and for helping people find  jobs. More about that at the end.

並幫助人們找到工作。最後會有更多關於這方面的內容。

Atomic orbitals have long been a source of  frustration for me. On the one hand, you  

長期以來，原子軌道一直是讓我感到沮喪的根源。一方面，你

have simple cartoon diagrams that make them feel  friendly... but which are so varied and vague they  

有簡單的卡通圖，使他們感到友好......但這些圖是如此多樣和模糊，他們

don't really convey much beyond the basic idea  that atoms have a nucleus and some electrons. Some  

除了原子有一個原子核和一些電子這一基本概念外，並沒有真正傳達多少東西。一些

people try to take the cartoony diagrams and make  them feel more random, or “quantum” – which is an  

人們試圖利用卡通式的圖表，使其感覺更加隨機，或 "量子"--這是一種

improvement – but they're still very much just  cartoon stand-ins for the vague idea of “atom”.

改進--但他們在很大程度上仍然只是 "原子 "這一模糊概念的卡通替身。

On the other hand, you have atomic orbitals  depicted as fuzzy clouds or balloons or  

另一方面，你的原子軌道被描繪成模糊的雲朵或氣球或

rainbow donuts, which are definitely more  technically accurate (or technically inspired),  

彩虹甜甜圈，這在技術上肯定更準確（或技術上的靈感）。

but none of which feel like they give me a sense  of what's actually going on - like, what does this  

但這些都沒有讓我感覺到實際發生了什麼--比如說，這到底是什麼？

blobby thing have to do with orbiting particles?  Is the electron inside it? Or on the surface? Why  

圓球狀的東西與軌道上的粒子有什麼關係？ 電子是在它裡面嗎？還是在表面？為什麼

do some of them have more blobs and others donuts?  And why are some of the donuts rainbow-colored?

是否有些人有更多的布盧姆，有些人有甜甜圈？ 還有，為什麼有些甜甜圈是彩虹色的？

I want to know what an atom looks like! And I  want that picture to actually have something  

我想知道原子是什麼樣子的!而且我希望那張照片真的有東西

to do with the nitty gritty reality of atoms  (since they are, indeed, real things). You know,  

與原子的細微現實有關（因為它們確實是真實的東西）。你知道的。

like how a diagram of the solar system is both  a totally-not-to-scale caricature and yet also  

就像太陽系的圖表既是完全不按比例的漫畫，又是

represents the very real idea that the planets  all orbit the sun in roughly the same plane,  

代表了一個非常真實的想法，即行星都在大致相同的平面內圍繞太陽運行。

and that some are farther out and some  are closer in; and if it's animated we  

有的地方比較遠，有的地方比較近；如果它是動畫，我們

get to see that the closer planets complete  their orbits more often. It's a nice picture!

可以看到，較近的行星更頻繁地完成它們的軌道。這是一幅很好的圖畫!

And that's what I want for atoms: a good picture. There are a few things I'd like that picture to  

而這就是我對原子的要求：一張好的照片。我希望這幅畫有以下幾點

get across, some of them because  they're important for the physics  

其中一些是因為它們對物理學很重要。

of atoms, and some of them because they're  questions my brain wants answers to. Like: 

的原子，而其中一些是因為它們是我的大腦想要回答的問題。比如說。

Where is the electron? How fast is it orbiting? 

電子在哪裡？它的軌道運行速度有多快？

How much energy does it have? How big is the picture relative to other pictures?

它的能量有多大？相對於其他圖片，該圖片有多大？

Of course, the wave-particle nature of quantum  mechanics means some of these ideas (like the  

當然，量子力學的波粒性質意味著其中一些觀點（如

electron's position) don't translate exactly from  our everyday intuition to the atomic scale...  

電子的位置）並不能完全從我們的日常直覺轉化為原子尺度......

BUT, there is a way of thinking about  wave-particle duality where you picture  

但是，有一種思考波粒二象性的方式，你可以想象一下

the wavefunction as a bunch of water, and the  particle as a speck of dust in that water;  

波函數是一束水，而粒子是水中的一粒灰塵。

the particle is mostly guided by where the water  goes (and the water is guided by the equations  

粒子主要是由水的去向引導的（而水是由方程式引導的）。

that determine how water behaves depending  on its circumstances). And, if you apply the  

這決定了水的行為方式取決於其環境）。)而且，如果你應用

mathematics of that idea to atomic orbitals,  and then render it in 3D, here's what you get.

將這一想法數學化到原子軌道上，然後用三維渲染，這就是你得到的結果。

Isn't it beautiful? Here's another. 

這不是很美嗎？這是另一個。

And another.

還有一個。

In fact, I made a bunch of these. And  they're all mesmerizing, and beautiful,  

事實上，我做了一大堆這樣的東西。它們都是令人著迷的，而且很美。

and isn't the ground state of the hydrogen atom  just so cute?? And aren't the excited states so  

氫原子的基態不是很可愛嗎？而激發態不也是如此

majestic? There's so much structure and detail in  them, I love it. You can see the patterns in the  

雄偉？它們有那麼多的結構和細節，我喜歡。你可以看到這些圖案在

orbitals, you can get a sense that they actually  ARE orbitals (I mean, something is orbiting!).

軌道，你可以感覺到它們實際上就是軌道（我的意思是，有東西在軌道上運行！）。

Ok, so I do have to be clear: the dots don't  each represent a separate electron - the whole  

好的，所以我必須明確：這些點並不代表一個單獨的電子--整個

collection represents the wavefunction of a single  electron, and the individual dots represent all  

集合代表單個電子的波函數，單個點代表所有的

the places that electron could be (a higher  density of dots means a higher probability of  

電子可能出現的地方（點的密度越高，意味著出現的概率越大）。

the electron being there). Electrons with more  energy are more likely to be far away from the  

電子在那裡）。)能量更大的電子更有可能遠離

nucleus, so higher energy orbitals are bigger.  The motion of the dots is showing the “flow” of  

核，所以高能量的軌道會更大。 點的運動顯示了 "流動 "的

the wavefunction, and DOES correspond to an extent  with its actual angular momentum, though they're  

波函數，並在一定程度上與它的實際角動量相對應，儘管它們是

NOT electron trajectories. Unless you think  Bohmian trajectories are real (in which case,  

不是電子軌跡。除非你認為波赫米亞軌跡是真實的（在這種情況下。

they really are electron trajectories!). I'll let  the philosophers of physics fight that one out.

它們真的是電子軌跡！）。)我會讓物理學的哲學家們去爭論這個問題的。

But the point is these visuals are created by  representing actual electron wavefunctions in a  

但問題是這些視覺效果是通過代表實際的電子波函數在一個

visual language that our brains can understand -  that of objects and light and shadows and motion  

我們的大腦能夠理解的視覺語言--物體、光影和運動的語言

in 3D space. There's actually stuff orbiting!!  And they're pretty! I hope you like them too.

在三維空間中。真的有東西在軌道上運行！？ 而且它們很好看!我希望你也喜歡它們。

Oh, one final thing - I 100% get that these  are not easy to draw. So if you want a cartoon  

哦，最後一件事--我100%明白，這些東西不容易畫。是以，如果你想要一個卡通片

representation of an atom that's simple  but more closely based in atomic physics,  

原子的表示方法很簡單，但更緊密地基於原子物理學。

here's my proposal: it's based on the three  “P” orbitals (the ones from the “P” block of  

這是我的建議：它基於三個 "P "軌道（來自 "P "區的軌道）。

the periodic table): one of them has the electron  orbiting one way, one in the opposite way, and in  

週期表）：其中一個電子以一種方式運行，一個以相反的方式運行，而在

the third one the electron is orbiting the same  amount but around some perpendicular direction,  

第三種情況下，電子在相同的軌道上運行，但在一些垂直方向上運行。

and we can't know which, which is why the points  aren't moving in the middle orbital, and why I've  

而我們無法知道是哪一個，這就是為什麼這些點在中間軌道上沒有移動，以及為什麼我已經

drawn a dotted line and question mark for the  sideways circle. And if you want you can add  

為側面的圓圈畫了一條虛線和問號。如果你願意，你可以添加

an electron to each orbital - or two electrons,  if one is oriented spin up and one spin down.  

每個軌道上有一個電子--或者兩個電子，如果一個是自旋向上的，一個是自旋向下的。

THIS is a MinutePhysics-approved  cartoon representation of an atom.

這是經MinutePhysics認可的原子的卡通表現。

Thanks to Google for sponsoring this portion  of my video. When Google reached out to  

感謝谷歌贊助我視頻的這一部分。當谷歌聯繫到

sponsor MinutePhysics, I immediately  said yes, because I use Google search  

贊助MinutePhysics，我立即說好，因為我用谷歌搜索

literally every day for everything from 3D  software tutorials, to physics equations,  

從3D軟件教程到物理學方程式，每天都有很多人在使用。

the weather, recipes, and of course coronavirus  vaccine information. And Google has been focusing  

天氣、菜單，當然還有冠狀病毒疫苗資訊。而谷歌一直在關注

a lot on supporting individuals and small  businesses over the last year - Google can  

在過去一年中，谷歌在支持個人和小企業方面做了很多工作--谷歌可以

even help *you* or your family and friends  discover opportunities and find jobs where  

甚至幫助*你*或你的家人和朋友發現機會並找到工作，在那裡

you live! Just search "jobs for physics  majors" or "jobs for veterans in Montana"  

你住的地方!只要搜索 "物理學專業的工作 "或 "蒙大拿州退伍軍人的工作"

or "jobs for" whatever it is you do, and Google  will help you find opportunities tailored to you!  

或 "工作機會"，不管你是做什麼的，谷歌都會幫你找到適合你的機會。

Thanks again to Google for sponsoring  this part of my video, for making it  

再次感謝谷歌贊助我視頻的這部分內容，使其成為

easy to convert centimeters to inches, and for  helping us all find the information we need.

解釋瞭如何將釐米轉換為英寸，並幫助我們找到我們需要的資訊。

Ok, the sponsored segment is  over and you're still here!  

好了，贊助的部分結束了，你還在這裡!

You probably want to know about the  rainbow donuts. The color there represents  

你可能想知道彩虹甜甜圈的情況。那裡的顏色代表

the "phase" of the wavefunction, which informs  how different wavefunctions interfere with  

波函數的 "相位"，它告訴人們不同的波函數是如何相互影響的。

each other, and it's essentially being  represented by motion in my 3D visuals.

彼此之間的關係，而且它基本上被我的3D視覺中的運動所代表。