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. 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. 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. 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. 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. 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." 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. 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. 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. 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. 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. 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.
