07.03 - 호킹 복사(Hawking Radiation)

07.03 - 호킹 복사(Hawking Radiation) [커세라 강의 페이지]

So far quantum mechanics seems pretty weird, okay? Niels Bohr responsible for planetary model of the hydrogen atom once said, anyone who is not shocked by quantum theory has not understood it.

* 보어 모형

Well that may be the case, another famous physicist Richard Feynman once said, I think I can safely say that nobody understands quantum mechanics.

Now, Feynman didn't mean that quantum mechanics is a useless theory, but that the quantum world behaved so strangely compared to our macroscopic world that our human intuitions cannot be relied upon to predict what will happen

Quantum tunnelling is just one such example of how strange quantum mechanics can be. How can tiny particles vanish on one side of a wall only to appear on the other side? Well, if we recall from our last lesson, we don’t know exactly where particles are as a result to the uncertainty principle. If we don’t know exactly where something is, how could a wall know either? That’s the basic principle behind quantum tunnelling. That indeterminacy or uncertainty can lead to a whole host of outcomes.

Play video starting at 1 minute 4 seconds and follow transcript1:04

But quantum tunnelling is related to a process within black holes called Hawking radiation. So we need to understand that in order to continue.

Play video starting at 1 minute 12 seconds and follow transcript1:12

As we saw previously, one of the fundamental relations of quantum mechanics is the Heisenberg Uncertainty Principle. In a practical sense, it states that no matter how accurate our instrumentation, the experiments we conduct will always be limited in the accuracy of their results by at least h bar / 2.

But it's not just our instruments, the entire universe obeys this uncertainty principle. The uncertainty principle has an important implication when we think about the vacuum. Normally, you'd think of the vacuum as a void, space that is completely devoid of material, matter, and energy of any kind.

In the context of quantum mechanics, that simply cannot be true. Because if there is absolutely nothing, that would imply certainty, certainty about the fact that there is no energy or mass in the vacuum. If you are certain that there's no energy in the vacuum, then you are saying that the uncertainty in the energy delta e is 0.

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However, the energy time version of the Heisenberg uncertainty principle states that delta E times delta t is greater than or equal to h bar divided by 2. In essence, you can never be totally certain that you have a true vacuum, since delta E has to be larger than 0. The uncertainty principle tells us that what we think is a vacuum actually has, for brief moments of time delta t, particles appearing and disappearing. This quantum view of the vacuum is sometimes called the quantum foam.

* Quantum Foam: Quantum foam or spacetime foam is the fluctuation of spacetime on very small scales due to quantum mechanics. The idea was devised by John Wheeler in 1955.

Play video starting at 2 minutes 33 seconds and follow transcript2:33

In general, the uncertainty principle is meaningless in everyday life. We never measure things so precisely that we run into such a limit. But what if instead we zoom down into the quantum world, what do you suspect we'd see? Let's shrink down in spatial dimensions to about the size of an atom and in the time dimension so that we are living through nanoseconds as if they were seconds.

Play video starting at 2 minutes 54 seconds and follow transcript2:54

Already you can see that spacetime itself is strange at the quantum scale. Scientists call this mess the quantum foam. This is an artist's illustration of the quantum foam. And as you can see, the foam appears to be frothing with activity. What's going on down here?

Play video starting at 3 minutes 8 seconds and follow transcript3:08

Since we've shrunk ourselves down in space and in time, we're living in the cold reality of what the uncertainty principle enforces on the universe, for lack of a better term, uncertainty.

Play video starting at 3 minutes 18 seconds and follow transcript3:18

Down here, the foam can essentially be anything, a proton antiproton pair here, an electron muon neutrino entanglement there. The quantum foam might even generate tiny wormholes. As long as these species last for only a short time, they can have lots of energy.

Play video starting at 3 minutes 34 seconds and follow transcript3:34

Physicists call particles born in the quantum foam, virtual particles. Because for all intents and purposes, they exist for such a short period of time that we in classical world barely measure their existence. We can borrow energy from the universe as long as we pay it back very quickly.

Play video starting at 3 minutes 49 seconds and follow transcript3:49

So now a question we might ask is, what happens if we put a black hole nearby and zoom in on the quantum world at the boundary of the event horizon? Do virtual particles get pulled across the event horizon? Classically, we'd say no. For one, the quantum foam is not a result of classical theories like general relativity.

But given its existence anyway, we generally thing that virtual particles don't last long enough to fall in. However, we also have to consider where a particle is because in this universe, we obey the laws of quantum mechanics.

Play video starting at 4 minutes 20 seconds and follow transcript4:20

So here we are among virtual particles in the quantum foam, and this black region is the event horizon of our black hole. Let's see if we can pin down an electron and its antiparticle, the positron, when they emerge from the quantum foam.

Play video starting at 4 minutes 32 seconds and follow transcript4:32

This particle pair is called positronium because it exists, albeit temporarily, as a quasi-atom until the universe decides its time is up. And it vanishes back into the quantum foam. But the diagram here doesn't show a complete picture because the electron and positron in the image have definite positions. If we were to truly draw this properly, each would have a much larger probability density, which is to say, regions within which the particles are likely to exist.

Play video starting at 4 minutes 59 seconds and follow transcript4:59

Probability densities characterized by something called the wave function are places where there are probably particles.

So for example, positronium, there's a 100% chance that we'd find them inside this boundary. But look, the way we've drawn this, there's a good chance that we could find the blue particle not just on the boundary of the event horizon but within it entirely.

That's a bit goofy, you might think. The particle, antiparticle pair have come into to existence. And before they can repay their energy to the universe, one of them vanished into the black hole.

So now we're in a pickle. We needed that blue particle to annihilate the red one. But instead, now we just have a red one left with no companion. And it doesn't want to stick around.

Essentially, what you've just witnessed is Hawking radiation, the process by which particles can kind of escape from a black hole. When a particle, antiparticle pair pop out of the quantum foam, right on the boundary of a black hole, the outgoing particle actually steals energy from the black hole system. It doesn't have to pay the universe back for that energy, instead the black hole had to pay for that part of the equation.

Play video starting at 6 minutes 1 second and follow transcript6:01

Not only does that mean that particles appear to come from the event horizon, but also that quantum mechanics allows black holes to evaporate slowly. So it's pretty obvious that quantum mechanics can do some pretty strange stuff. They can whittle away at a massive black hole until nothing remains.

In the next lessons, we'll develop a further understanding of this concept by examining a black hole's temperature, its entropy, and eventually, we'll determine how long a black hole has to live in the face of quantum mechanics.

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[인터뷰] [커세라 페이지]

What is Hawking Radiation?

호킹 복사란 무엇인가?

Interview with Dr. Don Page, Professor at the University of Alberta

앨버타 대학 교수 돈 페이지 박사와 인터뷰

There are different ways to think about hawking radiation.

호킹 복사를 이해하는 방법은 여러가지 있습니다.

But one way is to think that in quantum mechanics, because of the uncertainty principle, what you might think of empty space is not really an empty.

그중 한가지 방법이 양자역학으로 생각 하는 거지요. 불확정성 원리 때문인데 빈공간이 실제로 아무것도(에너지조차)없다고 생각하진 않습니다.

It's seething with particle, anti-particle pairs that form and then annihilate.

(빈공간이라도) 입자와 반입자의 생성과 소멸이  들끓고 있습니다.

In some sense, they borrow energy, but then, they have to return it back and so, they can exist for very short time.

에너지를 빌려왔다가 다시 되돌리기를 반복하면서 아주 짧은 동안 존재 합니다.

So you can have, for example, an electron positron pair that's produced, but it annihilates really quickly in the vacuum.

예를 들어 진공에서는 전자와 양전자 쌍이 생성되었다가 곧바로 소멸하죠.

But what happens is if you have a black hole, you have this black hole horizon and if one of the two particles in the pair falls behind the horizon, then it's no longer left outside to annihilate with what's outside, so that the other particle of the pair that's outside the black hole, can escape.

하지만 블랙홀의 사건 지평선 근처에서 입자 쌍이 생성되었다고 합시다. 쌍중 하나가 블랙홀로 빨려 들어갔다면 사건지평선 밖에 남아있던 나머지는 (쌍으로 생성되었다가 쌍으로 없어져야 하는데) 소멸될 기회가 없어져 블랙홀 밖으로 달아나 버립니다. 

So this escaping particle then is the hawking radiation. So that's one way to view it.

따라서 이 달아난 입자가 호킹 복사로 나타나는 겁니다. 이것이 바로 양자역학적으로 호킹복사에 대한 관점이죠.

There's other ways to talk about just evolving Quantum Field Theory in curved space-time, that the mathematics gets rather difficult.

또다른 방법으로는 굽은 시공간에 관한 양자장 이론입니다. 이해하기엔 아주 어려운 수학입니다.

 

* annihilate: 전멸시키다. [입자의] 쌍을 소멸시키다.

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