and asteroids and comets... The Solar System in short

以及小行星和彗星，簡言之，我們的太陽系

formed about 4.6 billion years ago from a nebulous cloud

在46億年前由星雲形成

of swirling gas and dust which coalesced thanks to the irresistibly

渦漩氣體與塵埃聚結在一起因受到了不可抗拒的

attractive force of gravity.

重力吸引

attractive force of gravity.

重力吸引

However, theis nebula started off more or less as a big shapeless blob

然而，星雲形成之初只是一個巨大、無定型的斑點

So how did our solar system end up with all the planets

為何最後我們太陽系上所有的行星

and their moons orbiting in a flat disk?

和衛星會繞著一個像是平盤的軌道呢

I mean, we've all seen the planetary model of the atom,

我們都看過原子的行星模型

which is definitely wrong when applied to atoms

當然，此模型應用在此上是完全錯誤的

but it also kind of suggests that planets might revolve

但這表示行星有可能從各種方向

around the sun every which way.

繞著太陽旋轉

So is our solar system somehow special in its flatness?

所以我們平盤狀的太陽系很特殊嗎

Or is the planetary model of the atom doubly wrong?

或者原子行星模型大錯特錯

Well, our solar system definitely isn't alone,

其實我們的太陽系不是唯一

many exoplanets; star systems are flat,

很多外部行星和星團都是扁平狀的

a lot of galaxies are flat,

許多星系也是

black hole accretion disks are flat,

黑洞的吸積盤是扁平的

Saturn's rings are flat,

土星環也是

etc.

等等都是

So why, when there's all of 3D space to fill,

但為何，宇宙不是呈現三維空間

does the universe have this preference for flatness?

難道宇宙傾向平面狀嗎

The answer has to do with two things, collisions

答案和兩樣東西有關，碰種

and the fact that we live in three dimensions.

以及我們身處在三維空間的事實

Bear with me.

請容我解釋

Anytime a bunch of objects held together by gravity are zooming and circling around

當一堆物體受到重力吸引並互繞旋轉時

their individual paths are nearly impossible to predict,

我們無法預測他們個別的路徑

and yet, collected together they have a single total amount

但將他們視為一體時

that they spin about their center of mass.

他們會繞著中心質量旋轉

It may be hard to figure out exactly what direction that rotation is in

或許很難找出確切的旋轉方向

but the mathematics implies there must be some plane

但我們由數學得知，一定有些平面

in which the cloud -taken as a whole- spins.

是由雲氣帶動整體旋轉的

Now, in two dimensions a cloud of particles rotating in a plane

當粒子旋轉在二維空間時

is flat by definition, it's in two dimensions.

它就是呈現平面狀

But in three dimensions, even though the rotation of the cloud is given

但在三維世界中，就算旋轉中的雲氣

by one plane, particles can whiz around far up and down from that plane.

是在一平面上，粒子會任意馳騁在平面上下

As the particles bump into each other, all the up and down motion

當粒子相撞，所有的上下運動

tends to cancel out. It's energy lost in crashing and clumping.

都會抵銷，其能量消耗在碰種與聚集上

Yet the whole mass must continue spinning inexorably,

然而整體質量仍持續劇烈旋轉

because in our universe, the total amount of spinning in any isolated system

因為宇宙中，任一獨立系統的旋轉總量

always stays the same.

都是 一樣

So over time through collisions and crashes, the cloud loses its loft

隨著時間推移，不停地碰撞使雲氣不再上下移動

and flattens into a spinning, roughly 2 dimensional disk shape, like a solar system or a spiral galaxy.

而成了一個旋轉的二維平面，就像太陽系或漩渦星系

However, in 4 spacial dimensions, the math works out such that

然而四維空間中，由數學證明出

there can be two separate and complementary planes of rotation

可以有兩個不同卻互輔的旋轉平面

which is both really really hard for our 3D-thinking brains to picture

我們的大腦實在無法想像

and also means there's no up and down direction in which particles lose energy by collisions.

這也表示，粒子不會因上下碰撞而失去能量

So a cloud of particles can continue being just that... a cloud.

所以雲氣依舊不變

And thus, only in three dimensions can a nebula or infant galaxy

因此，唯有在三維空間中，星雲或者初始星系

start out not flat and end up flat

才有可能在最終變成平面狀

which is definitely a good thing because we need all that matter to clump together

這絕對是件好事因為我們需要這些物質聚集

in order for stars and planets to form, and for us,

形成恆星、行星、我們

-even those of us who think atoms look like this-

以及那些認為原子長這樣的人

to exist.

才得以生存