Finally, we find that the velocity v, momentum P , and total energy E are related in a rather simple way. That the mass in motion atspeed v is the mass m0 at rest divided by (1−v2/c2)1/2, surprisingly enough, is rarely used. Instead, the followingrelations are easily proved, and turn out to be very useful:
E2 − P2c2=m02c4 (16.13)
and
Pc = Ev/c. (16.14)
最后，我们发现矢速 v 、动量P、及总能量 E 的相关方式，相当简单。以速度 v 运动时的质量，就是静止时的质量 m0 ，除以 (1−v2/c2)1/2, 这一点，足以让人惊奇，但很少被用到。相反，下面的关系，很容易被证明，结果发现，非常有用：
E2 − P2c2=m02c4 (16.13)
和：
Pc = Ev/c. (16.14)

1 Chapter17. Space-Time第17章空间—时间
17–1The geometry of space-time 17-1 空间时间的几何形状
The theory of relativity shows us that therelationships of positions and times as measured in one coordinate system and anotherare not what we would have expected on the basis of our intuitive ideas. It isvery important that we thoroughly understand the relations of space and timeimplied by the Lorentz transformation, and therefore we shall consider thismatter more deeply in this chapter.
在一个坐标系中，可测得位置和时间，在另一坐标系中，也可测得，两者之间，有一种关系，相对论理论，给我们指出，这种关系，并不是我们基于我们的直观想法，所期待的那种关系。洛伦兹变换，说明了一种空间和时间的关系，对我们来说，彻底理解之，很重要，因此，在本章中，我们将更深入地考虑此事。

好家伙

The Lorentz transformation between thepositions and times (x,y,z,t) as measured by an observer “standing still,” and the correspondingcoordinates and time (x′,y′,z′,t′) measured inside a “moving” space ship, moving with velocity uare
(17.1)
Let us compare these equations with Eq. (11.5), which also relates measurements in two systems,one of which in this instance is rotated relative to the other:
x′=xcosθ + y sinθ,
y′=ycosθ − xsinθ, (17.2)
z′=z
In this particular case, Moe and Joe are measuring with axes having anangle θ between the x′ - and x -axes. In each case, we note that the “primed” quantities are“mixtures” of the “unprimed” ones: the new x′ is a mixture of x and y , and the new y′ is also a mixture of x and y .
洛伦兹变换，是两个坐标系中，所测的位置和时间的变换，一个坐标系中，观察者“站着不动”，另一个坐标系，是一艘“移动中的太空飞船，其矢速为u，该变换就是：
(17.1)
让我们把这些方程，与方程（11.5）相比较，它也是与两个系统中的测量值有关，在此例中，其中一个，相对于另一个，有一个旋转，即：
x′=xcosθ + y sinθ,
y′=ycosθ − xsinθ, (17.2)
z′=z
在这个具体的案例中，Moe 的x轴，与Joe的x′ 轴之间的夹角，是θ。在每个案例中，我们都注意到，“原始的”量，都是“非原始的”量的混合：新的x′，是x和y的混合，新的 y′，也是x和 y 的混合。

An analogy is useful: When we look at anobject, there is an obvious thing we might call the “apparent width,” andanother we might call the “depth.” But the two ideas, width and depth, are not fundamentalproperties of the object, because if we step aside and look at the same thingfrom a different angle, we get a different width and a different depth, and wemay develop some formulas for computing the new ones from the old ones and theangles involved. Equations (17.2)are these formulas. One might say that a given depth is a kind of “mixture” ofall depth and all width. If it were impossible ever to move, and we always sawa given object from the same position, then this whole business would beirrelevant—we would always see the “true” width and the “true” depth, and theywould appear to have quite different qualities, because one appears as asubtended optical angle and the other involves some focusing of the eyes or evenintuition; they would seem to be very different things and would never getmixed up. It is because we can walk around that we realize that depthand width are, somehow or other, just two different aspects of the same thing.
做个类比，还是有用的：当我们观看一个对象时，有一个明显的事情，我们可称之为“明显的宽度”，另外一个，我们可以称之为“深度”。但是，这两个想法，即宽度和深度，并不是对象的基本属性，因为，如果我们走到一旁，从一个不同的角度，来看此同一事物，我们就会得到不同的宽度和深度，且我们可以开发出一些公式，以用老的值，来计算新的值，这里也会牵扯到角度。方程组（17.2）就是这些公式。有人可能会说，一个被给予的深度，就是所有深度和宽度的“混合”。如果移动{观察者的}，永远都是不可能的，且我们总是从同一个位置，来看被给予的对象，那么，此整个事情，就是不相关的--我们总是会看到“真正的”宽度和“真正的”深度，且它们将显现出，具有不同的特性，因为，一个特性，可能会显现出，是作为对着的光学的角度，而另一个特性，则会牵扯到某些眼睛的聚焦、甚至直观；它们似乎是完全不同的事物，永远也不会混在一起。正是因为我们可移步他处，我们才能意识到，深度和宽度，在某种意义上，只是同一事物的两个不同的方面。
{另外一种盲人摸象？}

Can we not look at the Lorentztransformations in the same way? Here also we havea mixture—of positions and the time. A difference between a space measurementand a time measurement produces a new space measurement. In other words, in thespace measurements of one man there is mixed in a little bit of the time, as seenby the other. Our analogy permits us to generate this idea: The “reality” of anobject that we are looking at is somehow greater (speaking crudely andintuitively) than its “width” and its “depth” because they depend upon howwe look at it; when we move to a new position, our brain immediatelyrecalculates the width and the depth. But our brain does not immediatelyrecalculate coordinates and time when we move at high speed, because we have hadno effective experience of going nearly as fast as light to appreciate the factthat time and space are also of the same nature. It is as though we were alwaysstuck in the position of having to look at just the width of something, notbeing able to move our heads appreciably one way or the other; if we could, we understandnow, we would see some of the other man’s time—we would see “behind,” so tospeak, a little bit.
难道，我们不能以同样的方式，来看洛伦兹变换？这里，我们也有一个混合，一个位置与时间的混合。位置测量与时间测量之间的区别，产生了新的空间测量。换句话说，在一个人对空间的测量中，在其他人看来，混有一点点时间。我们的类比，允许我们产生这样的想法：对于我们正在看着的对象，其“真实性”，从某种意义上说，要大于（照自然原状地和直观地）其“宽度”和“深度”，因为，它们依赖于我们如何看它；当我们移到一个新的位置时，我们的大脑，就立刻开始重新计算宽度和深度。但是，当我们高速移动时，我们的大脑，并不立刻重新计算坐标和时间，因为，我们并没有像光速走得那样块的实际经验，以能感觉到以下事实：空间和时间是同样的性质。情况好像是这样，即我们总是被困在一个位置，只能去看某物的宽度，而不能把我们的脑袋，明显地往这边或那边移动{？}；如果我们可以的话，我们现在就可以理解，我们能够看到其他人的时间--这么说吧，我们可以看到一点点“后面的”时间。{？}

Thus we shall try to think of objects in anew kind of world, of space and time mixed together, in the same sense that theobjects in our ordinary space-world are real, and can be looked at fromdifferent directions. We shall then consider that objects occupying space andlasting for a certain length of time occupy a kind of a “blob” in a new kind ofworld, and that we look at this “blob” from different points of view when we aremoving at different velocities. This new world, this geometrical entity inwhich the “blobs” exist by occupying position and taking up a certain amount oftime, is called space-time. A given point (x,y,z,t)in space-time is called an event. Imagine, for example, that weplot the x -positions horizontally, y and z in two other directions, both mutually at “right angles” and at “rightangles” to the paper (!), and time, vertically. Now, how does a movingparticle, say, look on such a diagram? If the particle is standing still, thenit has a certain x , and as time goes on, it has the same x , the same x , the same x ; so its “path” is a line that runs parallel to the t -axis (Fig. 17–1 a).（图17-1a）On the other hand, if itdrifts outward, then as the time goes on x increases (Fig. 17–1 b). Soa particle, for example, which starts to drift out and then slows up shouldhave a motion something like that shown in Fig. 17–1(c). Aparticle, in other words, which is permanent and does not disintegrate isrepresented by a line in space-time. A particle which disintegrates would berepresented by a forked line, because it would turn into two other things whichwould start from that point.
这样，就有了某种新的世界，空间和时间混在一起，我们将在这个新的世界中，尝试以同样的意义，来思考对象；此同样的意义，是指对象在我们普通的空间世界，是真实的，且能够从不同的方向，被观看。有些对象，占据了空间，在时间上也延续了一段长度，这些对象，在新的世界中，成为了某种“一团”，对于这些对象，当我们以不同的矢速运动时，就是从不同的观点，来考虑它们。这个新的世界，是一个几何实体，其中，“一团”，是通过占据位置和一定量的时间，来存在，故此新世界，被称为空间-时间。空间中一个被给予的点point (x,y,z,t)，被称为一个事件。例如，想象我们水平地画x位置，而y和z在另外两个方向，且都是在直角方向，且与纸张（！）和时间垂直。现在，一个运动的粒子，在这样一种示意图上，看上去应该是什么样？如果粒子站着不动，那么，它就有一个确定的x，随着时间的推移，它的x是一样的，一直一样；于是，其“路径”就是一条与t轴平行的线。另一方面，如果它向外漂移，那么，随着时间，x将增加（图17-1b）。例如，一个粒子，开始时，向外漂移，然后变慢，那么其运动，将如图17-1（c）所示。换句话说，一个粒子，如果是永久的且没有分裂，那么，它就会被空间中的一条线来表示。如果一个粒子分裂了，将被一个分叉线表示，因为它变成了两个其他事物，这两个事物，将从那个点开始{其自己的轨迹}。

Fig. 17–1.Three particle paths in space-time:(a) a particle at rest at x=x0 ; (b) a particle which starts at x=x0and moves with constant speed; (c) a particle which starts athigh speed but slows down; (d) a light path. 图7-1 空间中三个粒子的路径：（a）一个在x=x0处静止的粒子；（b）一个初始位置在x=x0，以恒速运动的粒子；（c）一个开始时高速，然后变慢的粒子；（d）一个光的路径。

What about light? Light travels at thespeed c , and that would be represented by a line having a certain fixed slope(Fig. 17–1d).
那么光呢？光以速度c在走，它会被一条直线代表，此线斜率，是固定的（图17-1d）。

Now according to our new idea, if a givenevent occurs to a particle, say if it suddenly disintegrates at a certainspace-time point into two new ones which follow some new tracks, and thisinteresting event occurred at a certain value of x and a certain value of t , then we would expect that, if this makes any sense, we just have totake a new pair of axes and turn them, and that will give us the new tand the new x in our new system, as shown in Fig. 17–2(a).But this is wrong, because Eq. (17.1)is not exactly the same mathematical transformation as Eq. (17.2).Note, for example, the difference in sign between the two, and the fact thatone is written in terms of cosθ and sinθ , while the other is written with algebraic quantities. (Of course, itis not impossible that the algebraic quantities could be written as cosine andsine, but actually they cannot.) But still, the two expressions are verysimilar. As we shall see, it is not really possible to think of space-time as areal, ordinary geometry because of that difference in sign. In fact, althoughwe shall not emphasize this point, it turns out that a man who is moving has touse a set of axes which are inclined equally to the light ray, using a specialkind of projection parallel to the x′ - and t′ -axes, for his x′ and t′ , as shown in Fig. 17–2(b).We shall not deal with the geometry, since it does not help much; it is easierto work with the equations.
现在，依据我们新的想法，如果一个粒子，发生了给定的事件，亦即，如果在某确定的空间-时间点上，它突然分裂成两个新的粒子，这两新粒子，各有其新的轨道，这个有趣的事件，发生在某确定的x值和确定的t值上，因此，我们就期望一件事，如果此事有什么意义的话，即我们只需取一对新的轴，并旋转它们，这样，将在新的系统中，给我们新的t和新的x，如图17-2（a）所示。但这是错的，因为方程（17.1）并不是像方程（17.2）那样，是完全的数学转换。例如，注意两组方程之间的符号差异，及如下事实：一个是用cosθ和sinθ来描述，而另一个，是用代数的量。（当然，代数的量，被写成cosθ和sinθ，并非不可能，但实际上不行）。但尽管如此，这两组表达式，还是非常类似。正如我们将看到，把空间-时间，思考为真正的、通常的几何图形，实际上是不可能的，这是因为那个符号的区别。事实上，虽然我们将强调这一点，但结果则是，一个运动中的人，必须利用一组轴，对于他的x′ 和 t′，这些轴，用一种特殊的平行于x′ 轴和 t′ 轴的投影，平等地倾斜于光线，如图17-2（b）所示。我们将不处理几何图形，由于它们，帮助不大；而只与方程打交道，这样更容易些。

Fig. 17–2.Two views of a disintegratingparticle. 图17-2 分裂中的粒子的两个视图。

17–2Space-time intervals 17-2 空间-时间的间隔
Although the geometry of space-time is notEuclidean in the ordinary sense, there is a geometry which is verysimilar, but peculiar in certain respects. If this idea of geometry is right,there ought to be some functions of coordinates and time which are independentof the coordinate system. For example, under ordinary rotations, if we take twopoints, one at the origin, for simplicity, and the other one somewhere else, bothsystems would have the same origin, and the distance from here to the otherpoint is the same in both. That is one property that is independent of theparticular way of measuring it. The square of the distance is x2+y2+z2. Now what about space-time? It is not hard to demonstrate that wehave here, also, something which stays the same, namely, the combination c2t2−x2−y2−z2is the same before and after the transformation:
c2t′2−x′2−y′2−z′2=c2t2−x2−y2−z2. (17.3)
This quantity is therefore something which, like the distance, is “real”in some sense; it is called the interval between the two space-timepoints, one of which is, in this case, at the origin. (Actually, of course, itis the interval squared, just as x2+y2+z2is the distance squared.) We give it a different name because it is ina different geometry, but the interesting thing is only that some signs are reversedand there is a c in it.
虽然空间-时间的几何，不是常规意义上的欧几里德的几何，而是，有一种非常类似的几何，在某些具体的方面，非常特别。如果关于这个几何的想法，是正确的，那么，就应该有一些关于坐标和时间的函数，它们是独立于坐标系统的。例如，在通常的旋转中，如果我们取两个点，为了简单，一个在原点，另外一个在其他地方，且两个系统，原点同样，那么，在两个系统中，两点间的距离，就是一样的。这个属性，独立于具体测量它的方法。距离的平方就是x2+y2+z2。现在，空间-时间中又如何呢？在这里，有些东西，同样保持不变，演证它们，并不困难，比如组合c2t2−x2−y2−z2，在变换前后，是一样的：
c2t′2−x′2−y′2−z′2=c2t2−x2−y2−z2. (17.3)
因此，这个量，在某种意义上，就像距离一样，是“真实的”，它被称为：两个空间-时间中的点之间的间隔{ interval }，在这个案例中，一个点，在原点（实际上，它当然是间隔的平方，正如x2+y2+z2是距离的平方一样）因为，它是在一种不同的几何中，所以，我们给它了一个不同的名字，但有趣的事情则是，只是一些符号相反了，及有一个c在其中。

Let us get rid of the c ; that is an absurdity if we are going to have a wonderful space with x’s and y ’s that can be interchanged. One of the confusions that could becaused by someone with no experience would be to measure widths, say, by theangle subtended at the eye, and measure depth in a different way, like thestrain on the muscles needed to focus them, so that the depths would bemeasured in feet and the widths in meters. Then one would get an enormouslycomplicated mess of equations in making transformations such as (17.2),and would not be able to see the clarity and simplicity of the thing for a verysimple technical reason, that the same thing is being measured in two differentunits. Now in Eqs. (17.1)and (17.3)nature is telling us that time and space are equivalent; time becomes space; theyshould be measured in the same units. What distance is a “second”? It iseasy to figure out from (17.3)what it is. It is 3×108 meters, the distance that light would go in one second.In other words, if we were to measure all distances and times in the sameunits, seconds, then our unit of distance would be 3×108 meters, and the equations would be simpler. Or another way thatwe could make the units equal is to measure time in meters. What is a meter oftime? A meter of time is the time it takes for light to go one meter, and istherefore 1/3×10−8 sec, or 3.3 billionths of a second! We would like, in other words, to putall our equations in a system of units in which c=1 . If time and space are measured in the same units, as suggested, thenthe equations are obviously much simplified. They are
(17.4)
t′2−x′2−y′2−z′2=t2−x2−y2−z2. (17.5)
If we are ever unsure or “frightened” that after we have this systemwith c=1 we shall never be able to get our equations right again, the answer isquite the opposite. It is much easier to remember them without the c’s in them, and it is always easy to put the c ’s back, by looking after the dimensions. For instance, in (1−u2)1/2, we know that we cannot subtract a velocity squared, which has units,from the pure number 1 , so we know that we must divide u2 by c2 in order to make that unitless, and that is the way it goes.
让我们抛弃 c；如果我们要有一个奇妙的空间，在其中，x ’和 y ’们，可以交换，那么，这就是荒谬的。没有经验的人，能引起的困惑之一，比如就是，通过眼睛对着的角度，来测量宽度，而以不同的方法来测量深度，如肌肉上的张力，需要聚焦于它们，这样，深度就可用英尺来测量，而宽度就可用米来测量。{？}因此，人们在做诸如（17.2）的变换时，就可以得到巨大复杂的方程，很混乱，由于某个非常简单的技术原因，将不会看到事情的清晰性和简单性，即同样的事情，正在被用两个不同的单位测量。现在，在方程（17.1）和（17.3）中，自然正在告诉我们，时间和空间，是等价的；时间变成空间；它们应该用同样的单位来测量。什么样的距离是一“秒”呢？从（17.3），很容易弄清楚，它是什么。它是3×108米，光在一秒中所走的距离。换句话说，如果我们要用同样的单位秒，来测量距离和时间，那么，我们距离的单位就是3×108米，则方程组将更简单。或者，另一种方式，我们可以让单位相等，是用米来测量时间。什么是一米的时间呢？一米的时间，就是光在一秒中所走的时间，因此，就是1/3×10−8 sec，或者三十三亿分之一秒！换句话说，我们将把所有的方程组，放进一个单位的系统中，在其中 c=1。如果时间和空间，按上面所建议，是用同样的单位来测量，那么，方程组将会明显被简化。它们就是：
(17.4)
t′2−x′2−y′2−z′2=t2−x2−y2−z2. (17.5)
在我们有了这个系统c=1之后，我们是否将永远不能得到正确的方程了，对此，如果我们无法保证或“被吓到了”，那么，答案恰是完全相反。没有c们在里面，记忆方程，会更容易，把c们放回去，也总是很容易，通过寻找维度就行。例如，在 (1−u2)1/2中，我们知道，我们不能从纯粹数1中，减去一个矢速的平方，矢速是有单位的，所以，我们就知道了，我们必须用u2除以c2，以让它变得没有单位，做法就是这样。

The difference between space-time andordinary space, and the character of an interval as related to the distance, isvery interesting. According to formula (17.5),if we consider a point which in a given coordinate system had zero time, and onlyspace, then the interval squared would be negative and we would have animaginary interval, the square root of a negative number. Intervals can beeither real or imaginary in the theory. The square of an interval may be eitherpositive or negative, unlike distance, which has a positive square. When aninterval is imaginary, we say that the two points have a space-like intervalbetween them (instead of imaginary), because the interval is more like spacethan like time. On the other hand, if two objects are at the same place in agiven coordinate system, but differ only in time, then the square of the timeis positive and the distances are zero and the interval squared is positive;this is called a time-like interval. In our diagram of space-time, therefore,we would have a representation something like this: at 45∘ there are two lines (actually, in four dimensions these will be“cones,” called light cones) and points on these lines are all at zero intervalfrom the origin. Where light goes from a given point is always separated fromit by a zero interval, as we see from Eq. (17.5).Incidentally, we have just proved that if light travels with speed cin one system, it travels with speed c in another, for if the interval is the same in both systems, i.e.,zero in one and zero in the other, then to state that the propagation speed oflight is invariant is the same as saying that the interval is zero.
下面两点，都很有趣，一、空间-时间，与普通空间的差别；二、间隔的一个特性，与距离有关。依据公式（17.5），如果我们考虑一个点，它在一个被给予的坐标系中，有零时间，且只有空间，那么，间隔的平方，将是负的，我们将有一个虚间隔（虚数的间隔），要对一个负数，求平方根。理论上，间隔既可以是实数，也可以使虚数。间隔的平方，既可以是正的，也可以是负数，而不像距离，其平方总为正。当间隔是虚数时，我们说，这两个点之间，有一种类空间隔（而不是虚数的），因为此间隔，更像空间，而不是更像时间。另一方面，如果在一个被给予的坐标系中，两个对象，在同一个地点，但是，只是在时间上有差别，那么，这个时间的平方就是正的，而距离就是零，且间隔的平方就是正的；这被称为类时间间隔。因此，在我们空间-时间的示意图中，我们将有一个代表，它就是类似这样的一个东西：在45度方向，有两条线（实际上，在四维中，这些将是“圆锥”，被称为光锥），这些线上的点，与原点都是零间隔。在这里，从一个被给予的点所走出的光，总是被零间隔，把它分割开来，正如我们在方程（17.5）所见{？}。顺便说一句，我们已经证明了，如果在一个系统里，光以速度c在走，那么，在另一个系统中，它也是以速度c在走，因为，如果在两个系统中，间隔是同样的，也就是说，在一个里面是零，在另一个里面也是零，那么，说‘光速的扩展是不变的’，就与说‘间隔是零’，是一样的。

17–3Past, present, and future 17-3 过去、现在和将来

Fig. 17–3.The space-time region surroundinga point at the origin. 图17-3 一个点，在原点处，绕着该点的空间-时间区域
The space-time region surrounding a givenspace-time point can be separated into three regions, as shown in Fig. 17–3. Inone region we have space-like intervals, and in two regions, time-likeintervals. Physically, these three regions into which space-time around a givenpoint is divided have an interesting physical relationship to that point: aphysical object or a signal can get from a point in region 2 to the event O by moving along at a speed less than the speed of light. Thereforeevents in this region can affect the point O , can have an influence on it from the past. In fact, of course, an objectat P on the negative t -axis is precisely in the “past” with respect to O ; it is the same space-point as O , only earlier. What happened there then, affects O now. (Unfortunately, that is the way life is.) Another object at Qcan get to O by moving with a certain speed less than c , so if this object were in a space ship and moving, it would be,again, the past of the same space-point. That is, in another coordinate system,the axis of time might go through both O and Q . So all points of region 2 are in the “past” of O , and anything that happens in this region can affect O. Therefore region 2 is sometimes called the affective past, or affecting past; itis the locus of all events which can affect point O in any way.
在空间-时间中，给定一点，绕着该点的空间-时间区域，可被分成三个部分，如图17-3所示。在一个区域中，我们有类空间隔，在两个区域中，有类时间间隔。物理上讲，这三个区域，是空间-时间绕着一个给定点，划分而成的，它们与那个点，有一种有趣的物理关系：一个物理对象或一个信号，可以从区域2中的一个点，通过以慢于光速的速度移动，而到达事件O。因此，在这个区域的事件，可以影响点 O，可以从过去，对它产生影响。当然，事实上，在负的t轴上、点P处的一个对象， 相对于O来说，就是精确地“过去”；它作为O，是同一个空间点，只是更早些罢了。那么，那里究竟发生了什么呢,影响到现在的O。（很不幸，生活的方式，就是这样。）在Q的另外一个对象，可以通过一个小于光速的确定速度运动，到达O，于是，如果这个对象，是在一艘太空飞船中运动，那么，就将又是：同样的空间点的过去{存在}。也就是说，在另一坐标系中，时间轴可能从O和 Q中都通过。于是，区域2中的所有点，都在O的“过去”中，且这个区域所发生的任何事，都能影响O。因此，区域2，有时就被称为有效的过去，或正影响着过去；它就是所有‘能以任何方式影响点O的事件’的中心。

Region 3 , on the other hand, is a region which we can affect from O, we can “hit” things by shooting “bullets” out at speeds lessthan c . So this is the world whose future can be affected by us, and we maycall that the affective future. Now the interesting thing about all therest of space-time, i.e., region 1 , is that we can neither affect it now from O , nor can it affect us now at O , because nothing can go faster than the speed of light. Of course,what happens at R can affect us later; that is, if the sun is exploding“right now,” it takes eight minutes before we know about it, and it cannot possiblyaffect us before then.
另一方面，对于区域3，我们可以从O来影响它，我们可以发射速度低于c的“子弹”，来“击打”事物。所以，我们可以影响这个世界的未来，我们可称其为感情的未来。现在，对于所有剩下的空间-时间、亦即区域1，关于它的有趣事情就是，我们即不能现在、从O来影响它，它也不能现在、早O处，影响我们，因为，没有什么，能比光速更快。当然，在R处发生的事情，可以在稍后，影响我们，也就是说，如果太阳“现在”爆炸，我们需要八分钟，才能知道，在此之前，它不可能影响我们。

What we mean by “right now” is a mysteriousthing which we cannot define and we cannot affect, but it can affect us later,or we could have affected it if we had done something far enough in the past. Whenwe look at the star Alpha Centauri, we see it as it was four years ago; wemight wonder what it is like “now.” “Now” means at the same time from our specialcoordinate system. We can only see Alpha Centauri by the light that has comefrom our past, up to four years ago, but we do not know what it is doing “now”;it will take four years before what it is doing “now” can affect us. Alpha Centauri“now” is an idea or concept of our mind; it is not something that is reallydefinable physically at the moment, because we have to wait to observe it; wecannot even define it right “now.” Furthermore, the “now” depends on thecoordinate system. If, for example, Alpha Centauri were moving, an observerthere would not agree with us because he would put his axes at an angle, andhis “now” would be a different time. We have already talked about thefact that simultaneity is not a unique thing.
我们说“立即现在”的意思就是，对于一个神秘的事物，我们不能定义它，也不能影响它，但是，它以后可以影响我们，或者，如果我们在足够远的过去，做过某事，那么，我们就可能已经影响它了。当我们看恒星阿尔法半人马座时，我们看到的，是四年前的它；我们可能想知道，它“现在”如何。“现在”意味着，与我们特定的坐标系的时间相同的时间。我们看到的阿尔法半人马座，是从我们的过去、大约四年前，发出的光，但是，我们并不知道它“现在”在做什么；它“现在”正在做的，要四年后，才能影响我们。阿尔法半人马座，“现在”只是我们心里的一个想法或概念；它并不是一个当前就能真正物理定义的东西，因为，要观察它，我们要等待；我们甚至都不能立即“现在”就定义它。另外，“现在”还依赖于坐标系。例如，如果阿尔法半人马座过去在运动，那里的一个观察者，不会与我们一致，因为，他可以让他的轴，有一个角度，那么，他的“现在”，就将是一个不同的时间。我们已经探讨了如下事实：同时性并不是一个独一无二的事物。