Within the past few years, just such atechnique was used to measure the lifetime of the π0 -meson. By observing in a microscope the minute tracks left in aphotographic emulsion in which π0 -mesons had been created one saw that a π0 -meson (known to be travelling at a certain speed nearly that of light)went a distance of about 10−7 meter, on the average, before disintegrating. It lived for onlyabout 10−16 sec. It should be emphasized that we have here used a somewhatdifferent definition of “time” than before. So long as there are no inconsistenciesin our understanding, however, we feel fairly confident that our definitionsare sufficiently equivalent.
在过去的几年中，正是这样一种技术，被用来计量π0介子的生命期。在一个照相乳液中，π0介子被创造出来，通过显微镜，来观察它所留下的极小的痕迹，我们就可以看到π0介子（其速度被认为是光的速度），在分化瓦解之前走过的距离，平均大约为10-7米。它只生存了约10-16秒。应该强调，我们在这里所使用的“时间”的定义，与以前的不同。然而，只要在我们的理解中，没有不一致，我们就还是比较有信心：我们的定义是充分相等的。

By extending our techniques—and ifnecessary our definitions—still further we can infer the time duration of stillfaster physical events. We can speak of the period of a nuclear vibration. Wecan speak of the lifetime of the newly discovered strange resonances(particles) mentioned in Chapter 2.Their complete life occupies a time span of only 10−24 second, approximately the time it would take light (which movesat the fastest known speed) to cross the nucleus of hydrogen (the smallestknown object).
通过扩展我们的技术，及有必要的话扩展我们的定义，我们还可以走得更远，即让时间，去关联更快的物理事件的持续期。我们可以谈原子核振动的周期。我们可以谈新发现的奇怪的共振态（粒子）的周期，它在第2章提到过。它们的完整生命所占据的时间段，只有10-24秒，近似于光（光速是已知速度中最快的）通过氢的原子核（已知的最小对象）的时间。

What about still smaller times? Does “time”exist on a still smaller scale? Does it make any sense to speak of smaller timesif we cannot measure—or perhaps even think sensibly about—something whichhappens in a shorter time? Perhaps not. These are some of the open questionswhich you will be asking and perhaps answering in the next twenty or thirtyyears.
那么更小的时间呢？“时间”是否在一个更小的尺度上存在呢？对于更小的时间，如果我们不能计量它，那么谈论它、甚至思考那些在它里面所发生的事情，还有意义吗？或许不是。在接下来的20到30年中，有一些公开的问题，你们可以问，或许也可以回答。

5–4Long times 5-4长的时间
Let us now consider times longer than oneday. Measurement of longer times is easy; we just count the days—so long asthere is someone around to do the counting. First we find that there is anothernatural periodicity: the year, about 365 days. We have also discovered that nature has sometimes provideda counter for the years, in the form of tree rings or river-bottom sediments.In some cases we can use these natural time markers to determine the time whichhas passed since some early event.
现在，我们考虑比一天更长的时间。较长时间的计量，比较容易，我们只需要去数天数就行了，当然，得有人去做这事儿才行。首先，我们发现，有另外一个自然的周期，那就是年，大约365天。我们还发现，自然以树的年轮、及河床里的沉积物的形式，为年提供了一个计数器。在有些情况下，我们可以使用这些自然的时间标记来决定：从某些早期的事件开始，直到后面某时，所经历的时间。

When we cannot count the years for the measurement of long times, we must look for other ways to measure. One of the mostsuccessful is the use of radioactive material as a “clock.” In this case we donot have a periodic occurrence, as for the day or the pendulum, but a new kindof “regularity.” We find that the radioactivity of a particular sample ofmaterial decreases by the same fraction for successive equal increasesin its age. If we plot a graph of the radioactivity observed as a function oftime (say in days), we obtain a curve like that shown in Fig. 5–3. Weobserve that if the radioactivity decreases to one-half in T days (called the “half-life”), then it decreases to one-quarter inanother T days, and so on. In an arbitrary time interval t there are t/T “half-lives,” and the fraction left after this time tis (12)t/T .
在计量长的时间时，如果我们不能对年计数，那么，我们就应该寻找其他计量的方法。一种成功的方法，就是使用辐射材料作为“时钟”，在这种情况下，我们并没有周期性的表现，例如天或钟摆，但却有一种新的“规则”。我们发现，一种特殊材料样品的辐射，随着其年龄的增加，衰减的比例相同。如果把观察到的辐射，作为时间的函数，来画一幅图，我们就会得到如图5-3所示的曲线。我们观察到，如果辐射在T天内（被称为“半衰期”），衰减一半，那么，在另外一个T天内，它就会衰减到1/4，如此等等。在任意一个时间段t内，就会有t/T的“半衰期”，在这个时间段t之后，剩下的部分，就是（1/2）t/T。

Fig. 5–3.The decrease with time of radioactivity.The activity decreases by one-half in each “half-life,” T . 图5-3 辐射随时间的衰减。每一个“半衰期”，辐射减少一半

If we knew that a piece of material, say apiece of wood, had contained an amount A of radioactive material when it was formed, and we found out by adirect measurement that it now contains the amount B , we could compute the age of the object, t , by solving the equation:(1/2)t/T=B/A.
对于一块材料，比如说一块木头，如果我们知道，它生成时，包含的辐射量为A，那么，我们通过直接计量，可以发现它现在包含的量为B，这样，通过解方程：(1/2)t/T=B/A，我们就可以计算出其年龄t。

There are, fortunately, cases in which we can know the amount of radioactivitythat was in an object when it was formed. We know, for example, that the carbondioxide in the air contains a certain small fraction of the radioactive carbonisotope C14 (replenished continuously by the action of cosmic rays). If we measurethe total carbon content of an object, we know that a certain fractionof that amount was originally the radioactive C14 ; we know, therefore, the starting amount A to use in the formula above. Carbon-14 has a half-life of 5000 years. By careful measurements we can measure the amount leftafter 20 half-lives or so and can therefore “date” organic objects whichgrew as long as 100,000 years ago.
幸运的是，在有些情况下，我们可以知道，一个对象在形成时所拥有的辐射量是多少。例如，我们知道空气中的二氧化碳，包含着比较小的、一定量的辐射性的碳同位素C14（通过宇宙射线，不断在补充）。如果我们计量一个对象中的碳的总量，我们就会知道，这个量的一些确定部分，最初就是辐射性的C14；因此，我们就知道了上面公式中所用到的开始时的量A。碳14的半衰期是5000年。通过仔细的计量，我们可以计量出20个半衰期之后，剩下的量，这样，对于那些已经生长了大约10万年的有机对象，就可以“确定其年代”。

We would like to know, and we think we doknow, the life of still older things. Much of our knowledge is based on themeasurements of other radioactive isotopes which have different half-lives. Ifwe make measurements with an isotope with a longer half-life, then we are ableto measure longer times. Uranium, for example, has an isotope whose half-lifeis about 109 years, so that if some material was formed with uranium in it109 years ago, only half the uranium would remain today. When the uraniumdisintegrates, it changes into lead. Consider a piece of rock which was formeda long time ago in some chemical process. Lead, being of a chemical naturedifferent from uranium, would appear in one part of the rock and uranium wouldappear in another part of the rock. The uranium and lead would be separate. Ifwe look at that piece of rock today, where there should only be uranium we willnow find a certain fraction of uranium and a certain fraction of lead. Bycomparing these fractions, we can tell what percent of the uranium disappearedand changed into lead. By this method, the age of certain rocks has been determinedto be several billion years. An extension of this method, not using particular rocksbut looking at the uranium and lead in the oceans and using averages over theearth, has been used to determine (within the past few years) that the age ofthe earth itself is approximately 4.5 billion years.
对于更古老的事物，我们想知道，而且我们也认为我们知道，它的生命。我们的很多知识，都基于其他放射性同位素的计量，这些同位素，拥有不同的半衰期。如果我们用一个有着较长半衰期的同位素，进行计量，那么，我们就可以计量更长的时间。例如，铀，就有一种同位素，其半衰期为109年，所以，如果某种材料，是109年前形成的，且含有铀，那么今天，铀的量就只会剩下一半。铀分解后，会变成铅。考虑一块岩们，是很久以前在化学反应中形成的。铅的化学性质，与铀不同，在这块岩石中，铅会出现在岩石的这一部分，而铀则会出现在岩石的另一部分。铀和铅应该是分开的。如果我们今天去看这块岩石，那么，在曾经只有铀的地方，就会发现既有一部分铅，又有一部分铀。通过比较这些部分，我们就可以得到，铀消失并变成铅的百分比。通过这种方法，特定岩石的年龄，就可以被规定为几十亿年。这个方法有种延伸，就是不用特别的岩石，而是在海洋中，寻找铀和铅，并且使用地球上的平均值，这种方法，可用来规定地球的年龄，大约是4.5亿年。
{译注：应该是海洋中底壳中的铀？}

It is encouraging that the age of the earthis found to be the same as the age of the meteorites which land on the earth,as determined by the uranium method. It appears that the earth was formed outof rocks floating in space, and that the meteorites are, quite likely, some ofthat material left over. At some time more than five billion years ago, the universestarted. It is now believed that at least our part of the universe had itsbeginning about ten or twelve billion years ago. We do not know what happenedbefore then. In fact, we may well ask again: Does the question make any sense?Does an earlier time have any meaning?
依据这种铀的方法，可以规定，地球的年龄，与那些落到地球上的陨石的年龄，是同样的，这种说法令人鼓舞。地球似乎是由漂浮在太空中的岩石，形成的，而这些陨石，完全有可能，是形成时剩下的一些材料。大约在50多亿年前的某时，宇宙开始了。现在公认的一点就是，我们的这部分宇宙，大约在10到12亿年之前开始。但在那之前，发生了什么，我们并不知道。事实上，我们完全可以再次追问：这个问题，有什么意义吗？更早的时间，会意味着什么呢？

5–5Units and standards of time 5-5 时间的单位和标准
We have implied that it is convenient if westart with some standard unit of time, say a day or a second, and refer allother times to some multiple or fraction of this unit. What shall we take as ourbasic standard of time? Shall we take the human pulse? If we compare pulses, wefind that they seem to vary a lot. On comparing two clocks, one finds they donot vary so much. You might then say, well, let us take a clock. But whoseclock? There is a story of a Swiss boy who wanted all of the clocks in his townto ring noon at the same time. So he went around trying to convince everyone ofthe value of this. Everyone thought it was a marvelous idea so long as all ofthe other clocks rang noon when his did! It is rather difficult to decide whoseclock we should take as a standard. Fortunately, we all share one clock—theearth. For a long time the rotational period of the earth has been taken as thebasic standard of time. As measurements have been made more and more precise,however, it has been found that the rotation of the earth is not exactly periodic,when measured in terms of the best clocks. These “best” clocks are those whichwe have reason to believe are accurate because they agree with each other. We nowbelieve that, for various reasons, some days are longer than others, some daysare shorter, and on the average the period of the earth becomes a little longeras the centuries pass.
我们曾暗示过，如果我们从一些标准的时间单位，比如说一天或一秒出发，来让其他的时间，都是这个标准的倍数、或者是部分，那么，将会很方便。我们应该用什么，来做我们时间的基本标准呢？我们将用人类的脉搏吗？如果我们比较脉搏的话，就会发现，变化很大。比较两个钟表，我们可以发现，它们的变化则没有那么大。因此，有人可能会说，好吧，那么让我们来选一个时钟。但用谁的时钟呢？有这么一个故事，一个瑞士男孩，他想让城里的所有时钟，都在中午的同一时间报时。于是，他就挨家游说，想让所有的人都相信这件事的价值。每个人都想，只要所有其他人的时钟，都在中午报时，这是一个奇妙的想法，但他自己的时钟不报就行！选谁的时钟作为标准，非常困难。幸运的是，我们共享着一个时钟，那就是地球。很久以来，地球的转动，就被当作一个时间的基本标准。然而，随着计量方法越来越精确，已经发现，如果用最好的时钟来计量的话，地球的转动并不是一个准确的周期。对于这些最好的时钟，我们有理由相信它们是准确的，因为它们相互之间是一致的。出于各种不同的原因，我们现在相信，有些天，比其他的天要长一些，有些则要短一些，从平均值看，地球的周期，在过去的几个世纪中，变得长了。

Until very recently we had found nothing muchbetter than the earth’s period, so all clocks have been related to the lengthof the day, and the second has been defined as 1/86,400 of an average day. Recently we have been gaining experience withsome natural oscillators which we now believe would provide a more constant timereference than the earth, and which are also based on a natural phenomenon availableto everyone. These are the so-called “atomic clocks.” Their basic internalperiod is that of an atomic vibration which is very insensitive to thetemperature or any other external effects. These clocks keep time to anaccuracy of one part in 109 or better. Within the past two years an improved atomic clock whichoperates on the vibration of the hydrogen atom has been designed and built byProfessor Norman Ramsey at Harvard University. He believes that this clockmight be 100 times more accurate still. Measurements now in progress willshow whether this is true or not.
直到不久之前，我们还是没有找到比地球周期更好的东西，所以，所有的时钟，都一直依赖于地球的长度，而秒则被定义为一天平均长度之一，即1/86400。最近我们有了一些自然的振荡器的经验，我们现在相信，它们可以给我们提供一个比地球更恒定的时间参考，且此震荡器，基于一个所有人都可得到的现象。就是所谓的原子钟。它们的基本内部周期，就是原子振动的周期，它对温度或任何其他的外部影响，都非常敏感。这些时钟，可以让时间达到109或更好。在过去的两年里，哈佛教授诺曼·拉姆齐，设计并建造了一种改进型的原子钟，它是基于氢原子的震动。他相信，这个钟比现在的要精确100多倍。现在正在进行的计量，将会指出，这个说法是否正确。

We may expect that since it has been possibleto build clocks much more accurate than astronomical time, there will soon bean agreement among scientists to define the unit of time in terms of one of theatomic clock standards.
由于建造比天文时间更准确的时钟，已经可能，所以我们可以期待，不久的将来，科学家们会达成协议：用一台原子钟，作为标准，来定义时间的单位。

5–6Large distances 5-6 大的距离
Let us now turn to the question of distance.How far, or how big, are things? Everybody knows that the way you measuredistance is to start with a stick and count. Or start with a thumb and count.You begin with a unit and count. How does one measure smaller things? How doesone subdivide distance? In the same way that we subdivided time: we take asmaller unit and count the number of such units it takes to make up the longerunit. So we can measure smaller and smaller lengths.
现在，我们转向距离。事物有多远，或有多大呢？每个人都知道，计量距离，是从用一个棍子开始，然后数数。或用拇指开始，然后数数。就是你从一个单位开始，然后开始数数。如何计量较小的事物呢？如何把距离分成较小的部分呢？这与我们分时间的方法相同：我们拿一个较小的单位，然后，看较长的单位中，有多少个此较小的单位。于是我们就可以计量越来越小的长度。

But we do not always mean by distance what one gets by counting off with a meter stick. It would be difficult to measure the horizontal distance between two mountain tops using only a meter stick. We have found by experience that distance can be measured in another fashion: by triangulation. Although this means that we are really using a different definition of distance, when they can both be used they agree with each other. Space is more or less what Euclid thought it was, so the two types of definitions of distance agree. Since they do agree on the earth it gives us some confidence in using triangulation for still larger distances. For example, we were able to use triangulation to measure the height of the first Sputnik. We found that it was roughly 5×105 meters high. By more careful measurements the distance to the moon can be measured in the same way. Two telescopes at different places on the earth can give us the two angles we need. It has been found in this way that the moon is 4×108 meters away.
但是，通过距离，我们并不总是意味着：人们通过米尺量出来的东西。两座山峰之间的距离，用米尺量，将会非常困难。通过经验，我们发现，距离可以通过另外一种方式，即三角测量来计量。虽然，这意味着我们确实在用另外一种距离的定义，但是，当这两种方法都可以被使用的时候，它们是一致的。空间，或多或少，就是欧几里德所想的那样，所以，这两种距离定义的类型，是一致的。鉴于它们在地球上是一致的，所以，我们有信心，把三角测量，用到更大的距离上。例如，我们可以把三角测量，用在人造卫星的高度上。我们发现，它大约是5×10的5次方米高。通过更仔细的计量方法，到月亮的距离，也可以用这种方法来测出。在地球上两个不同地点的望远镜，可以给我们提供我们需要的两个角度。以这种方式，已经发现，月亮的距离是4×10的8次方米。

Fig. 5–4.The height of a Sputnik isdetermined by triangulation. 图5-4 用三角测量来计算人造卫星的高度

We cannot do the same with the sun, or atleast no one has been able to yet. The accuracy with which one can focus on agiven point on the sun and with which one can measure angles is not good enoughto permit us to measure the distance to the sun. Then how can we measure the distanceto the sun? We must invent an extension of the idea of triangulation. We measurethe relative distances of all the planets by astronomical observations of wherethe planets appear to be, and we get a picture of the solar system with the properrelative distances of everything, but with no absolute distance.One absolute measurement is then required, which has been obtained in a numberof ways. One of the ways, which was believed until recently to be the mostaccurate, was to measure the distance from the earth to Eros, one of the smallplanetoids which passes near the earth every now and then. By triangulation onthis little object, one could get the one required scale measurement. Knowingthe relative distances of the rest, we can then tell the distance, for example,from the earth to the sun, or from the earth to Pluto.
对于太阳，我们没法做同样的事情，至少现在还没有人能够做到。因为用这种方法，我们需要在太阳上有一个准确的点，给我们提供一个准确的角度，但这做不到，所以，我没法测量到太阳的距离。那么，我们如何才能测量到太阳的距离呢？我们应该对三角测量这种想法，做一些扩展。通过天文学的观察，我们可以得到行星出现的位置，然后计算所有这些行星的相对距离。因此，就需要一种绝对的计量方法，现在，已经有若干方式，可以得到它。方式之一，直到最近，都被认为是最精确的，它就是计量从地球到爱欲星的距离，该星是小行星，不断地经过地球。通过对这个小对象的计量，人们就可以得到他们所期待的计量尺度。知道了其他行星的相对距离，我们就可以得到：地球到太阳的、或者地球到冥王星的距离。