* 앞선 동영상편에서 폭포수의 두마리 물고기의 예를 들어 시공간의 사고 실험의 소재로 삼았다. 물이 가진 의미를 따져 보자.
Suppose we have two fish swimming in a gentle stream above a waterfall. Let's assume that since the fish are immersed in the water, they don't really have a concept of what water is. They consider water to be a natural immutable part of their environment.
천천히 흐르는 강에 물고기 두마리가 헤엄치고 있다. 물속에 잠겨 있는 물고기의 입장에서 물의 의미는 당연한 것이다. 물고기의 입장에서 물은 필수 불가결한 환경요소다.
As you well know, water is not the framework of the universe. But to a fish, it might as well be. So, our two happy fish are living their fishy lives exchanging fishy details about fish stuff by communicating through sound waves in the water. We'll assume now that the fish don't communicate visually and that all of their communication is limited to sound. Maybe it's night in the stream or maybe the fish are unable to see because of mud in the water. Consider the speed of the stream. Since it's flowing slowly, the fish can stay relatively stationary with just a few swishes of their tails. The motion of the water is similar to the effects that we perceive as spacetime.
물이 우주의 기본 틀(framework)가 될수는 없지만 두 물고기에게 중요한 환경이고 수중 음파를 통해 서로 대화할 것이다. 물고기는 시각적 인지능력은 없이 오직 소리만을 사용한다고 가정하자. 강물의 속도는 아주 느리기 때문에 물고기는꼬리만 조금 흔들면 정지할 수 있다. 물의 움직임은 우리가 시공간 이라고 인식하는 것과 유사하다. [우리가 시공간을 당연히 인지하듯 물고기에게 물은 당연한 것이다. 물의 표면이 만들수 있는 유연한 형상과 연속성을 감안하면 왜곡된 시공간의 비유에 적절하다.]
Keep in mind, both the fish and the water can have independent speeds and that there's no universal limit for how fast they can go. So it's possible for the fish and the water itself to exceed the speed of sound in water. Our fish can't swim that fast. But perhaps, one of our fish is researching a faster than sound jetpack.
물고기와 물살의 속도는 서로 무관하고 속도에 제한이 없다고 하자. 물고기와 물살은 수중음파의 속도보다 빠르게 움직일 수는 있다. 하지만 우리의 상황에 등장하는 물고기들은 빠르게 헤엄치지 못한다. 그대신 음파 돌파 제트 추진장치를 달 수도 있다고 하자.
At one end of the stream, the current is drawn into a rushing waterfall. The water pouring over the top of the waterfall gets faster as it falls, traveling faster and faster towards the bottom. The waterfall can be divided into two regions with a short transition between them. The first region is the top, where the stream's water begins to accelerate. But the water flows slower than the speed of sound. Below this first region, there's a transition, where the speed of the water is equal to the speed of sound in water. In the lower region, the water is flowing faster than the speed of sound.
강의 끝에는 폭포가 있다. 폭포수가 떨어지는 속도는 매우 빠르다. 폭포를 두 구역으로 나누는데 윗부분은 물이 가속되기 시작한다. 하지만 아직 소리의 속도에 도달하지 못했다. 그 아래로 천이 구간인데 마침내 폭포수의 속도가 음파속도에 이른다. 이어서 물의 속도는 음파속도보다 빠른 구역이다.
When both fish are above the waterfall, they can carry out a fishy conversation without any difficulty. When they speak, the speed of the stream has very little effect on how the sound travels between them. But what do you think will happen if one of the fish is carried over the top of the waterfall? Let's examine what the two fish experience as the traveling fish descends through the two regions of the waterfall.
폭포위 하천에서 두마리의 물고기는 하천의 속도가 빠르지 않아서 어려움 없이 대화 할 수 있다. 만일 물고기 한마리가 폭포에 빠지면 둘 사이에 어떻게 대화할 수 있을까? 폭포수의 속도 구역에 따라 달라질 것이다.
In the first region of the waterfall, where the water is gently accelerating over the edge, our adventurist fish is heard yelling for the help of his friend, "Help me. I'm being swept over a waterfall." The sound waves emitted by the yelling fish propagate back up the stream towards the stationary fish upstream. Since the velocity of the water in this region is lower than the speed of sound, the fish can still be heard by its companion. However, since the fish is yelling in flowing water, the sound waves travel at the speed of sound minus the speed of the water in the waterfall. The stationary fish will hear the falling fish's voice as being deeper the faster the water flows in the waterfall. This is due to the Doppler effect. <deep voice> "Help me. I continued to be swept further down this waterfall."
폭포가 시작되는 구간은 물의 속도가 가속을 시작했지만 음파보다 느리다. 빨간 물고기의 구조신호가 위로 전달되어 파란 물고기는 이를 들을 수 있다. 하지만 음파의 속도는 물의 속도에서 뺀 값이 되므로 정지한 물고기에게 떨어지는 물고기의 소리는 저음으로 들린다. 바로 도플러 효과 때문이다.
At the transition between the two regions, the speed of water is equal to the speed of sound. At this point, any sounds emitted by the falling fish would appear to be completely stationary. This corresponds to an infinite Doppler shift, and the sound waves would be stretched by the motion of the water. The sound emitted by the falling fish would be so low. It would become inaudible to the fish upstream.
떨어지는 물고기가 천이 구역에 이를 수록 떨어지는 물고기 속도가 소리속도에 도달하면 무한대 도플러 편이가 되어 위의 서 있는 물고기는 아무소리도 들지 못하게 된다.
So, what exactly happens when the falling fish is carried beyond this point? At the point in the waterfall where the speed of the water is equal to the speed of sound, the infalling fish's calls can no longer be heard by the fish upstream. This region in the waterfall is similar to the event horizon of a black hole. Recall that the speed of light is the escape velocity from an event horizon. So, similarly, the part of the waterfall where the stream flows at the speed of sound is just like an event horizon. Since the information carried by sound is trapped, we can call this a sonic event horizon.
마치 블랙 에서 탈출속도가 빛의 속도와 같아지는 '사건 지평선'과 유사한 상황이 벌어진다. 폭포수가 떨어지는 속도와 음파속도가 같아지는 지점을 음파 사건지평선 이라하자.
What does the infalling fish experience? Well, beyond the awareness that it's going over a waterfall, its experience is almost indistinguishable from the stationary fish. Since the infalling fish is accelerated at the same rate as the water around it, it feels like it's in a perfectly still environment, oblivious to the peril that it's in. Not only that, but the infalling fish would continue to hear its companion upstream.
떨어지는 물고기는 폭포수와 함께 가속되기 때문에 아무 위험을 느끼지 못한다. 게다가 위에 있는 동료 물고기의 소리도 들을 수 있다.
Why? Because the upstreams fish's sound waves are being carried along and accelerated with the flow of the water instead of against it. So, communication into the sonic event horizon is possible just like it's possible to send light rays into a black hole.
위의 물고기 소리가 폭포수의 흐름과 함께 가속되고 있다. 따라서 마치 블랙홀 안으로 빛을 들여 보낼 수 있듯이 소리사건지평선에 이르기까지 두 물고기 사이의 대화는 가능하다.
This analogy illustrates a couple of important points about black holes, but it does have some limitations that we need to consider.
First and foremost, a black hole has a singularity at its core. Unlike a waterfall, which has a bottom and a region for water to flow outwards, there is no escape from a fall into a black hole. We might try to illustrate this by adding sharp rocks at the bottom of the waterfall, which obliterate anything including the fish that encounter it. However, we also said that the speed of light is the universal limit, not the speed of sound. In fact, this gives our adventurous little fish an opportunity to escape.
블랙홀을 물고기와 폭포수의 비유에 있어서 몇 가지 고려사항:
가장 중요한 사항을 꼽자면 블랙홀의 중심은 특이점 (무한히 작은 점에 거대 질량이 몰려 있음)이라는 점이다. 한번 빠지면되돌아 나올수 없다. 게다가 빛의 속도는 우주 불변의 상수다. 이에 비해 똑똑한 물고기는 제트 추진장치를 메고 폭포를 거슬러 오를 수 있다.
Perhaps the motivation for the falling fish to go over the waterfall is because it's an inventor fish who has discovered the secret to underwater rocket technology. Perhaps this inventor fish accidentally dropped a rocket pack over the waterfall and was on a mission to retrieve it. If the fish reaches its rocket pack before hitting the rocks at the bottom of the waterfall, it can accelerate to a speed faster than that of the water's flow and return to the safety of the stream where its companion anxiously awaits. This analogy does demonstrate some key physics with respect to the behavior of sound waves in the region around an event horizon, similar to the behavior of light around black holes.
Some scientists have created bathtub drain black holes in the laboratory in order to gain a better understanding of the environment around black holes. These drain holes probe the behavior of event horizons in much the same way that our fish encountered a sonic event horizon. So, why did the fish cross the waterfall? Well, to rescue his jetpack, of course. So long and thanks for all the fish.
어떤 과학자들은 배수구에 물이 회오리 치며 빠져나가는 모형을 블랙홀에 비유하기도 한다.
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