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• The Heisenberg Uncertainty Principle is one of a handful of ideas

海森堡測不準原理，或&quot;不確定性原理&quot; 是少數可以從量子物理領域

• from quantum physics to expand into general pop culture.

拓展到普羅大眾文化的物理原理之一

• It says that you can never simultaneously know the exact position

它指出我們無法既確定一個物體的位置

• and the exact speed of an object and shows up as a metaphor in everything

又同時精準測得這它的速率。 這在許多領域被當成隱喻使用

• from literary criticism to sports commentary.

從藝文評論到體育播報領域都有

• Uncertainty is often explained as a result of measurement,

測不準原理常常被認為源自於測量行為

• that the act of measuring an object's position changes its speed, or vice versa.

測量物體位置的動作 同時會改變其速度，反之亦然

• The real origin is much deeper and more amazing.

但是真正的原理更加深奧 也更加驚奇有趣

• The Uncertainty Principle exists because everything in the universe

之所以會有測不準原理 是因為宇宙中的任何東西

• behaves like both a particle and a wave at the same time.

都同時兼具「粒子」和「波」的兩種性質

• In quantum mechanics, the exact position and exact speed of an object

在量子力學中，一個物體的 確切位置和速度是沒有意義的

• have no meaning.

為了理解它

• To understand this,

我們需要釐清一下： 表現得像「粒子」或像「波」的含意

• we need to think about what it means to behave like a particle or a wave.

粒子可在某一時間存在於特定位置

• Particles, by definition, exist in a single place at any instant in time.

我們能利用在特定位置 發現此物體的機率圖形

• We can represent this by a graph showing the probability of finding

來呈現這個定義 圖形上會有一個高峰值

• the object at a particular place, which looks like a spike,

物體在某個特定位置 出現的機率是 100%，在他處則都是 0%

• 100% at one specific position, and zero everywhere else.

而波則是「擾動」在空間中傳播的現象

• Waves, on the other hand, are disturbances spread out in space,

就像是湖面上的漣漪

• like ripples covering the surface of a pond.

我們可將「波」視為整體 然後確認其性質

• We can clearly identify features of the wave pattern as a whole,

其中最重要的就是波長

• most importantly, its wavelength,

波長是相鄰兩個波峰或波谷之間的距離

• which is the distance between two neighboring peaks,

但是我們無法確認波的位置

• or two neighboring valleys.

波在各種不同的位置出現的機率都很大

• But we can't assign it a single position.

波長在量子物理學不可或缺的

• It has a good probability of being in lots of different places.

因為物體的(物質波)波長與其動量有關

• Wavelength is essential for quantum physics

動量 = 質量 Χ 速度

• because an object's wavelength is related to its momentum,

一個快速運動的物體具有很大的動量

• mass times velocity.

伴隨著波長很短的物質波

• A fast-moving object has lots of momentum,

很重的物體即使動得不快 仍具有很大的動量

• which corresponds to a very short wavelength.

同樣的，也代表了它的波長很短

• A heavy object has lots of momentum even if it's not moving very fast,

這就是我們無法察覺 日常物體波動性質的原因

• which again means a very short wavelength.

如果你丟出一個棒球

• This is why we don't notice the wave nature of everyday objects.

它的波長是1公尺的10的33次方之一

• If you toss a baseball up in the air,

因為實在是太小了，所以不可能被測到

• its wavelength is a billionth of a trillionth of a trillionth of a meter,

但微小的物體，例如原子或電子束

• far too tiny to ever detect.

波長就大到足以用物理實驗量測出來

• Small things, like atoms or electrons though,

如果我們有一個純粹的波 就可以測量它的波長

• can have wavelengths big enough to measure in physics experiments.

進而算出它的動量 但是卻無法測出它的確實位置

• So, if we have a pure wave, we can measure its wavelength,

另一方面，我們很容易確知粒子的位置

• and thus its momentum, but it has no position.

但它卻並沒有波長 所以我們不知道它的動量大小

• We can know a particles position very well,

為了同時得到 一個粒子的位置與動量

• but it doesn't have a wavelength, so we don't know its momentum.

我們需要融合兩種圖像

• To get a particle with both position and momentum,

創造一個侷限 在很小區域的波圖像

• we need to mix the two pictures

那該如何進行呢？

• to make a graph that has waves, but only in a small area.

方法是：藉由疊加數個不同波長的的波

• How can we do this?

因為一個波一種動量 這代表賦予物體具備不同動量的可能性

• By combining waves with different wavelengths,

當我們將兩個波疊加起來時

• which means giving our quantum object some possibility of having different momenta.

波峰對齊的地方會形成更高的波峰

• When we add two waves, we find that there are places

在另外一些位置 因波峰與波谷對齊而相互抵銷

• where the peaks line up, making a bigger wave,

結果就是有些地方我們看得到波

• and other places where the peaks of one fill in the valleys of the other.

另一些地方，則什麼都沒有

• The result has regions where we see waves

如果我們再加上第三個波

• separated by regions of nothing at all.

那些波被抵銷的區域變大了

• If we add a third wave,

加上第四個，持續變大 而有波的區域逐漸變窄

• the regions where the waves cancel out get bigger,

如果我們持續疊加更多的波 就能得到一個波包

• a fourth and they get bigger still, with the wavier regions becoming narrower.

在一個很小的區域內有一個確定的波長

• If we keep adding waves, we can make a wave packet

這就得到了一個 同時擁有波與粒子屬性的物體

• with a clear wavelength in one small region.

但是這樣一來 位置和動量都無法準確測得

• That's a quantum object with both wave and particle nature,

物體並非侷限在一個單一位置上

• but to accomplish this, we had to lose certainty

在波包內的範圍裡 我們發現物體的機率都很高

• about both position and momentum.

我們透過疊加多個波得到波包

• The positions isn't restricted to a single point.

意味著我們就有可能找到 與其中一個物體相對應的動量

• There's a good probability of finding it within some range

導致位置與動量都無法精確測量

• of the center of the wave packet,

這都與測不準原理有關

• and we made the wave packet by adding lots of waves,

如果你想更精確的測量位置

• which means there's some probability of finding it

就得用更多的波疊加起來， 加以建造出更小的波包

• with the momentum corresponding to any one of those.

波數增加使動量更不確定

• Both position and momentum are now uncertain,

如果你想更明確的得到動量值 就需要一個更大的波包

• and the uncertainties are connected.

結果位置就更不確定

• If you want to reduce the position uncertainty

這就是海森堡測不準原理

• by making a smaller wave packet, you need to add more waves,

最初由德國物理學家 Werner Heisenberg 於1927 年提出

• which means a bigger momentum uncertainty.

這種測不準的特性與測量的精確度無關

• If you want to know the momentum better, you need a bigger wave packet,

是結合波和粒子 兩種性質之後不可避免的結果

• which means a bigger position uncertainty.

測不準原理不僅僅 是測量上的實際限制

• That's the Heisenberg Uncertainty Principle,

它是物體只能表現出 一種(波或粒子)性質的限制

• first stated by German physicist Werner Heisenberg back in 1927.

已被建入宇宙基本構造之中

• This uncertainty isn't a matter of measuring well or badly,

• but an inevitable result of combining particle and wave nature.

• The Uncertainty Principle isn't just a practical limit on measurment.

• It's a limit on what properties an object can have,

• built into the fundamental structure of the universe itself.

The Heisenberg Uncertainty Principle is one of a handful of ideas

B2 中高級 中文 美國腔 TED-Ed 動量 波長 物體 位置 原理

# 【TED-Ed】什麼是海森堡不確定性原理？- Chad Orzel (【TED-Ed】What is the Heisenberg Uncertainty Principle? - Chad Orzel)

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稲葉白兎 發佈於 2021 年 01 月 14 日