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Let's say I'm heading towards a star 10 ly away but I am traveling at 298289729 m/s (~99.49% of light), so that I will reach the star in 1 year from my perspective. This would cause the length to contract in the direction of motion.

If I were to peer out the front windshield at the beginning of my journey, I would still see the star I am heading towards as if it was 10 light years away, right? In other words, the length contraction does not make the size of the star increase in my field of view as if was closer to it than I am from a timelike/static perspective.

I would assume you could use trigonometry to find the distance to the target star. Would it not then be correct to say that you are experiencing a speed increase, in the sense that even though the star is 10 ly away—and can visually be confirmed to be so—you will nevertheless cover that distance in 1 year.

I understand that our measurement of c will not change, so what resolves this apparent paradox.

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I am afraid that you are misunderstanding the implications of SR. You have said that you can complete your journey to the star in 1 year. That means the star is about a light year away from you in your frame of reference at the start of your journey. The fact that it might be some other distance away in some other frame is irrelevant.

You are overlooking the relativity of simultaneity. If you ask at the start of your journey 'where is the star now?', now means a moment in time which is simultaneous with your question in your frame of reference. To someone passing you at that instant in the star's frame 'where is the star now?' means where is the star at a completely different time which happens to be simultaneous in their frame. The reason why you think the star is 1ly away while the passing person believes it is 10ly away is that you are each considering its position at different times.

If you could magically decelerate in an instant to be in the star's rest frame, your plane of simultaneity would tilt significantly, and would intersect with the star's worldline at a point roughly 9 years earlier, so in this new frame the star 'now' is about 10ly away.

You might ask, then, how would all that look through your windscreen? Before you decelerated you had a stream of photons entering your eye giving the impression you were looking at a star 1ly away, and an instant later, after you decelerated, the same stream of photons, more or less, must give you the impression the star is now 10ly away, so how can that work?

The answer lies in the fact that the photons were greatly blue-shifted when you were travelling rapidly towards the star. That would have had the effect of making time on the star appear to be running fast by about a factor of ten, and it would also affect the apparent subtended angles of light beams focussed by your eye. When you slow, all those effects vanish.

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  • $\begingroup$ Are you saying then that if I look out the front windshield I will experience the star to be larger on my horizon and if I slow down to a timelike frame then it will shrink on my horizon? I find that difficult to believe. The photons entering my eye are the same regardless of my speed, surely. $\endgroup$
    – GodProbablyExists
    Commented Jun 12, 2022 at 7:10
  • $\begingroup$ What you are overlooking is the relativity of simultaneity. I will add a para to my answer to explain. $\endgroup$
    – Professor Sushing
    Commented Jun 12, 2022 at 7:12
  • $\begingroup$ I should also mention blue-shifting. I will add that too. I hope it makes sense. $\endgroup$
    – Professor Sushing
    Commented Jun 12, 2022 at 7:40
  • $\begingroup$ Thank you for your answer. $\endgroup$
    – GodProbablyExists
    Commented Jun 12, 2022 at 8:01
  • $\begingroup$ My pleasure. It was an interesting question, particularly the point about how the star must appear to shrink if you slow to a stop- I hadn't thought about that before. $\endgroup$
    – Professor Sushing
    Commented Jun 12, 2022 at 9:03
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Actually talking about what you would see in special relativity is pretty complicated. Way too many books and resources use the term "see" or "observe" to talk about what is being referred to when things like length contraction and so forth are discussed and this really makes it misleading.

Relativity is really a theory of spacetime. Not space+time. The splitting up into space+time is an artificial construct, in that there is no one way to do it that is inherently "more correct" than another. Your eyes (or better, the eyes+light system) splits up spacetime in a way that is different from the way that is talked about in relativity books when length contraction is discussed, and that means that you cannot straightforwardly apply the "length contraction" talk to that.

In fact, an observer that could "see" such length contraction, and produce an image like that your eyes give you, would have to be using a method of sensing that is either apparently physically impossible (tachyonic particles), or else it would have to essentially be reconstructing its view at a point far into the future of the actual events in question using recorded data, or else still, the "observer" would have to be a giant structure filling and encompassing the whole area over which the relativistic phenomena are to be observed.

What your eyes would see would look pretty trippy. There's some simulated videos of it on youtube. It's not clearly about things being "bigger" or "smaller" but rather it looks instead much more akin to looking through a fisheye lens, and the fisheye distortion grows as your speed approaches $c$.

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