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• The setup for the twins paradox is as followssuppose I sit on earth while you head

• off on a rocketship at a constant speed for a while, then turn around and come back.

• We know that moving things experience time more slowly, so I'll think that when you get

• back, you should be younger than me.

• But from your perspective, the earth (with me on it) is doing the moving, receding and

• then returning, so you think that I should be younger than you.

• Who's right?

• We'll use the fact that time rotates to sort this all out.

• Ok, so from my perspective, every second that passes I stay in the same place, while every

• second that passes, you get farther away, and then closer.

• Simple enough.

• From my perspective, you'll take ten seconds to get back.

• And since you're moving, I'll think that time is passing more slowly for you, so I'll calculate

• that your journey, for you, takes eight seconds.

• Nowand this is the important bitsince you're moving, what you think of as the forward

• direction of time will be rotated relative to _my_ perception of time.

• So on your outward journey, the seconds will tick away like this.

• And on your return journey, the seconds will look like this.

• From your perspective, your journey does indeed take eight seconds!

• But almost immediately, we also see the solution to the twins paradox: right here.

• This bit of my time is unaccounted for by you.

• During your entire journey, you'll think that time is passing more slowly for me than for

• you (and indeed it ishere, and here, add up to only 6.4 seconds), but because of

• your change in velocity when you turn around to come home, your notion of time rotates

• and skips right over a large swath of my time.

• Which amounts to preciselyyou guessed itthe missing 3.6 seconds.

• And this is the resolution to the twins paradox: because you changed velocity, your notion

• of simultaneous times rotates, so your accounting of how time passes in parts of the universe

• far away from you will have gaps in it.

• Well, in reality it wouldn't have gaps, because you couldn't instantaneously change direction

• you'd have to fire your rockets to start heading home, and during that acceleration

• your notion of time would have very very quickly rotated through the missing gap in my journey,

• allowing you to properly account for the missing time.

• In summary: during your outward and return journeys, ten seconds would pass for me, and

• I'd calculate eight seconds as passing for you.

• Eight seconds _would_ pass for you, and you'd calculate 6.4 seconds as passing for me during

• your outward and return journeys, and 3.6 seconds as passing for me during your acceleration

• (even if it was basically instantaneous).

• So we both agree that when you come home, you'll be younger!

• And indeed, this is what happens when you send an atomic clock flying around in in an

• airplane: it records less time as having passed than a twin atomic clock that stays on the

• ground.

• PS the time rotations I've been talking about are actually called "Lorentz Transformations",

• and they're the way that most working physicists think about special relativity and things

• like time dilation, relativistic doppler shifts, and so on.

• Trying to understand relativity just by using basic equations for time dilation and length

• contraction (like is often done in beginning physics classes) will often lead to confusing

• apparent contradictions, because they don't take into account the full changing of simultaneity

• of events, and so on.

The setup for the twins paradox is as followssuppose I sit on earth while you head

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# Complete Solution To The Twins Paradox

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林宜悉 posted on 2020/03/28
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