《费曼物理学讲义》笔记讲课稿
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2Basic Physics2–1IntroductionIn this chapter, we shall examine the most fundamental ideas that we have about physics—the nature of things as we see them at the present time. We shall not discuss the history of how we know that all these ideas are true; you will learn these details in due time.The things with which we concern ourselves in science appear in myriad forms, and with a multitude of attributes. For example, if we stand on the shore and look at the sea, we see the water, the waves breaking, the foam, the sloshing motion of the water, the sound, the air, the winds and the clouds, the sun and the blue sky, and light; there is sand and there are rocks of various hardness and permanence, color and texture. There are animals and seaweed, hunger and disease, and the observer on the beach; there may be even happiness and thought. Any other spot in nature has a similar variety of things and influences. It is always as complicated as that, no matter where it is. Curiosity demands that we ask questions, that we try to put things together and try to understand this multitude of aspects as perhaps resulting from the action of a relatively small number of elemental things and forces acting in an infinite variety of combinations.For example: Is the sand other than the rocks? That is, is the sand perhaps nothing but a great number of very tiny stones? Is the moon a great rock? If we understood rocks, would we also understand the sand and the moon? Is the wind a sloshing of the air analogous to the sloshing motion of the water in the sea? What common features do different movements have? What is common to different kinds of sound? How many different colors are there? And so on. In this way we try gradually to analyze all things, to put together things which at first sight look different, with the hope that we may be able to reduce the number of different things and thereby understand them better.A few hundred years ago, a method was devised to find partial answers to such questions. Observation, reason, and experiment make up what we call the scientific method. We shall have to limit ourselves to a bare description of our basic view of what is sometimes called fundamental physics, or fundamental ideas which have arisen from the application of the scientific method.What do we mean by ―understanding‖ something? We can imagine that this complicated array of moving things which constitutes ―the world‖ is something like a great chess game being played by the gods, and we are observers of the game. We do not know what the rules of the game are; all we are allowed to do is to watch the playing. Of course, if we watch long enough, we may eventually catch on to a few of the rules. The rules of the game are what we mean by fundamental physics. Even if we knew every rule, however, we might not be able to understand why a particular move is made in the game, merely because it is too complicated and our minds are limited. If you play chess you must know that it is easy to learn all the rules, and yet it is often very hard to select the best move or to understand why a player moves as he does. Soit is in nature, only much more so; but we may be able at least to find all the rules. Actually, we do not have all the rules now. (Every once in a while something like castling is going on that we still do not understand.) Aside from not knowing all of the rules, what we really can explain in terms of those rules is very limited, because almost all situations are so enormously complicated that we cannot follow the plays of the game using the rules, much less tell what is going to happen next. We must, therefore, limit ourselves to the more basic question of the rules of the game. If we know the rules, we consider that we ―understand‖ the world.How can we tell whether the rules which we ―guess‖ at are really right if we cannot analyze the game very well? There are, roughly speaking, three ways. First, there may be situations where nature has arranged, or we arrange nature, to be simple and to have so few parts that we can predict exactly what will happen, and thus we can check how our rules work. (In one corner of the board there may be only a few chess pieces at work, and that we can figure out exactly.)A second good way to check rules is in terms of less specific rules derived from them. For example, the rule on the move of a bishop on a chessboard is that it moves only on the diagonal. One can deduce, no matter how many moves may be made, that a certain bishop will always be on a red square. So, without being able to follow the details, we c an always check our idea about the bishop’s motion by finding out whether it is always on a red square. Of course it will be, for a long time, until all of a sudden we find that it is on a black square (what happened of course, is that in the meantime it was captured, another pawn crossed for queening, and it turned into a bishop on a black square). That is the way it is in physics. For a long time we will have a rule that works excellently in an over-all way, even when we cannot follow the details, and then some time we may discover a new rule. From the point of view of basic physics, the most interesting phenomena are of course in the new places, the places where the rules do not work—not the places where they do work! That is the way in which we discover new rules.The third way to tell whether our ideas are right is relatively crude but probably the most powerful of them all. That is, by rough approximation. While we may not be able to tell why Alekhine moves this particular piece, perhaps we can roughly understand that he is gathering his pieces around the king to protect it, more or less, since that is the sensible thing to do in the circumstances. In the same way, we can often understand nature, more or less, without being able to see what every little piece is doing, in terms of our understanding of the game.At first the phenomena of nature were roughly divided into classes, like heat, electricity, mechanics, magnetism, properties of substances, chemical phenomena, light or optics, x-rays, nuclear physics, gravitation, meson phenomena, etc. However, the aim is to see complete nature as different aspects of one set of phenomena. That is the problem in basic theoretical physics, today—to find the laws behind experiment; to amalgamate these classes. Historically, we have always been able to amalgamate them, but as time goes on new things are found. We were amalgamating very well, when all of a sudden x-rays were found. Then we amalgamated some more, and mesons were found. Therefore, at any stage of the game, it always looks rathermessy. A great deal is amalgamated, but there are always many wires or threads hanging out in all directions. That is the situation today, which we shall try to describe.Some historic examples of amalgamation are the following. First, take heat and mechanics. When atoms are in motion, the more motion, the more heat the system contains, and so heat and all temperature effects can be represented by the laws of mechanics. Another tremendous amalgamation was the discovery of the relation between electricity, magnetism, and light, which were found to be different aspects of the same thing, which we call today the electromagnetic field. Another amalgamation is the unification of chemical phenomena, the various properties of various substances, and the behavior of atomic particles, which is in the quantum mechanics of chemistry.The question is, of course, is it going to be possible to amalgamate everything, and merely discover that this world represents different aspects of one thing? Nobody knows. All we know is that as we go along, we find that we can amalgamate pieces, and then we find some pieces that do not fit, and we keep trying to put the jigsaw puzzle together. Whether there are a finite number of pieces, and whether there is even a border to the puzzle, is of course unknown. It will never be known until we finish the picture, if ever. What we wish to do here is to see to what extent this amalgamation process has gone on, and what the situation is at present, in understanding basic phenomena in terms of the smallest set of principles. To express it in a simple manner, what are things made of and how few elements are there?2–2Physics before 1920It is a little difficult to begin at once with the present view, so we shall first see how things looked in about 1920 and then take a few things out of that picture. Before 1920, our world picture was something like this: The ―stage‖ on which the universe goes is the three-dimensional space of geometry, as described by Euclid, and things change in a medium called time. The elements on the stage are particles, for example the atoms, which have some properties. First, the property of inertia: if a particle is moving it keeps on going in the same direction unless forces act upon it. The second element, then, is forces, which were then thought to be of two varieties: First, an enormously complicated, detailed kind of interaction force which held the various atoms in different combinations in a complicated way, which determined whether salt would dissolve faster or slower when we raise the temperature. The other force that was known was a long-range interaction—a smooth and quiet attraction—which varied inversely as the square of the distance, and was called gravitation. This law was known and was very simple. Why things remain in motion when they are moving, or why there is a law of gravitation was, of course, not known.A description of nature is what we are concerned with here. From this point of view, then, a gas, and indeed all matter, is a myriad of moving particles. Thus many of the things we saw while standing at the seashore can immediately be connected. First the pressure: this comes from the collisions of the atoms with the walls or whatever; the drift of the atoms, if they are all moving in one direction on the average, is wind; the random internal motions are the heat. There are waves of excess density,where too many particles have collected, and so as they rush off they push up piles of particles farther out, and so on. This wave of excess density is sound. It is a tremendous achievement to be able to understand so much. Some of these things were described in the previous chapter.What kinds of particles are there? There were considered to be 92 at thattime: 92 different kinds of atoms were ultimately discovered. They had different names associated with their chemical properties.The next part of the problem was, what are the short-range forces? Why does carbon attract one oxygen or perhaps two oxygens, but not three oxygens? What is the machinery of interaction between atoms? Is it gravitation? The answer is no. Gravity is entirely too weak. But imagine a force analogous to gravity, varying inversely with the square of the distance, but enormously more powerful and having one difference. In gravity everything attracts everything else, but now imagine that there are two kinds of ―things,‖ and that this new force (which is the electrical force, of course) has the property that likes repel but unlikes attract. The ―thing‖ that carries this stron g interaction is called charge.Then what do we have? Suppose that we have two unlikes that attract each other, a plus and a minus, and that they stick very close together. Suppose we have another charge some distance away. Would it feel any attraction? It would feel practically none, because if the first two are equal in size, the attraction for the one and the repulsion for the other balance out. Therefore there is very little force at any appreciable distance. On the other hand, if we get very close with the extra charge, attraction arises, because the repulsion of likes and attraction of unlikes will tend to bring unlikes closer together and push likes farther apart. Then the repulsion will be less than the attraction. This is the reason why the atoms, which are constituted out of plus and minus electric charges, feel very little force when they are separated by appreciable distance (aside from gravity). When they come close together, they can ―see inside‖ each other and rearrange their charges, with the result that they have a very strong interaction. The ultimate basis of an interaction between the atoms is electrical. Since this force is so enormous, all the plusses and all minuses will normally come together in as intimate a combination as they can. All things, even ourselves, are made of fine-grained, enormously strongly interacting plus and minus parts, all neatly balanced out. Once in a while, by accident, we may rub off a few minuses or a few plusses (usually it is easier to rub off minuses), and in those circumstances we find the force of electricity unbalanced, and we can then see the effects of these electrical attractions.To give an idea of how much stronger electricity is than gravitation, consider two grains of sand, a millimeter across, thirty meters apart. If the force between them were not balanced, if everything attracted everything else instead of likes repelling, so that there were no cancellation, how much force would there be? There would be a force of three million tons between the two! You see, there is very, very little excess or deficit of the number of negative or positive charges necessary to produce appreciableelectrical effects. This is, of course, the reason why you cannot see the difference between an electrically charged or uncharged thing—so few particles are involved that they hardly make a difference in the weight or size of an object.With this picture the atoms were easier to understand. They were thought to have a ―nucleus‖ at the center, which is positively electrically charged and very massive, and the nucleus is surrounded by a certain number of ―electrons‖ which are very light and negatively charged. Now we go a little ahead in our story to remark that in the nucleus itself there were found two kinds of particles, protons and neutrons, almost of the same weight and very heavy. The protons are electrically charged and the neutrons are neutral. If we have an atom with six protons inside its nucleus, and this is surrounded by six electrons (the negative particles in the ordinary world of matter are all electrons, and these are very light compared with the protons and neutrons which make nuclei), this would be atom number six in the chemical table, and it is called carbon. Atom number eight is called oxygen, etc., because the chemical properties depend upon the electrons on the outside, and in fact only upon how many electrons there are. So the chemical properties of a substance depend only on a number, the number of electrons. (The whole list of elements of the chemists really could have been called 1, 2, 3, 4, 5, etc. Instead of saying ―carbon,‖ we could say ―element six,‖ meaning six electrons, but of course, when the elements were first discovered, it was not known that they could be numbered that way, and secondly, it would make everything look rather complicated. It is better to have names and symbols for these things, rather than to call everything by number.)More was discovered about the electrical force. The natural interpretation of electrical interaction is that two objects simply attract each other: plus against minus. However, this was discovered to be an inadequate idea to represent it. A more adequate representation of the situation is to say that the existence of the positive charge, in some sense, distorts, or creates a ―condition‖ in space, so that when we put the negative charge in, it feels a force. This potentiality for producing a force is called an electric field. When we put an electron in an electric field, we say it is ―pulled.‖ We then have two rules: (a) charges make a field, and (b) charges in fields have forces on them and move. The reason for this will become clear when we discuss the following phenomena: If we were to charge a body, say a comb, electrically, and then place a charged piece of paper at a distance and move the comb back and forth, the paper will respond by always pointing to the comb. If we shake it faster, it will be discovered that the paper is a little behind, there is a delay in the action. (At the first stage, when we move the comb rather slowly, we find a complication which is magnetism. Magnetic influences have to do with charges in relative motion, so magnetic forces and electric forces can really be attributed to one field, as two different aspects of exactly the same thing. A changing electric field cannot exist without magnetism.) If we move the charged paper farther out, the delay is greater. Then an interesting thing is observed. Although the forces between two charged objects should go inversely as the square of the distance, it is found, when we shake acharge, that the influence extends very much farther out than we would guess at first sight. That is, the effect falls off more slowly than the inverse square.Here is an analogy: If we are in a pool of water and there is a floating cork very close by, we can move it ―directly‖ by pushing the water with another cork. If you looked only at the two corks, all you would see would be that one moved immediately in response to the motion of the other—there is some kind of ―interaction‖ between them. Of course, what we really do is to disturb the water; the water then disturbs the other cork. We could make up a ―law‖ that if you pushed the water a little bit, an object close by in the water would move. If it were farther away, of course, the second cork would scarcely move, for we move the water locally. On the other hand, if we jiggle the cork a new phenomenon is involved, in which the motion of the water moves the water there, etc., and waves travel away, so that by jiggling, there is an influence very much farther out, an oscillatory influence, that cannot be understood from the direct interaction. Therefore the idea of direct interaction must be replaced with the existence of the water, or in the electrical case, with what we call the electromagnetic field.The electromagnetic field can carry waves; some of these waves are light, others are used in radio broadcasts, but the general name is electromagnetic waves. These oscillatory waves can have various frequencies. The only thing that is really different from one wave to another is the frequency of oscillation. If we shake a charge back and forth more and more rapidly, and look at the effects, we get a whole series of different kinds of effects, which are all unified by specifying but one number, the number of oscillations per second. The usual ―pickup‖ that we get from electric currents in the circuits in the walls of a building have a frequency of about onehundred cycles per second. If we increase the frequency to 500 or 1000 kilocycles (1 kilocycle=1000cycles) per second, we are ―on the air,‖ for this is the frequency range which is used for radio broadcasts. (Of course it has nothing to do with the air! We can have radio broadcasts without any air.) If we again increase the frequency, we come into the range that is used for FM and TV. Going still further, we use certain short waves, for example for radar. Still higher, and we do not need an instrument to ―see‖ the stuff, we can see it with the human eye. In the range offrequency from 5×1014 to 1015 cycles per second our eyes would see the oscillation of the charged comb, if we could shake it that fast, as red, blue, or violet light, depending on the frequency. Frequencies below this range are called infrared, and above it, ultraviolet. The fact that we can see in a particular frequency range makes that part of the electromagnetic spectrum no more impressive than the other parts from a physicist’s standpoint, but from a human standpoint, of course, it is more interesting. If we go up even higher in frequency, we get x-rays. X-rays are nothing but very high-frequency light. If we go still higher, we get gamma rays. These two terms, x-rays and gamma rays, are used almost synonymously. Usually electromagnetic rays coming from nuclei are called gamma rays, while those of high102 Electrical disturbanceField 5×105 – 106 Radio broadcastWaves 108 FM —TV 1010 Radar5×1014 – 1015 Light1018X-rays Particle 1021γ-rays, nuclear 1024γ-rays, ―artificial‖ 1027 γ-rays, in cosmic rays2–3Quantum physicsHaving described the idea of the electromagnetic field, and that this field cancarry waves, we soon learn that these waves actually behave in a strange way whichseems very unwavelike. At higher frequencies they behave much morelike particles! It is quantum mechanics , discovered just after 1920, which explainsthis strange behavior. In the years before 1920, the picture of space as athree-dimensional space, and of time as a separate thing, was changed by Einstein,first into a combination which we call space-time, and then still further intoa curved space-time to represent gravitation. So the ―stage‖ is changed intospace-time, and gravitation is presumably a modification of space-time. Then it wasalso found that the rules for the motions of particles were incorrect. The mechanicalrules of ―inertia‖ and ―forces‖ are wrong —Newton’s laws are wrong —in the world ofatoms. Instead, it was discovered that things on a small scale behave nothinglike things on a large scale. That is what makes physics difficult —and very interesting.It is hard because the way things behave on a small scale is so ―unnatural‖; we haveno direct experience with it. Here things behave like nothing we know of, so that it isimpossible to describe this behavior in any other than analytic ways. It is difficult, andtakes a lot of imagination.Quantum mechanics has many aspects. In the first place, the idea that a particlehas a definite location and a definite speed is no longer allowed; that is wrong. Togive an example of how wrong classical physics is, there is a rule in quantummechanics that says that one cannot know both where something is and how fast it ismoving. The uncertainty of the momentum and the uncertainty of the position are complementary, and the product of the two is bounded by a small constant. We canwrite the law like this: ΔxΔp≥ℏ/2, but we shall explain it in more detail later. This rule is the explanation of a very mysterious paradox: if the atoms are made out of plus and minus charges, why don’t the minus charges simply sit on top of the plus charges (they attract each other) and get so close as to completely cancel them out? Why are atoms so big? Why is the nucleus at the center with the electrons around it? It was first thought that this was because the nucleus was so big; but no, the nucleus is verysmall. An atom has a diameter of about 10−8 cm. The nucleus has a diameter ofabout 10−13 cm. If we had an atom and wished to see the nucleus, we would have to magnify it until the whole atom was the size of a large room, and then the nucleus would be a bare speck which you could just about make out with the eye, but very nearly all the weight of the atom is in that infinitesimal nucleus. What keeps the electrons from simply falling in? This principle: If they were in the nucleus, we would know their position precisely, and the uncertainty principle would then require that they have a very large (but uncertain) momentum, i.e., a very large kinetic energy. With this energy they would break away from the nucleus. They make a compromise: they leave themselves a little room for this uncertainty and then jiggle with a certain amount of minimum motion in accordance with this rule. (Remember that when a crystal is cooled to absolute zero, we said that the atoms do not stop moving, they still jiggle. Why? If they stopped moving, we would know where they were and that they had zero motion, and that is against the uncertainty principle. We cannot know where they are and how fast they are moving, so they must be continually wiggling in there!) Another most interesting change in the ideas and philosophy of science brought about by quantum mechanics is this: it is not possible to predict exactly what will happen in any circumstance. For example, it is possible to arrange an atom which is ready to emit light, and we can measure when it has emitted light by picking up a photon particle, which we shall describe shortly. We cannot, however, predict when it is going to emit the light or, with several atoms, which one is going to. You may say that this is because there are some internal ―wheels‖ which we have not looked at closely enough. No, there are no internal wheels; nature, as we understand it today, behaves in such a way that it is fundamentally impossible to make a precise prediction of exactly what will happen in a given experiment. This is a horrible thing; in fact, philosophers have said before that one of the fundamental requisites of science is that whenever you set up the same conditions, the same thing must happen. This is simply not true, it is not a fundamental condition of science. The fact is that the same thing does not happen, that we can find only an average, statistically, as to what happens. Nevertheless, science has not completely collapsed. Philosophers, incidentally, say a great deal about what is absolutely necessary for science, and it is always, so far as one can see, rather naive, and probably wrong. For example, some philosopher or other said it is fundamental to the scientific effort that if an experimentis performed in, say, Stockholm, and then the same experiment is done in, say, Quito, the same results must occur. That is quite false. It is not necessary that science do that; it may be a fact of experience, but it is not necessary. For example, if one of the experiments is to look out at the sky and see the aurora borealis in Stockholm, you do not see it in Quito; that is a different phenomenon. ―But,‖ you say, ―that is something that has to do with the outside; can you close yourself up in a box in Stockholm and pull down the shade and get any difference?‖ Surely. If we take a pendulum on a universal joint, and pull it out and let go, then the pendulum will swing almost in a plane, but not quite. Slowly the plane keeps changing in Stockholm, but not in Quito. The blinds are down, too. The fact that this happened does not bring on the destruction of science. What is the fundamental hypothesis of science, the fundamental philosophy? We stated it in the first chapter: the sole test of the validity of any idea is experiment. If it turns out that most experiments work out the same in Quito as they do in Stockholm, then those ―most experiments‖ will be used to formulate some general law, and those experiments which do not come out the same we will say were a result of the environment near Stockholm. We will invent some way to summarize the results of the experiment, and we do not have to be told ahead of time what this way will look like. If we are told that the same experiment will always produce the same result, that is all very well, but if when we try it, it does not, then it does not. We just have to take what we see, and then formulate all the rest of our ideas in terms of our actual experience.Returning again to quantum mechanics and fundamental physics, we cannot go into details of the quantum-mechanical principles at this time, of course, because these are rather difficult to understand. We shall assume that they are there, and go on to describe what some of the consequences are. One of the consequences is that things which we used to consider as waves also behave like particles, and particles behave like waves; in fact everything behaves the same way. There is no distinction between a wave and a particle. So quantum mechanics unifies the idea of the field and its waves, and the particles, all into one. Now it is true that when the frequency is low, the field aspect of the phenomenon is more evident, or more useful as an approximate description in terms of everyday experiences. But as the frequency increases, the particle aspects of the phenomenon become more evident with the equipment with which we usually make the measurements. In fact, although we mentioned many frequencies, no phenomenon directly involving a frequency has yet been detected above approximately 1012 cycles per second. We only deduce the higher frequencies from the energy of the particles, by a rule which assumes that the particle-wave idea of quantum mechanics is valid.Thus we have a new view of electromagnetic interaction. We have a new kind of particle to add to the electron, the proton, and the neutron. That new particle is called a photon. The new view of the interaction of electrons and photons that is electromagnetic theory, but with everything quantum-mechanically correct, is called quantum electrodynamics. This fundamental theory of the interaction of light and matter, or electric field and charges, is our greatest success so far in physics. In。
加州理工学院费曼物理学讲义加州理工学院(California Institute of Technology, 缩写为Caltech)"Physics is to math what sex is to masturbation."(“物理之于数学好比性爱之于手淫。
”)"Physics is like sex: sure, it may give some practical results, but that's not why we do it."(“物理跟性爱有相似之处:是的,它可能会产生某些实在的结果,但这并不是我们做它的初衷。
”)理查·费曼与“草包族科学”理查·费曼曾经在1974年,于加州理工学院的一场毕业典礼演说中叙述“草包族科学”(Cargo cult science)时提到:从过往的经验,我们学到了如何应付一些自我欺骗的情况。
举个例子,密立根做了个油滴实验,量出了电子的带电量,得到一个今天我们知道是不大对的答案。
他的资料有点偏差,因为他用了个不准确的空气粘滞系数数值。
于是,如果你把在密立根之后、进行测量电子带电量所得到的资料整理一下,就会发现一些很有趣的现象:把这些资料跟时间画成坐标图,你会发现这个人得到的数值比密立根的数值大一点点,下一个人得到的资料又再大一点点,下一个又再大上一点点,最后,到了一个更大的数值才稳定下来。
为什么他们没有在一开始就发现新数值应该较高?——这件事令许多相关的科学家惭愧脸红——因为显然很多人的做事方式是:当他们获得一个比密立根数值更高的结果时,他们以为一定哪里出了错,他们会拼命寻找,并且找到了实验有错误的原因。
另一方面,当他们获得的结果跟密立根的相仿时,便不会那么用心去检讨。
因此,他们排除了所谓相差太大的资料,不予考虑。
我们现在已经很清楚那些伎俩了,因此再也不会犯同样的毛病。
目录第1章原子的运动 (5)§1-1引言 (5)§1-2物质是原子构成的 (5)§1-3原子过程 (5)§1-3化学反应 (6)第2章基本物理 (6)§2-1引言 (6)§2-2 1920年以前的物理学 (6)附录 (7)理查德.费曼 (7)目录 (9)[编辑] 生平简介 (9)[编辑] 费曼的著作 (10)[编辑] 传记 (12)[编辑] 参考资料 (12)[编辑] 外部链接 (12)第1章原子的运动§1-1 引言问:为什么不能直截了当的列出基本定律,然后再就一切可能的情况说明定律的应用呢?答:第一,我们还不知道所有的基本定律:未知领域的边界在不断地扩展;第二,正确地叙述物理定律要涉及到一些非常陌生的概念,而叙述这些概念有要用到高等数学。
三一文库()〔费曼物理学讲义中文版〕*篇一:费曼物理学讲义中文版费曼物理学讲义费曼物理学讲义(TheFeynmansLecturesonPhysics)被誉为本世纪最经典的物理导引。
《费曼物理学讲义》是根据诺贝尔物理学奖获得者-理查德·菲利普·费曼(RichardPhillipsFeynman,又译作费恩曼),在1961年9月至1963年5月在加利福尼亚工学院讲课录音整理编辑的。
删除了原录音中费曼教授对惯性导航的精彩解说(可以到网上找录音)和应对做题的解决思路(单独成书)。
《费曼物理学讲义》成书几十年,导引了千千万万物理学工作者进入物理殿堂。
我国自82年开始引进并翻译,并由上海科学技术出版社刊印。
近年来上海科学技术出版社与上海世纪出版股份有限公司合作出版、发行该书,2005年6月推出第一版,截至2010年已经是第八次印刷。
世界图书出版公司北京公司也出版了该书的影印版,译名为《费恩曼物理学讲义》。
这部书虽然基础,理解时,仍需反复研读。
简介20世纪60年代初,美国一些理工科大学鉴于当时的大学基础物理教学与现代科学技术的发展不相适应,纷纷试行教学改革,加利福尼亚理工学院就是其中之一。
该校于1961年9月至1963年5月特请著名物理学家费恩曼主讲一二年级的基础物理课,事后又根据讲课录音编辑出版了《费恩曼物理学讲义》。
本讲义共分三卷,第1卷包括力学、相对论、光学、气体分子动理论、热力学、波等,第2卷主要是电磁学,第3卷是量子力学。
全书内容十分丰富,在深度和广度上都超过了传统的普通物理教材。
引申当时美国大学物理教学改革试图解决的一个主要问题是基础物理教学应尽可能反映近代物理的巨大成就。
《费恩曼物理学讲义》在基础物理的水平上对20世纪物理学的两大重要成就——相对论和量子力学——作了系统的介绍,对于量子力学,费恩曼教授还特地准备了一套适合大学二年级水平的讲法。
教学改革试图解决的另一个问题是按照当前物理学工作者在各个前沿研究领域所使用的方式来介绍物理学的内容。
《费曼讲物理:入门》个人笔记1918-1988.2.15《费曼讲物理:入门》是从著名的费曼《物理学讲义》节选的六节物理课。
内容包括“运动着的原子”、“基础物理学”、“物理学与其他学科的关系”、“能量守恒”、“万有引力理论”、“量子行为”六部分。
费曼:物理学与其他学科的关系∙“理解某种事情”指的是?组成这个“世界”的运动物体的复杂排列似乎有点像是天神们所下的一盘伟大的国际象棋,我们则是这盘棋的观众….当我们观看了足够长的时间,总能看出几条规则来,而弈棋规则就是我们所说的基础物理。
但是,即使我们知道了每条规则,仍然可能不理解为什么下棋时要走这一步,这仅仅是因为情况太复杂了,而我们的智力确实有限的。
除了我们还在知道所有规则以外,我们真正能用已知规则来解释的事情也非常有限,因为几乎所有的情况都是极其复杂的,我们不能领会这盘棋中应用这些规则的走法,更无法预言下一步将要怎样。
所以,如果我们知道了这些规则,就认为“理解”了世界。
∙实验是任何观念的正确性的唯一试金石。
∙如果一件事情不是科学,这并不意味着其中有什么错误的地方,它只是意味着其它不是科学而已。
1. 化学:受到物理学影响最深;①理论化学最深刻的部分必定会归结到量子力学;②统计力学;③有机化学→生物化学→生物学(无机化学:物理化学,量子化学)2. 生物学:生物过程中有很多物理现象,比如神经放电3. 天文学4. 地质学5. 心理学如果我们微不足道的有限智力为了某种方便将这个宇宙分为几个部分:物理,化学,生物,地理,天文,心理等,那么记住,大自然并不知道这一切。
P32 有时候,我真搞不清楚人是怎么回事:他们都不是透过了解而学习,而且靠背诵死记或其他方法,因此知识的基础都很薄弱。
P79 就这样,我学到一点关于生物学的特性:你可以很轻易便提出一个非常有趣的问题,而没有人知道答案。
但在物理学,你必须先稍微深入学习,才有可能问一些大家都无法回答的问题。
P87 我居然在哈佛大学的生物系里发表演讲呢!事实上,这可以作为我一生中的写照:我永远会一脚踏进某个事情中,看看到底能做到什么地步。
第28卷第5期 唐山师范学院学报 2006年9月 Vol. 28 No.5 Journal of Tangshan Teachers College Sep. 2006 ────────── 收稿日期:2005-02-29作者简介:王贺清(1965-),女,河北唐山人,唐山师范学院物理系讲师。
- 137 -本科物理“双语教学”的范本——《费曼物理学讲义》王贺清(唐山师范学院 物理系,河北 唐山 063000)摘 要:费曼独特的教学理念对物理教学的启迪是非同寻常的,其《费曼物理学讲义》中深刻的物理学思想和精练的阐述,是物理系本科学生双语学习难得的经典教材,而且还能为学生毕业后从事物理教学和科研打下良好的基础。
关键词:费曼物理学讲义;双语教学;启迪中图分类号:G658.3 文献标识码:B 文章编号:1009-9115(2006)05-0137-021 《费曼物理学讲义》为创设“双语教学”环境提供了良好的开端物理系“双语教学”课程是为大三学生开设的。
经过大一和大二两年的大学英语学习,学生已经具有了基本的听、说、读、写的语言能力,有些学生已经具备了较高的英语水平;同时学生也具备了物理专业背景知识。
《费曼物理学讲义》能把学生从“做题,过级”的怪圈中解放出来,以一种既符合学生学习心理特点,也符合英语教学规律的方式来创设“双语教学”环境。
《费曼物理学讲义》的前言用了很长篇幅介绍了费曼的生平、费曼对科学和教育的贡献及《费曼物理学讲义》产生的背景,使学生在“双语”环境中不仅能轻松地感受到费曼多方面的个性,而且更能体会到费曼简单而巧妙的教学技巧。
例如,在一次讲座中,他试图解释为什么千万不能用第一次提出的观点所用的数据来证明这个观点。
费曼开始谈论汽车车牌,看上去像是漫不经心偏离了主题,实际上已经严密地论证了他所论述的物理内容:Once, during a public lecture, he was trying to explain why one must not verify an idea using the same data that suggested the idea in the first place. Seeming to wander off the subject. Feynman began talking about the license plates. “You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!”(“你知道吗!今天晚上发生了最令我惊奇的事情。
费曼讲物理:通过《费曼物理学讲义》学习物理概念介绍费曼是一位杰出的物理学家,也是一位优秀的科普作家。
他以其独特的教学风格和幽默感而闻名于世。
《费曼物理学讲义》是费曼在加州理工学院教授初级大学物理课程时所编写的教材,以其简洁、生动、易于理解的方式展示了物理学的核心概念。
1. 物理学简介在开始深入探讨《费曼物理学讲义》之前,我们先来了解一下物理学的基本内容和重要性。
涵盖了经典力学、电磁学、热力学等领域,它是自然科学中最基础和最重要的一个分支。
2.《费曼物理学讲义》概述这本书是由费曼亲自撰写,分为三卷。
每卷都以清晰明了的语言描述了各个领域中的重要概念,配有丰富的例题和插图,便于读者更好地理解。
2.1 第一卷:力与运动原则第一卷主要介绍了经典力学方面的知识,讲解了运动规律、牛顿定律、万有引力等基础内容。
2.2 第二卷:电与磁第二卷则涵盖了电磁学的内容,详细讲解了静电学、电流、磁场以及电磁辐射等相关概念。
2.3 第三卷:量子物理最后一卷则涉及到量子物理学领域,包括粒子的性质、波粒二象性、原子结构和核物理等内容。
3. 学习《费曼物理学讲义》的建议•掌握数学基础:由于物理学与数学紧密相关,建议读者在阅读本书之前具备扎实的数学基础。
•系统化地学习:将书籍分为多个部分,每次深入研究一个主题,并进行总结和复习。
•注重实践:通过大量的例题和实验来巩固所学知识并加深理解。
•结合其他资源:除了《费曼物理学讲义》,还可以参考其他教材、视频教程等来帮助更好地理解难点。
•交流与讨论:可以参加物理学习小组或者与同学共同探讨问题,相互促进学习。
4. 结语《费曼物理学讲义》是一本值得推荐的物理学自学教材,以其独特的风格和深入浅出的讲解方法,帮助读者更好地理解物理学中的核心概念。
通过系统化地阅读和实践,相信读者能够从中获得丰富的知识和启发。
同时也希望读者在深入研究物理学领域时能够保持求知的好奇心和兴趣。
《费曼物理学讲义》笔记费曼物理学讲义第一章原子的运动引言:两学年的物理课,200年以来空前蓬勃发展的知识领域。
1、我们还不知道所有的基本定律:未知领域的边界在不断地扩展、涉及一些陌生的概念,需要高数。
大量的预备性的训练 2实验是一切知识的试金石。
理论、实验物理学家1、正确的、陌生的定律以及有关的奇特而困难的定律,例如相对论,四维空间等等之。
2、简单的质量守恒定律,虽然只是近似,但并不包含那种困难的观念的定律那我们世界的总体图像是怎样的呢,原子的假设(一言以蔽之),证明原子的存在,布朗运动从原子的观点来描写固体、液体和气体。
假设有一滴水,贴近观察,光滑连续的水,没有任何其它东西。
用最好的光学显微镜放大2000倍,相当于一个大房间,可以看到草履虫摆动的纤毛与卷曲的身体。
再放大2000倍,像从远处看挤在足球场上的人群。
再放大250倍,放大10亿倍后的水的图像。
蒸发、溶解与淀积化学反应、化学物质从原子角度考虑这个世界最基本的物质,那么首先想到的自然是太阳,这个由氢氦元素组成的巨大熔炉,源源不断地发生着核聚变;以至于地球的组分、人的化学组分第二章基本物理引言:我们在科学上所关心的事物具有无数的形式和许多属性:或许是由较少量的基本事物和相互作用以无穷多的方式组合后所产生的结果。
沙粒与月亮,岩石;风与水流,流动;不同的运动有什么共同特征;究竟有多少颜色,我们就是试图这样地逐步分析所有的事情,把那些乍看起来似乎不相同的东西联系起来,希望有可能减少不同类事物的数目,从而能更好地理解它们。
世界是一盘伟大的象棋,我们不知道弈棋的规则,所有能做的事就是观看这场棋赛。
(张志豪的三维弹球;lol里的小细节也是一步一步探索出来的) 人们首先把自然界中的现象大致分为几类,如热、电、力学、磁、物性、化学、光、核物理等等现象,这样做的目的是将整个自然界看作是一系列现象的不同侧面。
基础理论物理:发现隐匿在实验后的定律;把各类现象综合起来。
费曼物理学讲义中文pdf费曼物理学讲义是一套备受推崇的物理教材,由著名物理学家理查德·费曼编著。
这套讲义涵盖了广泛的知识领域,包括力学、相对论、光学、气体分子动理论、热力学、波、电磁学以及量子力学等。
其特点是内容通俗易懂,叙述条理清晰,深入浅出,避免了运用高深烦琐的数学方程。
因此,无论是普通物理水平的读者,还是物理专业的学者,都能从这套讲义中获得丰富的知识和启发。
费曼物理学讲义的第一卷主要讲述了原子的运动等基本物理概念。
在第一卷中,费曼先生通过生动的例子和简洁的语言,使读者对物理学的基本原理有了直观的理解。
此外,讲义还介绍了物理学与其他科学的关系,以及各门学科之间的相互联系,帮助读者建立起全面的科学素养。
第二卷则涵盖了力学、相对论、光学等方面的内容。
在这一卷中,费曼先生详细讲解了牛顿定律、万有引力定律等基本定律,以及相对论的基本原理。
此外,他还介绍了光的性质和光学现象,使读者对光学有了更深入的认识。
第三卷主要涉及气体分子动理论、热力学、波、电磁学以及量子力学等领域。
在这一卷中,费曼先生讲解了气体分子的运动规律、热力学定律、波动现象以及电磁学的基本原理。
此外,他还深入浅出地介绍了量子力学的基本概念,使读者对这一神秘的领域有了更为清晰的认识。
总之,费曼物理学讲义是一套极具价值的物理教材,适用于广大读者学习。
这套讲义不仅能够帮助读者掌握物理学的基本知识,还能激发他们对物理学的兴趣和热情。
无论你是高中生、大学生,还是物理工作者,都可以从这套讲义中获得丰富的教益。
值得一提的是,费曼物理学讲义的全三卷已经被翻译成中文,并提供了PDF高清中文版下载。
广大读者可以借此机会,深入了解这套备受推崇的物理教材,感受费曼先生独特的教学风格和物理智慧。
在当前的科学研究中,费曼物理学讲义仍然具有很高的指导意义。
这套讲义对于培养新一代物理学家和提高全社会的科学素养具有重要意义。
希望更多的读者能够通过学习费曼物理学讲义,走进物理学的殿堂,探索这个神奇而美妙的世界。
费曼物理学讲义第一章原子的运动引言:两学年的物理课,200年以来空前蓬勃发展的知识领域。
1、我们还不知道所有的基本定律:未知领域的边界在不断地扩展2、涉及一些陌生的概念,需要高数。
大量的预备性的训练实验是一切知识的试金石。
理论、实验物理学家1、正确的、陌生的定律以及有关的奇特而困难的定律,例如相对论,四维空间等等之。
2、简单的质量守恒定律,虽然只是近似,但并不包含那种困难的观念的定律那我们世界的总体图像是怎样的呢?原子的假设(一言以蔽之),证明原子的存在,布朗运动从原子的观点来描写固体、液体和气体。
假设有一滴水,贴近观察,光滑连续的水,没有任何其它东西。
用最好的光学显微镜放大2000倍,相当于一个大房间,可以看到草履虫摆动的纤毛与卷曲的身体。
再放大2000倍,像从远处看挤在足球场上的人群。
再放大250倍,放大10亿倍后的水的图像。
蒸发、溶解与淀积化学反应、化学物质从原子角度考虑这个世界最基本的物质,那么首先想到的自然是太阳,这个由氢氦元素组成的巨大熔炉,源源不断地发生着核聚变;以至于地球的组分、人的化学组分第二章基本物理引言:我们在科学上所关心的事物具有无数的形式和许多属性:或许是由较少量的基本事物和相互作用以无穷多的方式组合后所产生的结果。
沙粒与月亮,岩石;风与水流,流动;不同的运动有什么共同特征;究竟有多少颜色?我们就是试图这样地逐步分析所有的事情,把那些乍看起来似乎不相同的东西联系起来,希望有可能减少不同类事物的数目,从而能更好地理解它们。
世界是一盘伟大的象棋,我们不知道弈棋的规则,所有能做的事就是观看这场棋赛。
(张志豪的三维弹球;lol里的小细节也是一步一步探索出来的)人们首先把自然界中的现象大致分为几类,如热、电、力学、磁、物性、化学、光、核物理等等现象,这样做的目的是将整个自然界看作是一系列现象的不同侧面。
基础理论物理:发现隐匿在实验后的定律;把各类现象综合起来。
1、热与力学的综合,当原子运动时,运动得越是剧烈,系统包含的热量就越多,这样热和所有的温度效应可以用力学定律来说明2、电、磁、光,同一件事物的不同方面,电磁场3、量子化学。
费曼物理学讲义第一章原子的运动引言:两学年的物理课,200年以来空前蓬勃发展的知识领域。
1、我们还不知道所有的基本定律:未知领域的边界在不断地扩展2、涉及一些陌生的概念,需要高数。
大量的预备性的训练实验是一切知识的试金石。
理论、实验物理学家1、正确的、陌生的定律以及有关的奇特而困难的定律,例如相对论,四维空间等等之。
2、简单的质量守恒定律,虽然只是近似,但并不包含那种困难的观念的定律那我们世界的总体图像是怎样的呢?原子的假设(一言以蔽之),证明原子的存在,布朗运动从原子的观点来描写固体、液体和气体。
假设有一滴水,贴近观察,光滑连续的水,没有任何其它东西。
用最好的光学显微镜放大2000倍,相当于一个大房间,可以看到草履虫摆动的纤毛与卷曲的身体。
再放大2000倍,像从远处看挤在足球场上的人群。
再放大250倍,放大10亿倍后的水的图像。
蒸发、溶解与淀积化学反应、化学物质从原子角度考虑这个世界最基本的物质,那么首先想到的自然是太阳,这个由氢氦元素组成的巨大熔炉,源源不断地发生着核聚变;以至于地球的组分、人的化学组分第二章基本物理引言:我们在科学上所关心的事物具有无数的形式和许多属性:或许是由较少量的基本事物和相互作用以无穷多的方式组合后所产生的结果。
沙粒与月亮,岩石;风与水流,流动;不同的运动有什么共同特征;究竟有多少颜色?我们就是试图这样地逐步分析所有的事情,把那些乍看起来似乎不相同的东西联系起来,希望有可能减少不同类事物的数目,从而能更好地理解它们。
世界是一盘伟大的象棋,我们不知道弈棋的规则,所有能做的事就是观看这场棋赛。
(张志豪的三维弹球;lol里的小细节也是一步一步探索出来的)人们首先把自然界中的现象大致分为几类,如热、电、力学、磁、物性、化学、光、核物理等等现象,这样做的目的是将整个自然界看作是一系列现象的不同侧面。
基础理论物理:发现隐匿在实验后的定律;把各类现象综合起来。
1、热与力学的综合,当原子运动时,运动得越是剧烈,系统包含的热量就越多,这样热和所有的温度效应可以用力学定律来说明2、电、磁、光,同一件事物的不同方面,电磁场3、量子化学。
这场游戏是否有底1920年以前的物理学(一开始就从现在的观点讲起是有点困难)1920年以前,我们的世界图像:宇宙活动的舞台是欧几里得所描绘的三维几何空间,一切事物在称为时间的一种媒介里变化,舞台上的基本元素是粒子,例如原子,他们具有某些特性,首先一个是惯性,动则同方向一直动下去,除非有力;第二个基本元素就是力,第一类力是分子间原子间作用力,确定温度升高食盐溶解变快,另一为长程相互作用,是与距离平方成反比的变化平缓的作用力,称为万有引力。
这些为我们所知,它是简单的,但为什么物体运动一旦开始就能保持,或者为什么存在一条万有引力定律,我们就不清楚了。
粒子有哪些种类?在当时92种,按照各自的化学性质被赋予不同的名称。
其次短程力是什么?为什么一个碳吸引一个而不是三个氧,相互作用的机制是万有引力吗,不,太弱了。
关于电的两条规则1、电荷产生电场2、电荷在电场中会受到里的作用,例木塞于水。
电磁波,频率越快,由场(电扰动)到波(无线电、FM、雷达、光)到粒子(X射线)第三章物理学与其他科学的关系(如果说某件事不是科学,这并不意味着其中有什么错误的地方,这只是意味着它不是科学而已。
数学不是科学,它的正确性不是用实验来检验的;爱好不是科学)我们知道,精确预言某个化学反应中出现什么情况是十分困难的,然而,理论化学最深刻部分必定会归结到量子力学。
与生物学。
所有的物质都是由原子组成的,并且生命体所做的每一件事都可以从原子摆动和晃动中来理解。
与天文学是的,此刻我是世界上唯一知道为什么她们会发光的人。
孤独真理远比以往任何艺术家的想象更为奇妙!物理学的历史问题:这些定律是怎么变化而来的“整个宇宙就存在一杯葡萄酒中。
”第四章能量守恒有一个事实,如果你愿意的话,也可以说一条定律,支配着至今我们所知道的一切自然现象,没有什么例外,这条定律称为能量守恒定律。
淘气的丹尼斯只有当我们的公式包含了所有形式的能量时才能理解能量守恒。
我想在这里讨论一下地球表面附近的重力势能的公式,与历史无关,这种推导方式只是为这堂课想出来的,也就是说一种推理思路。
为的是要向你们说明一个值得注意的情况,从几个事实和严密的推理出发可以推断出很多有关大自然的知识。
虚功原理,为了运用能量守恒的原理,我们用了很小的假想运动为了说明另一种形式的能量,我们来考虑一个单摆。
E=mc2守恒定律,能量守恒定律,线动量守恒,角动量守恒;微妙的,与空间和时间有关电荷守恒定律,重子的守恒,轻子守恒定律;进行计数的意义上是简单的第五章时间与距离运动。
很多人都喜欢把伽利略在350年前所做的工作看作是物理学的开端,在此之前对运动的研究是哲学上的事情,大部分的论据是由亚里士多德和其他希腊哲学家提出的,伽利略做实验,球沿着斜面滚下,对于时间的测量用脉搏。
时间。
时间的定义建立在某种明显是周期性的事件的重复性上。
短的时间,伽利略断定只要一个摆的摆幅很小,则以相等的时间间隔来回摆动,即可划分出一个小时的几分之一。
假如我们利用一个机械装置计点摆动次数,并且保持摆动进行下去,那么就得到我们祖先一代所用的那种摆钟。
电学摆第六章几率“我们这个世界的真正逻辑寓于几率的计算之中。
”JG麦克斯韦,活到100岁,明天下雨,明年发生地震,下一个10秒盖革计数器,下一个十年核战。
这个世界是现实的,可逆过程只是最理想的状态绝对不可能实现,而唯有判断、几率的计算才是真正的生活;在理论物理无处可走的现在,实验就是判断选择了。
信息information 又是能够计算几率的最基础的条件,正如福尔摩斯小脑袋只是对信息的整理和判断,不过他有自己的独特而高效的思路。
Head-Tail 帕斯卡三角形无规行走距离的平方来表示这种量度的进度第七章万有引力理论开普勒定律,基于第谷的星表。
每个行星沿着一条称为椭圆的曲线绕太阳运行,而太阳处于椭圆的一个焦点。
椭圆不仅仅是一个呈现为一个卵形的东西,而是一条非常独特的精确的曲线,两只平头钉,一束线和铅笔。
开普勒三定律1、太阳,椭圆焦点2、等时等面卡文迪许称地球引力与相对论。
依照牛顿的观点,引力效应是瞬间发生的,爱因斯坦证明我们不能发送比光更快的信号第八章运动人龟赛跑;速率第九章牛顿的动力学定律直线运动行星运动第十章动量守恒线性气垫相对论性动量,质量随速度而改变。
在量子力学中,动量是另一回事,它不再是mv了。
物体的速度的含义已难于确切定义,但是动量仍然存在。
在量子力学中,差别在于当粒子表现为波时,动量就用每厘米的波数来量度,波数越大,动量就越大。
第十一章矢量使用物理学中的所有概念需要具备一定的常识,它们不纯粹是数学的或抽象的概念。
物理定律的对称性,物理定律对于平移是对称的。
人造卫星上摆钟根本不走第十二章力的特性任何简单的概念都是近似的。
作为例子,考虑一个客体;什么是客体,哲学家这样说,嗯,就拿一张椅子来作为例子吧。
那么椅子是什么。
哪些原子属于油漆,哪些原子属于灰尘摩擦。
从原子情况来看,相互接触的两个表面是不平整的,它们有很多接触点,在这些接触点上,原子好像粘接在一起,于是当我们拉动一个正在滑动的物体时,原子啪的忽然打开,随即发生振动。
动力损耗的机理是当滑动体撞击突起部分时,突出部分发生形变,接着在两个物体之间产生波和原子运动,过了一会儿产生热。
摩擦系数,公式分子力。
这些力是原子之间的力,也是摩擦的根本起因。
图中将两个原子之间的力作为两个原子之间的距离的函数。
同时,还存在着不同的情况:例如在水分子中氧带有较多负电荷,所以负电荷在正电荷的平均位置不在同一点上,结果附近的另一个分子感受到比较大的力,这个力称为偶极-偶极力。
然而,对许多系统来说,电荷平衡得非常好,特别是氧气,它是完全对称的。
对于所有非极性分子(其中所有的电力被中和),在较大距离上的作用力仍然是引力,而且与距离的7次方成反比,正是这个力使得我们不会落到地板下面去。
在一定距离形成固体。
胡克定律基本力,场下面我们来讨论唯一剩下的基本力。
我们把他们称作基本力是由于他们遵从的定律从根本上说是简单的。
我们首先讨论电力。
在分析比较基本的一类力时形成了一种有趣的、非常重要的概念。
因为乍看起来,力比反平方定律所指出的要复杂得多,而这些定律仅当相互作用物体处于静止时才成立,所以就需要一种改进的方法来处理当物体开始以一种复杂的方式运动时所产生的非常复杂的力。
经验表明,用所谓“场”的概念这种方法,对于分析这种类型的力是非常有用的。
第十三章功与势能(上)能量守恒最简单的例子是一个垂直下落的物体,动能加势能总和为恒量,如何证明?动能的变化率拓展到更一般的情况首先讨论三维情况下一般的动能变化率现在我们来讲一讲单位第十四章(下)在学习任何一个与数学有关的技术性课题中,人们面临着弄懂并记住大量事实和概念的任务。
可以“证明”存在着某些关系将这些事实和概念联系起来,人们容易把证明本身与它们之间所建立起来的关系混淆起来。
很清楚,要学习和记住的要点是事实和概念之间的关系,而不是证明本身。
在任何特定情况下,我们可以或者说“能够证明”某某是正确的,或者直接来证明它。
几乎在所有情况中,我们所采用的那种特殊证明首先是为了能将它很快地和容易地写在黑板上或纸上,并且使它尽可能地清楚,结果看上去似乎这个证明很简单。
当看到一个证明时,要记住的并不是证明本身,而是那些能够证明是正确的东西。
一个作者在一门课程中所作的全部论证,并不是他从学习大学一年级物理时就记住的。
完全相反,他只记得某某是正确的,而在说明如何去证明的时候,需要的话,他就自己想出一个证明方法。
无论哪个真正学过一门课程的人,都应遵循类似的步骤去做,而死记证明是无用的。
约束运动。
固定的无摩擦约束运动保守力势和场第十五章狭义相对论第一次看出牛顿所阐明的运动方程存在一个谬误、并找到修正它的方法是在1905年,这两件事都是爱因斯坦。
牛顿第二定律如右:即使速度大到像绕地球运转的卫星,约5英里/秒,对质量修正只是20亿到30亿分之一。
相对性原理是牛顿在他的运动定律的一个推论中首先提出的:“封闭在一个给定空间中的物体,它们的运动彼此之间是同一的,无论这个空间是处于静止状态还是均匀地沿一直线向前运动。
”相对性原理在力学中已应用了很长一段时间,惠更斯应用它来求出弹子球碰撞的规则。
在上一世纪中,由于对电、磁以及光等现象的研究,人们对于这条定理的兴趣更加浓厚了。
许多人对这些现象所作的一系列精心研究,其结晶就是麦克斯韦方程组似乎并不遵循相对性原理。
这就是说,如果我们用上式代入麦克斯韦方程组并对它进行变换,那么它们的形式不再保持相同;因此,在飞行的宇宙飞船中,光与电的现象应当与飞船静止时不同。