I mean, we can go very close, but we can never ever reach the speed of light.

我的意思是，我們可以非常接近光速，但永遠不可能達到光速。

Why is that?

為什麼會這樣？

The most common explanation I got is if you take the graph of the kinetic energy versus the speed, look, as the speed approaches C, kinetic energy goes to infinity, so it takes infinite energy.

我得到的最常見的解釋是，如果用動能與速度的關係圖來表示，那麼當速度接近 C 時，動能就會達到無窮大，所以需要的能量是無限的。

But my problem is that that's not an explanation.

但我的問題是，這不是一種解釋。

I don't have an intuition behind why that is true.

我也不知道為什麼會這樣。

Another explanation was mass goes to infinity, but again, there's no evidence for that.

另一種解釋是品質無窮大，但同樣沒有證據證明這一點。

So what's really going on?

到底發生了什麼？

What's the physically happening that's limiting that ship from going towards the speed of light?

是什麼物理現象限制了飛船向光速前進？

That's what we're gonna try and answer in this video.

這就是我們要在本視頻中嘗試回答的問題。

And so if you're ready for it, let's begin.

如果你準備好了，那就開始吧。

So Einstein, where do we start?

那麼，愛因斯坦，我們從哪裡開始呢？

Einstein says, imagine you are inside a very fast-moving ship and you have a photon clock with you.

愛因斯坦說，想象一下，你在一艘高速行駛的飛船裡，身邊有一個光子鍾。

Now at this point, I say, wait a second, Einstein.

此時此刻，我要說，等一下，愛因斯坦。

I don't wanna deal with hypothetical clocks.

我不想和假設的時鐘打交道。

I wanna talk about real clocks.

我想談談真正的時鐘。

Einstein says, well, buddy, patience.

愛因斯坦說，好吧，夥計，耐心點。

If you understand photon clocks, you'll be able to understand everything else.

如果理解了光子鍾，就能理解其他一切。

I'm like, okay, cool, let's trust him.

我想，好吧，那就相信他吧。

So what's a photon clock?

那麼光子鍾是什麼呢？

It's a clock where you have two mirrors and photon bounces between the two.

這是一個有兩面鏡子的時鐘，光子在兩面鏡子之間反彈。

And we can say that, hey, when the photon hits the bottom mirror, it hits a tick.

我們可以說，嘿，當光子擊中底部鏡面時，它擊中了一個刻度。

So we get tick, tick, tick, tick, tick, and so on and so forth.

於是，我們就有了嘀嗒、嘀嗒、嘀嗒、嘀嗒、嘀嗒，等等等等。

Now Einstein asks, what would the same clock look like if you are seeing the whole thing from outside the ship?

現在愛因斯坦要問，如果你從船外看到整個過程，同樣的時鐘會是什麼樣子？

Well, let's see.

讓我想想

At first, I'm like, hey, it looks the same to me.

一開始，我想，嘿，我看都一樣。

The photon is bouncing between the two mirrors.

光子在兩面鏡子之間跳動。

But Einstein says, if you look carefully, you see the photon is now traveling a diagonal path.

但愛因斯坦說，如果你仔細觀察，就會發現光子現在正沿著對角線軌跡移動。

This means it's gonna travel a longer distance.

這意味著它的飛行距離會更長。

But remember, the photon always travels with the speed of light.

但請記住，光子始終以光速傳播。

See, the speed of light is the same in all reference frames, which means the photon now is gonna take a longer time between the ticks.

你看，光速在所有參照系中都是一樣的，這就意味著現在的光子在 "嘀 "和 "嘀 "之間需要更長的時間。

In other words, we will see that photon clock ticks slower.

換句話說，我們會看到光子時鐘的滴答聲變慢了。

So again, let's compare.

那麼，我們再來比較一下。

Here's what the photon clock would look like from inside the ship.

這是光子鍾在飛船內的樣子。

Look at the ticks.

看看蝨子。

Tick, tick, tick, tick.

滴答 滴答 滴答

Now from outside.

現在從外面。

Tick, tick, tick.

滴答，滴答，滴答

You can see it has become slower.

你可以看到它變得更慢了。

And now what happens if the ship moves even faster?

現在，如果飛船移動得更快，會發生什麼呢？

Well, it will travel even longer path, as you will see.

那麼，它將走更長的路，你會看到的。

And therefore, the ticks will become even slower.

是以，滴答聲會變得更慢。

So the photon clock shows that clocks slow down when they are moving.

是以，光子時鐘表明，時鐘在運動時會變慢。

And at this point, I say, cool, photon clocks tick slower.

這時候，我說，酷，光子鐘的滴答聲變慢了。

That's great.

好極了

Now what about real physical clocks, Einstein?

那麼真正的物理時鐘呢，愛因斯坦？

Well, Einstein says, if you look at this clock, and if you zoom in to the second hand, what would the animation look like from the atomic scale?

愛因斯坦說，如果你看這個時鐘，如果你放大秒針，從原子尺度上看，動畫會是什麼樣子？

And I say, well, if the second hand is just ticking like this, then the animation would look something like this.

我說，好吧，如果秒針像這樣滴答作響，那麼動畫就會像這樣。

But Einstein says, that can't happen.

但愛因斯坦說，這不可能發生。

You can't have something like this.

你不能擁有這樣的東西。

And the reason is when, say, this atom accelerates, this atom in particular accelerates, all the other atoms cannot accelerate at the same time.

原因在於，當這個原子加速時，尤其是這個原子加速時，其他所有原子都無法同時加速。

Information takes time to travel.

資訊的傳播需要時間。

These atoms are bonded electromagnetically.

這些原子以電磁方式結合在一起。

So when one atom accelerates, we need to wait for an electromagnetic wave to go from one atom to another, and only then the other atom can accelerate.

是以，當一個原子加速時，我們需要等待電磁波從一個原子傳到另一個原子，只有這樣，另一個原子才能加速。

An electromagnetic wave is basically a photon.

電磁波基本上就是一個光子。

So the better way to think about this is, when this atom accelerates, it actually sends a photon, and only then the next atom accelerates, and then the next one, and the next one, and so on, and so forth.

是以，更好的思考方式是，當這個原子加速時，它實際上會發出一個光子，然後下一個原子才會加速，再下一個，再下一個，以此類推。

So you see, the whole thing is not instantly going, but it's so fast, it feels like it's instantly going.

所以，你看，整個過程並不是瞬間完成的，但它是如此之快，感覺就像是瞬間完成的。

But now Einstein asks,

但現在愛因斯坦問

Mahesh, what if now this set of atoms were moving?

馬赫什，如果現在這組原子在移動呢？

What would the animation look like now?

現在的動畫會是什麼樣子？

Wait a second.

等一下

This also is very similar to the photon clock, which means if this was moving, the photons would end up taking a diagonal path again, and therefore the whole thing slows down.

這也與光子鍾非常相似，也就是說，如果它在移動，光子最終會再次走對角線路徑，是以整個速度會變慢。

Well, let's look at it.

讓我們來看看。

Let's look at it, here we go.

讓我們來看看，開始了。

Yes, the photons are slowing down.

是的，光子正在減速。

The photon is not slowing down, the transfer is slowing down, because the photons are taking a diagonal path just like before, and therefore, real physical clocks actually slow down.

光子並沒有變慢，而是傳輸變慢了，因為光子走的是對角線路徑，就像以前一樣，是以，真正的物理時鐘實際上變慢了。

Look at this, this one is ticking slower than this one.

看看這個，這個的滴答聲比這個慢。

Real physical clocks slow down when they're moving.

真正的物理時鐘在移動時會變慢。

Whoa.

哇哦

But at this point, we could ask Einstein, is there evidence for this?

但此時此刻，我們可以問愛因斯坦，有證據證明這一點嗎？

This is just a theory, right?

這只是一種理論，對嗎？

So Einstein says, well, probably not in his time, but today we do.

所以愛因斯坦說，也許在他那個時代不會，但今天我們會。

You see, we've actually taken atomic clocks, which are synced on Earth, and then we put them on planes, and then we flew around the world, and then we brought them back, they went out of sync.

你看，我們實際上是把地球上同步的原子鐘放在飛機上，然後飛到世界各地，再把它們帶回來，它們就不同步了。

And we did this multiple times, and every time we checked, we saw that the amount they went out of sync perfectly predicts, is perfectly predicted by special relativity.

我們這樣做了多次，每次檢查都發現，它們脫節的程度完全符合狹義相對論的預測。

Now, of course, gravity also affects it, which is dealt in general relativity, so there is this additional effect that's happening, but when you put all of that together, there is evidence that suggests that time dilation is real.

當然，萬有引力也會對其產生影響，這在廣義相對論中也有論述，是以還有額外的影響正在發生，但當你把所有這些放在一起時，有證據表明時間膨脹是真實存在的。

So with this, we know that time itself is slowing down, or is it?

是以，我們知道時間本身正在變慢，還是這樣？

You see, clocks are slowing down, but how does it tell us that the time itself is slowing down, Einstein?

愛因斯坦，你看，時鐘在變慢，但它怎麼能告訴我們時間本身在變慢呢？

Einstein says, for that, let's look at radioactivity.

愛因斯坦說，為此，讓我們來看看放射性。

Radioactive decay is where you have an unstable atom that spontaneously splits.

放射性衰變是指不穩定原子自發分裂。

The cool thing about radioactivity is that they have something called the half-life.

放射性的神奇之處在於它們有一種叫做半衰期的東西。

For example, if you take a particular radium isotope, it has a half-life of about 1,600 years, which means that if you take a billion radium isotopes, wait for 1,600 years, half of them would have decayed, and the rest half would have stayed.

例如，如果你使用一種特定的鐳同位素，它的半衰期約為 1600 年，這意味著如果你使用 10 億個鐳同位素，等待 1600 年，其中一半會衰變，剩下的一半會保持不變。

Wait for another 1,600 years, another half would have decayed, and so on and so forth.

再等 1600 年，又有一半會腐爛，如此循環往復。

Now, it turns out that if you take elementary particles like muons, they have a half-life of about 1 1⁄2 microseconds.

現在，事實證明，像μ介子這樣的基本粒子，它們的半衰期約為 1 1⁄2 微秒。

We did that in lab, we have tested this in labs, but we also get muons in our atmosphere due to the cosmic rays colliding with our atmosphere.

我們在實驗室裡做過，我們在實驗室裡測試過，但由於宇宙射線與我們的大氣層相撞，我們的大氣層中也會出現μ介子。

Turns out that these muons, when we looked at them, they have a half-life of 10 times more.

結果發現，當我們觀察這些μ介子時，它們的半衰期是原來的10倍。

At first, I'm like, Einstein, why is that a problem?

一開始，我想，愛因斯坦，這怎麼會是個問題呢？

Like, these are maybe different muons, and Einstein says, no.

比如，這些可能是不同的μ介子，而愛因斯坦說，不。

Just like how the charge of an electron stays the same, regardless of where the electrons come from, or when you do the experiment, or where you do it, the half-life of radioactive sample of a particular radioactive isotope would be the same, regardless of where that isotope comes from.

就像電子的電荷如何保持不變一樣，無論電子來自哪裡、何時做實驗、在哪裡做實驗，某種放射性同位素的放射性樣本的半衰期都是一樣的，無論該同位素來自哪裡。

So, how is it possible that these muons would have 10 times more half-life?

那麼，這些μ介子的半衰期怎麼可能多出 10 倍呢？

Well, it turns out that's because they're traveling close to speed of light.

原來，這是因為它們的速度接近光速。

And so, if you, again, plug in the numbers according to special relativity, you get the exact same result.

是以，如果你再次根據狹義相對論輸入數字，就會得到完全相同的結果。

Time dilation.

時間膨脹

Time dilation is literally making these muons age slower.

時間膨脹確實讓這些μ介子的老化速度變慢了。

But what's physically going on?

但實際上發生了什麼呢？

Something very similar to what we saw in the photon clock.

與我們在光子鍾中看到的非常相似。

The fact that these muons are moving, this means that photons are taking longer, or whatever that force carrier, photons are not the force carrier, this is a weak nuclear force, but whatever the force carriers are, they will now take a longer time, and therefore the radioactive process gets slowed down.

事實上，這些μ介子在移動，這意味著光子需要更長的時間，或者說，不管是什麼力載體，光子不是力載體，這是一種弱核力，但不管是什麼力載體，它們現在都需要更長的時間，是以放射性過程會變慢。

And that's why muons are literally aging slower because they're moving.

這就是為什麼μ介子的老化速度會變慢，因為它們在移動。

Time dilation.

時間膨脹

And if muons can age slower, if radioactivity process can slow down, all biochemical processes can also slow down.

如果μ介子可以減緩衰老，如果放射性過程可以減緩，那麼所有的生化過程也可以減緩。

And that means living beings will age slower.

這意味著生物衰老的速度會變慢。

So, if you have two twins, one baby, sorry, two twins, one moving, then you will see the moving twin will age much slower than the twin that's at Earth.

是以，如果你有兩個雙胞胎，一個嬰兒，對不起，兩個雙胞胎，一個在移動，那麼你會發現移動的雙胞胎會比在地球上的雙胞胎衰老得慢得多。

This is a real process.

這是一個真實的過程。

And the fact that muons age slower somewhat gives us an indirect evidence that this is a real, real phenomenon.

μ介子的衰老速度較慢這一事實給了我們一個間接證據，證明這是一個真實存在的現象。

Whoa.

哇哦

And we could still argue that Einstein, the processes are slowing down over here, and because the force carriers take a longer time because of the motion, but that doesn't mean that the time itself slows down.

我們仍然可以爭辯說，愛因斯坦，這裡的過程變慢了，由於運動，力的載體需要更長的時間，但這並不意味著時間本身變慢了。

And at this point, Einstein says, well, Mahesh, in science, you need some process to measure anything.

這時，愛因斯坦說，好吧，馬赫什，在科學中，你需要一些過程來測量任何東西。

And so if you believe that time exists beyond the processes and measurements, then it's now beyond the realm of science, and now we're going into philosophical debate, and that's meaningless for science.

是以，如果你認為時間的存在超越了過程和測量，那麼它現在就超越了科學的範疇，現在我們進入了哲學辯論，而這對科學來說毫無意義。

So science deals with the measurables.

是以，科學只處理可測量的數據。

And so as far as we can measure, everything that is affected by time is being slowed down, and so we say time itself slows down.

是以，在我們所能測量的範圍內，一切受時間影響的事物都在變慢，所以我們說時間本身也在變慢。

Okay.

好的

Einstein, now, how does this whole time dilation thing explain why objects can never be accelerated to speed of light?

愛因斯坦，那麼，時間膨脹這件事又如何解釋物體永遠無法加速到光速呢？

Einstein says, for that, let's first derive the expression for this time dilation, and at first, I'm like, no, no, no,

愛因斯坦說，為此，讓我們先推導出時間膨脹的表達式，一開始，我想，不，不，不、

I want an intuitive explanation, and Einstein says, don't worry, it will only add to the intuition.

我想要一個直觀的解釋，愛因斯坦說，別擔心，這隻會增加直覺。

And it's also cool to actually derive it because we can do it logically as well.

實際推導出來也很酷，因為我們可以從邏輯上進行推導。

So let's quickly do that.

所以，讓我們快點做吧。

So for that, we're gonna use distance equals speed over time, and if you look at our clock from inside the space, when the, inside the spaceship, when the clock is at rest, the distance traveled by the photon is just speed into time, so c into t.

是以，我們將使用距離等於速度與時間的關係，如果你從太空中觀察我們的時鐘，當飛船內的時鐘處於靜止狀態時，光子所走過的距離就是速度與時間的關係，即c與t的關係。

So this is the time that we see from inside the ship.

這就是我們從飛船內部看到的時間。

Now, when we look at it from outside the ship, this is what it would look like.

現在，當我們從船外看它時，它就會是這個樣子。

And so if the time taken now is longer, and let's call that time as t dash, this distance would now again be the speed of light into this new time, the time that we see from outside the ship, t dash.

是以，如果現在所花的時間更長，讓我們把這個時間稱為 t dash，那麼這個距離將再次成為進入這個新時間的光速，也就是我們從飛船外看到的時間 t dash。

And now you can see, you have two sides of the triangle.

現在你可以看到，三角形有兩條邊。

If you can figure out the third side, we're done.

如果你能想出第三面，我們就大功告成了。

But what is that third side?

但第三面是什麼呢？

The third side is the distance traveled by the mirror in the time t dash, or the distance traveled by the ship in the time t dash, and we know the speed of the ship is v, then it'll become v times t dash.

第三面是鏡子在 t 衝刺時間內的移動距離，或者說是飛船在 t 衝刺時間內的移動距離，我們知道飛船的速度是 v，那麼它就變成了 v 乘以 t 衝刺。

And now it's just the Pythagoras theorem.

現在只剩下勾股定理了。

We can use Pythagoras theorem to isolate t dash, and we can figure it out.

我們可以用畢達哥拉斯定理分離出 t 個破折號，就可以算出來了。

Great idea for you to pause and derive this historical expression yourself.

你能停下來，自己推導出這一歷史表述，真是個好主意。

It's such a proud moment.

這是多麼值得驕傲的時刻。

But if you've tried it, here it goes.

但如果你已經試過了，那就來吧。

So we'll just use Pythagoras theorem.

所以我們就用畢達哥拉斯定理。

And now we're just gonna do some algebra to isolate t dash.

現在我們要做一些代數運算來分離出 t dash。

And boom, this is the time dilation equation.

這就是時間膨脹方程。

And let's pause here because this gives me goosebumps.

讓我們暫停一下，因為這讓我起雞皮疙瘩。

It's one of the cornerstones of physics, and what did we use?

這是物理學的基石之一，我們用了什麼？

Pythagoras theorem to derive it.

勾股定理推導出來的。

And yet, more than 150 years ago, even the smartest folks couldn't comprehend this.

然而，150 多年前，即使是最聰明的人也無法理解這一點。

They had no idea that universe behaved this way.

他們不知道宇宙會有這種行為。

Oh my God.

我的天啊

Wow.

哇

It can be confusing when you're first learning it, and so Einstein says, let's make sure that we're on the same page with the vocabulary.

剛開始學的時候可能會很困惑，所以愛因斯坦說，讓我們來確保我們的詞彙量是一致的。

This t is what we call the proper time.

這個 t 就是我們所說的適當時間。

This is the time that we see when the clock is at rest.

這就是時鐘靜止時我們看到的時間。

And since when things are at rest, we see time flowing normally for us, that's why it's called the proper time.

由於在靜止狀態下，我們看到時間在正常流動，是以這被稱為 "正常時間"。

Anybody inside the spaceship will basically say nothing weird is happening.

飛船裡的人基本上都會說沒有發生什麼奇怪的事情。

The time is proper for me, so proper time.

對我來說，時機已經成熟，時機已經成熟。

And this t dash is what we call the dilated time.

這個 "t "就是我們所說的擴張時間。

This is the time that we see when we're looking at things from outside the spaceship.

這就是我們從飛船外觀察事物時所看到的時間。

And to make this equation slightly more intuitive, this is how we like to write it.

為了讓這個等式更直觀，我們喜歡這樣寫。

This is the usual notation as well, so let's familiarize ourselves with this.

這也是常用的符號，讓我們先熟悉一下。

Gamma is what we call the Lorentz factor.

伽馬就是我們所說的洛倫茲係數。

And we like to talk in terms of gamma because gamma is a number that's bigger than one.

我們喜歡用伽馬來表示，因為伽馬是一個比 1 大的數字。

And again, it makes sense.

同樣，這也是有道理的。

The dilated time must be bigger than the proper time by the factor gamma.

擴張時間必須比正常時間大伽馬因子。

And now let's look at what are some values for gamma for different values of speed.

現在我們來看看不同速度值下的伽瑪值。

So let's do that.

那就這麼辦吧。

And you can immediately see, even at 50% the speed of light, gamma is so small, 1.2.

你馬上就能看到，即使在光速為 50%的情況下，伽瑪也是如此之小，只有 1.2。

And so for lower speeds, gamma is almost one.

是以，對於較低的速度，伽馬值幾乎為 1。

And that's the reason why Newtonian physics works because if gamma is almost one, dilated time is the same as the proper time and we don't see any discrepancy, we just have one time.

這也是牛頓物理學行之有效的原因，因為如果伽馬值幾乎為一，則擴張時間與正常時間相同，我們不會看到任何差異，我們只有一個時間。

But notice as you go closer and closer to the speed of light, gamma value increases.

但請注意，當你越來越接近光速時，伽馬值就會增加。

So for example, at 87% the speed of light, gamma is two.

例如，在光速為 87% 的情況下，伽馬值為 2。

This means the dilated time is twice the proper time.

這意味著擴張時間是正常時間的兩倍。

That means when I'm looking at the ship, in my clock when two seconds tick, in that ship I will see one second ticking.

也就是說，當我看著這艘飛船時，在我的時鐘中，兩秒滴答作響，而在這艘飛船上，我將看到一秒滴答作響。

It's dilated twice.

它擴張了兩倍。

Similarly, I'd say 99.9% the speed of light, gamma is 22.

同樣，我認為光速為 99.9%，伽馬為 22。

It means I have to wait 22 seconds for one second to tick in that moving clock.

這意味著我必須等待 22 秒鐘，才能讓移動時鐘上的一秒鐘滴答作響。

Does that make sense?

有道理嗎？

All right, so we have the intuition for where the time dilation comes from because the photon ends up traveling a longer distance.

好了，我們有了時間膨脹產生的直覺，因為光子最終傳播了更長的距離。

We have the numbers now.

我們現在有數字了。

Einstein, it's time to answer the question.

愛因斯坦，是時候回答這個問題了。

Why can't objects be accelerated to the speed of light?

為什麼物體不能加速到光速？

So Einstein says, well, imagine we have a spaceship, very advanced spaceship that is accelerating at say 1,000 kilometers per second per second.

所以愛因斯坦說，好吧，想象一下我們有一艘飛船，非常先進的飛船，正在以比如每秒1000公里的速度加速。

This means that every second that spaceship is gaining a velocity of 1,000 kilometers per second.

這意味著飛船每秒鐘的速度增加了 1000 公里。

This will happen if there's a constant force acting on the spaceship, okay?

如果飛船上有持續的力，就會出現這種情況，明白嗎？