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I have a twin who stays on Earth, and I will move to another planet 4 ly away. I will travel at a certain relativistic speed towards this planet. What I just described here is the first half of the Twin Paradox, isn’t it?

Now, I understand that, due to time dilation, the clock of everything that is moving relative to an observer ticks more slowly than the observer’s clock.

Since my twin on Earth watched me move away at such high speed to the planet, my clock ticks more slowly compared to his clock. So, when I arrive at the planet, I will be younger than him. But, from my point of view, my twin on Earth moves away from me at the same speed. So, his clock would tick more slowly than mine during the trip, and when I arrive my twin would be younger than me.

I know that the full version of the Twin Paradox is not really a paradox in special relativity. But just can’t make sense of the seemingly paradoxical case that I just described which is actually just the first half of the Twin Paradox.

Would anyone please help me point out the mistakes that I made in my thought process?

Qmechanic
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Mr Deevid
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2 Answers2

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The answer is that you are younger than your twin in his frame, and he is younger than you in yours. There is no paradox here. The reason why this happens is that you and your twin have different 'nows' owing to the relativity of simultaneity. When you compare your ages, what you are effectively asking is how old is my twin 'now', where 'now' is whatever time it happens to be where you are. Because you and your twin are moving relative to each other, you have tilted planes of simultaneity, so 'now' for you on a distant planet is not the same time as 'now' for your twin back on Earth.

If you decelerate to come to rest relative to your twin, then you break the symmetry and you become younger than your twin in what is now your common rest frame. Alternatively, your twin could accelerate to reach your speed relative to the Earth and become stationary relative to you in that way, in which case it would be your twin who would be younger in the common frame.

Professor Sushing
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"So, his clock would tick more slowly than mine during the trip," Yes, this is correct.

"and when I arrive my twin would be younger than me." This does not follow. A clock that has just spent the last hour ticking slower than yours can show either an earlier or a later time than yours does.

WillO
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