## 字幕列表 影片播放

• One of the fundamental principles in modern physics is that there's no absolute time.

現代物理學的一個基本原則是，沒有絕對的時間。

• And I'm not even talking about relativity making time go at different rates if you're

我甚至不是在談論相對論使時間以不同的速度流逝，如果你是

• going near light speed – I just mean that any time is as good as any other to set your

接近光速--我的意思是，任何時候都可以設置你的

• clock to zero.

時鐘為零。

• The predictions of physics work all the same, and it's not like there's someabsolute

物理學的預測都是一樣的，並不像有什麼 "絕對的"。

• starting time” – I mean, if there were, time zones wouldn't work!

我的意思是，如果有的話，時區就不起作用了！"。

• In addition to allowing time zones, the fact that there's no absolute time also implies

除了允許時區之外，沒有絕對時間的事實也意味著

• the law of conservation of energy.

能量守恆定律。

• Here's a simple proof to show that if a force doesn't depend explicitly on time,

這裡有一個簡單的證明，表明如果一個力不明確地依賴於時間。

• then that force conserves energy!

那麼這股力量就會節約能量!

• First, conserving energy just means that there's a certain number, called the energy, which

首先，節約能源只是意味著有一個一定的數字，稱為能量，這

• doesn't change as time passesif you compare the energy at two different times

不會隨著時間的推移而改變--如果你比較兩個不同時間的能量

• you'll see no difference.

你會看到沒有任何區別。

• And the total energy of a system is the sum of its energy of motion, or kinetic energy,

而一個系統的總能量是其運動能量，或動能的總和。

• and its energy due to positionthe potential energy.

和它由於位置而產生的能量--勢能。

• So all we need is to find the change in kinetic and potential energies over time, and add

是以，我們所需要的是找到動能和勢能隨時間的變化，並加上

• them up!

他們了!

• Ok, we know the kinetic energy of an object is half of its mass times its velocity squared.

好吧，我們知道一個物體的動能是其品質的一半乘以其速度的平方。

• So the change in kinetic energy over time is just one half m times the difference of

是以，動能隨時間的變化只是半米的差異，即

• the squares of the velocities.

速度的平方值。

• Some clever algebra can rearrange this expression to become the average velocity times m times

一些巧妙的代數可以重新排列這個表達式，成為平均速度乘以m乘以

• the CHANGE in velocity.

速度的變化。

• But a change of velocity over time is just an acceleration, and mass times acceleration

但速度隨時間的變化只是一個加速度，而品質乘以加速度

• is equal to the force on the object.

等於物體上的力。

• So the change in kinetic energy of an object over time is just velocity times force.

是以，一個物體的動能隨時間的變化只是速度乘以力。

• On the other hand, the change in the potential energy of an object is negative the amount

另一方面，一個物體的勢能的變化是負數。

• of work it takes to get the object to its current position from its previous position

將物體從之前的位置移至當前位置所需的工作量

• independent of the path taken – that is, potential energy is the negative of the force

與所走的路徑無關，也就是說，勢能是力的負值。

• applied times the change in position.

適用於位置變化的兩倍。

• This is where thethere's no absolute timepart comes into playyou can't

這就是 "沒有絕對的時間 "這一部分發揮作用的地方--你不能

• have potential energy for a force that changes over time.

對一個隨時間變化的力有勢能。

• And just to be clear, “no changing over timedoesn't mean that an object can't

為了明確起見，"不隨時間變化 "並不意味著一個物體不能

• experience a changing force along the course of its journey: the force might be different

在其旅程中經歷了一個不斷變化的力量：這個力量可能是不同的

• at different places, but at any particular place, the force must remain the same.

在不同的地方，但在任何特定的地方，力必須保持相同。

• Anyway, this is all just to say that the change in potential energy is negative F times the

總之，這一切只是為了說明，勢能的變化是負的F倍。

• change in position.

改變立場。

• The negative comes from the fact that if you let the force push you along your potential

負面因素來自於這樣一個事實：如果你讓力量推著你走，你的潛力

• energy decreases, while if you fight in opposition to the force your potential energy increases.

勢能會減少，而如果你與力對抗，你的勢能會增加。

• So the change in potential energy over time is the negative of the force times the change

是以，隨著時間的推移，勢能的變化是力的負值乘以變化量

• in position over time, but change in position over time is velocity!

在時間上的位置變化，但在時間上的位置變化是速度!

• Which means change in potential energy of an object over time is negative velocity times

這意味著物體隨時間變化的勢能是負速度乘以

• force.

力。

• And thus the change in the total energy over time, which is the sum of the changes in the

是以，隨著時間的推移，總能量的變化，也就是以下變化的總和

• kinetic and potential energies over time, is v*F plus negative v*F, which equals zero!

隨著時間的推移，動能和勢能，是v*F加上負v*F，等於零!

• And zero change in energy over time is precisely conservation of energy!

而能量隨時間的變化為零，正是能量守恆!

• All for the same reason that time zones work.

所有的原因都與時區的作用相同。

• This video is brought to you in part by Audible.com, the leading provider of audiobooks across

本視頻部分內容由Audible.com提供，Audible.com是全球領先的有聲讀物提供商。

• all types of literature, including fiction, non-fiction and periodicals.

所有類型的文學作品，包括小說、非小說和期刊。

• If you go to audible.com/minutephysics, you can try audible out by downloading a free

如果你進入 audible.com/minutephysics，你可以通過下載免費的audible來嘗試。

• audiobook of your choice.

您選擇的有聲讀物。

• I'd like to recommend the book Unruly Places: Lost Spaces, Secret Cities, and Other Inscrutable

我想推薦《不守規矩的地方》這本書。失落的空間，祕密的城市，和其他不可告人的地方。

• Geographies by Alastair Bonnett [called Off the Map in the UK] – it's a tour of all

阿拉斯泰爾-博內特（Alastair Bonnett）的《地理學》[在英國稱為《地圖之外》]--它是對所有國家的巡禮。

• sorts of weird, abandoned or disregarded places around the world, from the unrecognized self-declared

世界各地各種奇怪的、被遺棄的或被忽視的地方，從未被承認的自稱的

• island nation of Sealand to traffic islands, and beyond.

從海島國到交通島，甚至更遠。

• Again, you can download your free audiobook at audible.com/minutephysics and thanks to

同樣，你可以在audible.com/minutephysics下載你的免費有聲書，並感謝

• audible for helping me continue to make these videos.

有聲有色，幫助我繼續製作這些視頻。

• As a followup, I'll admit that I skimmed over some details in this derivation and it's

作為後續，我承認我略過了這個推導中的一些細節，它是

• much easier to do with calculus.

用微積分來做要容易得多。

• You just have to know that the time derivative of kinetic energy is m times v times a which

你只需知道，動能的時間導數是m乘以v乘以a，即

• is F*v, and the time derivative of potential energy is -F times dx/dt, or -F*v, and so

是F*v，而勢能的時間導數是-F乘以dx/dt，或-F*v，是以

• the time derivative of the total energy, dE/dt, is F*v-F*v = 0, which means energy doesn't

總能量的時間導數，dE/dt，是F*v-F*v=0，這意味著能量沒有

• change over time.

隨時間變化。

• And as a final followup, the most legit and robust version of this proof as it applies

作為最後的跟進，這個證明的最合法和最有力的版本，因為它適用於

• to ALL OF PHYSICS is called Noether's theorem, discovered by Emmy Noether in 1915.

在所有的物理學中，諾特定理被稱為諾特定理，由埃米-諾特在1915年發現。

• It's beautiful physics.

這是美麗的物理學。

One of the fundamental principles in modern physics is that there's no absolute time.

B1 中級 中文 變化 時間 動能 物體 能量 速度

# 能量守恆的簡單證明 (A Simple Proof of Conservation of Energy)

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Summer 發佈於 2021 年 10 月 08 日