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• In our universe, when you change from a non-moving perspective to a moving one, or vice versa,

• that change of perspective is represented by a what's called Lorentz transformation,

• which is a kind of squeeze-stretch rotation of spacetime that I've mechanically implemented

• with this spacetime globe.

• The spacetime globe illustrates many of the features of special relativity, like length

• contraction and time dilation and the twins paradox is...

• The twins paradox is a linguistically confusing situation that can arise in special relativity

• when somebody learns about time dilation - the fact that in our universe,...(that) things

• moving relative to each other each view the other's time as passing more slowly (which

• is calledtime dilation”).

• As the paradox goesif each person views time as passing more slowly for the other,

• then if my twin travels away from earth for a while and then comes back, who's actually

• younger when we meet again?”

• When you have a potentially confusing situation in relativity, it's really helpful to actually

• draw a spacetime diagram to understand what's going on.

• So we'll use the spacetime globe.

• The situation is this: you're sitting on earth for, let's say, 12 seconds.

• Your twin travels out at a third of the speed of light for what you measure to be 6 seconds,

• then they turn around and come back at a third the speed of light for what you again measure

• to be 6 seconds.

• So what does your twin think?

• Well, to understand the situation from their moving perspective we need to transform the

• spacetime diagram so they no longer appear to be movingthat is, so that their worldline

• is vertical.

• That's what it means for the spacetime diagram to represent their perspective.

• Having done so for the outward leg of their journey, it's clear that your twin would say

• that leg of their journey took them – I dunno, what's that look like?

• About 5 and 2/3 seconds?

• And then they turned around and headed back to earth, which corresponds to a different

• moving perspective.

• Let's transform things to see how they look from that perspective; that is, so that the

• worldline of that leg of the journey is vertical.

• Having done so, it's clear that your twin would say that the return leg of their journey

• took themagain, looks like about 5 and 2/3 seconds.

• So from the perspective of your twin, their whole journey takes 5.66+5.66=11.3 seconds,

• while for you it took 12 seconds.

• So you, who stayed put, are older.

• The key to why the two of you do in fact age differently is that your traveling twin has

• two separate perspectives during their journey, while you, staying put, only have one.

• And that's the resolution to the linguistically confusing twins situation, demonstrated with

• a hands-on spacetime diagram - I want to say that even though I knew and understood the

• math and physics behind this, my belief in the true-ness of the solution to the twins

• paradox went up a million times the first time I actually measured the times each twin

• experienced with my hands, in real life like this.

• So I hope that I've managed to capture even a small percentage of that gut level belief

• in this video.

• You also don't have to use Lorentz transformations to figure out the solution to the twins paradox

• if you know about proper time (spacetime intervals), because spacetime intervals are/proper time

• is a way of calculating the time that passes for somebody according to their perspective.

• So in the case of your twin, on each leg of their journey they take 6 seconds to travel

• the distance light would travel in two seconds (or, 2 light-seconds), and taking the square

• root of the difference of those numbers squared gives a proper time of 5.66 seconds for each

• leg of their journeyexactly what we measured on the spacetime globe!

• If you're interested in a little more insight into how theeach person views time as

• passing more slowly for the otherpart of the paradox actually makes sense (and I

• promise, it does), I have another pair of videos diving into more detail on the twins

• paradox that I highly recommend you check out!

• And to deepen your personal understanding of the resolution to the twins paradox, I

• highly recommend Brilliant.org's course on special relativity.

• There, you can work through the calculations I've glossed over in a step-by-step guided

• exploration, giving you essential hand-on experience with spacetime intervals and other

• tools of relativity along the way.

• The special relativity questions on Brilliant.org are specifically designed to help you go deeper

• on the topics I'm including in this series, and you can get 20% off of a Brilliant subscription

• by going to Brilliant.org/minutephysics.

• of Brilliant's courses and puzzles, and lets Brilliant know you came from here.

In our universe, when you change from a non-moving perspective to a moving one, or vice versa,

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# The Twins Paradox Hands-On Explanation | Special Relativity Ch. 8

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林宜悉 posted on 2020/03/28
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