If both craft suddenly accelerate the same amount at the same time, they should stay

如果兩艘飛船在同一時間突然加速，它們應該保持相同的速度。

the same distance apart.

相隔相同的距離。

Except, now they're moving... and in our universe moving objects undergo length contraction

只是，現在它們在移動......而在我們的宇宙中，移動的物體會發生長度收縮。

and get shorter in the direction of motion.

並在運動的方向上變短。

The spacecraft and string should each have their lengths contracted, and be shorter.

航天器和繩子的長度應該各自收縮，並且變短。

So do the spacecraft and string as a whole contract, with the two spacecraft closer to

航天器和繩索作為一個整體也會收縮，兩個航天器更接近於

each other?

彼此之間？

Or do the spacecraft individually contract but stay separated the same amount, while

還是航天器單獨收縮但保持相同的分離量，而

the string shortens & risks snapping?

繩子縮短並有斷裂的危險？

Assuming the string has no significant strength, the spacecraft shouldn't move any differently

假設繩子沒有明顯的強度，航天器的移動應該不會有任何變化

than if there were no string at all - and since they both underwent the same acceleration,

比起根本沒有繩子的情況下，它們都經歷了同樣的加速度。

they should stay separated the same as when they started.

他們應該保持與開始時一樣的分離。

Which means when the string shortens, it must snap.

這意味著當繩子縮短時，它必須折斷。

But how?

但怎麼做呢？

Is length contraction a real, physical, force?

長度收縮是一種真實的、物理的力嗎？

Yes, yes it is - from a certain point of view.

是的，是的，它是--從某種角度來看。

The electromagnetic forces which hold the string together undergo length contractions,

將繩子固定在一起的電磁力經歷了長度收縮。

too, and so the very atoms and intermolecular separations within the string are contracted,

也是如此，是以弦內的原子和分子間的分離也被收縮了。

literally pulling the string shorter - or tearing it apart if its ends are tied to,

從字面上看，就是把繩子拉短--如果繩子的兩端綁在一起，就會把它撕開。

I dunno, two heavy spacecraft.

我不知道，兩個重型航天器。

So length contraction makes the string tear itself apart.

是以，長度收縮使繩子自己撕裂。

But...from another point of view, the string breaks for a different reason.

但是......從另一個角度來看，繩子斷裂的原因不同。

Because, from the perspective of a moving object, events that used to be simultaneous

因為從一個運動物體的角度來看，過去是同時發生的事件

no longer are - in this case, from a perspective moving along with the spacecraft's final speeds,

不再是--在這種情況下，從一個與航天器最終速度一起移動的角度來看。

the front spacecraft actually accelerates first, and so for a while is moving away from

前面的航天器實際上首先加速，是以有一段時間是在遠離

the back spacecraft - by the time the back one catches up, the rockets are farther apart

後面的航天器--當後面的航天器追上時，火箭的距離更遠了

than when they started!

比起他們開始的時候!

All this is much more easy to keep track of if you use spacetime diagrams to correctly

如果你用時空圖來正確記錄這一切，那就更容易掌握了。

describe the whole situation (rather than just trying to think about length contraction

描述整個情況（而不是僅僅試圖思考長度收縮的問題

on its own, or relativity simultaneity on its own, or whatever).

在其本身，或相對論同時性在其本身，或其他）。)

But the point is, from a moving perspective, it's the spacecraft that snap the string.

但問題是，從移動的角度來看，是航天器扣住了繩子。

OK, so then why don't the spacecraft tear themselves apart when they accelerate?

好吧，那麼為什麼航天器在加速時不會自我撕碎？

If the string snaps, why don't ALL objects explode whenever they move?

如果繩子斷了，為什麼所有的物體在移動時都不會爆炸？

Well, that can only happen if different pieces of the object independently accelerate, like

那麼，這隻能發生在物體的不同部分獨立加速的情況下，例如

how the two spacecraft each have their own propulsion.

這兩個航天器如何各自擁有自己的推進力。

Normal objects aren't like that; instead, one part is pushed or pulled, and then the

普通物體不是這樣的；相反，一個部分被推或拉，然後是

intermolecular forces in the object transmit that acceleration to the other bits of the

物體中的分子間力將該加速度傳遞到其他位的

object.

對象。

And when those intermolecular forces experience length contraction, the object as a whole

而當這些分子間力經歷了長度收縮時，物體作為一個整體

simply contracts instead of being torn apart.

簡單地收縮，而不是被撕碎。

But any time there are multiple sources of acceleration on multiple parts of an object...

但任何時候，在一個物體的多個部分上有多個加速度源...

in principle it could get torn apart by length contraction.

原則上，它可以被長度收縮撕碎。

Or you might say perhaps it gets torn apart because those different parts start accelerating

或者你可以說也許它被撕裂了，因為那些不同的部分開始加速。

at different times.

在不同的時間。

It depends on your point of view - literally.

這取決於你的觀點--從字面上看。

In our universe, it's not just space and time that are relative - in some cases, it's

在我們的宇宙中，不僅僅是空間和時間是相對的--在某些情況下，它是

also whether you're torn apart, or tear yourself apart.

也不管你是被撕裂，還是把自己撕裂。

In putting together this video, it was really helpful for me to work out the spacetime diagram

在拼湊這段視頻時，對我來說，算出時空圖真的很有幫助

for bell's spaceship paradox myself - and that's exactly the idea behind Brilliant,

我自己也是為了貝爾的飛船悖論--而這正是《輝煌》背後的想法。

this video's sponsor.

本視頻的贊助商。

Brilliant is based off the principle that active problem solving is the fastest path

輝煌是基於這樣的原則：主動解決問題是最快的途徑。

towards mastery of a new concept or skill - and now they've taken it to the next level

掌握一個新的概念或技能--而現在他們又將其提升到了新的水準

with tons of visual interactivity across their math and science courses.

在他們的數學和科學課程中，有大量的視覺互動性。

You can interact with the math of gears and pulleys and computer programming and the pythagorean

你可以與齒輪和滑輪的數學、計算機編程和勾股定理進行互動。

theorem!

定理!

To gain a deeper understanding of science and mathematics and to sign up for free, go

為了更深入地瞭解科學和數學，並免費註冊，請訪問

to Brilliant.org/MinutePhysics.

到Brilliant.org/MinutePhysics。

The first 200 people will get 20% off an annual Premium subscription with full access to all

前200人將獲得20%的年度高級訂閱，可以完全訪問所有的

of Brilliant's courses and puzzles.

的Brilliant的課程和謎題。

Again, that's Brilliant.org/MinutePhysics - and thanks to Brilliant for their support.

同樣，這就是Brilliant.org/MinutePhysics--感謝Brilliant的支持。