back and forth and the distances would just keep getting shorter on both sides. $\endgroup$
    – Jacques Le Normand
    Commented May 10, 2022 at 22:21
  • $\begingroup$ @JacquesLeNormand : Only if your speed keeps increasing. $\endgroup$
    – WillO
    Commented May 11, 2022 at 1:11
  • $\begingroup$ ahh, makes sense now. It's not only the position of A and B that count, but their relative speed to myself $\endgroup$
    – Jacques Le Normand
    Commented May 11, 2022 at 3:04
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Imagine a very long rod (2 light years) from object A to object B. When you pass by this rod (parallel to it) at a significant fraction of the speed of light, you will see its length contract, uniformly. Now if it were two 1-lightyear lengths, one from you to A, and one from you to B, hopefully you can see one would expect both distances to contract.

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