giant orbs attached to it by springs.

一些巨型球體由彈簧連接到它身上。

His actual drawings, compared night after night, show these bright spots moving back

他的手繪圖，比對每個夜晚 表明這些亮點來回移動過

and forth past Jupiter, exactly the same as if they were balls hanging off of springs.

木星， 跟球掛在彈簧上一樣。

I mean, yeah Galileo was looking at the moons of Jupiter, but if you plot their motion back

我的意思是，伽利略當時看著的是 木星的衛星，但如果你繪製他們來回

and forth and back and forth over time, it forms a sine wave.

又來回的運動一段時間， 它會形成一個正弦波。

And that motion is mathematically identical to the motion of something bouncing up and

而這個以彈簧上下彈跳的運動是有數學根據的

down on a spring with a linear restoring force - also sine waves over time.

具有續力 - 和正弦波隨著時間的推移。

From a side-on perspective that projects two dimensions down to one, things in circular

把物體的側面從二次元降到一次元，在軌道循環上

orbits look exactly like they’re springing back and forth on giant coils of wire.

看起來就像被巨大的線圈拉著來回彈跳。

Now, I’m not saying that we should think of the moons of Jupiter as being held on by

現在，我不是說我們應該覺得木星的衛星被無形

giant invisible springs, but it’s a valid mathematical model when viewing them from

的巨型彈簧拉著，而是它可以應用為數學的公式當你在

a distance – it’ll make the same predictions about the motions of the moons as the “orbiting

遠處觀察 - 而它會有相同的衛星運動軌跡預測為

in circles due to invisible gravity” model, and one can be mathematically transformed

"因為無形的引力造成循環的軌道"公式 且其中一個可以由數學轉換

into the other.

為另一個。

The moons of Jupiter aren’t alone in having multiple mathematical descriptions: projectiles

木星的衛星不是唯一一個有複雜的數學描述：

and storms on earth experience a force (called the Coriolis effect) that causes them to turn,

拋物線和地球上的風暴受到力的作用（叫 科里奧利效應），使它們轉彎

but viewed from an external perspective, the projectiles and storms are what goes in a

但由外部的角度看， 拋物線和風暴會直直的走

straight line while the earth turns beneath them.

當地球讓他們向下彎

Both models, if you use them carefully, make correct predictions about reality.

這兩種公式， 如果你仔細的運用它們，會與現實相同的正確預測。

And quantum phenomena can be modeled in at least three different ways that all give the

量子現象可以用至少三種不同的公式模擬，都會是

same predictions: as a particle being guided by a spread-out “pilot wave”, or as a

同樣的預測：1. 粒子被一個展開的“導航波”引導，或

spread out probability wave that collapses to a single point, or as a particle exploring

2. 一個展開的機率波坍塌為一個點，或者

all possible paths it could take and interfering with itself along the way.

3. 一個粒子的所有可能的路徑和所有一路上所有的干擾

All three of these mathematical models suggest different ways of thinking about what’s

所有這三個數學公式 都提供不同的想法關於

“actually” going on in quantum mechanics, and the fact that all of them give the same

在量子系統中“實際上”是發生了什麼事 而事實上，他們顯示出相同的

experimental predictions suggests that perhaps none of them is the “right” way to picture

實驗預測，表明著 也許他們都不是“正確”的方式來描繪

what’s happening in quantum systems.

在量子系統發生了什麼事。

Mathematical models give us nice, easy-to-digest pictures of how the universe works: moons

數學公式給了我們不錯又很好吸收 關於宇宙如何運作的想像：衛星

orbit around planets, atoms bind together into molecules, electrons are clouds of probability,

繞著行星轉，原子聚在一起成分子，電子變成電子雲，

and so on.

之類的。

But we need to be careful how much weight we give to the models in our heads (or on

但是，我們必須要小心在想像中的這些東西有多少重量 （或

our blackboards, or computer screens).

我們的黑板或電腦螢幕）。

Do Jupiter’s moons move like they’re pulled back and forth by the invisible force of springs?

木星的衛星像被無形的彈簧力量拉扯來回移動?

Or held in orbits by the invisible force of gravity?

或者是由無形的引力軌道？

Or are they following helical paths which are actually straight lines in curved spacetime?

或者他們螺旋的路徑 實際上在彎曲的時空中是種直線？

The way we describe the world influences the way we think the world is, even when there

我們描述這世界的方式影響著我們眼中的世界，即使

are other, equally correct ways of describing the world that paint entirely different pictures

有其他大致相同且正確的描述卻畫出完全不同的想像

from our own.

從我們之中。

That’s not to say we should accept wrong ideas, but we should be aware that sometimes

這並不是說我們應該接受錯誤 的想法，但我們應該意識到，有時

a different correct picture, one we haven’t considered, is the one we need to see.

不同的正確想像，一個我們沒有 考慮到的，是我們需要去了解的。

Hey, Henry here, thanks for watching.

嘿，我是亨利，感謝收看。

This video has been supported by Audible.com, as you may know, a leading provider of audiobooks

該視頻已被Audible.com的支持， 正如你可能知道，有聲讀物的主要供應商

including fiction, non-fiction and periodicals.

包括小說，非小說類和期刊。

You can get a free 30-day trial at audible.com/minutephysics, and I’d like to recommend the book “The

你可以在audible.com/minutephysics獲得免費試用30天，我想推薦一本

Power of Habit” by Charles Duhigg, which explores how we form habits, how to break

"查爾斯．杜希格 - 習慣的力量:為什麼我們這樣生活，那樣工作?" ，探索我們如何形成的習慣，如何突破他們

them, and how to use them to your advantage – it’s a good one.

以及如何利用它們變成你的優勢

You can listen to “The Power of Habit” or another book of your choice, with a free

你可以聽“習慣的力量” 或者您選擇的另一本書，以免費

30-day trial at Audible.com/minutephysics.

30天試用版在Audible.com/minutephysics。

Thanks again for watching, and thanks to audible for supporting these videos.

再次感謝您的收看，也謝謝發聲支持這些視頻。 - f8702111翻譯