It is a very beautiful line of reasoning. The only problem is thatperhaps it is not true. (After all, nature does not have to go alongwith our reasoning.) For example, perhaps perpetual motion is, in fact,possible. Some of the assumptions may be wrong, or we may have made a mistakein reasoning, so it is always necessary to check. It turns outexperimentally, in fact, to be true.
这条推理思路，非常漂亮。唯一的问题就是，或许它不是真的。（毕竟自然没有必要按我们的思路走。）例如，永动机事实上或许是可能的。有些假定可能是错的，或者，我们在推理时犯了错，所以，检查总是必要的。事实上，从实验的角度看，是真的。

The general name of energy which has to dowith location relative to something else is called potential energy. Inthis particular case, of course, we call it gravitational potential energy.If it is a question of electrical forces against which we are working, insteadof gravitational forces, if we are “lifting” charges away from other chargeswith a lot of levers, then the energy content is called electrical potentialenergy. The general principle is that the change in the energy is the forcetimes the distance that the force is pushed, and that this is a change inenergy in general:
(change inenergy)=(force)×(distanceforceacts through).(4.4)
有些能量，与相对于其它某物的位置有关，这种能量，我们称之为势能。当然，在这种特殊情况下，我们称之为重力势能。如果我们所谈的问题，是与电力有关，而不是与重力有关，如果我们是用很多杠杆，把电荷从其它电荷中“提升”，那么，这个能量的内容，我们称之为电势能。一般的原理就是，能量的变化，是力乘以力所作用的距离，这就是一般能量的变化：
能量中的变化=(力)×(力所作用的距离).(4.4)

Fig. 4–3.Inclined plane. 倾斜的平面
The principle of the conservation of energyis very useful for deducing what will happen in a number of circumstances. Inhigh school we learned a lot of laws about pulleys and levers used in differentways. We can now see that these “laws” are all the same thing, and thatwe did not have to memorize 75 rules to figure it out. A simple example is a smooth inclined planewhich is, happily, a three-four-five triangle (Fig. 4–3). Wehang a one-pound weight on the inclined plane with a pulley, and on the otherside of the pulley, a weight W . We want to know how heavy W must be to balance the one pound on the plane. How can we figure thatout? If we say it is just balanced, it is reversible and so can move up anddown, and we can consider the following situation. In the initial circumstance,(a), the one pound weight is at the bottom and weight W is at the top. When W has slipped down in a reversible way, (b), we have a one-pound weightat the top and the weight W the slant distance, or five feet, from the plane in which it wasbefore. We lifted the one-pound weight only three feet and we loweredW pounds by five feet. Therefore W=3/5 of a pound. Note that we deduced this from the conservation ofenergy, and not from force components. Cleverness, however, is relative. Itcan be deduced in a way which is even more brilliant, discovered by Stevinusand inscribed on his tombstone. Figure 4–4explains that it has to be 35 of a pound, because the chain does not go around. It is evidentthat the lower part of the chain is balanced by itself, so that the pull of thefive weights on one side must balance the pull of three weights on the other,or whatever the ratio of the legs. You see, by looking at this diagram, that Wmust be 3/5 of a pound. (If you get an epitaph like that on your gravestone, youare doing fine.)

Fig. 4–4.The epitaph of Stevinus. 斯蒂维纽司的墓志铭
很多情况下，究竟会发生什么，都可以用能量守恒原理来解释。在高中，我们学了滑轮和杠杆在不同方式下使用的规律。现在我们可以看到，这些规律，都是同一个事情，这样，我们就没必要去记75条规则，以把它搞清楚了。一个简单的例子，就是一个光滑的斜面，它恰好是3、4、5三角形，见图4-3。我们在斜面上，用一个滑轮，吊着一磅重，在滑轮的另一面，是重量W。我们想知道，W应该有多重，才能平衡斜面上的那一磅。我们如何才能搞清楚呢？如果我们说，它刚好已经平衡了，那么，它就是可反转的，于是就可以来回移动，这样我们就可以考虑下面的情况。在初始情况下，（a），一磅重，在底部，重量W，在顶部。当W以一种可反转的方式，滑动到下面时，（b），一磅重，在顶部，而重量W，距其先前所在位置的距离，就是斜面的长度，或五英尺。我们把一磅重抬高了三英尺，把W降低了五英尺。因此W是1磅的3/5。注意，我们是从能量守恒，推出这点的，而不是从力的构成。然而，聪明是相对的。还有一种更加才华横溢的方法，可以推出它。该方法由斯蒂维纽司发现，且刻在他的墓碑上。图4-4解释了，确实应该是一磅的3/5，因为链子并不是转着圈走。很明显，下部的链子，是自平衡的，于是，在一侧拉这五个重量的，与另一侧拉三个重量的，应该平衡，且不论这个绳子的比例是多少。你看，通过看这个图，W应该是一磅的3/5。（如果你的墓碑上，有这么一个墓志铭，说明你很棒。）

Let us now illustrate the energy principle with a more complicated problem, the screw jack shown in Fig. 4–5. A handle 20 inches long is used to turn the screw, which has 10 threads to the inch. We would like to know how much force would be needed at the handle to lift one ton (2000 pounds). If we want to lift the ton one inch, say, then we must turn the handle around ten times. When it goes around once it goes approximately 126 inches. The handle must thus travel 1260 inches, and if we used various pulleys, etc., we would be lifting our one ton with an unknown smaller weight W applied to the end of the handle. So we find out that W is about 1.6 pounds. This is a result of the conservation of energy.

Fig. 4–5.A screw jack. 图4-5 一个螺丝千斤顶
现在，我们用一个更复杂的问题，即一个螺丝千斤顶，如图4-5，来说明这个能量原理。一个20英寸长的手柄，被用来转这个螺丝，这个螺丝有10条螺线/英寸。我们希望知道，把一吨（2000磅）举高，在手柄上要加多少力。如果我们想把这一吨，抬高一英寸，那么，我们应该把手柄转十次。手柄转一圈，约走126英寸。这样，手柄就应该走了1260英寸，如果我们使用各种不同的滑轮等等，作用于手柄末端，我们就是高用一个较小的重量W，来举此一吨。所以我们发现，W约为1.6磅。这是一个能量守恒的结果。

Fig. 4–6.Weighted rod supported on one end.图4-6 一端有支持的重锤杆
Take now the somewhat more complicated exampleshown in Fig. 4–6. A rodor bar, 8 feet long, is supported at one end. In the middle of the bar isa weight of 60 pounds, and at a distance of two feet from the support there isa weight of 100 pounds. How hard do we have to lift the end of the bar in orderto keep it balanced, disregarding the weight of the bar? Suppose we put apulley at one end and hang a weight on the pulley. How big would theweight W have to be in order for it to balance? We imagine that the weightfalls any arbitrary distance—to make it easy for ourselves suppose it goes down4 inches—how high would the two load weights rise? The centerrises 2 inches, and the point a quarter of the way from the fixed endlifts 1 inch. Therefore, the principle that the sum of the heights timesthe weights does not change tells us that the weight W times 4 inches down, plus 60 pounds times 2 inches up, plus 100 pounds times 1 inch has to add up to nothing:
−4W+(2)(60)+(1)(100)=0,W=55 lb.(4.5)
Thus we must have a 55 -pound weight to balance the bar. In this way we can work out the lawsof “balance”—the statics of complicated bridge arrangements, and so on. Thisapproach is called the principle of virtual work, because in order toapply this argument we had to imagine that the structure moves alittle—even though it is not really moving or even movable. Weuse the very small imagined motion to apply the principle of conservation ofenergy.
现在我们看一个更复杂的例子，见图4-6。杆长八英尺，一端有支点。杆的中间，有60磅的重量，距支点两英尺处，有100磅的重量。为了在杆的另一端举起它，以保持平衡，我们要用多大的力呢？杆重忽略不计。假设我们在另一端放一个滑轮，把重量吊在滑轮上。那么，要保持平衡，W应有多重？我们假设这个重量，可以下降任意的距离，为了方便，我们假设是四英寸，那么？杆上的这两个重量，能被抬多高呢？中间的抬高两英寸，与固定支点相距1/4杆长的那个，抬高一英寸。因此，高度乘以重量之和不变这条原理，告诉我们，重量W乘以4英寸向下，加上60磅乘以两英寸向上，再加上100磅乘以1英寸，应为零。
−4W+(2)(60)+(1)(100)=0，W=55 lb。 (4.5)
这样，要让杆平衡，我们就要有55磅的重量。以这种方式，我们就得出了“平衡”的规律，即复杂的桥的安排的静态{力学}，等等。这一解决方案，被称为虚拟的工作原理，因为，为了应用这种论证，我们必须想象这个结构，移动了一点，虽然，它可能并未真正地移动，或者根本不能移动。我们利用很小的想象出来的运动，来应用能量守恒的原理。

4–3Kinetic energy 4-3 动能
To illustrate another type of energy weconsider a pendulum (Fig. 4–7). If wepull the mass aside and release it, it swings back and forth. In its motion, itloses height in going from either end to the center. Where does the potentialenergy go? Gravitational energy disappears when it is down at the bottom;nevertheless, it will climb up again. The gravitational energy must have goneinto another form. Evidently it is by virtue of its motion that it is ableto climb up again, so we have the conversion of gravitational energy into someother form when it reaches the bottom.

Fig. 4–7.Pendulum. 图4-7 单摆
为了示例另外一种能量，我们考虑单摆（图4-7）。如果我们把那个圆块，拉到一边，然后放开它，那么，它就会来回摆动。在其运动中，无论从哪边到中间，它都会失去高度。潜在的能量去了哪里呢？当它在底部时，重力势能消失，尽管如此，它还是会再升起来。重力势能应该是变成了另外一种形式。最终，正是由于运动，它才能重新升起，所以，我们就得到，当它到达底部的时候，重力势能转换成了某种其他形式的能量。

We must get a formula for the energy ofmotion. Now, recalling our arguments about reversible machines, we can easilysee that in the motion at the bottom must be a quantity of energy which permitsit to rise a certain height, and which has nothing to do with the machineryby which it comes up or the path by which it comes up. So we have anequivalence formula something like the one we wrote for the child’s blocks. Wehave another form to represent the energy. It is easy to say what it is. Thekinetic energy at the bottom equals the weight times the height that it couldgo, corresponding to its velocity: K.E.=WH . What we need is the formula which tells us the height by some rulethat has to do with the motion of objects. If we start something out with acertain velocity, say straight up, it will reach a certain height; we do notknow what it is yet, but it depends on the velocity—there is a formula forthat. Then to find the formula for kinetic energy for an object moving withvelocity V , we must calculate the height that it could reach, and multiply bythe weight. We shall soon find that we can write it this way:
K.E.=WVV/2g.(4.6)
我们应该为运动的能量，找到一个公式。现在，回想我们关于可反转机器的论证，我们很容易看到，在底部的运动中，应该有一定量的能量，能让物体，上升一定高度，且此能量，与物体到这个地方的机制和其上升的路径，都无关。所以，我们就有了一个等价性的公式，与我们给孩子的积木所写的公式，有点类似。我们还有另外一种形式，可以代表这个能量。说它是什么，很容易。在底部的动能，等于重量乘以它能达到的高度，与其速度相应：K.E.=WH。我们需要的，是这样一个公式，它可以通过一些与对象的运动有关的规则，来告诉我们高度。如果我们以一定的速度，启动某物，比如说直接向上，那么，它它将达到一定的高度，我们并不知道，此高度是多少，但是，它依赖于速度，对此，应该有一个公式。因此，对于一个以速度V运动着的物体，要找出关于其动能的公式，我们就应该计算它能达到的高度，然后乘以重量。我们很快将发现，我们可以这样表示:
K.E.=W*V*V/2g. (4.6)

Of course, the fact that motion has energy has nothing to do with thefact that we are in a gravitational field. It makes no difference wherethe motion came from. This is a general formula for various velocities. Both (4.3)and (4.6)are approximate formulas, the first because it is incorrect when the heights aregreat, i.e., when the heights are so high that gravity is weakening; thesecond, because of the relativistic correction at high speeds. However, when wedo finally get the exact formula for the energy, then the law of conservationof energy is correct.
当然，运动有能量这一事实，与我们处于重力场中这一事实，没有任何关系。运动从何而来，无所谓。这个公式，对各种运动，普遍适用。(4.3)和(4.6)，都是近似的，第一个，因为当高度很高的时候，它就不对了，因为很高时，重力变弱了；至于第二个，因为在非常高的速度时，它就是相对正确的。然而，对于动能，当我们最终找到准确的公式时，那么，能量守恒规律就是正确的。

4–4Other forms of energy 4-4 能量的其他形式
We can continue in this way to illustratethe existence of energy in other forms. First, consider elastic energy. If wepull down on a spring, we must do some work, for when we have it down, we canlift weights with it. Therefore in its stretched condition it has a possibilityof doing some work. If we were to evaluate the sums of weights times heights,it would not check out—we must add something else to account for the fact thatthe spring is under tension. Elastic energy is the formula for a spring when itis stretched. How much energy is it? If we let go, the elastic energy, as thespring passes through the equilibrium point, is converted to kinetic energy andit goes back and forth between compressing or stretching the spring and kineticenergy of motion. (There is also some gravitational energy going in and out,but we can do this experiment “sideways” if we like.) It keeps going until thelosses—Aha! We have cheated all the way through by putting on little weights tomove things or saying that the machines are reversible, or that they go onforever, but we can see that things do stop, eventually. Where is the energy whenthe spring has finished moving up and down? This brings in another formof energy: heat energy.
能量的存在，还有各种其他形式，我们可以继续以上述方式，来展示它们。首先，考虑弹性能量。如果我们压一个弹簧，我们就应该做些工，因为，当我们把它压下时，我们就可以用它来举起重量。所以，当它伸展时，弹簧就有可能做一些工。如果我们要估算重量乘以高度的和，这不会有结果，我们应该增加一些其他的东西，以说明弹簧处于压缩状态这一事实。弹性能量，是弹簧展开之后的公式。它有多少能量呢？如果我们让弹簧开始弹，那么，当弹簧超过平衡点的时候，弹性能量就被转换成动能，这样，弹簧就在压缩和伸展之间变化，能量就在运动的动能和弹性能量之间变化。{？意译}（在此期间，还会有重力能量的进出，但是，如果我们愿意的话，我们可以用“侧面”的方式，来做这个实验{平躺？}。弹簧会不断地弹，直到最后松散不动--啊哈！我们一直也有一点儿小的欺诈，即通过放一点小的重量，以让弹簧移动，或者，说这个机器呢是可反转的，或者，说它可以永远运动，但是，我们可以看到，最终它还是停了下来。当弹簧停止运动时，能量去了哪里呢？这就带来了能量的另一种的形式：热能。

Inside a spring or a lever there are crystalswhich are made up of lots of atoms, and with great care and delicacy in thearrangement of the parts one can try to adjust things so that as somethingrolls on something else, none of the atoms do any jiggling at all. But one mustbe very careful. Ordinarily when things roll, there is bumping and jiggling becauseof the irregularities of the material, and the atoms start to wiggle inside. Sowe lose track of that energy; we find the atoms are wiggling inside in a randomand confused manner after the motion slows down. There is still kinetic energy,all right, but it is not associated with visible motion. What a dream! How dowe know there is still kinetic energy? It turns out that with thermometersyou can find out that, in fact, the spring or the lever is warmer, and thatthere is really an increase of kinetic energy by a definite amount. We callthis form of energy heat energy, but we know that it is not really a newform, it is just kinetic energy—internal motion. (One of the difficulties withall these experiments with matter that we do on a large scale is that we cannotreally demonstrate the conservation of energy and we cannot really make ourreversible machines, because every time we move a large clump of stuff, the atomsdo not remain absolutely undisturbed, and so a certain amount of random motiongoes into the atomic system. We cannot see it, but we can measure it withthermometers, etc.)
在一个滑轮或一个杠杆的内部，有晶体，晶体由很多原子构成，通过对滑轮或杠杆的各部分，做非常仔细地安排，就可以调整事物，让一个东西在另外一个上面滚动，而没有任何原子在摇动。但是，人们必须非常仔细。通常，当事物开始滚动的时候，因为材料的不规则，就会有撞击和摆动，原子就会开始在里面摇动。于是，我们就失去了能量的踪迹。我们发现，在运动变慢之后，原子在材料里面，以一种随机的和让人迷惑的方式在摆动。动能当然还有，但是，它们并没有与看得到的运动相联。这是一个什么样的梦啊！我们如何才能知道还有动能呢？结果就是，借助温度计，你会发现，弹簧或滑轮变热了，动能有了一定量的增加。这种能量的形式，我们称之为热能，但是，我们知道，它并不真正是一种新的形式，它只是动能--一种内部的运动。（在较大的尺度上，对物质做这些实验，所遇到的困难之一就是，我们不能真正地演示能量守恒，我们不能做出真正的可反转的机器，因为，每次我们移动一个大的东西，都绝对不可能不干扰原子，于是，一定量的随机运动，就会进入到原子系统中。这点我们看不到，但是，我们可以用温度计测到它，等等。）

There are many other forms of energy, andof course we cannot describe them in any more detail just now. There iselectrical energy, which has to do with pushing and pulling by electric charges.There is radiant energy, the energy of light, which we know is a form ofelectrical energy because light can be represented as wigglings in theelectromagnetic field. There is chemical energy, the energy which is releasedin chemical reactions. Actually, elastic energy is, to a certain extent, likechemical energy, because chemical energy is the energy of the attraction of theatoms, one for the other, and so is elastic energy. Our modern understanding isthe following: chemical energy has two parts, kinetic energy of the electrons insidethe atoms, so part of it is kinetic, and electrical energy of interaction ofthe electrons and the protons—the rest of it, therefore, is electrical. Next wecome to nuclear energy, the energy which is involved with the arrangement ofparticles inside the nucleus, and we have formulas for that, but we do not havethe fundamental laws. We know that it is not electrical, not gravitational, andnot purely kinetic, but we do not know what it is. It seems to be an additionalform of energy. Finally, associated with the relativity theory, there is a modificationof the laws of kinetic energy, or whatever you wish to call it, so that kineticenergy is combined with another thing called mass energy. An object hasenergy from its sheer existence. If I have a positron and an electron,standing still doing nothing—never mind gravity, never mind anything—and theycome together and disappear, radiant energy will be liberated, in a definiteamount, and the amount can be calculated. All we need know is the mass of the object.It does not depend on what it is—we make two things disappear, and we get acertain amount of energy. The formula was first found by Einstein; it is E=mcc.
能量还有很多其他形式，当然，现在对它们，我们还不可能做更细致的讨论。有电能，它与对电荷的推拉有关。有辐射能、光能，我们知道它是一种电能的形式，因为光可以被表现为在电磁场中的摆动。有化学能，这是在化学反应中，释放出来的能量。实际上，在某种意义上说，弹性能量更像化学能，因为化学能是原子相互之间的吸引，即一个原子对其他原子的吸引，弹性能量也如此。我们现代的理解如下：化学能有两部分，一部分，是原子内部电子的动能，所以是动能；另一部分，是电子和质子之间的相互作用，所以是电能。下面，我们来到原子能，它与原子核内部粒子的排列有关，对此，我们有公式，但是并没有基础规律。我们知道，它不是电能，不是重力能，也不是纯粹的动能，但它究竟是什么，我们不知道。它似乎是能量的另一种形式。最后，根据与相对论的关系，动能规律有所修改，或者，不论你称它是什么，动能都与另外一个被称为质能的东西有关。一个对象，由于它只是存在，就具有能量。如果我有一个正电子和一个电子，它们在那里什么都不做，--不考虑重力能，或者其他事情--，那么，当它们相碰，就会消失，辐射能就会以一定的量，被释放出来，此量是可计算的。我们所需要知道的，就是对象的质量。对象是什么，并不重要，我们让两个东西消失，就会得到一定量的能量。此公式，最初由爱因斯坦发现，即E=mcc。

It is obvious from our discussion that thelaw of conservation of energy is enormously useful in making analyses, as we haveillustrated in a few examples without knowing all the formulas. If we had all theformulas for all kinds of energy, we could analyze how many processes should workwithout having to go into the details. Therefore conservation laws are veryinteresting. The question naturally arises as to what other conservation lawsthere are in physics. There are two other conservation laws which are analogousto the conservation of energy. One is called the conservation of linear momentum.The other is called the conservation of angular momentum. We will find out moreabout these later. In the last analysis, we do not understand the conservationlaws deeply. We do not understand the conservation of energy. We do notunderstand energy as a certain number of little blobs. You may have heard thatphotons come out in blobs and that the energy of a photon is Planck’s constanttimes the frequency. That is true, but since the frequency of light can beanything, there is no law that says that energy has to be a certain definiteamount. Unlike Dennis’ blocks, there can be any amount of energy, at least as presentlyunderstood. So we do not understand this energy as counting something at themoment, but just as a mathematical quantity, which is an abstract and ratherpeculiar circumstance. In quantum mechanics it turns out that the conservationof energy is very closely related to another important property of the world, thingsdo not depend on the absolute time. We can set up an experiment at a givenmoment and try it out, and then do the same experiment at a later moment, andit will behave in exactly the same way. Whether this is strictly true or not, wedo not know. If we assume that it is true, and add the principles of quantummechanics, then we can deduce the principle of the conservation of energy. Itis a rather subtle and interesting thing, and it is not easy to explain. Theother conservation laws are also linked together. The conservation of momentumis associated in quantum mechanics with the proposition that it makes nodifference where you do the experiment, the results will always be thesame. As independence in space has to do with the conservation of momentum,independence of time has to do with the conservation of energy, and finally, ifwe turn our apparatus, this too makes no difference, and so the invarianceof the world to angular orientation is related to the conservation of angularmomentum. Besides these, there are three other conservation laws, that areexact so far as we can tell today, which are much simpler to understandbecause they are in the nature of counting blocks.
我们前面的讨论，展示了几个例子，且不用知道所有的公式，据此，很明显，能量守恒规律，在分析方面非常有用。如果对所有种类的能量，我们都有公式，那么，我们就可以分析，究竟有多少{能量守恒的}过程在运行，且不用陷入到具体的细节中去。因此，守恒规律，非常有趣。但通常会产生的问题则是，在物理学中，还有哪些其他的守恒规律呢？可与能量守恒规律类比的，有两个守恒规律。一个是线性动量的守恒。另一个是角动量的守恒。后面我们会讲到它们。在前一个分析中，我们并未深刻地理解守恒规律。我们并不理解能量守恒。我们并不把能量理解为一定数量的小团块。你可能听说过，光子是一块一块地出来的{一束一束的？}，而光子的能量，就是普朗克常数乘以频率。这是真的，但是，由于光的频率可以是任意值，所以，没有任何规律可以告诉我们，能量必须是某一确定的量。与丹尼斯的积木不同，可能有任何数量的能量，至少，现在是这么理解的。所以，我们把能量，并不理解为是在数某物，而只是能理解为一种数学的量，它是抽象的，且与特殊环境有关。在量子力学中，结果就是，能量守恒，与世界上另外一个重要的特性，密切相关，此特性就是：事情的并不依赖于绝对时间。我们可以在某一时间，做一个实验，然后在另一时间，做同样的实验，那么，两者表现，应基本相同。这点是不是严格真实的，我们并不知道。如果我们假定它是真的，然后，增加量子力学的原理，那么，我们就可以减少能量守恒的原理。这是一个很精巧和很有趣的事情，但解释起来并不容易。其他的守恒规律，都是连接在一起的。动量守恒，在量子力学中，与一个命题相结合来，该命题就是：你在哪里做这个实验，并无区别，结果总是一样。正如空间中的独立，与动量守恒有关一样，时间的独立，则与能量守恒有关，最终，如果我们开动我们的仪器，那么，这一点将不会产生任何不同，于是，世界对于角度方位的不变性，与角动量的守恒有关。除此之外，还有三个守恒规律，是我们今天能够准确告诉的，理解它们，要简单的多，因为，它们的本质，与数积木是一样的。

The first of the three is the conservationof charge, and that merely means that you count how many positive, minushow many negative electrical charges you have, and the number is never changed.You may get rid of a positive with a negative, but you do not create any net excessof positives over negatives. Two other laws are analogous to this one—one iscalled the conservation of baryons. There are a number of strangeparticles, a neutron and a proton are examples, which are called baryons. Inany reaction whatever in nature, if we count how many baryons are coming into aprocess, the number of baryons2which come out will be exactly the same. There is another law, the conservationof leptons. We can say that the group of particles called leptons are:electron, muon, and neutrino. There is an antielectron which is a positron, thatis, a −1 lepton. Counting the total number of leptons in a reactionreveals that the number in and out never changes, at least so far as we know atpresent.
这三个守恒规律中的第一个，就是电荷的守恒，它只意味着，你计数得到的正电荷的数目，减去你所有的负电荷的数目，这个数目差，总是不变。你可以用一个负电荷，除掉一个正电荷，但是，对于正电荷减去负电荷的部分，你永远不能创造出任何净增长。另外两个守恒规律，与此类似，其中一个，被称为重子守恒。有若干奇怪的粒子，中子和质子就是例子，它们被称为重子。在自然的任何实验中，对于一个过程，如果有多少个重子到来，那么，产生重子的地方，就一定会有同样多的重子数目（脚注2）。另一条守恒规律，就是轻子的守恒。我们可以说，被称为轻子的粒子组，就是：电子、介子和中微子。还有一个反电子，它也就是正电子，也就是说，是一个-1 轻子。在一个反应中，对所有的轻子计数，就会揭示，进出的轻子数目，永远不变，至少，就我们目前所知，是如此。
These are the six conservation laws, threeof them subtle, involving space and time, and three of them simple, in thesense of counting something.
这些就是六个守恒规律，其中三个很精巧，与空间和时间有关，另外三个很简单，其意义，就是对某种东西的计数。

With regard to the conservation of energy,we should note that available energy is another matter—there is a lot ofjiggling around in the atoms of the water of the sea, because the sea has acertain temperature, but it is impossible to get them herded into a definitemotion without taking energy from somewhere else. That is, although we know fora fact that energy is conserved, the energy available for human utility is notconserved so easily. The laws which govern how much energy is available arecalled the laws of thermodynamics and involve a concept called entropyfor irreversible thermodynamic processes.
就能量守恒而言，我们应该注意到，{现实中}有多少能量，能够获得，则是另外回事--在水中原子的周围，有很多摆动，因为海水有一定的温度，但是，要把它们{原子的摆动}，牧化为一种确定的运动，而不从其他地方得到能量，则是不可能的。也就是说，虽然我们知道，能量守恒，作为一个事实，是有的，但是，对于人类的使用来说，那些可获得的能量，还不是这么容易守恒的。有多少能量，可以获得，管这事的规律，被称为热力学的规律，它牵扯到一个概念，被称为熵，这是一个对不可逆的热力学过程而言的概念。