14–4 Nonconservative forces 14-4 非保守力
We have spent a considerable timediscussing conservative forces; what about nonconservative forces? We shalltake a deeper view of this than is usual, and state that there are nononconservative forces! As a matter of fact, all the fundamental forces innature appear to be conservative. This is not a consequence of Newton’s laws.In fact, so far as Newton himself knew, the forces could be nonconservative, asfriction apparently is. When we say friction apparently is, we aretaking a modern view, in which it has been discovered that all the deep forces,the forces between the particles at the most fundamental level, areconservative.
我們討論保守力，所花時間，相當可觀，那麼，非保守力如何呢？我們將對它，做一個比通常更深入的視察，然後聲明：沒有非保守力！作為一種事實情況，自然中所有基礎力的表現，都是保守性的。這不是牛頓規律的後果。事實上，就牛頓本人所知，力可以是非保守的，如摩擦力，顯然就是。當我們說摩擦力，明顯就是的時候，我們是用了一個現代的視角，在其中，已經發現，所有深的力，如在最基礎層面的粒子之間的力，是保守的。
If, for example, we analyze a system likethat great globular star cluster that we saw a picture of, with the thousands ofstars all interacting, then the formula for the total potential energy is simplyone term plus another term, etc., summed over all pairs of stars, and the kineticenergy is the sum of the kinetic energies of all the individual stars. But theglobular cluster as a whole is drifting in space too, and, if we were farenough away from it and did not see the details, could be thought of as asingle object. Then if forces were applied to it, some of those forces mightend up driving it forward as a whole, and we would see the center of the wholething moving. On the other hand, some of the forces can be, so to speak, 「wasted」in increasing the kinetic or potential energy of the 「particles」 inside. Let ussuppose, for instance, that the action of these forces expands the wholecluster and makes the particles move faster. The total energy of the wholething is really conserved, but seen from the outside with our crude eyes whichcannot see the confusion of motions inside, and just thinking of the kineticenergy of the motion of the whole object as though it were a single particle,it would appear that energy is not conserved, but this is due to a lack ofappreciation of what it is that we see. And that, it turns out, is the case:the total energy of the world, kinetic plus potential, is a constant when welook closely enough.
例如，如果我們分析一個系統，比如巨大的球形星簇--我們通過照片看到的那種，它由上千個交互作用的恆星組成，那麼，其總勢能的公式，簡單說就是：一個恆星對的勢能，加上另外一個的，如此等等，遍歷所有的恆星對，而動能，就是所有個別恆星動能的總和。但是，球形星簇，也是作為一個整體，漂在空中，如果我們離它足夠遠，看不清細節，那麼，它就可以被思考為一個單獨的對象。因此，如果有力，作用於它，那麼，這些力的一部分，可能會用來驅動它，作為一個整體，向前移動，那麼，我們就可以看到，整個星簇的中心，在移動。另一方面，力的另外一部分，這麼說吧，可能被「浪費了」，因為它們增加了內部某些粒子的動能和勢能。例如，讓我們假設，這些力的作用，可以擴展到整個星簇，讓粒子移動地更快。整個事物的總能量，確實是保守的，但是，我們的裸眼，看不到內部混亂運動，用我們的裸眼，從外面看，只能把整個對象，當作一個單獨的粒子，從而會想，其運動的動能，似乎是不保守的，但是，這要歸於，我們並不了解我們所看到的東西。結果就是：對於這個世界，當我們足夠近地觀察它時，其總能量，即動能加勢能，是一個常數。
When we study matter in the finest detailat the atomic level, it is not always easy to separate the total energyof a thing into two parts, kinetic energy and potential energy, and such separationis not always necessary. It is almost always possible to do it, so letus say that it is always possible, and that the potential-plus-kinetic energyof the world is constant. Thus the total potential-plus-kinetic energy insidethe whole world is constant, and if the 「world」 is a piece of isolated material,the energy is constant if there are no external forces. But as we have seen,some of the kinetic and potential energy of a thing may be internal, forinstance the internal molecular motions, in the sense that we do not notice it.We know that in a glass of water everything is jiggling around, all the parts aremoving all the time, so there is a certain kinetic energy inside, which weordinarily may not pay any attention to. We do not notice the motion of theatoms, which produces heat, and so we do not call it kinetic energy, but heatis primarily kinetic energy. Internal potential energy may also be in the form,for instance, of chemical energy: when we burn gasoline energy is liberatedbecause the potential energies of the atoms in the new atomic arrangement arelower than in the old arrangement. It is not strictly possible to treat heat asbeing pure kinetic energy, for a little of the potential gets in, and viceversa for chemical energy, so we put the two together and say that the totalkinetic and potential energy inside an object is partly heat, partly chemicalenergy, and so on. Anyway, all these different forms of internal energy aresometimes considered as 「lost」 energy in the sense described above; this willbe made clearer when we study thermodynamics.
對於物質，當我們在原子層這一最詳細的部分，來研究它時，把總的能量分成兩部分，即動能和勢能，並不總是很容易，且這種分開，並非總是必要的。做這種區分，幾乎總是可能的，所以，讓我們說，這總是可能的，且世界的勢能加動能，是一個常數。這樣，在一個整體世界的內部，總的勢能加動能，是一個常數，如果此「世界」，是一個孤立體，那麼，如果沒有外部力的話，能量就是常數。但是，正如我們看到的，一個事物的某些動能和勢能，可能是內部的，例如內部分子的運動，這種意義，我們並沒有注意到。我們知道，在一杯水中，所有東西都在搖動，所有的部分，都一直在運動，所以，其內部就有一定的動能，對此，我們通常並未注意。我們並未注意到原子的運動，它會產生熱，所以，我們並沒有把它稱為動能，但熱主要是動能。再例如，內部勢能，也可以化學能的形式存在，當我們燃燒汽油時，能量就被釋放，因為，原子的勢能，在新原子中的排列，比在舊原子中的排列，要低。把熱當做純粹的動能來對待，並不是嚴格意義上可能的，因為一些勢能會進來，對化學能也如此，所以，我們把這兩個放在一起，說一個對象中的總的動能和勢能，部分是熱能，部分是化學能等。總之，所有這些內部能量的不同形式，有時，按照上面所描述的意義，而被考慮為「消失了」的能量；這一點，當我們研究熱力學時，就會更清楚了。
As another example, when friction is presentit is not true that kinetic energy is lost, even though a sliding object stopsand the kinetic energy seems to be lost. The kinetic energy is not lostbecause, of course, the atoms inside are jiggling with a greater amount ofkinetic energy than before, and although we cannot see that, we can measure itby determining the temperature. Of course if we disregard the heat energy, thenthe conservation of energy theorem will appear to be false.
作為另一個例子，當摩擦力在場時，動能消失了這種說法，並不正確，儘管一個滑動對象停止了，且動能似乎消失了。動能沒有消失，當然是因為，內部原子，正在用比以前更大的動能，在搖動，雖然我們看不到，但我們可以通過測溫，來計量它。當然，如果我們忽視熱能，那麼，能量守恆原理，似乎就是錯的。
Another situation in which energy conservationappears to be false is when we study only part of a system. Naturally, theconservation of energy theorem will appear not to be true if something is interactingwith something else on the outside and we neglect to take that interaction intoaccount.
還有一種情況，在其中，能量守恆看上去是錯的，這是因為我們研究的，只是系統的一部分。如果外部有某物與某物交互作用，而我們卻沒有把這種交互計算在內，那麼自然，能量守恆原理，看上去就不正確。
In classical physics potential energyinvolved only gravitation and electricity, but now we have nuclear energy andother energies also. Light, for example, would involve a new form of energy inthe classical theory, but we can also, if we want to, imagine that the energyof light is the kinetic energy of a photon, and then our formula (14.2)would still be right.
在經典物理學中，勢能只包含萬有引力和電力，但現在，我們又有了原子能和其他能量。但是，如果我們想的話，我們也能夠想像，光能是光子的動能，那麼，公式（14.2），就仍正確，那麼，在經典理論中，光就將包含一種新的能量形式。