Chapter 5 Entropy and Thermodynamics of Black Holes

黑洞的熵和热力学

You are what you eat

人如其食

It is often said that you are what you eat. Thus if your diet is purely junk food and chocolate, then your complexion, not to mention your physical and mental well-being, will be rather different than if you subsist on a healthy diet of salad andMediterranean food.However, it seems that black holes are not fussy eaters. Whether they are hoovering up a vast expanse of interstellar dust or a cubic light-year of fried eggs, their mass will similarly increase inexorably. In fact, after a black hole has finished its sumptuous meal, you have no way of telling what it was eating, only how much it has consumed (although you could tell if what it ate had charge or angular momentum). You only know the quantity of its diet, not about the quality. The `no-hair theorem' described in Chapter 2 says that the black hole is only characterized by a very few parameters (mass, charge, and angular momentum), and thus we cannot talk about what the black hole is made of. 

人们常说人如其食。因此，如果你的饮食纯粹是垃圾食品和巧克力，那么你的气色和身心健康都将与你食用以沙拉和地中海式饮食为主的健康食品时大不相同。但是，黑洞似乎并不挑食。无论是吸收广阔的星际尘埃还是吸收一整个立方光年的煎蛋，它们的质量都会无可避免地增加。实际上，在黑洞吃完丰盛的食物后，你无法分辨它吃了什么，只能知道它吃了多少(不过你可以分辨它吃的东西是否带有电荷或角动量)。你只知道饮食的数量，而不是饮食的品质。第2章中描述的“无毛定理”说，黑洞仅有很少的参数(质量、电荷和角动量)表征，因此我们无法去讨论黑洞是由什么构成的。 

This lack of knowledge about the nature of what has been sucked in by a black hole may seem like a trivial observation, but it is actually rather profound. Information about a black hole's lunch menu has been fundamentally lost. Any matter which has fallen into the black hole has surrendered its identity.We can't perform measurements on that matter, or discern any details about it. 

缺乏对黑洞所吸入的物质性质的了解，看起来似乎是个微不足道的事情，但实际却有深远影响。有关黑洞午餐菜单的信息从根本上丢失了。落入黑洞的任何事物都已放弃了自己的特性，我们无法对它进行探测，也无法了解关于它的任何细节。 

Black holes and engine

黑洞与引擎

This situation is eerily familiar to those who have studied the beautiful subject of thermodynamics. In that field it is quite common to understand how information can become lost or dissipated through physical processes. Thermodynamics has a long and interesting history. The modern theory began during the industrial revolution when people were trying to work out how to make steam engines more efficient. `Energy' could be defined in such a way that it was always conserved and could be converted between different forms. This is known as the first law of thermodynamics. However, although you can make some conversions between different types of energy, there are particular conversions you are not permitted to make. For example, although you are allowed to convert mechanical work completely into heat(you do that every time you use the brakes to bring your car to a complete stop), you cannot convert heat completely into mechanical work, which unfortunately is precisely what we would like to do with a steam engine. Therefore a steam engine in a train only succeeds in making a partial conversion of heat from the furnace into mechanical work which turns the wheels. It was ultimately realized that heat is a type of energy involving the random motion of atoms, while mechanical work involves the coordinated motion of some large bit of matter, like a wheel or a piston. Therefore, a crucial component of the nature of heat is randomness: because of the jiggling of atoms in a hot body, you lose track of the motion of the individual atoms. This random motion cannot simply be unrandomized without additional cost.The randomness, or to give it the technical name, entropy, in any isolated system never decreases but must always either stay the same or increase in every physical process. (This is the second law of thermodynamics.) One way of looking at this is to say that our information about the world always decreases because we cannot keep track of the motion of all the atoms in a large system. As energy moves from macroscopic scales to microscopic scales, from a simple moving piston to the random motion of huge numbers of atoms, then information is lost to us. Thermodynamics allows us to make this vague-sounding notion completely quantitative.This information loss turns out to be exactly analogous to what we've been describing for matter falling into a black hole. 

对于那些研究过热力学这门美丽的学科的人来说，以下情况再熟悉不过了。在该领域，理解信息是如何通过物理过程丢失或耗散掉是很容易的。热力学有着悠久而有趣的历史。关于热力学的现代理论始于工业革命，当时人们试图研究如何提高蒸汽机的效率。在对“能量”进行定义时，应要求其始终保持守恒，并且可以在不同形式之间进行转换，这被称为热力学第一定律。尽管你可以让能量在不同类型之间进行一些转换，有些特殊的转换却是不被允许的。例如，尽管你可以将机械功完全转换为热(每当你踩刹车令汽车完全停住时都在这样做)，但你无法将热量完全转化为机械功;不幸的是，这正是我们想用蒸汽机做到的事情。因此，火车中的蒸汽机只能将炉子中的热量部分地转化为使车轮转动的机械功。人们最终意识到，热是一种涉及原子随机运动的能量，而机械功则涉及一些诸如轮子或者活塞这种大块物质的协同运动。因此，热的本质中的一个重要部分就是随机性:由于热的物体内原子的振动，你将无法跟踪单个原子的运动轨迹。这种随机运动不可能在没有任何额外代价的情况下被非随机化。在任何孤立系统的各种物理过程中，专业名称为熵的这种随机性都不会减少，且必须始终保持不变或增加——这就是热力学第二定律。对这种现象的一个解释是，由于无法跟踪大型系统中所有原子的运动，我们所知的关于世界的信息总是在减少。随着能量从宏观尺度转移到微观尺度，也就是从简单的活塞运动转化为大量原子的随机运动， 对于我们来说信息就丢失了。热力学使我们能够将这个模糊的概念完全定量化。事实证明，这种信息的丢失与我们所描述的物质落入黑洞是完全类似的。