Within the past year there has been a bigimprovement in our knowledge of the scale of the solar system. At the Jet PropulsionLaboratory the distance from the earth to Venus was measured quite accuratelyby a direct radar observation. This, of course, is a still different type ofinferred distance. We say we know the speed at which light travels (andtherefore, at which radar waves travel), and we assume that it is the samespeed everywhere between the earth and Venus. We send the radio wave out, andcount the time until the reflected wave comes back. From the time weinfer a distance, assuming we know the speed. We have really anotherdefinition of a measurement of distance.
在过去的这一年里，我们关于太阳系的尺度的知识，有了很大的提高。在“喷气推进实验室”，地球到金星的距离，通过一个直接的雷达观测，被准确地测量。当然，这个距离，仍是推出的，类型不同而已。我们说我们知道光传播的速度（从而，知道雷达波传播的速度），我们假定在金星和地球之间的任何地方，其速度都一样。我们发射雷达波出去，然后开始计时，直到反射的波回来。假设我们知道速度，我们就可以从时间，推出距离。我们确实有另外一个关于距离测量的定义。

How do we measure the distance to a star, whichis much farther away? Fortunately, we can go back to our triangulation method,because the earth moving around the sun gives us a large baseline for measurementsof objects outside the solar system. If we focus a telescope on a star insummer and in winter, we might hope to determine these two angles accuratelyenough to be able to measure the distance to a star.
到恒星的距离，要远的多，我们如何测量呢？幸运的是，我们可以回退到三角测量的方法，因为地球绕着太阳转，这给我们测量太阳系外的对象，提供了一个大的基线。如果在冬天和夏天，我们用望远镜，聚焦于一个恒星，我们那就可以希望得到两个角度，它们足够精确，可用来测量到恒星的距离。

Fig. 5–5.The distance of nearby stars canbe measured by triangulation, using the diameter of the earth’s orbit as abaseline. 图5-5 到附近恒星的距离，可通过三角测量来测量，用地球轨道的直径，作为基线。

What if the stars are too far away for us to use triangulation? Astronomers are always inventing new ways of measuring distance. They find, for example, that they can estimate the size and brightness of a star by its color. The color and brightness of many nearby stars—whose distances are known by triangulation—have been measured, and it is found that there is a smooth relationship between the color and the intrinsic brightness of stars (in most cases). If one now measures the color of a distant star, one may use the color-brightness relationship to determine the intrinsic brightness of the star. By measuring how bright the star appears to us at the earth (or perhaps we should say how dim it appears), we can compute how far away it is. (For a given intrinsic brightness, the apparent brightness decreases with the square of the distance.) A nice confirmation of the correctness of this method of measuring stellar distances is given by the results obtained for groups of stars known as globular clusters. A photograph of such a group is shown in Fig. 5–6. Just from looking at the photograph one is convinced that these stars are all together. The same result is obtained from distance measurements by the color-brightness method.
如果行星太远，无法使用三角测量，那该如何？天文学家总在发明新的测距方法。例如，他们发现，他们可以通过一颗恒星的颜色，来估计其尺寸和亮度。很多附近的恒星，其距离，已经通过三角测量得到，其颜色和亮度，也已经被测量，故此发现，恒星的颜色，与内在亮度，有一个光滑的关系（在大多数情况下）。如果一个人，测量一颗恒星的颜色，那么，他就可以使用颜色-亮度关系，来得到该星的内部亮度。通过测量，恒星对地球上的我们来说有多亮（或者，对我们来说，显得有多暗），我们就可以计算出它有多远。（对于一个被给与的内部亮度，明显的亮度，随着距离的平方而减少。）这一计算星际距离的方法，是否正确，下面的结果，给出了满意的回答：有一组星，被称为格拉星族，我们有关于它们的结果。这样一组星的照片，如图5-6所示。通过看这张照片，人们可以确定，这些恒星是在一起的。通过颜色亮度方法所做的距离测量，结果相同。

Fig. 5–6.A cluster of stars near the center of our galaxy. Their distance from the earth is 30,000 light-years, or about 3×1020 meters. 图5-6 接近我们银河系中心的一个星簇。它们到地球的距离为30,000光年，或3*10的20次方米。

A study of many globular clusters givesanother important bit of information. It is found that there is a highconcentration of such clusters in a certain part of the sky and that most ofthem are about the same distance from us. Coupling this information with otherevidence, we conclude that this concentration of clusters marks the center ofour galaxy. We then know the distance to the center of the galaxy—about 1020 meters.
对星簇的研究，还提供了另外一些重要的信息。研究发现，这类星簇集中于天空的某一区域，且其中的大部分，与我们的距离基本相同。把这些信息，与其他的证据，结合起来看，我们就可以得出结论：这类星的集中，标志着银河系的中心。因此，我们就知道，距银河系中心的距离，大约为10的20次方米。

Knowing the size of our own galaxy, we havea key to the measurement of still larger distances—the distances to other galaxies.Figure 5–7is a photograph of a galaxy, which has much the same shape as our own. Probablyit is the same size, too. (Other evidence supports the idea that galaxies are allabout the same size.) If it is the same size as ours, we can tell its distance.We measure the angle it subtends in the sky; we know its diameter, and we computeits distance—triangulation again!
知道了我们星系的大小，对于测量更大的距离、即到其他星系的距离，我们就有了一把钥匙。图5-7，就是一个星系的图片，其形状，与我们星系的非常相似。或许大小就是一样的。（其他证据支持：所有星系，基本上都是同样大小这一想法。）如果其大小与我们的相同，那么，我们就可以得到其距离。我们测量它在天空中所延伸的角度；我们就可知道其直径；然后就可计算出其距离--又是三角测量。

Fig. 5–7.A spiral galaxy like our own. Presumingthat its diameter is similar to that of our own galaxy, we may compute itsdistance from its apparent size. It is 30 million light-years (3×1023meters) from the earth. 图5-7 一个类似于我们星系的旋转星系。假设其直径，与我们的类似，我们就可以从其显示出来的大小出发，计算出其距离。距地球大约是3千万光年（3*10的23次方米）。

Photographs of exceedingly distant galaxieshave recently been obtained with the giant Palomar telescope. One is shown inFig. 5–8.It is now believed that some of these galaxies are about halfway to the limit ofthe universe—1026 meters away—the largest distance we can contemplate!
极其遥远的星系的照片，最近，已经用巨大的帕洛玛望远镜得到。图5-8所示，就是其中之一。据宇宙的限制，大约为10的26次方米，这是我们现在所能思考的最大距离；现在相信，这些星系中的一些，{由于是在宇宙的中心}，所以它们距宇宙的边界，在各个方向，都差不多。

Fig. 5–8.The most distant object, 3C 295 inBoötes (indicated by the arrow), measured by the 200 -inch telescope to date (1960). 图5-8 距离最远的对象，3C 295，在牧夫座（由箭头所示），由当时（1960）的200英寸的望远镜所测。

5–7Short distances 5-7 短的距离
Now let’s think about smaller distances.Subdividing the meter is easy. Without much difficulty we can mark off onethousand equal spaces which add up to one meter. With somewhat more difficulty,but in a similar way (using a good microscope), we can mark off a thousand equalsubdivisions of the millimeter to make a scale of microns (millionths of a meter).It is difficult to continue to smaller scales, because we cannot “see” objectssmaller than the wavelength of visible light (about 5×10−7 meter).
现在，我们思考较短的距离。把米分小，很容易。划分出米的千分之一，并不困难。以同样的方式（使用更好的显微镜），虽然稍微困难点，但我们还是可以划分出毫米的千分之一，以造出微米（一米的百万分之一）的尺寸。继续划分出更小的尺寸，就困难了，因为我们“看不到”比可见光波（约5*10的-7次方）更小的对象。

Fig. 5–9.Electron micrograph of some virusmolecules. The “large” sphere is for calibration and is known to have adiameter of 2×10−7 meter (2000 Å). 图5-9 病毒分子的电子显微图片。“大的”区域是用来校准的，其直径为2*10的-7次方米（2000 Å）。
We need not stop, however, at what we cansee. With an electron microscope, we can continue the process by makingphotographs on a still smaller scale, say down to 10−8 meter (Fig. 5–9). Byindirect measurements—by a kind of triangulation on a microscopic scale—we cancontinue to measure to smaller and smaller scales. First, from an observationof the way light of short wavelength (x-radiation) is reflected from a patternof marks of known separation, we determine the wavelength of the light vibrations.Then, from the pattern of the scattering of the same light from a crystal, wecan determine the relative location of the atoms in the crystal, obtainingresults which agree with the atomic spacings also determined by chemical means.We find in this way that atoms have a diameter of about 10−10 meter.
我们无须止步于我们所能看到的东西。利用一个电子显微镜，我们可以通过制造出更小尺寸、即比10的-8次方米还小的照片，来继续这个过程。通过间接的测量，即通过一种微观尺度的三角测量，我们可以继续测量越来越小的尺寸。首先，我们有一些已知的分开的东西，它们构成一种标记的模型，用来反射波短波长的光（x辐射），通过对这种反射的观察，我们可以确定光振动的波长。然后，让同样的光，经过一个水晶，形成一种散射的模型，从此模型出发，我们就可以得到，原子在晶体中的相对位置；这样所获得的结果，与通过化学方法所确定的原子的空间状态，是一致的。以这种方式，我们发现原子的直径，约为10的-10次方米。

There is a large “gap” in physical sizesbetween the typical atomic dimension of about 10−10 meter and the nuclear dimensions 10−15 meter, 10−5 times smaller. For nuclear sizes, a different way of measuring sizebecomes convenient. We measure the apparent area, σ , called the effective cross section. If we wish the radius, wecan obtain it from σ=πr2 , since nuclei are nearly spherical.
经典的原子的维数，大约是10的-10次方米，原子核的维数，大约是10的-15次方米，要小10的-5次方倍，这两个物理尺寸之间，有一个很大的“沟”。对于原子核的尺寸，一种不同的计量尺寸的方法，变得很方便。我们测量可视面积，σ，它被称为有效的横截面积。如果我们希望得到半径，我们可以从σ=π*r*r获得，因为原子核，近乎球形。

Measurement of a nuclear cross section canbe made by passing a beam of high-energy particles through a thin slab ofmaterial and observing the number of particles which do not get through. Thesehigh-energy particles will plow right through the thin cloud of electrons andwill be stopped or deflected only if they hit the concentrated weight of anucleus. Suppose we have a piece of material 1 centimeter thick. There will be about 108 atomic layers. But the nuclei are so small that there is littlechance that any nucleus will lie behind another. We might imagine that ahighly magnified view of the situation—looking along the particle beam—wouldlook like Fig. 5–10.
对一个原子核的横截面积的测量，可以这样：让一束高能的粒子光束，通过一个薄的材料板，然后，观察没有通过这个板的粒子数。这些高能的粒子，会像犁地一样，穿过薄的电子云，然后，由于原子核的重量，是高度浓缩的，如果粒子撞上，就会停止，或被反射。假定我们有一片一厘米厚的材料。那么原子层，将有10的8次方层。但是，由于原子核是如此之小，以至于，一个原子核正好排在另一个后面的机会很小。对于这种情况，即沿着粒子光束去看，我们可以想象一个放大的视图，就会是如图5-10所示。

Fig. 5–10.Imagined view through a block ofcarbon 1 cm thick if only the nuclei were observed. 图5-10 如果只有原子核被观察的话，想象通过一块1厘米厚的碳板，所得到的视图。

The chance that a very small particle willhit a nucleus on the trip through is just the total area covered by theprofiles of the nuclei divided by the total area in the picture. Suppose thatwe know that in an area A of our slab of material there are N atoms (each with one nucleus, of course). Then the fraction of thearea “covered” by the nuclei is Nσ/A . Now let the number of particles of our beam which arrive at the slabbe n1 and the number which come out the other side be n2 . The fraction which do not get through is (n1−n2)/n1, which should just equal the fraction of the area covered. We canobtain the radius of the nucleus from the equation1
πr2 = σ =(A/N)*((n1−n2)/n1).
一个小粒子，在其旅途中，撞上原子核的机会，正是：原子核覆盖的面积，除以该区域的总面积。假设我们知道，在面积为A的材料版中，有N个原子（当然每一个都有一个原子核）。因此，被原子核“覆盖”的面积的分数就是 Nσ/A。现在，假设到达板上的光束中的粒子数目是n1，而从板的另一侧出来的粒子数是n2。那么，没有通过的粒子的分数就是： (n1−n2)/n1，它应该等于被覆盖的面积的分数。从下面的方程，我们就可以获得原子核的半径：（脚注1）
Πrr = σ =(A/N)*((n1−n2)/n1)
From such an experiment we find that the radii of the nuclei are fromabout 1 to 6 times 10−15 meter. The length unit 10−15 meter is called the fermi, in honor of Enrico Fermi(1901–1954).
从这样的实验中，我们得出，原子核的半径大概是1*10的-15到6*10的-15次方米。为了纪念恩里克·费米，10的-15次方米这个单位长度，被称为费米子。

What do we find if we go to smaller distances?Can we measure smaller distances? Such questions are not yet answerable. It hasbeen suggested that the still unsolved mystery of nuclear forces may be unravelledonly by some modification of our idea of space, or measurement, at such smalldistances.
如果我们来到较小的距离，我们能发现什么呢？我们能测量较小的距离吗？这类问题，尚未可知。原子核的力，还是一个尚未解决的谜团，有建议说，要搞清它，只有对于这么小的距离，我们关于空间的想法、或者测量，得到改变之后，才可能。

It might be thought that it would be a goodidea to use some natural length as our unit of length—say the radius of theearth or some fraction of it. The meter was originally intended to be such aunit and was defined to be (π/2)×10−7 times the earth’s radius. It is neither convenient nor very accurateto determine the unit of length in this way. For a long time it has been agreedinternationally that the meter would be defined as the distance between twoscratches on a bar kept in a special laboratory in France. More recently, ithas been realized that this definition is neither as precise as would beuseful, nor as permanent or universal as one would like. It is currently beingconsidered that a new definition be adopted, an agreed-upon (arbitrary) numberof wavelengths of a chosen spectral line.
或许会想，使用某些自然长度，比如说地球的半径，或其分数，作为我们的长度单位，会是一个好主意。其实最初，就是打算用米，来做这样的单位，且它就被定义为：(π/2)×10−7乘以地球的半径。以这种方式来定义长度的单位，既不方便，也不准确。很久以来，国际上达成的一致就是：米的定义，就是保存在一个法国特殊实验室中的特殊棍棒上的两个刻痕之间的距离。更近一些时候，我们意识到，这个定义，既不像实用上那么精确，也不如我们所期待那样持久、或普遍。现在，正在考虑采用一种新的定义，即选择某种光谱线，用它的一定数目的波长。

Measurements of distance and of time giveresults which depend on the observer. Two observers moving with respect to eachother will not measure the same distances and times when measuring what appearto be the same things. Distances and time intervals have different magnitudes,depending on the coordinate system (or “frame of reference”) used for makingthe measurements. We shall study this subject in more detail in a later chapter.
距离测量和时间测量所给出的结果，依赖于观察者。一个事物，很明显是一个，但是，如果两个观察者，相向而行，那么，测量出的距离和时间将不同。距离和时间的间隔，有不同的等级，依赖于测量所使用的坐标系或参考框架。在后面的章节中，我们将更仔细地研究这一主题。

Perfectly precise measurements of distancesor times are not permitted by the laws of nature. We have mentioned earlierthat the errors in a measurement of the position of an object must be at leastas large as
Δx≥ℏ/2Δp,
where ℏ is a small fundamental physical constant called the reduced Planckconstant and Δp is the error in our knowledge of the momentum (mass times velocity) ofthe object whose position we are measuring. It was also mentioned that theuncertainty in position measurements is related to the wave nature ofparticles.
对于距离或时间的完全精确的测量，并不被自然规律所允许。早先我们曾提到过，对象位置测量中的错误，至少应该与下面公式中的Δx一样大：
Δx≥ℏ/2Δp,
这里ℏ是一个小的基础物理常数，被称为缩减的普朗克常数，Δp是我们关于一个对象的动量（质量乘以速度）的知识中的错误，这个对象的位置，就是我们正在测量的。同样也提到过，在位置测量中的不确定性，与粒子的波的特性有关。