We said that the laws of nature are approximate:that we first find the “wrong” ones, and then we find the “right” ones. Now,how can an experiment be “wrong”? First, in a trivial way: if something is wrongwith the apparatus that you did not notice. But these things are easily fixed,and checked back and forth. So without snatching at such minor things, how canthe results of an experiment be wrong? Only by being inaccurate. For example,the mass of an object never seems to change: a spinning top has the same weightas a still one. So a “law” was invented: mass is constant, independent ofspeed. That “law” is now found to be incorrect. Mass is found to increase withvelocity, but appreciable increases require velocities near that of light. A truelaw is: if an object moves with a speed of less than one hundred miles a secondthe mass is constant to within one part in a million. In some such approximateform this is a correct law. So in practice one might think that the new lawmakes no significant difference. Well, yes and no. For ordinary speeds we cancertainly forget it and use the simple constant-mass law as a goodapproximation. But for high speeds we are wrong, and the higher the speed, themore wrong we are.
我们说过，自然的规律，只是近似的：我们首先发现“错误”的规律，然后,发现“正确”的。现在，一个实验，如何才会是“错误”的呢？首先，是一些小事情，例如仪器出了问题，而你没有注意到。但是这类小事，很容易解决，来回检查就行。所以，如果不被这种小事情所干扰，那么，一个实验的结果，如何才“能”是错误的呢？只能是由于不精确。例如，一个物体的质量，永远不变：一个旋转的陀螺，与一个静止的陀螺，重量相等。于是，就得到一条定律：质量是守恒的，它独立于速度。现在发现，这条定律，并不正确。质量被发现，随着速度的增加而增加，但是，只有速度到达光速时，才有显著的增加。一条“真正”的定律就是:如果物体的运动速度，在每秒100英里之内，那么，质量就是守恒的，因为只有百万分之一的变化。在一些这类近似的形式中，这就是一条正确的定律。所以，在实践中，有人可能会想，新的定律，并没有什么显著的不同。对此，你可以说是，也可以说否。对于普通速度，我们完全可以忘记这条规律，而是把简单的质量守恒定律，当作一种近似。但在高速的情况下，我们就错了，且速度越高，我们的错误就越大。

Finally, and most interesting, philosophicallywe are completely wrong with the approximate law. Our entire picture of theworld has to be altered even though the mass changes only by a little bit. Thisis a very peculiar thing about the philosophy, or the ideas, behind the laws. Evena very small effect sometimes requires profound changes in our ideas.
最后，也最有趣的，就是对于近似性的规律，从哲学意义上说，我们完全错了。因为即便物质，只改变了一点点，我们关于世界的图像，也会发生彻底改变。这与规律后面的哲学或想法有关，非常奇特。有时一个很小的结果，也会要求我们的想法，产生深刻的改变。

Now, what should we teach first? Should weteach the correct but unfamiliar law with its strange and difficultconceptual ideas, for example the theory of relativity, four-dimensionalspace-time, and so on? Or should we first teach the simple “constant-mass” law,which is only approximate, but does not involve such difficult ideas? The firstis more exciting, more wonderful, and more fun, but the second is easier to getat first, and is a first step to a real understanding of the first idea. Thispoint arises again and again in teaching physics. At different times we shallhave to resolve it in different ways, but at each stage it is worth learningwhat is now known, how accurate it is, how it fits into everything else, andhow it may be changed when we learn more.
那么，首先我们应该教什么呢？我们是否应该教那些正确的、但却是不熟悉的规律呢？因为这些规律，比较奇怪，而且，有着比较困难的概念性的想法，例如，相对论、四维时空等。或者，我们首先应该教这种简单的“质量守恒”规律，它是近似的，但却不牵扯到困难的概念。第一种教法，更刺激、更有好奇性、也更有趣，但第二种教法，则更容易一些，并且，要真正理解第一种教法中的想法，这也是第一步。这一问题，在教授物理学的时候呢，不断会浮起。在不同的时期，我们将以不同的方式，来解决它，但在每个阶段，有些事情，都值得知道，那就是：现在知道了些什么？它有多准确？它与其他的东西，有多适合？以及，当我们学到更多的东西时，它会发生什么样的变化？
{它=它们}

Let us now proceed with our outline, orgeneral map, of our understanding of science today (in particular, physics, butalso of other sciences on the periphery), so that when we later concentrate onsome particular point we will have some idea of the background, why thatparticular point is interesting, and how it fits into the big structure. So,what is our overall picture of the world?
今天的科学，对世界是如何理解的？现在，让我们看看这个大纲，或者说一般的地图（主要是物理学，当然也包括其他的边缘科学），这样，在后面，当我们集中在某些特别的点上的时候，我们对于其背景也会有想法、为什么这个特别的点会很有趣、以及它与整个大的结构是如何适应的。于是，我们关于世界的整个图像，究竟是什么呢？

Matter is made of atoms 物质由原子构成
If, in some cataclysm, all of scientificknowledge were to be destroyed, and only one sentence passed on to the nextgenerations of creatures, what statement would contain the most information inthe fewest words? I believe it is the atomic hypothesis (or the atomic fact,or whatever you wish to call it) that all things are made of atoms—littleparticles that move around in perpetual motion, attracting each other when theyare a little distance apart, but repelling upon being squeezed into one another.In that one sentence, you will see, there is an enormous amount ofinformation about the world, if just a little imagination and thinking areapplied.
假设某种灾难发生，导致所有的科学知识，都被摧毁，只有一句话，可以流传给下一代造物，它用最少的词，包含最多的信息，那么，会是什么呢？我相信，它就是原子假设（或原子事实，不论你把它叫什么吧），即所有事物，都由原子构成，而原子，就是小的粒子，它们绕着圆周，做永恒运动，当它们之间的距离比较远时，就相互吸引，但当把它们挤压在一起时，它们就相互排斥。如果使用一点想象力或思考能力的话，那么你将看到，这句话包含着关于这个世界的巨量信息。

Figure 1–1 图1–1 水放大10亿倍
To illustrate the power of the atomic idea,suppose that we have a drop of water a quarter of an inch on the side. If welook at it very closely we see nothing but water—smooth, continuous water. Evenif we magnify it with the best optical microscope available—roughly twothousand times—then the water drop will be roughly forty feet across, about asbig as a large room, and if we looked rather closely, we would still seerelatively smooth water—but here and there small football-shaped thingsswimming back and forth. Very interesting. These are paramecia. You may stop atthis point and get so curious about the paramecia with their wiggling cilia andtwisting bodies that you go no further, except perhaps to magnify the parameciastill more and see inside. This, of course, is a subject for biology, but forthe present we pass on and look still more closely at the water materialitself, magnifying it two thousand times again. Now the drop of water extendsabout fifteen miles across, and if we look very closely at it we see a kind ofteeming, something which no longer has a smooth appearance—it looks something likea crowd at a football game as seen from a very great distance. In order to seewhat this teeming is about, we will magnify it another two hundred and fiftytimes and we will see something similar to what is shown in Fig. 1–1. Thisis a picture of water magnified a billion times, but idealized in several ways.In the first place, the particles are drawn in a simple manner with sharpedges, which is inaccurate. Secondly, for simplicity, they are sketched almostschematically in a two-dimensional arrangement, but of course they are movingaround in three dimensions. Notice that there are two kinds of “blobs” orcircles to represent the atoms of oxygen (black) and hydrogen (white), and thateach oxygen has two hydrogens tied to it. (Each little group of an oxygen withits two hydrogens is called a molecule.) The picture is idealized further inthat the real particles in nature are continually jiggling and bouncing,turning and twisting around one another. You will have to imagine this as adynamic rather than a static picture. Another thing that cannot be illustratedin a drawing is the fact that the particles are “stuck together”—that theyattract each other, this one pulled by that one, etc. The whole group is “gluedtogether,” so to speak. On the other hand, the particles do not squeeze througheach other. If you try to squeeze two of them too close together, they repel.
为了说明此想法的力量，假设我们有一滴水，尺寸有1/4英寸。如果我们非常仔细的观察它的话，那么，我们看到的无非还是水—光滑而连续的水。即便我们用现在能得到的最好的显微镜，大概2000倍，来放大它，那么，这个水滴的尺寸大概就是40英尺，约像一个房间那么大，如果我们更仔细地看，我们看到的仍是光滑的水，但是，这里或那里，会有小的足球形状的东西，在来回游动。非常有趣。它们是草履虫。你可以停在这里，对这些摆动着纤毛、扭动着身躯的草履虫，充满好奇，不再继续前行，除非把草履虫也放大，看看里面究竟有什么。当然，这是一个生物学的课题，而当前的我们，要继续往前走，把水再放大2000倍，看水里面究竟有什么。现在这滴水，尺寸扩展到相当于15英里，如果我们仔细观察，我们就看到某种团队，很热闹，已经没有光滑的外观了，就像是从远处，看橄榄球运动中挤在一堆的人群。为了搞清楚这个团队，究竟是怎么回事，我们继续把它放大250倍，我们将看到某种与图1-1类似的东西。这就是水滴放大10亿倍的样子，但是，在几个方面，做了理想化处理。首先，是用一种简单的方式来画这些粒子的，边缘比较锋利。其次，为了简单起见，草图把它们示意为在一个平面中，实际上，它们是在三维空间中移动。注意，有两种“块”或圆，黑的代表着氧原子，白的代表着氢原子，每个氧原子上，捆着两个氢原子。（每个由一个氧原子、两个氢原子组成的小组，被称为一个分子。）在现实中，真正的粒子，不断地摇动、弹跳着，一个绕着一个不断地旋转和纽动，此图对这点也做了理想化。你要把这个图，想象成动态的，而不是静态的。还有一件事情，无法用图来示例，那就是，这些粒子是“粘在一起的”，即它们相互吸引，这个被那个拉着，如此等等。这么说吧，整个一组，“被胶水粘在了一起”。另一方面，这些粒子，并没有互相挤过{互相切入}。如果你尝试把两个离子，挤压在一起，当距离很近时，它们就会互相排斥。

The atoms are 1 or 2×10−8 cm in radius. Now 10−8 cm is called an angstrom (just as another name), so wesay they are 1 or 2 angstroms (Å) in radius. Another way to remember theirsize is this: if an apple is magnified to the size of the earth, then the atomsin the apple are approximately the size of the original apple.
原子的半径是1或2X10-200px。现在，10-8被称为一个埃米（另一个名字），于是我们说原子的半径是1或2个埃米(Å)。记住它们大小的另外一个方法就是：如果一个苹果，被放大到地球那么大，那么，苹果中的原子，大约就是原来的苹果那么大。

Now imagine this great drop of water withall of these jiggling[A1] particles stuck together and tagging along with each other. Thewater keeps its volume; it does not fall apart, because of the attraction ofthe molecules for each other. If the drop is on a slope, where it can move fromone place to another, the water will flow, but it does not just disappear—thingsdo not just fly apart—because of the molecular attraction. Now the jigglingmotion is what we represent as heat: when we increase the temperature,we increase the motion. If we heat the water, the jiggling increases and thevolume between the atoms increases, and if the heating continues there comes atime when the pull between the molecules is not enough to hold them togetherand they do fly apart and become separated from one another. Of course,this is how we manufacture steam out of water—by increasing the temperature;the particles fly apart because of the increased motion.
现在，想象这么一大滴水，其中所有振动着的粒子，都相互粘在一起，并相互跟随在一起。水保持着它的体积；由于分子间的相互吸引力，所以它不会散开。如果水滴是在一个斜面上，它就可以从一个地方移动到另外一个地方，这就是水的流动，但是，水滴并不会消失—事物并不会飞散，这是因为分子间的吸引力。现在，振动这种运动，我们通常用热来代表它:当我们增加温度的时候，我们就是增加这种运动。如果我们加热水，那么，振动就会增加，原子之间的空间就会增加，如果持续加热，那么到了一定时候，当分子间的引力不足以把它们聚在一起的时候，它们就会飞散，相互之间分开。当然，这就是我们如何从水产生水蒸气的道理，即增加温度；因为运动增加，所以水就飞散开来。
[A1]

Figure 1–2 图1-2 水蒸汽
In Fig. 1–2 we havea picture of steam. This picture of steam fails in one respect: at ordinaryatmospheric pressure there certainly would not be as many as three watermolecules in this figure. Most squares this size would contain none—but we accidentallyhave two and a half or three in the picture (just so it would not be completelyblank). Now in the case of steam we see the characteristic molecules more clearlythan in the case of water. For simplicity, the molecules are drawn so thatthere is a 120∘ angle between the hydrogen atoms. In actual fact the angle is105∘3′ , and the distance between the center of a hydrogen and the center ofthe oxygen is 0.957 Å, so we know this molecule very well.
图1-2是水蒸汽的图。该图在下面这一方面是失败的:在常规大气压下，在这种图中，不会有多达三个水分子。大多数情况下，这个尺寸的面积内，一个水分子都没有，但在图中，我们碰巧拥有了两个半或三个，这样，就使得它不是空的。现在，在水蒸汽的情况下，我们看到的水分子的特点，比在水的情况下看到的，更清楚。为简明起见，分子被画成：氢原子之间是120∘。实际上，这个角度是105∘3′，氢原子中心与氧原子中心的距离是0.957 Å，这样，对这个分子，我们就了解的很清楚了。

Let us see what some of the properties ofsteam vapor or any other gas are. The molecules, being separated from oneanother, will bounce against the walls. Imagine a room with a number of tennisballs (a hundred or so) bouncing around in perpetual motion. When they bombardthe wall, this pushes the wall away. (Of course we would have to push the wallback.) This means that the gas exerts a jittery force which our coarse senses(not being ourselves magnified a billion times) feel only as an average push.In order to confine a gas we must apply a pressure. Figure 1–3 shows astandard vessel for holding gases (used in all textbooks), a cylinder with apiston in it. Now, it makes no difference what the shapes of water moleculesare, so for simplicity we shall draw them as tennis balls or little dots. Thesethings are in perpetual motion in all directions. So many of them are hittingthe top piston all the time that to keep it from being patiently knocked out ofthe tank by this continuous banging, we shall have to hold the piston down by acertain force, which we call the pressure (really, the pressure timesthe area is the force). Clearly, the force is proportional to the area, for ifwe increase the area but keep the number of molecules per cubic centimeter thesame, we increase the number of collisions with the piston in the sameproportion as the area was increased.
让我们看看水蒸气和其他气体的一些特性。当分子被相互之间分开之后，它们就会弹向墙壁。想象一个房间，里面有若干网球（大约100多个），在不停地做着弹跳运动。当它们高速撞击墙的时候，就把墙往外推。（当然，我们得把墙推回来。）这就意味着，气体产生了一种抖动的力量，而我们粗糙的感觉（我们自己并没有被放大十亿倍），只能感觉到一种平均的推力。为了限制气体，我们必须使用压力。图1-3就显示了一种装气体的标准容器（所有课本中都使用），一个带活塞的圆筒。现在，水分子的形状是什么，已经无所谓了，所以，为了简明，我们将把它们画成网球或小圆点。这些东西，在所有的方向上，不停地运动着。它们的数量众多，一直不停地击打着上方的活塞，为了防止活塞被这种连续的撞击，踢出容器，我们将在活塞的上方，往下施加一个力，我们称之为压力。（确实呢，压力乘以面积就是力）。很明显，力与面积成比例，因为，如果我们增加面积，同时保持每立方厘米的分子数量不变，那么，由于撞击的比例{单位面积的撞击次数}，与面积增加之前相同，所以，就等于我们增加了对活塞的撞击次数。

Figure 1–3 图1–3

Now let us put twice as many molecules inthis tank, so as to double the density, and let them have the same speed, i.e.,the same temperature. Then, to a close approximation, the number of collisionswill be doubled, and since each will be just as “energetic” as before, the pressureis proportional to the density. If we consider the true nature of the forcesbetween the atoms, we would expect a slight decrease in pressure because of theattraction between the atoms, and a slight increase because of the finitevolume they occupy. Nevertheless, to an excellent approximation, if the densityis low enough that there are not many atoms, the pressure is proportional tothe density.
现在，我们把罐子中的分子数加倍，于是密度加倍，且让分子的速度相同，即温度相同。这样，粗略近似地说，撞击的数量会加倍，由于每个分子都像以前一样，具有同样的“活力”，所以压力与密度成比例。原子之间，具有引力，如果我们考虑到此真实本质，那么我们就会认为，由于原子间的引力，会让压力，稍有减少；而由于所占体积是有限的，则会让压力，稍有增加。尽管如此，精确近似地说，如果密度足够低，亦即没有很多原子的话，那么，压力与密度成比例。

We can also see something else: If weincrease the temperature without changing the density of the gas, i.e., if weincrease the speed of the atoms, what is going to happen to the pressure? Well,the atoms hit harder because they are moving faster, and in addition they hitmore often, so the pressure increases. You see how simple the ideas of atomic theoryare.
我们还可以看到一些其他的事情，如果我们不改变气体的密度，而增加温度，亦即增加原子的速度，那么，对压力会有什么影响呢？结果就是，原子撞击的更狠了，因为它们移动的更快了，另外，它们撞击的次数也增加了，于是压力就增加了，你看原子理论的想法，多么简单啊！

Let us consider another situation. Supposethat the piston moves inward, so that the atoms are slowly compressed into asmaller space. What happens when an atom hits the moving piston? Evidently itpicks up speed from the collision. You can try it by bouncing a ping-pong ballfrom a forward-moving paddle, for example, and you will find that it comes offwith more speed than that with which it struck. (Special example: if an atomhappens to be standing still and the piston hits it, it will certainly move.)So the atoms are “hotter” when they come away from the piston than they werebefore they struck it. Therefore all the atoms which are in the vessel willhave picked up speed. This means that when we compress a gas slowly, thetemperature of the gas increases. So, under slow compression, a gaswill increase in temperature, and under slow expansion it will decreasein temperature.
下面，我们再考虑另外一种情况，假设活塞向里移动，于是原子就慢慢的被压缩到一个更小的空间。当原子撞击到移动中的的活塞时，会发生什么事情呢？很明显，通过碰撞，原子提高了速度。你可以做一个实验，用一个球拍，不断向前移动，来推挡一个乒乓球，你会发现球离开的速度，要比它来的速度更快（特殊例子，如果一个原子，碰巧是静止的，那么当活塞碰到它的时候，它肯定就会移动）。于是，当原子离开活塞时，比其撞上活塞时，会更“热”。所以，容器内的所有原子，最终都会选择增加速度。这就意味着，当我们慢慢地压缩气体时，气体的温度就会增加。所以，缓慢压缩气体时，其温度就会增加，而缓慢扩大它时，其温度就会减小。

Figure 1–4 冰
We now return to our drop of water and lookin another direction. Suppose that we decrease the temperature of our drop ofwater. Suppose that the jiggling of the molecules of the atoms in the water issteadily decreasing. We know that there are forces of attraction between theatoms, so that after a while they will not be able to jiggle so well. What willhappen at very low temperatures is indicated in Fig. 1–4: the moleculeslock into a new pattern which is ice. This particular schematic diagramof ice is wrong because it is in two dimensions, but it is right qualitatively.The interesting point is that the material has a definite place for every atom,and you can easily appreciate that if somehow or other we were to hold all theatoms at one end of the drop in a certain arrangement, each atom in a certainplace, then because of the structure of interconnections, which is rigid, theother end miles away (at our magnified scale) will have a definite location. Soif we hold a needle of ice at one end, the other end resists our pushing itaside, unlike the case of water, in which the structure is broken down becauseof the increased jiggling so that the atoms all move around in different ways.The difference between solids and liquids is, then, that in a solid the atomsare arranged in some kind of an array, called a crystalline array, andthey do not have a random position at long distances; the position of the atomson one side of the crystal is determined by that of other atoms millions ofatoms away on the other side of the crystal. Figure 1–4 is aninvented arrangement for ice, and although it contains many of the correctfeatures of ice, it is not the true arrangement. One of the correct features isthat there is a part of the symmetry that is hexagonal. You can see that if weturn the picture around an axis by 60∘ , the picture returns to itself. So there is a symmetry in theice which accounts for the six-sided appearance of snowflakes. Another thing wecan see from Fig. 1–4 is whyice shrinks when it melts. The particular crystal pattern of ice shown here hasmany “holes” in it, as does the true ice structure. When the organizationbreaks down, these holes can be occupied by molecules. Most simple substances,with the exception of water and type metal, expand upon melting, becausethe atoms are closely packed in the solid crystal and upon melting need moreroom to jiggle around, but an open structure collapses, as in the case ofwater.
我们现在返回到那个水滴，换个角度看。假设我们增加了水滴的温度，假设水中原子的分子振动，稳定下降。我们知道，原子之间有吸引力，那么，过段时间后，它们的振动，就不会这么好了。温度非常低的时候，会发生什么事情呢？见图四：分子会被困住，形成一个新的模型，这就是冰。这个冰分子的规划图是错的，因为它是二维的，但定性地说是对的。有趣的一点是，材料中的每个原子都有一个确定的位置，你很容易判断，如果以某种方式，我们能拿住某一边的所有原子，每个原子都在一个确定的地方，那么，由于内部连接的结构--这是刚性的，那么，几英里外的另一端（按我们放大的那个尺寸看），将在一个确定的位置。对于水滴，如果我们用手挤压，它就会被挤破，原子就会向不同的方向移动，而在冰的情况下，如果我们拿住它的一端，但是它的另一端，并不会受到挤压。因此，固体和液体的区别就是，在固体中，原子是以某种阵列的方式被安排的，这称为晶体阵列，在一个长的距离内，它们的位置，并不是随机的，某一端的一个原子的位置，是由几英里之外的一个原子决定的。图1-4中，对冰的安排，是虚拟的，虽然它们包含了很多冰的正确特征，但不是真实的。正确的属性之一，就是有一部分对称是六边形的，如果我们把这个图转60度，你就可以看到，那个图就又回来了。所以，冰里面的这个对称，就可以用来解释雪花的六边形显现。从图1-4可以看到的另一点，就是为什么冰融化的时候，会收缩。这里所显示的冰的粒子晶体模型中，有很多“洞”，正如真正冰的结构一样。当此结构被破坏时，这些洞就被分子占领。除了水和铅字合金外，大部分简单的实质{substance},在融化时，都会扩张，因为固态晶体中，原子被紧密地压在一起，而融化时，它们需要更多的空间来振动，于是，正如在水中那样，一个开放的结构就垮掉了。

Now although ice has a “rigid” crystallineform, its temperature can change—ice has heat. If we wish, we can change theamount of heat. What is the heat in the case of ice? The atoms are not standingstill. They are jiggling and vibrating. So even though there is a definite orderto the crystal—a definite structure—all of the atoms are vibrating “in place.”As we increase the temperature, they vibrate with greater and greateramplitude, until they shake themselves out of place. We call this melting.As we decrease the temperature, the vibration decreases and decreases until, atabsolute zero, there is a minimum amount of vibration that the atoms can have,but not zero. This minimum amount of motion that atoms can have is notenough to melt a substance, with one exception: helium. Helium merely decreasesthe atomic motions as much as it can, but even at absolute zero there is still enoughmotion to keep it from freezing. Helium, even at absolute zero, does notfreeze, unless the pressure is made so great as to make the atoms squashtogether. If we increase the pressure, we can make it solidify.
现在，虽然冰有着“刚性”的晶体形式，但其温度，却可以改变--冰有热。如果我们愿意，我们可以改变此热的量。那么，在冰这种情况下，它的热又是什么呢？原子并不是静止的。它们在摇动震动。所以对于晶体来说，即便有一个确定的命令—即它有一个确定的结构，但是，所有的原子还是在其“位置上”震动着。随着温度的增加，其振动幅度，越来越大，直到把它们自己摇出那个地方。这我们称为融化。当我们降低温度时，震动逐渐减小，直到绝对0度，在这里，原子有一个最小的震动，但并不是零。这个原子所能拥有的最小震动，不足以让一个实质体{substance}融化，只有一个例外,那就是氦。氦尽其所能，降低原子的运动，但即便在绝对0度，也还有足够的运动，以保持它不会结冰。即便是在绝对0度，氦也不结冰，除非压力增加，把原子挤压在一起。如果我们增加压力，就可以把氦固体化。
{vibrate:震动，原地震动？单摆？}