诺贝尔奖获得者全书【1911】【物理学奖】
【获奖类别】物理学奖【获奖年代】1911年
【获得情况】威廉·维恩（Wilhelm Wien）
[img]http://nobelprize.org/physics/laureates/1911/wien.jpg[/img]
威廉·维恩（Wilhelm Wien）
1864年1月13日出生于Fischhausen, in East Prussia
1928年8月30日逝世
【获奖理由】因发现热辐射规律——维恩位移定律和建立黑体辐射的维恩公式，获得了1911年度诺贝尔物理学奖。
【研究成果】
19世纪末，人们已经认识到热辐射和光辐射都是电磁波，并对辐射能量在不同频率范围内的分布问题，特别是黑体辐射，进行了较深入的理论和实验研究。维恩和拉梅尔发明了第一个实用黑体——空腔发射体，为他们的实验研究提供了所需的“完全辐射”。维恩在前人研究的基础上于1893年提出了理想黑体辐射的位移定律：lmaxT=常数。该定律指出，随着温度的升高，与辐射能量密度极大值对应的波长向短波方向移动。由于辐射通量密度与辐射能量密度之比为c/4，所以在测出对应辐射通量密度极大值的lmax后，就可以根据维恩位移定律确定辐射体的温度。光测温度计就是根据这一原理制成的。
接着，维恩研究了黑体辐射能量按波长的分布问题。他从热力学理论出发，在分析了实验数据之后，得到了一个半经验的公式：
即维恩公式。其中，El为在波长l处单位波长间隔的辐射能量；C1和C2是两个经验参数，通过符合实验曲线来确定；T为平衡时的温度。维恩公式在短波波段与实验符合得很好，但在长波波段与实验有明显的偏离。后来，在进一步探索更好的辐射公式的过程中，普朗克建立了与所有的实验都符合的辐射量子理论。但是，在利用光学高温计测量温度时，人们仍经常采用维恩公式，因为它计算简单且足够精确。
【获奖感言】
大家都知道，一个物体之所以看上去是白色的，那是因为它反射所有频率的光波；反之，如果看上去是黑色的，那是因为它吸收了所有频率的光波的缘故。物理上定义的“黑体”，指的是那些可以吸收全部外来辐射的物体，比如一个空心的球体，内壁涂上吸收辐射的涂料，外壁上开一个小孔。那么，因为从小孔射进球体的光线无法反射出来，这个小孔看上去就是绝对黑色的，即是我们定义的“黑体”。
19世纪末，人们开始对黑体模型的热辐射问题发生了兴趣。其实，很早的时候，人们就已经注意到对于不同的物体，热和辐射似乎有一定的对应关联。比如说金属，有过生活经验的人都知道，要是我们把一块铁放在火上加热，那么到了一定温度的时候，它会变得暗红起来（其实在这之前有不可见的红外线辐射），温度再高些，它会变得橙黄，到了极度高温的时候，如果能想办法不让它汽化了，我们可以看到铁块将呈现蓝白色。也就是说，物体的热辐射和温度有着一定的函数关系（在天文学里，有“红巨星”和“蓝巨星”，前者呈暗红色，温度较低，通常属于老年恒星；而后者的温度极高，是年轻恒星的典范）。
问题是，物体的辐射能量和温度究竟有着怎样的函数关系呢？
最初对于黑体辐射的研究是基于经典热力学的基础之上的，而许多著名的科学家在此之前也已经做了许多基础工作。美国人兰利（samuel pierpont langley）发明的热辐射计是一个最好的测量工具，配合罗兰凹面光栅，可以得到相当精确的热辐射能量分布曲线。“黑体辐射”这个概念则是由伟大的基尔霍夫（gustav robert kirchhoff）提出，并由斯特藩（josef stefan）加以总结和研究的。到了19世纪80年代，玻尔兹曼建立了他的热力学理论，种种迹象也表明，这是黑体辐射研究的一个强大理论武器。总而言之，这一切就是当威廉？维恩（wilhelm wien）准备从理论上推导黑体辐射公式的时候，物理界在这一课题上的一些基本背景。
维恩是东普鲁士一个地主的儿子，本来似乎命中注定也要成为一个农场主，但是当时的经济危机使他下定决心进入大学学习。在海德堡、哥廷根和柏林大学度过了他的学习生涯之后，维恩在1887年进入了德国帝国技术研究所（physikalisch technische reichsanstalt，ptr），成为了赫尔姆霍兹实验室的主要研究员。就是在柏林的这个实验室里，他准备一展他在理论和实验物理方面的天赋，彻底地解决黑体辐射这个问题。
维恩从经典热力学的思想出发，假设黑体辐射是由一些服从麦克斯韦速率分布的分子发射出来的，然后通过精密的演绎，他终于在1893年提出了他的辐射能量分布定律公式：
u = b（λ^-5）（e^-a/λt）（其中λ^-5和e^-a/λt分别表示λ的-5次方以及e的-a/λt次方。u表示能量分布的函数，λ是波长，t是绝对温度，a，b是常数。当然，这里只是给大家看一看这个公式的样子，对数学和物理没有研究的朋友们大可以看过就算，不用理会它具体的意思）。
这就是著名的维恩分布公式。很快，另一位德国物理学家帕邢（f.paschen）在兰利的基础上对各种固体的热辐射进行了测量，结果很好地符合了维恩的公式，这使得维恩取得了初步胜利。
【其它事件】
维恩的分子假设使得经典物理学家们十分地不舒服。因为辐射是电磁波，而大家已经都知道，电磁波是一种波动，用经典粒子的方法去分析，似乎让人感到隐隐地有些不对劲，有一种南辕北辙的味道。
果然，维恩在帝国技术研究所（ptr）的同事很快就做出了另外一个实验。卢梅尔（otto richard lummer）和普林舍姆（ernst pringsheim）于1899年报告，当把黑体加热到1000多k的高温时，测到的短波长范围内的曲线和维恩公式符合得很好，但在长波方面，实验和理论出现了偏差。很快，ptr的另两位成员鲁本斯（heinrich rubens）和库尔班（ferdinand kurlbaum）扩大了波长的测量范围，再次肯定了这个偏差，并得出结论，能量密度在长波范围内应该和绝对温度成正比，而不是维恩所预言的那样，当波长趋向无穷大时，能量密度和温度无关。在19世纪的最末几年，ptr这个由西门子和赫尔姆霍兹所创办的机构似乎成为了热力学领域内最引人瞩目的地方，这里的这群理论与实验物理学家，似乎正在揭开一个物理内最大的秘密。
维恩定律在长波内的失效引起了英国物理学家瑞利（还记得上次我们闲话里的那位苦苦探究氮气重量，并最终发现了惰性气体的爵士吗？）的注意，他试图修改公式以适应u和t在高温长波下成正比这一实验结论，最终得出了他自己的公式。不久后另一位物理学家金斯（j.h.jeans）计算出了公式里的常数，最后他们得到的公式形式如下：
u = 8π（υ^2）kt / c^3这就是我们今天所说的瑞利-金斯公式（rayleigh-jeans），其中υ是频率，k是玻尔兹曼常数，c是光速。同样，没有兴趣的朋友可以不必理会它的具体涵义，这对于我们的故事没有什么影响。
这样一来，就从理论上证明了u和t在高温长波下成正比的实验结果。但是，也许就像俗话所说的那样，瑞利-金斯公式是一个拆东墙补西墙的典型。因为非常具有讽刺意义的是，它在长波方面虽然符合了实验数据，但在短波方面的失败却是显而易见的。当波长λ趋于0，也就是频率υ趋向无穷大时，大家可以从上面的公式里看出我们的能量辐射也将不可避免地趋向无穷大。换句话说，我们的黑体将在波长短到一定程度的时候释放出几乎是无穷的能量来。
这个戏剧性的事件无疑是荒谬的，因为谁也没见过任何物体在任何温度下这样地释放能量辐射（如果真要这样的话，那么原子弹什么的就太简单了）。这个推论后来被加上了一个耸人听闻的，十分适合在科幻小说里出现的称呼，叫做“紫外灾变”。显然，瑞利－金斯公式也无法给出正确的黑体辐射分布。
我们在这里遇到的是一个相当微妙而尴尬的处境。我们的手里现在有两套公式，但不幸的是，它们分别只有在短波和长波的范围内才能起作用。这的确让人们非常的郁闷，就像你有两套衣服，其中的一套上装十分得体，但裤腿太长；另一套的裤子倒是合适了，但上装却小得无法穿上身。最要命的是，这两套衣服根本没办法合在一起穿。
总之，在黑体问题上，如果我们从经典粒子的角度出发去推导，就得到适用于短波的维恩公式。如果从类波的角度去推导，就得到适用于长波的瑞利－金斯公式。长波还是短波，那就是个问题。
研究文献原文存放：
范德瓦尔斯 的讲演稿（Prize Lecture）:
Wilhelm Wien – Nobel Lecture
Nobel Lecture, December 11, 1911
On the Laws of Thermal Radiation
The kind recognition which my work on thermal radiation has received in the views of your ancient and famous Academy of Sciences gives me particular pleasure to speak to you about this subject which is again attracting the attention of all physicists because of the difficulty of the problems involved. As soon as we step beyond the established boundaries of pure thermodynamic theory, we enter a trackless region confronting us with obstacles which even the most astute of us are almost at a loss to tackle.
If, as is the custom, I speak mainly about my own researches, I must say that I was fortunate in finding that not everything had yet been gleaned in the field of general thermodynamic radiation theory. Using known physical laws it was possible to derive a general law of radiation theory which has, under the name of the displacement law, been acclaimed by fellow workers. In applying thermodynamics to the theory of radiation, we make use of the ideal processes which have been found so fruitful elsewhere. These are mental experiments whose realization is frequently impracticable and which nevertheless lead to reliable results. Such deliberations can only be undertaken if all the processes on which, governed by laws, the mental experiments are based, are known, so that the effect of any change can be stated accurately and completely. Further, to be allowed to idealize, we must neglect all non-essential secondary phenomena, while considering only everything indissolubly connected with the processes under examination. In the application of mechanical heat theory, this method has proved to be extremely fruitful. Helmholtz used it in the theory of concentration flows, Van 't Hoff used it in applying thermodynamics to the theory of solutions. It is necessary, in these deliberations, to presuppose the existence of a so-called semi-permeable membrane which permits the solvent to pass, but not the substance dissolved. Although it is impossible to prepare membranes which strictly satisfy this requirement, we can assume them as possible in the ideal processes, because the laws of Nature set no limit to approximation to semipermeability. The conclusions drawn from these assumptions have in any case always been in agreement with experience. In radiation theory, analogous deliberations can be made if we assume perfectly reflecting bodies as possible in the ideal processes. Kirchhoff used them for proving his famous theorem of the constancy of the ratio of emission and absorption power. This theorem has become one of the most general of radiation theory and expresses the existence of a certain temperature equilibrium for radiation. According to it, there must exist, in a cavity surrounded by bodies of equal temperature, a radiation energy that is independent of the nature of the bodies. If in the walls surrounding this cavity a small aperture is made through which radiation issues, we obtain a radiation which is independent of the nature of the emitting body, and is wholly determined by the temperature. The same radiation would also be emitted by a body which does not reflect any rays and which is therefore designated as completely black, and this radiation is called the radiation of a black body or black-body radiation.
The Kirchhoff theorem is not limited to radiation caused by thermal processes. It seems to be valid for most, if not all luminous processes. That the temperature concept can be applied to all luminous processes is beyond doubt. Since we can produce all types of light by means of hot bodies, we can ascribe, to the radiation in thermal equilibrium with hot bodies, the temperature of these bodies, and thus every radiation, even that issueing from a phosphorescent body, has a certain temperature for every colour. This temperature has however no connection whatever with that of the body, nor is it possible as yet to state how e.g. a phosphorescent body comes into equilibrium with radiation. These conditions are bound to be very complicated, in particular in the case of bodies which convert the absorbed radiation and emit it after a long interval of time.
Again using ideal processes and assuming radiation pressure, which at that time had been deduced from the electromagnetic theory of light, Boltzmann derived from thermodynamics the law, previously empirically formulated by Stefan, that the radiation of a black body is proportional to the fourth power of the absolute temperature.
This did not exhaust the conclusions to be drawn from thermodynamics. There remained the determination of the changes undergone by the colours present in radiation with changes of temperature. Computation of this change is again based on an ideal process. For this, we must assume wholly reflecting bodies as possible that scatter all incident radiation and which can therefore be described as completely white. If we allow the radiation coming from a black body to enter a space of this kind, it will in the end propagate exactly as if the walls of the space were themselves radiant and had the same temperature as the black body. If we then seal off the black body from the white space, we obtain the unrealisable case of a radiation permanently reciprocated between mirroring walls. In our thoughts, we continue the experiment. We imagine the volume of our space to be reduced by movement of the walls, so that the entire radiation is concentrated in a smaller space. Since radiation exercises a certain pressure, the pressure of light, on the walls it strikes, it follows that some work must have been expended in size reduction, as if we had compressed a gas. Because of the low magnitude of the pressure of light, this work is very small, but it can be computed accurately, which is all that matters in the case under discussion. In accordance with the principle of the conservation of energy, this work cannot be lost, it is converted into radiation, which further increases the radiation concentration. This change of radiation density due to the movement of the white walls is not the only change to which the radiation is subjected. When a light ray is reflected by a moving mirror, it undergoes a change of the colour dictated by the oscillation frequency. This change in accordance with the so-called Doppler principle plays a substantial part in astrophysics. The spectrum line emitted by an approaching celestial body appears to be displaced in the direction of shorter wavelengths in the ratio, its velocity: the velocity of light. This is also the case when a ray is reflected by a moving mirror, except that the change is twice as great. We are therefore able to calculate completely the change undergone by the radiation as a result of the movement of the walls. The pressure of light which is essential to these deliberations was demonstrated at a much later date, Lebedev being the first to do so. Arrhenius used it to explain the formation of comet tails. Before that, it was only a conclusion drawn from Maxwell's electromagnetic theory. We now calculate both the change of radiation density due to movement, and the change of the various wavelengths. From this mental experiment, we can draw an important conclusion. We can conclude from the second law of mechanical heat theory that the spectral composition of the radiation which we have changed by compression in the space with mirror walls is exactly the same as it would be had we obtained the increased density of radiation by raising the temperature, because we would otherwise be able to produce, by means of colour filters, unequal radiation densities in the two spaces, and to generate work from heat without compensation. Since we can calculate the change of individual wavelengths due to compression, we can also derive the manner in which the spectral composition of black-body radiation varies with temperature. Without discussing this calculation in detail, let me give you the result: the radiation energy of a certain wavelength varies with changing temperature so that the product of temperature and wavelength remains constant.
Using this displacement law it is easy to calculate the distribution of the intensity of thermal radiation over the various wavelengths for any temperature, as soon as it is known for one temperature.
The shift of the maximum of intensity in particular is directly accessible to observation. Since the wavelength at which the maximum intensity lies also defines the principal area of the wavelength which is most intense at this temperature, we can, by changing the temperature, shift the principal area of radiation in the direction of short or long wavelengths of any desired magnitude. Of the other derivations of the displacement law, I shall only mention that by H.A. Lorentz. If, in the electromagnetic equations of Maxwell, we imagine all spatial dimensions as being displaced in time in the same ratio, these equations show that the electromagnetic energy must decrease in proportion to the fourth power of displacement. Since, according to the Stefan-Boltzmann law, energy increases with the fourth power of absolute temperature, the linear dimensions must vary inversely proportionately to the absolute temperature. Each characteristic length must vary in this ratio, from which the displacement law follows.
From the displacement law, we can calculate the temperature of the sun if we are entitled to assume that the radiation of the sun must be ascribed to heat, and if we know the position of the maximum of the energy of solar radiation. Different figures are given for this position by different observers, i.e. 0.532 m according to Very, and 0.433 m according to Abbot and Fowle. Depending on the figure used, the temperature of the sun works out at 5,530° and 6,790°. However much the observers may differ, there can be no doubt that the maximum of solar radiation is situated in the visible range of wavelengths. This is to say that the temperature of the sun is the most favourable utilization of the radiant energy of a black body for our illumination and that, in our artificial light sources which utilize thermal radiation we must aim at achieving this temperature, from which we are admittedly far removed as yet.
I wish to discuss yet another application of the displacement law, i.e. the possibility of calculating the wavelength of X-rays. As we know, X-rays are produced by the impact of electrons on solid bodies, and their wavelength must be a function of the velocity of the electrons. According to the kinetic theory of gases, the mean kinetic energy of a molecule is a measure of absolute temperature. If, as is done in the theory of electrons, we assume that this is also valid for the kinetic energy of the electrons, the electric energy of the cathode rays would be a measure of their temperature. If we substitute the temperature thus calculated in the displacement law, we find that the wavelength of the maximum of the intensity indicates a wavelength range of X-rays which agrees well with the wavelengths found by other arguments. It might be objected that we must not ascribe a temperature to the electrons. The permissibility of our procedure can however be justified by an inversion of the above argument. Radiation in an enclosed space must necessarily release electrons whose velocity according to Einstein's law is proportional to the oscillation frequency. The energy maximum of radiation generates electrons whose velocity is so great that their kinetic energy comes very close to the temperature associated with the maximum of energy.
The displacement law exhausts the conclusions that can be drawn from pure thermodynamics with respect to radiation theory. All these conclusions have been confirmed by experience. The individual colours present in the radiation are mutually wholly independent. The manner in which at a given temperature the intensity of radiation is distributed over the individual wavelengths cannot be determined from thermodynamics. For this, one must examine the mechanism of the radiation process in detail. Similar conditions obtain in the theory of gases. Thermodynamics can tell us nothing about the magnitude of the specific heat of the gases; what is required, is to examine molecular motion. But the kinetic theory of gases which is based on probability calculations has made much greater progress than the corresponding theory of radiation. The statistical theory of gases has set itself the task of accounting also for the laws of thermodynamics. I do not wish to discuss here the extent to which the task may be considered as having been solved, and whether we are entitled to consider the reduction of the second law to probability as a wholly satisfactory theory. It has in any case been very successful, in particular since a theoretical explanation has been found of the deviations from the thermodynamic state of equilibrium, the so-called fluctuations, e.g. in Brownian movement. None of the statistical theories of radiation has however as yet even attempted to derive the Stefan-Boltzmann law and the displacement law, which must always be introduced into theory from outside. Quite apart from this, we are as yet far removed from a satisfactory theory to account for the distribution of radiation energy over the individual wavelengths.
I myself made the first attempt in this direction. I endeavoured to bypass the problem of applying probability calculation to radiation theory by imagining radiation as resulting from gas molecules moving according to laws of probability. Instead of these we could also imagine electrons generating radiation on striking molecules. What is essential is the further assumption that such a particle will only emit radiation of a certain wavelength dictated by velocity, and that the velocity distribution of the particles obeys Maxwell's law. With the assistance of the radiation laws derived from thermodynamics we obtain a radiation law which shows good agreement with experience for a wide range of wavelengths, i.e. for the range in which the product of temperature and wavelength is not unduly large.
Imperfect as this first attempt was, a formula had been obtained which considerably deviates from reality for large wavelengths only. Since observations however establish these deviations beyond doubt, it was clear that the formula had to be modified.
Lord Rayleigh was the first to approach the problem from an entirely different angle. He made the attempt to apply to the radiation problem a very general theorem of statistical mechanics, i.e. the theorem of the uniform distribution of energy over the degrees of freedom of the system in the state of statistical equilibrium. The meaning of this theorem is as follows:
In the state of thermal equilibrium, all movements of the molecules are so completely irregular that there exists no movement which would be preferred over any other. The position of the moving parts can be established by geometrical parameters which are mutually independent and in the direction of which the movement falls. These are called the degrees of freedom of the system. As regards the kinetic energy of movement, no degree of freedom is preferred over another, so that each contains the same amount of the total energy.
Radiation present in an empty space can be represented so that a given number of degrees of freedom is allocated to it. If the waves are reflected back and forth by the walls, systems of standing waves are established which adapt themselves to the distances between two walls. This is most easily understood if we consider a vibrating string which can execute an arbitrary number of individual vibrations, but whose half wavelengths must be equal to the length of the string divided by an integer.
The individual standing waves possible represent the determinants of the processes and correspond to the degrees of freedom. If we allocate to each degree of freedom its proper amount of energy, we obtain the Rayleigh radiation law, according to which the emission of radiation of a given wavelength is directly proportional to the absolute temperature, and inversely proportional to the fourth power of the wavelength. The law agrees with observation at exactly the point where the law discussed above failed, and it was at first considered to be a radiation law of limited validity. But if the process of radiation obeys the general laws of electromagnetic theory or of the theory of electrons, we must necessarily arrive at Rayleigh's radiation law, as Lorentz has shown. Viewed as a general radiation law, it directly contradicts all experience, because, according to it, energy would have to accumulate increasingly at the shortest wavelengths. The possibility that we are not dealing in reality with a true state of equilibrium of radiation, but that it very gradually approaches the state where all energy is only present in the shortest wavelengths, is also contradicted by experience. In the case of the visible rays, to which the Rayleigh formula no longer applies at attainable temperatures, we can easily calculate, according to the Kirchhoff law, that the state of equilibrium must be attained in the shortest time, which state however remains far removed from the Rayleigh law. We thus obtain an inkling of the extraordinary difficulties which confront exact definition of the radiation formula. The knowledge that current general electromagnetic theory is insufficient, that the theory of electrons is inadequate, to account for one of the most common of phenomena, i.e. the emission of light, remains purely negative as yet. We only know how the thing cannot be done, but we lack the signposts that would enable us to find our way. We do however know that none of the models whose mode of action is based on purely electromagnetic principles can lead to correct results.
It is the merit of Planck to have introduced new hypotheses which enable us to avoid Rayleigh's radiation law. For long waves, this law is undoubtedly correct, and the right radiation formula must have a form such that, for very long waves, it passes into Rayleigh's law, and for short waves into the law formulated by me. Planck therefore retains as starting point the distribution of energy over the degrees of freedom of the system, but he subjects this distribution of energy to a restriction by introducing the famous hypothesis of elements of energy, according to which energy is not infinitely divisible, but can only be distributed in rather large quantities which cannot be divided further. This hypothesis would probably have been accepted without difficulty, if unchangeable particles, e.g. atoms of energy had been involved. It is an assumption that has proved inevitable for matter and electricity. The energy elements of Planck are however no atoms of energy; on the contrary, the displacement law requires that they are inversely proportional to the wavelength of a given vibration. This represents great difficulty for the understanding of these energy elements. Once we accept the hypothesis, we arrive at an entirely different distribution of energy over the radiating centres, if we search for them according to the laws of probability. This does not however give us the radiation law. All we know is how much energy the radiating molecules possess on average at a certain temperature, but not how much energy they emit. To derive emission at a given energy, we need a definite model which emits radiation. We can only construct such a model on the foundation of the known electromagnetic laws, and it is at this early point that the difficulty of the theory starts. On the one hand we relinquish the electromagnetic laws by introducing the energy elements; on the other hand we make use of these same laws for discovering the relationship between emission and energy. It could admittedly be argued that the electromagnetic laws are only valid for mean values taken over extended periods, whereas the energy elements relate to the elementary radiation process itself. An oscillator radiating in accordance with the electromagnetic laws will indeed have little similarity with the real atoms. Planck however rightly argues that this does not matter precisely because radiation in the equilibrium state is independent of the nature of the emitting bodies. It will however be required of a model which is to stand for the real atoms that it should lack none of the essential characteristics of the event under consideration. Every body that emits thermal rays has the characteristic that it is able to convert thermal rays of one wavelength into thermal rays of a different wavelength. It is on this that there rests the possibility of a specific spectral composition being established in the radiation at all times. The Planck oscillator lacks this ability, and doubts are bound to be raised as to whether it can properly be used for establishing the relationship between energy and emission. This difficulty can be avoided, and the oscillator can be done without, if, with Debye, we decompose the radiation energy in a hollow cube into Planck energy elements and distribute these energy elements over the oscillation frequencies of the standing waves formed in the cube according to the laws of probability. The logarithm of this probability will then be proportional to entropy, and the law of radiation results, if we search for the maximum of this entropy. This result is proof of the extremely general nature of Planck's concepts.
There are however further difficulties. The energy elements increase with decreasing wavelength, and an oscillator exposed to incident radiation will, at low intensity, need a very long time before it absorbs a full energy element. What happens if the incident radiation ceases, before an entire energy element has been absorbed? The difficulties implicit in answering this question have recently induced Planck to reformulate his original theory. He now assumes of emission only that it can occur exclusively by whole energy elements. Absorption is assumed to occur continuously according to the electromagnetic laws, and the energy content of an oscillator is assumed to have energy values capable of continuous change. The difficulty of the long absorption time is indeed avoided in this manner. On the other hand the close relationship between emission and absorption for the elementary process is relinquished, and this relationship now becomes valid statistically only. Every atom which only emits whole energy elements and absorbs continuously would therefore in the event of emission suddenly expend energy from its own reserve and would supplement this but little in the event of short irradiation. The special hypothesis must be made that, taken as a whole for many atoms in the stationary state, the absorbed energy after all becomes equal to that emitted. Whereas in the original form of the Planck theory the introduction of the hypothesis of energy elements was sufficient to permit the radiation laws to be derived, the new theories include uncertainties which can only be removed by further hypotheses. On the other hand the new fundamental hypothesis provides the possibility of further application, e.g. to electron emission.
It will be seen from the few observations I am able to offer in this context how great are the difficulties that remain in radiation theory. But the reference to these difficulties which it is the duty of the scientific approach to emphasize must not prevent us from paying tribute to the great positive achievements which the Planck theory has already accomplished.
It has produced a law of radiation which accomodates all observed data and includes the Rayleigh formula and my own formula as limiting cases. In addition, it has thrown unexpected light on an entirely different subject, i.e. the theory of specific heats.
It has long been known that the specific heats do not strictly obey the Dulong-Petit law and that they decrease at low temperatures. Diamonds do not obey the Dulong-Petit law even at normal temperatures. This law can be derived from the theorem of the distribution of kinetic energy over the degrees of freedom and states that, in solid bodies, every atom possesses, in accordance with its three degrees of freedom, three times the amount of energy, and, because of the potential energy, altogether six times the amount of energy of a degree of freedom. If however we apply Planck's distribution of energy by energy elements, we obtain, according to Einstein, a formula for the specific heat which does in fact show the drop of temperature. This result is characteristic of the Planck theory. This theory of specific heats is not derived from the radiation formula, but from the formula for the mean energy of an oscillator which is based directly on the hypothesis of the energy elements. Unfortunately, difficulties are beginning to appear. The exact measurements of specific heats at low temperatures made in Nernst's laboratory have shown that the Einstein formula does not agree with observation. The formula which satisfies the experimental data contains half energy elements in addition to the whole energy elements, which cannot be interpreted satisfactorily as yet. There can however be no doubt that the Planck radiation theory provides the first step to the theory of specific heats.
That the theory should remain in many respects incomplete and provisional, is in the nature of the problem which is perhaps the most difficult which has ever confronted theoretical physics. What is involved is to leave behind the laws of theoretical physics confirmed by direct observation, which alone have been applied in the past, and to enter areas which are beyond the reach of direct observation.
The difficulties which beset radiation theory also emerge in an entirely different approach. Einstein investigated the fluctuations to which radiation is continuously subjected even in the state of equilibrium as a result of the irregularities of the thermal processes. If we imagine a small plate in a cavity filled with radiation, this plate will be subjected to a radiation pressure which is the same on average on both sides of the plate. Since the radiation must contain irregularities, the pressure will alternately be greater on one or the other side so that the plate will execute small irregular movements, similar to the Brownian movement of a dust particle suspended in a liquid. These fluctuations can be derived from probability calculations. According to the Boltzmann theorem there is a simple relationship between entropy and probability. The entropy of radiation is known from the radiation law, so that the probability of state is also known, from which the fluctuations can be calculated. The mathematical expression for these fluctuations consists, in a peculiar manner, of two members. The first is readily understandable: it is due to irregularities which arise as a result of the mutual interference of the many independent beams which meet in one point. Where the density of radiation energy is high, this term alone predominates; it corresponds to the radiation range that obeys Rayleigh's law.
The other term, which cannot be directly explained by the undulation theory, predominates at low density of radiation energy, where the radiation obeys the law formulated by me. It would be understandable if the radiation consisted of the Planck energy elements which would be localized even in an empty space. We cannot however pursue this line of thought. We cannot shake the undulation theory of light, which is one of the most firmly established constructions in the whole of physics. Moreover, the term to be explained by localized energy elements, is not present by itself, and it is a priori impossible to introduce a dualistic approach into optics, e.g. to assume simultaneously Huyghens' wave theory and Newton's emanation theory. All we can do is to relinquish the Boltzmann method of applying probability calculations to this type of fluctuations, or to assume that a new irregularity is introduced into radiation with the process of reflection.
In view of the magnitude of the difficulties it is natural that opinions about the path to be pursued should differ greatly. Some are of the opinion that the fundamental principles of electrodynamics must be changed. And yet, previous theory embraces a vast range of facts, it accounts for events even in the most rapid movements of the b-rays, it has proved itself in the most precise optical measurements. In my view, all the signs suggest that the deviations from current theory are due to events within the atom. None of the processes in which the interior of the atom participates are amenable to current theory.
Sommerfeld made an attempt in this direction: He would ascribe to the constant h of the radiation law, which together with the oscillation frequency dictates the magnitude of the energy element, a simple significance for the interior of the atom. It is alleged to determine the period in which an electron entering the atom comes to a stop, as a function of its velocity. On this view, the constant h expresses a universal characteristic of the atoms. This theory permits calculation of the wavelength of X-rays, and it connects two previously independent attempts made by me to carry out this calculation. One method is based on the Planck theory of energy elements in that it assumes that the energy of the so-called secondary electrons released by Xrays is dictated by the energy element. The second method is based on the theory of electrons by means of which it calculates the energy radiated in the X-rays by sudden braking of an electron. From the determination of the energy of the cathode rays and the X-rays we can then calculate the brake path of the electrons and consequently the wavelength of the X-rays. The Sommerfeld theory connects these two theories. It has the great advantage of explaining the generation of X-rays with the aid of electromagnetic theory. A number of conclusions can then be drawn from this which are in complete agreement with observation, e.g. the polarisation of X-rays, the diversity of emission and of hardness in various directions.
The Sommerfeld theory has the great advantage that it attempts to invest the universal constant h of the Planck radiation theory with physical significance. It has the disadvantage that it has been applied so far only to electron emission and absorption, but cannot yet solve the problem of thermal radiation.
We must admit that the result of radiation theory todate is not a very good one for theoretical physics. As we have seen, only the general thermodynami theories have proved satisfactory as yet. The theory of electrons has come to grief over the radiation problem, the Planck theory has not yet been brought into a definite form. Research is faced with exceptional difficulties and we cannot discern when and how they can be overcome. In science, the redeeming idea often comes from an entirely different direction, investigations in an entirely different field often throw unexpected light on the dark aspects of unresolved problems. We must base our hope in the future in the expectation that the present era which has proved so fruitful for physics may not pass without a complete solution being found for the problem of thermal radiation. Far-reaching and new thoughts will have to set to work, but the result will be great, because we shall obtain a profound insight into the world of the atom and the elementary processes within it.
维恩的演讲
Wilhelm Wien – Banquet Speech
Wilhelm Wien's speech at the Nobel Banquet in Stockholm, December 10, 1911 (in German)
K鰊igliche Hoheiten, meine verehrten Damen und Herren! Für uns, die wir den Nobel-Preis erhalten haben, wird das erste Gefühl ein tiefer Dank sein, aber wir werden auch Veranlassung haben, unsere eigne Stellung zu den Arbeiten, die mit dem Preise gekr鰊t sind, zu untersuchen. Wir werden nicht ganz mit dem günstigen Urteil der schwedischen Akademie übereinstimmen, denn in der Wissenschaft tritt noch mehr als anderswo das grosse Missverh鋖tnis zwischen dem, was man gewollt, und dem, was man vollbracht hat, hervor. Jeder, der auf seine wissenschaftlichen Leistungen zurückblickt, wird das was noch zu leisten ist, und das was nicht gelungen ist, so überwiegend im Vergleich mit dem finden, was er ausführen konnte, dass er sich sagen wird, was Du getan hast war doch recht wenig. Aber es kommt noch ein anderes hinzu. Die Wissenschaft ist ein Organismus, der sich nach seinen innern Gesetzen entwickeln muss. Ich m鯿hte sie mit einem Baum vergleichen, der eine grosse Krone bekommen hat und weiter w鋍hst, der sich aber nur die Stoffe zu assimilieren vermag, die er für seine Entwicklung brauchen kann. Und so kann auch die Wissenschaft nur die Ideen in sich aufnehmen, die ihrer Entwicklung gem鋝s sind. Alles andere wird ausgeschieden und versinkt im Meere der Vergessenheit.
So habe ich meine eigene Arbeiten nur so lange auf einem Gebiet getrieben, als ich Wege sah, die zu einer natürlichen Weiterentwicklung führten. Wenn es meiner Begabung nicht entsprach, solche zu finden habe ich nur mehr als Zuschauer beobachtet, wie die Arbeit durch andere fortgeführt wurde und mich gefreut, wenn es gelang weiterzukommen. Für mich selbst habe ich dann ein anderes Arbeitsgebiet gesucht.
Bei der Auszeichnung durch die Nobelpreise stimmt aber noch ein anderes zum Nachdenken. Nicht immer sind die wissenschaftlichen Bestrebungen so anerkannt worden, und es liegt die Zeit noch nicht weit zurück, wo bedeutende Leistungen vergeblich auf Anerkennung warteten. Heute ist der Baum der Wissenschaft gross geworden, er tr鋑t sch鰊e Früchte und ist weithin sichtbar. So wird er mehr beachtet als früher. Aber es ist doch keineswegs so, dass überall die Wissenschaft so geehrt wird wie hier bei der Nobelfeier. Dieses Fest und die allgemeine Teilnahme sind ein Beweis für den weit vorgeschrittenen Idealismus des schwedischen Volkes. Hoffen wir, dass die 鋘dern V鰈ker folgen werden.
Die Verteilung, der Nobelpreise legt eine schwere Verantwortung auf die Schultern der schwedischen M鋘ner der Wissenschaft. Sie haben eine grosse Arbeit zu leisten; aber eine sch鰊e und beneidenswerte Arbeit. Einen grossen Einfluss auf die Wissenschaft k鰊nen sie ausüben, auf die Jüngern M鋘ner der Wissenschaft, indem sie sie anspornen, Arbeiten zu schaffen, die gekr鰊t werden k鰊nen. Und es wird immer ein Anreiz sein, wenn man etwas schaffen kann, das als nützlich anerkannt wird. Aber auch die M鋘ner, welche den Vorzug schon erreicht haben, mit dem Nobelpreis gekr鰊t zu werden, werden beeinflusst, indem sie veranlasst werden, ihren Dank abzustatten. Und diesen Dank kann ich mir nur in einer Weise vorstellen, n鋗lich dadurch, dass man seine ganzen Kr鋐te zur F鰎derung seiner Wissenschaft weiter einsetzt. So wird die schwedische Akademie in eigenartigem und immer zunehmendem Masse den Wert wissenschaftlicher Arbeit einzusch鋞zen und die Wissenschaft selbst dadurch zu f鰎dern haben. Ich fordere sie auf, auf die schwedische Akademie der Wissenschaften anzustossen.
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