The Twin's paradox is a well known paradox in which there is a difference in the ages of twins after one twin travels a round trip around the space and returns back while the other twin stays put. I understood how the gap in their ages arises because of the finite acceleration time taken during the change of velocity while the travelling twin takes a turn. But my question is, when he starts decelerating/ accelerating, won't he observe the other twin decelerating/ accelerating too? I mean, if I'm accelerating away from a reference position, that point will also accelerate in the opposite direction in my frame, right? I searched the internet for relevant answers to this question to which I didn't find anything concrete. Any help is appreciated. Thanks.
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The central thing you're missing here is that you can tell when you're in an accelerating frame.
If one twin notices that objects that aren't tied down begin to accelerate without being acted upon by any forces, then he knows that he is in a non-inertial frame, and that his observation that the other twin is accelerating is due to his own acceleration.
probably_someone
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The "without being acted upon by any forces" is an interesting reservation. If you feel a force, you may not know if you're being accelerated or feeling the force of gravity of some external object - to you, both feel exactly the same. This is why general relativity predicts time dilation is caused by gravity as well - see https://en.wikipedia.org/wiki/Gravitational_time_dilation. It is curious we don't think that other 1/r^2 forces (e.g., EM force) cause time dilation - but I don't know why, or whether this was actually tested. – Nadav Har'El Sep 16 '19 at 11:27
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What if the amount of acceleration is so very small as to not be detected by you? Then how would you know? – Brad S Aug 04 '20 at 13:26
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1@BradS There is no need for your brain to know... "nature" knows (ofc the effect continiously gets smaller and smaller). – Quillo Apr 24 '23 at 07:37