Chapter 4 Chapter Two Dark Clouds

one On April 27, 1900, the weather in London was still a bit cold.In the coffee shop on the side of the road, people were talking about the Universal Exposition being held in Paris at that time.Newsboys on the street were hawking newspapers, which were discussing the latest developments in China's Boxer Rebellion and the status of personnel in embassies in Beijing.A gentleman politely helped the lady into the carriage and rushed to listen to Puccini's opera "La Bohème".The two old ladies looked enviously at the carriage and admired the style of the lady's hat, but soon they found a new topic and began to comment on Earl Russell's divorce case.It seems that even the arrival of the new century cannot change the old and traditional way of life in this city.

In contrast, the presentation at the Royal Institution, Albemarle Street, received little attention.London's upper class seemed to have so poured out their enthusiasm for science on Sir Humphry Davy that they remained remarkably indifferent for decades to come.Still, it's a big deal for the scientific community.Famous scientists in Europe came here to listen to the speech of the respected but famous old man, Lord Kelvin. Kelvin's lecture was titled "Nineteenth-Century Dark Clouds Over the Dynamic Theory of Heat and Light".Already 76 years old at the time, the gray-haired man began his speech with his characteristic Irish accent. His first sentence was as follows:

"The dynamical theory asserts that heat and light are modes of motion. But the beauty and clarity of this theory are now overshadowed by two dark clouds..." ('The beauty and clarity of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds.') This dark cloud metaphor has since become so famous that it has been quoted over and over in almost every book on the history of physics, becoming a stereotyped statement.Linked to people's optimism about the unification of physics at that time, many times this expression became "two small dark clouds floating in the sunny sky of physics".These two famous dark clouds respectively refer to the difficulties encountered by classical physics in light ether and Maxwell-Boltzmann energy equipartition theory.To be more specific, it refers to the plight of people in the Michelson-Morley experiment and the research of black body radiation.

The purpose of the Michelson-Morley experiment is to detect the drift speed of light-ether to the earth.In people's minds at the time, the ether represented an absolutely static frame of reference, and the movement of the earth through the ether in space was like a ship traveling at high speed, blowing a strong "ether wind" head-on.Michelson conducted an experiment in 1881 to measure this relative velocity, but the result was not very satisfactory.So he teamed up with another physicist, Morey, to arrange a second experiment in 1886.This may be the most sophisticated experiment ever conducted in the history of physics at that time: they used the latest interferometers, and in order to improve the sensitivity and stability of the system, they even managed to get a large stone slab and put it in a mercury tank In this way, the interference factors are minimized.

However, the experimental results shocked and disappointed them: the two beams of light did not show any time difference at all.The aether seems to have no effect on the light passing through it.Unwillingly, Michelson and Morley observed for four days in a row. They even wanted to observe continuously for a year to determine the difference in the ether wind caused by the four seasons of the earth’s orbit around the sun. was reluctantly canceled. The Michelson-Morley experiment is the most famous "failed experiment" in the history of physics.It caused a sensation in the physics world at that time, because the concept of ether, as a representative of absolute motion, is the basis of classical physics and classical space-time theory.And this beam supporting the building of classical physics is ruthlessly negated by the result of an experiment, which immediately means the collapse of the entire physical world.However, no matter how pessimistic people were at that time, they did not think that classical physics, which had just achieved a great victory and reached its peak of glory, would collapse inexplicably, so people still proposed many compromise methods. The Irish physicist Fitzgerald ( George tzGerald and Dutch physicist Hendrik Antoon Lorentz independently put forward a hypothesis that the length of the object will shrink in the direction of motion, so that the relative motion speed of the ether cannot be measured.Although these hypotheses have allowed the concept of ether to continue to be preserved, they have raised strong questions about its meaning, because it is difficult to imagine how much of a "hypothetical physical quantity" with only theoretical significance is necessary.Kelvin's "first dark cloud" was put forward in this sense, but he thought that the hypothesis of length contraction had "get out of the woods" anyway, and all that had to be done was to modify the existing theory to better use The interaction between ether and matter is self-consistent.

As for the "second dark cloud", it refers to the inconsistency between black body radiation experiments and theories.It will play a very important part in our story, so we will discuss it carefully in later chapters.At the time of Kelvin's speech, there was still no sign of a solution to the problem.However, Kelvin's attitude towards this is also optimistic, because he himself does not believe in Boltzmann's theory of equal distribution of energy. He believes that the best way to dispel this dark cloud is to deny Boltzmann's theory (and To be honest, Boltzmann's theory of molecular motion was indeed controversial at the time, so that this rare genius was depressed and had mental problems. Boltzmann tried to commit suicide but failed, but he finally 6 years later, he personally ended his life in a small forest, leaving behind a great tragedy in the history of science).

The aged Kelvin stood on the podium, and the audience applauded his speech warmly.At the time, however, none of them (including Kelvin himself) would have understood what these two little dark clouds meant to physics.They can never imagine that it is these two inconspicuous dark clouds that will soon bring an unprecedented storm, lightning and thunder to the world, and cause terrible fires and floods, completely destroying the current prosperity and beauty.They also have no way of knowing that these two dark clouds will soon drive them out of the luxurious and comfortable theoretical palace, and exile them to the wilderness full of thorns and traps to live a wandering life for twenty years.What's more, they can't foresee that it is these two dark clouds that will eventually bring a great new life to physics, realize nirvana in the fire and rainstorm, and rebuild two more magnificent and beautiful castles.

The first dark cloud eventually led to the outbreak of the relativity revolution. The second dark cloud finally led to the outbreak of the quantum theory revolution. From today's perspective, Kelvin's speech back then is simply like a mysterious prophecy, which seems to have a sense of fate in the dark.Science took a big turn under his prediction, but the direction was completely unexpected by Kelvin.If the old jazz could live to this day and read the history of the development of physics in the new century, wouldn’t he be deeply shocked by his prophecy back then, and shudder in his heart?

**********After-dinner gossip: The great "accidental" experiment Let's talk about those famous "accidental" experiments in the history of physics today.By using the word "accident", I mean that the experiment failed to achieve the expected results, and it may be called a "failed" experiment to some extent. We have already talked about the Michelson-Morley experiment above. The results of this experiment were so shocking that its experimenters could not believe the correctness of their results for a considerable period of time.But it is precisely this negative evidence that finally makes the concept of "light ether" come to an end, and makes the birth of the theory of relativity possible.The failure of this experiment should be said to be a great victory in the history of physics. Science has always only believed in facts.

In the history of modern science, there have been many similar accidental experiments of great significance.Maybe we can start with AL Laroisier.At that time, people generally believed that the burning of objects was the result of "phlogiston" leaving the object.But one day in 1774, Lavoisier decided to measure the specific weight of this "phlogiston".He weighed a piece of tin with his scales and lit it.After the metal was completely burned to ashes, Lavoisier carefully collected every grain of ashes and weighed it again. The result made everyone at the time dumbfounded.According to phlogiston, the ash after burning should be lighter than before burning.Ten thousand steps back, even if phlogiston has no weight at all, it should still be the same weight.But Lavoisier's balance said: the ash is heavier than the metal before burning, and measuring the weight of phlogiston has become nonsense.However, when Lavoisier was surprised, he did not blame his own balance, but turned his suspicious eyes to the behemoth of phlogiston theory.Under his impetus, modern chemistry was finally established amidst the crash of this system.

By 1882, experimental difficulties had also begun to plague JWS Rayleigh, a professor of chemistry at the University of Cambridge.For a subject, he needed to accurately measure the specific gravity of various gases.When it came to nitrogen, however, Rayleigh ran into trouble.Here's the thing: To make sure the results were accurate, Rayleigh used two different methods to separate the gases.One is to produce nitrogen from ammonia by a method well known to chemists, and the other is to remove as much oxygen, hydrogen, water vapor, and other gases as possible from ordinary air, so that what is left should be pure nitrogen up.However, Rayleigh was distressed to find that the weights of the two were not the same, and the latter was two thousandths heavier than the former. Although a small difference, it was intolerable to a precise scientist like Rayleigh.In order to eliminate this difference, he tried his best, checked almost all his instruments, and repeated dozens of experiments, but the two-thousandth difference stubbornly existed there, and became more accurate with each measurement. .This obstacle made Rayleigh nearly go crazy. In desperation, he wrote to another chemist, William Ramsay, for help.The latter keenly pointed out that this weight difference may be caused by an imperceptible heavy gas mixed in the air.With the joint efforts of the two, argon (Ar) was finally discovered, and eventually led to the discovery of the entire noble gas group, which became a major evidence for the existence of the periodic table of elements. Another experiment worth talking about was done by Antoine Herni Becquerel in 1896.At that time, X-rays had just been discovered, and people were not very clear about its origin.Someone suggested that fluorescent substances could produce X-rays when exposed to sunlight, so Becquerel conducted research on this. He chose a kind of uranium oxide as a fluorescent substance, exposed it to the sun, and found that it did make black paper The film in the film was photosensitive, so he came to a preliminary conclusion: sunlight shining on fluorescent substances can indeed produce X-rays. However, just as he was about to study further, something unexpected happened.The weather turned cloudy, with dark clouds blocking the sun for several days.Becquerel had to put all his experimental equipment, including negatives and uranium salts, into the safe.However, on the fifth day, the weather still did not turn sunny. Becquerel couldn't bear it anymore and decided to develop the negatives.The uranium salt has been irradiated with a little light, and there should be some blurred marks on the film anyway, right? In getting his hands on the picture, however, Becquerel experienced that moment of surprise and delight that every scientist dreams of.His mind was dizzy: the negative was so thoroughly exposed, and the patterns on it were so clear, even a hundred times stronger than under strong sunlight.It was a historic moment when radioactive elements were discovered for the first time, albeit under dramatic circumstances.Becquerel's surprise finally opened the door to the interior of the atom, making people see a whole new world soon. Later in the story of quantum theory, we will see more such surprises.These accidents have added a brilliant legendary color to the history of science, and also made people more interested in the mysterious nature.That is one of the joys that science brings us. two As mentioned last time, Kelvin mentioned two "little dark clouds" in physics at the beginning of the century.The first one refers to the amazing results of the Michelson-Morley experiment, and the second one refers to the difficulties people encounter in the study of black body radiation. Our story is finally on the right track, and all of this begins with that confusing "black body". Everyone knows that the reason why an object looks white is because it reflects light waves of all frequencies; conversely, if it looks black, it is because it absorbs light waves of all frequencies.The "black body" defined in physics refers to objects that can absorb all external radiation, such as a hollow sphere, the inner wall is coated with radiation-absorbing paint, and a small hole is opened on the outer wall.Then, because the light entering the object from the small hole cannot be reflected, the small hole looks absolutely black, which is what we define as a "black body". At the end of the 19th century, people began to be interested in the thermal radiation problem of the blackbody model.In fact, very early on, people have noticed that for different objects, heat and radiation seem to have a certain corresponding relationship.For example, metals, anyone with life experience knows that if we heat a piece of iron on a fire, it will turn dark red when it reaches a certain temperature (in fact, there is invisible infrared radiation before this) , if the temperature is higher, it will become orange-yellow. When it reaches extremely high temperature, if we can find a way to prevent it from vaporizing, we can see that the iron block will appear blue-white.That is to say, there is a certain functional relationship between the thermal radiation of an object and its temperature (in astronomy, there are "red giant stars" and "blue giant stars", the former is dark red and has a lower temperature, and usually belongs to old stars; while the latter has an extremely high temperature. high, a model of young stars). The question is, what is the functional relationship between the radiated energy of an object and its temperature? The initial research on black body radiation is based on classical thermodynamics, and many famous scientists have done a lot of basic work before that.The thermal radiation meter invented by American Langley (Samuel Pierpont Langley) is the best measurement tool. With the Roland concave grating, a very accurate thermal radiation energy distribution curve can be obtained. The concept of "black body radiation" was proposed by the great Kirchhoff (Gustav Robert Kirchhoff), and was summarized and studied by Josef Stefan.In the 1880s, Boltzmann established his thermodynamic theory, and there are indications that this is a powerful theoretical weapon for the study of black body radiation.All in all, this was some basic background in physics on the subject when Wilhelm Wien was about to theoretically derive the black body radiation formula. Wien, the son of a landowner in East Prussia, seemed destined to become a farmer too, but the economic crisis at the time made him determined to study at university.After spending his studies at the Universities of Heidelberg, Göttingen and Berlin, Wien entered the German Reich Institute of Technology (Physikalisch Technische Reichsanstalt, PTR) in 1887, becoming principal investigator in the Helmholtz laboratory .It was in this laboratory in Berlin that he prepared to show his talents in theoretical and experimental physics and solve the problem of black body radiation once and for all. Starting from the idea of ​​classical thermodynamics, Wien assumed that the black body radiation was emitted by some molecules obeying Maxwell's velocity distribution, and then through precise deduction, he finally proposed his formula for the law of radiation energy distribution in 1893: u = b(λ^-5)(e^-a/λT) (where λ^-5 and e^-a/λT respectively represent the -5 power of λ and the -a/λT power of e. u represents The function of energy distribution, λ is the wavelength, T is the absolute temperature, a, b are constants. Of course, here is just to show everyone what this formula looks like. Friends who have no research in mathematics and physics can read it, no need pay attention to its specific meaning). This is the famous Wien distribution formula.Soon, another German physicist, F. Paschen, measured the thermal radiation of various solids on the basis of Langley, and the results were well in line with Wien's formula, which made Wien obtain initial victory. However, Wien faced a fundamental difficulty: his starting point seemed to be at odds with accepted reality. In other words, his molecular hypothesis made classical physicists very uncomfortable.Because radiation is electromagnetic waves, and as we all know, electromagnetic waves are a kind of fluctuations. Analyzing them with the method of classical particles seems to make people feel that there is something faintly wrong, and there is a taste of opposites. Sure enough, Wien's colleagues at the Imperial Institute of Technology (PTR) soon came up with another experiment.Otto Richard Lummer and Ernst Pringsheim reported in 1899 that when the black body was heated to a high temperature of more than 1000 K, the measured curve in the short wavelength range was in good agreement with the Wien formula OK, but when it comes to long wavelengths, experiment and theory diverge.Soon, the other two members of PTR, Heinrich Rubens and Ferdinand Kurlbaum, expanded the measurement range of the wavelength, reaffirmed this deviation, and concluded that the energy density in the long-wave range should be the same as The absolute temperature is directly proportional, not what Wien predicted, when the wavelength tends to infinity, the energy density has nothing to do with the temperature.In the last years of the 19th century, the PTR, an institution founded by Siemens and Helmholtz, seemed to be the most eye-catching place in the field of thermodynamics. Here, this group of theoretical and experimental physicists seemed to be uncovering Uncover one of physics' greatest secrets. The failure of Wien's law in long waves attracted the attention of the British physicist Rayleigh (remember the Sir who studied the weight of nitrogen and finally discovered the inert gas in our gossip last time?), he tried to modify The formula adapts to the experimental conclusion that u and T are proportional to high temperature and long waves, and finally draws his own formula.Not long after, another physicist, JH Jeans, calculated the constants in the formula, and finally they got the formula as follows: u = 8π(υ^2)kT / c^3 This is what we call the Rayleigh-Jeans formula today, where υ is the frequency, k is the Boltzmann constant, and c is the speed of light.Similarly, friends who are not interested can ignore its specific meaning, which has no effect on our story. In this way, the experimental result that u and T are proportional to high temperature and long wave is theoretically proved.However, perhaps, as the saying goes, the Rayleigh-Jins formula is a typical example of removing one thing for another.Because it is very ironic that although it conforms to the experimental data in the long wave, the failure in the short wave is obvious.When the wavelength λ tends to 0, that is, the frequency υ tends to infinity, you can see from the above formula that our energy radiation will inevitably tend to infinity.In other words, our black body will release almost infinite energy when the wavelength is short to a certain extent. This dramatic event is undoubtedly absurd, because no one has ever seen any object emit such energy radiation at any temperature (if this is the case, then the atomic bomb or something is too simple).This inference was later added a sensational title that is very suitable for appearing in science fiction, called "ultraviolet catastrophe".Obviously, the Rayleigh-Jins formula cannot give the correct black body radiation distribution. What we have here is a rather delicate and awkward situation.We now have two sets of formulas in our hands, but unfortunately, they only work in the shortwave and longwave ranges respectively.It really frustrates people, like you have two sets of clothes, one has a nice top but the pant legs are too long, and the other has nice pants but the top is too small to fit.The worst part is that these two sets of clothes can't be worn together at all. In short, on the black body problem, if we deduce it from the perspective of classical particles, we can get the Wien formula suitable for short waves.If deduced from the angle of similar waves, the Rayleigh-Jins formula applicable to long waves can be obtained.Long wave or short wave, that is the question. This conundrum has plagued physicists like this, with a dark sense of humor.When Kelvin described the "second dark cloud" on stage, people didn't know how this question would be answered in the end. However, after all, the bell of the new century has sounded, and a great revolution in physics is about to come.At this time, the first protagonist in our story, a slightly bald German with a mustache—Max Planck stepped onto the stage, and a new scene in physics finally opened. three As mentioned last time, we have two sets of formulas for the research on the blackbody problem.Unfortunately, one set is only effective in the longwave range, while the other is only effective in the shortwave range.When people were having a headache for this Dilemma, Max Planck stepped onto the stage of history.As fate would have it, this name will illuminate the history of physics throughout the 20th century. Max Carl Ernst Ludwig Planck was born in 1858 into a scholarly family in Kiel, Germany.His grandfather and great-grandfather were both professors of theology, and his father was a well-known law professor who had participated in the drafting of Prussian civil law. In 1867, the Planck family moved to Munich, where the young Planck attended middle school and university.When Bismarck's empire was flourishing, Planck retained the fine style of the classical period, was very interested in literature and music, and also showed extraordinary genius. Soon, however, his interest turned to nature.In the classroom of middle school, his teacher vividly described to the students how a worker moved the bricks to the roof, and the effort the worker expended was stored in the potential energy of the high place. Once the bricks fell down, the energy would follow. unleash….The magical conversion and conservation of energy greatly attracted the curious Planck, making him turn his attention to the mysterious laws of nature, which also became the starting point of his career.Germany lost a musician, but she gained a great master of science who pioneered the world. However, as we said in the previous chapter, theoretical physics did not look like a very promising job at the time.Planck's tutor at the university, Philipp von Jolly, persuaded him that the physical system had already been established very mature and complete, and there were no big discoveries to be made, so there was no need to waste time on this little discovery. meaning work above.Planck euphemistically stated that he studied physics out of interest in nature and rationality, and he just wanted to figure out the existing things, and he didn't expect to make any great achievements.Ironically, from today's point of view, this "very unpromising" expression has achieved one of the biggest breakthroughs in the physics world, and has achieved the fame of Planck's life.We should really be lucky with this decision. In 1879, Planck received a doctorate from the University of Munich, and then he successively taught at the Universities of Kiel, Munich and Berlin, and succeeded Kirchhoff.Planck's research interests were originally concentrated in the field of classical thermodynamics, but in 1896, he read Wien's paper on black body radiation and showed great interest in it.In Planck's view, the internal law of the object embodied by Wien's formula—the absolute law that has nothing to do with the nature of the object itself—represents something objective and eternal.It exists independently of people and the material world, and is not affected by the external world. It is the most noble goal pursued by science.Planck's preference is just a tradition and style of classical physics, an admiration for absolutely strict laws.This classical and conservative thought has passed through Newton, Laplace and Maxwell, with all the aristocratic atmosphere of the golden age, and penetrated deeply into Planck's bones.However, this venerable old-school scientist did not realize that he had unknowingly come to the forefront of the times, and his fate had arranged for him a deviant role. Let's get down to business.At the turn of the century, Planck decided to completely solve the problem of black body radiation, which has troubled people for a long time.He already has Wien's formula in his hand, but unfortunately this formula can only correctly predict the experimental results in the short-wave range.On the other hand, although Planck himself claimed that he did not know Rayleigh's formula at that time, he undoubtedly also knew the fact that u and T have a simple proportional relationship in the long wave range.This was told to him at noon on October 7, 1900 by a good friend of his, the experimental physicist Heinrich Rubens (mentioned in the previous chapter).By that date, Planck had been working on the problem for six years (he had begun investigating the field in 1894, before he had learned of Wien's work), but all All efforts seemed to be in vain. Now, please be quiet, and let our Mr. Planck think about the problem.The whole fact before him is that we have two formulas, each of which works only within a limited range.However, if we investigate the derivation of the two formulas fundamentally, we cannot find any problems.And our purpose is to find a generally applicable formula. Germany in October has entered mid-autumn.The weather is getting more and more gloomy, thick clouds are piling up in the sky, and the night is getting longer every day.The fallen leaves are colorful, covering the streets and fields, and occasionally the cool wind blows, and they rustle.During the day, Berlin is bustling and noisy, and at night, Berlin is quiet and solemn, but in this quiet and noisy, no one ever thought that a great historical moment is coming. In an office full of drafts at the University of Berlin, Planck brooded over the two irreconcilable formulas.Finally one day, he decided not to make those fundamental assumptions and derivations, anyway, we first try to come up with a formula that can satisfy all bands.Let's talk about other issues later. So, using mathematical interpolation, Planck began to play with the two formulas in his hand.What needs to be done is to make the influence of the Wien formula disappear as much as possible in the range of the long wave, and "exclusively" play out in the short wave.After trying for a few days, Planck finally came across a Bingo Moment, and he came up with a formula that seemed to fit the bill.At long waves, it behaves like a proportional relationship.On shortwave, it degenerates into the original form of Wien's formula. On October 19, Planck made this fresh formula public at a meeting of the German Physical Society (Deutschen Physikalischen Gesellschaft) in Berlin.That night, Rubens carefully compared the formula with the experimental results.As a result, to his surprise and joy, Planck's formula won a big victory. In every band, the data given by this formula are very accurate in line with the experimental value.The next day, Rubens notified Planck himself of the result, and Planck himself couldn't help being taken aback by this complete success.He didn't expect that this empirical formula, which was pieced together by luck, would have such a powerful power. Of course, he also thought that this shows that the success of the formula is not just a fluke.This shows that behind that mysterious formula, there must be some unknown secrets hidden.There must be some kind of universal principle postulated to support this formula, which makes it display such powerful force. Planck looked at his formula again. What kind of physical meaning does it represent?He found himself in a rather embarrassing position, knowing what was happening but not knowing why.Planck was like an unlucky candidate who glanced at the reference book beforehand, but when he was defending, he found that he only remembered the conclusion, but had no idea how to prove and explain it.The results of the experiment are conclusive, and it unequivocally proves the correctness of the theory, but why is this theory correct, what is it based on, and what does it explain?But no one could answer. However, Planck knew that there is a crucial thing hidden in it, which is related to the foundation of the entire thermodynamics and electromagnetism.Planck has vaguely realized that there seems to be a storm coming, and the analysis of this humble formula will change some aspects of physics.A sixth sense told him that the most important period of his life had arrived. Years later, Planck wrote to him: "At that time, I had been struggling with the problem of radiation and matter for 6 years, but to no avail. But I knew that this problem was crucial to the whole of physics, and I had also found the formula to determine the energy distribution. So, no matter what you pay At what cost, I must find a theoretical explanation for it. And I know very well that classical physics cannot solve this problem..." (Letter to RW Wood, 1931) At the watershed in his life, Planck finally decided to show his greatest determination and courage to open the Pandora's box in front of him, no matter what was inside.In order to solve this mystery, Planck has the spirit of breaking the boat.Except for the two laws of thermodynamics that he believes are unshakable, he is ready to abandon even the entire universe.However, even so, when he finally understood the meaning behind the formula, he was still so surprised that he couldn't believe it and accepted everything he found.Planck never dreamed at the time that his work was much more than just changing the face of physics.In fact, the whole of physics and chemistry will be completely destroyed and rebuilt, and a new era will come. In the last months of 1900, the black body, a dark cloud floating in the physical sky, began to roil inside. *********After dinner gossip: World Science Center In our history, we have seen many great men of science, from which we can also clearly see the continuous migration of world science centers. At the beginning of modern science, that is, in the 17th and 18th centuries, Britain was the undisputed center of world science (formerly Italy).Newton, as a representative of a generation of scientists, needless to say, Boyle, Hooke, until later David, Cavendish, Dalton, Faraday, Thomas Young, are the world's leading scientists.But soon, the center shifted to France.The Rise of France by Bernoulli Bernoulli), D'Alembert (JRdAlembert), Lavoisier, Lamarck, etc., to Ampere (Andre Marie Ampere), Fresnel, Carnot (Nicolas Carnot), Laplace, Foucault, Poisson, La The era of Grange has already dominated Europe.However, in the second half of the 19th century, Germany began to catch up, and a large number of geniuses emerged, Gauss, Ohm, Humboldt, Waller (Friedrich) Wohler), Helmholtz, Clausius, Boltzmann, Hertz... Although the UK even produced great men like Faraday, Maxwell, and Darwin, it was not enough to regain its original status.At the beginning of the 20th century, Germany's achievements in science reached its peak and became a sacred place in the minds of scientists from all over the world. Berlin, Munich and Göttingen became the well-deserved world centers of natural science at that time.In the future history, we will see more and more German names.Unfortunately, after the Nazis came to power, Germany's scientific and technological status plummeted, and a large number of scientists fled abroad, which directly caused the rise of the United States until today. I just don't know, who will be the next overlord? Four As mentioned last time, when Planck was studying black bodies, he accidentally discovered a universal formula, but he didn't know the physical meaning behind this formula. In order to be able to explain his new formula, Planck had decided to cast aside all conventional preconceived notions in his mind.He repeatedly chewed on the meaning of the new formula, and realized its connection and difference with the original two formulas.我们已经看到了，如果从玻尔兹曼运动粒子的角度来推导辐射定律，就得到维恩的形式，要是从纯麦克斯韦电磁辐射的角度来推导，就得到瑞利－金斯的形式。那么，新的公式，它究竟是建立在粒子的角度上，还是建立在波的角度上呢？ 作为一个传统的保守的物理学家，普朗克总是尽可能试图在理论内部解决问题，而不是颠覆这个理论以求得突破。更何况，他面对的还是有史以来最伟大的麦克斯韦电磁理论。但是，在种种尝试都失败了以后，普朗克发现，他必须接受他一直不喜欢的统计力学立场，从玻尔兹曼的角度来看问题，把熵和几率引入到这个系统里来。 那段日子，是普朗克一生中最忙碌，却又最光辉的日子。20年后，1920年，他在诺贝尔得奖演说中这样回忆道： “……经过一生中最紧张的几个礼拜的工作，我终于看见了黎明的曙光。一个完全意想不到的景象在我面前呈现出来。”（…until after some weeks of the most intense work of my life clearness began to dawn upon me， and an unexpected view revealed itself in the distance） 什么是“完全意想不到的景象”呢？原来普朗克发现，仅仅引入分子运动理论还是不够的，在处理熵和几率的关系时，如果要使得我们的新方程成立，就必须做一个假定，假设能量在发射和吸收的时候，不是连续不断，而是分成一份一份的。 为了引起各位听众足够的注意力，我想我应该把上面这段话重复再写一遍。事实上我很想用初号的黑体字来写这段话，但可惜论坛不给我这个功能。 “必须假定，能量在发射和吸收的时候，不是连续不断，而是分成一份一份的。” 在了解它的具体意义之前，不妨先了解一个事实：正是这个假定，推翻了自牛顿以来200多年，曾经被认为是坚固不可摧毁的经典世界。这个假定以及它所衍生出的意义，彻底改变了自古以来人们对世界的最根本的认识。极盛一时的帝国，在这句话面前轰然土崩瓦解，倒坍之快之彻底，就像爱伦·坡笔下厄舍家那间不祥的庄园。 好，回到我们的故事中来。能量不是连续不断的，这有什么了不起呢？ 很了不起。因为它和有史以来一切物理学家的观念截然相反（可能某些伪科学家除外，呵呵）。自从伽利略和牛顿用数学规则驯服了大自然之后，一切自然的过程就都被当成是连续不间断的。如果你的中学物理老师告诉你，一辆小车沿直线从A点行驶到B点，却不经过两点中间的C点，你一定会觉得不可思议，甚至开始怀疑该教师是不是和校长有什么裙带关系。自然的连续性是如此地不容置疑，以致几乎很少有人会去怀疑这一点。当预报说气温将从20度上升到30度，你会毫不犹豫地判定，在这个过程中间气温将在某个时刻到达25度，到达28度，到达29又1/2度，到达29又3/4度，到达29又9/10度……总之，一切在20度到30度之间的值，无论有理的还是无理的，只要它在那段区间内，气温肯定会在某个时刻，精确地等于那个值。 对于能量来说，也是这样。当我们说，这个化学反应总共释放出了100焦耳的能量的时候，我们每个人都会潜意识地推断出，在反应期间，曾经有某个时刻，总体系释放的能量等于50焦耳，等于32.233焦耳，等于3.14159……焦耳。总之，能量的释放是连续的，它总可以在某个时刻达到范围内的任何可能的值。这个观念是如此直接地植入我们的内心深处，显得天经地义一般。 这种连续性，平滑性的假设，是微积分的根本基础。牛顿、麦克斯韦那庞大的体系，便建筑在这个地基之上，度过了百年的风雨。当物理遇到困难的时候，人们纵有怀疑的目光，也最多盯着那巍巍大厦，追问它是不是在建筑结构上有问题，却从未有丝毫怀疑它脚下的土地是否坚实。而现在，普朗克的假设引发了一场大地震，物理学所赖以建立的根本基础开始动摇了。 普朗克的方程倔强地要求，能量必须只有有限个可能态，它不能是无限连续的。在发射的时候，它必须分成有限的一份份，必须有个最小的单位。这就像一个吝啬鬼无比心痛地付帐，虽然他尽可能地试图一次少付点钱，但无论如何，他每次最少也得付上1个penny，因为没有比这个更加小的单位了。这个付钱的过程，就是一个不连续的过程。我们无法找到任何时刻，使得付帐者正好处于付了1.00001元这个状态，因为最小的单位就是0.01元，付的帐只能这样“一份一份”地发出。我们可以找到他付了1元的时候，也可以找到他付了1.01元的时候，但在这两个状态中间，不存在别的状态，虽然从理论上说，1元和1.01元之间，还存在着无限多个数字。 普朗克发现，能量的传输也必须遵照这种货币式的方法，一次至少要传输一个确定的量，而不可以无限地细分下去。能量的传输，也必须有一个最小的基本单位。能量只能以这个单位为基础一份份地发出，而不能出现半个单位或者四分之一单位这种情况。在两个单位之间，是能量的禁区，我们永远也不会发现，能量的计量会出现小数点以后的数字。 1900年12月14日，人们还在忙活着准备欢度圣诞节。这一天，普朗克在德国物理学会上发表了他的大胆假设。他宣读了那篇名留青史的《黑体光谱中的能量分布》的论文，其中改变历史的是这段话： 为了找出N个振子具有总能量Un的可能性，我们必须假设Un是不可连续分割的，它只能是一些相同部件的有限总和……（die Wahrscheinlichkeit zu finden， dass die N Resonatoren ingesamt Schwingungsenergie Un besitzen， Un nicht als eine unbeschr？nkt teilbare， sondern al seine ganzen Zahl von endlichen gleichen Teilen aufzufassen…） 这个基本部件，普朗克把它称作“能量子”（Energieelement），但随后很快，在另一篇论文里，他就改称为“量子”（Elementarquantum），英语就是quantum。这个字来自拉丁文quantus，本来的意思就是“多少”，“量”。量子就是能量的最小单位，就是能量里的一美分。一切能量的传输，都只能以这个量为单位来进行，它可以传输一个量子，两个量子，任意整数个量子，但却不能传输1又1/2个量子，那个状态是不允许的，就像你不能用现钱支付1又1/2美分一样。 那么，这个最小单位究竟是多少呢？从普朗克的方程里可以容易地推算出这个常数的大小，它约等于6.55×10^-27尔格*秒，换算成焦耳，就是6.626×10^-34焦耳*秒。这个单位相当的小，也就是说量子非常的小，非常精细。因此由它们组成的能量自然也十分“细密”，以至于我们通常看起来，它就好像是连续的一样。这个值，现在已经成为了自然科学中最为重要的常数之一，以它的发现者命名，称为“普朗克常数”，用h来表示。 请记住1900年12月14日这个日子，这一天就是量子力学的诞辰。量子的幽灵从普朗克的方程中脱胎出来，开始在欧洲上空游荡。几年以后，它将爆发出令人咋舌的力量，把一切旧的体系彻底打破，并与联合起来的保守派们进行一场惊天动地的决斗。我们将在以后的章节里看到，这个幽灵是如此地具有革命性和毁坏性，以致于它所过之处，最富丽堂皇的宫殿都在瞬间变成了断瓦残垣。物理学构筑起来的精密体系被毫不留情地砸成废铁，千百年来亘古不变的公理被扔进垃圾箱中不得翻身。它所带来的震撼力和冲击力是如此地大，以致于后来它的那些伟大的开创者们都惊吓不已，纷纷站到了它的对立面。当然，它也决不仅仅是一个破坏者，它更是一个前所未有的建设者，科学史上最杰出的天才们参予了它成长中的每一步，赋予了它华丽的性格和无可比拟的力量。人类理性最伟大的构建终将在它的手中诞生。 一场前所未有的革命已经到来，一场最为反叛和彻底的革命，也是最具有传奇和史诗色彩的革命。暴风雨的种子已经在乌云的中心酿成，只等适合的时候，便要催动起史无前例的雷电和风暴，向世人昭示它的存在。而这一切，都是从那个叫做马克斯？普朗克的男人那里开始的。 *********饭后闲话：连续性和悖论 古希腊有个学派叫做爱利亚派，其创建人名叫巴门尼德（Parmenides）。这位哲人对运动充满了好奇，但在他看来，运动是一种自相矛盾的行为，它不可能是真实的，而一定是一个假相。why?因为巴门尼德认为世界上只有一个唯一的“存在”，既然是唯一的存在，它就不可能有运动。因为除了“存在”就是“非存在”，“存在”怎么可能移动到“非存在”里面去呢？所以他认为“存在”是绝对静止的，而运动是荒谬的，我们所理解的运动只是假相而已。 巴门尼德有个学生，就是大名鼎鼎的芝诺（Zeno）。他为了为他的老师辩护，证明运动是不可能的，编了好几个著名的悖论来说明运动的荒谬性。我们在这里谈谈最有名的一个，也就是“阿喀琉斯追龟辩”，这里面便牵涉到时间和空间的连续性问题。 阿喀琉斯是史诗里的希腊大英雄。有一天他碰到一只乌龟，乌龟嘲笑他说：“别人都说你厉害，但我看你如果跟我赛跑，还追不上我。” 阿喀琉斯大笑说：“这怎么可能。我就算跑得再慢，速度也有你的10倍，哪会追不上你？” 乌龟说：“好，那我们假设一下。你离我有100米，你的速度是我的10倍。现在你来追我了，但当你跑到我现在这个位置，也就是跑了100米的时候，我也已经又向前跑了10米。当你再追到这个位置的时候，我又向前跑了1米，你再追1米，我又跑了1/10米……总之，你只能无限地接近我，但你永远也不能追上我。” 阿喀琉斯怎么听怎么有道理，一时丈二和尚摸不着头脑。 这个故事便是有着世界性声名的“芝诺悖论”（之一），哲学家们曾经从各种角度多方面地阐述过这个命题。这个命题令人困扰的地方，就在于它采用了一种无限分割空间的办法，使得我们无法跳过这个无限去谈问题。虽然从数学上，我们可以知道无限次相加可以限制在有限的值里面，但是数学从本质上只能告诉我们怎么做，而不能告诉我们能不能做到。 但是，自从量子革命以来，学者们越来越多地认识到，空间不一定能够这样无限分割下去。量子效应使得空间和时间的连续性丧失了，芝诺所连续无限次分割的假设并不能够成立。这样一来，芝诺悖论便不攻自破了。量子论告诉我们，“无限分割”的概念是一种数学上的理想，而不可能在现实中实现。一切都是不连续的，连续性的美好蓝图，其实不过是我们的一种想象。 Fives 我们的故事说到这里，如果给大家留下这么一个印象，就是量子论天生有着救世主的气质，它一出世就像闪电划破夜空，引起众人的惊叹及欢呼，并摧枯拉朽般地打破旧世界的体系。如果是这样的话，那么笔者表示抱歉，因为事实远远并非如此。 我们再回过头来看看物理史上的伟大理论：牛顿的体系闪耀着神圣不可侵犯的光辉，从诞生的那刻起便有着一种天上地下唯我独尊的气魄。麦克斯韦的方程组简洁深刻，倾倒众生，被誉为上帝谱写的诗歌。爱因斯坦的相对论虽然是平民出身，但骨子却继承着经典体系的贵族优雅气质，它的光芒稍经发掘后便立即照亮了整个时代。这些理论，它们的成功都是近乎压倒性的，天命所归，不可抗拒。而伟人们的个人天才和魅力，则更加为其抹上了高贵而骄傲的色彩。但量子论却不同，量子论的成长史，更像是一部艰难的探索史，其中的每一步，都充满了陷阱、荆棘和迷雾。量子的诞生伴随着巨大的阵痛，它的命运注定了将要起伏而多舛。量子论的思想是如此反叛和躁动，以至于它与生俱来地有着一种对抗权贵的平民风格；而它显示出来的潜在力量又是如此地巨大而近乎无法控制，这一切都使得所有的人都对它怀有深深的惧意。 而在这些怀有戒心的人们中间，最有讽刺意味的就要算量子的创始人：普朗克自己了。作为一个老派的传统物理学家，普朗克的思想是保守的。虽然在那个决定命运的1900年，他鼓起了最大的勇气做出了量子的革命性假设，但随后他便为这个离经叛道的思想而深深困扰。在黑体问题上，普朗克孤注一掷想要得到一个积极的结果，但最后导出的能量不连续性的图象却使得他大为吃惊和犹豫，变得畏缩不前起来。 如果能量是量子化的，那么麦克斯韦的理论便首当其冲站在应当受置疑的地位，这在普朗克看来是不可思议，不可想象的。事实上，普朗克从来不把这当做一个问题，在他看来，量子的假设并不是一个物理真实，而纯粹是一个为了方便而引入的假设而已。普朗克压根也没有想到，自己的理论在历史上将会有着多么大的意义，当后来的一系列事件把这个意义逐渐揭露给他看时，他简直都不敢相信自己的眼睛，并为此惶恐不安。有人戏称，普朗克就像是童话里的那个渔夫，他亲手把魔鬼从封印的瓶子里放了出来，自己却反而被这个魔鬼吓了个半死。 有十几年的时间，量子被自己的创造者所抛弃，不得不流浪四方。普朗克不断地告诫人们，在引用普朗克常数h的时候，要尽量小心谨慎，不到万不得已千万不要胡思乱想。这个思想，一直要到1915年，当玻尔的模型取得了空前的成功后，才在普朗克的脑海中扭转过来。量子论就像神话中的英雄海格力斯（Hercules），一出生就被抛弃在荒野里，命运更为他安排了重重枷锁。他的所有荣耀，都要靠自己那非凡的力量和一系列艰难的斗争来争取。作为普朗克本人来说，他从一个革命的创始者而最终走到了时代的反面，没能在这段振奋人心的历史中起到更多的积极作用，这无疑是十分遗憾的。在他去世前出版的《科学自传》中，普朗克曾回忆过他那企图调和量子与经典理论的徒劳努力，并承认量子的意义要比那时他所能想象的重要得多。 不过，我们并不能因此而否认普朗克在量子论所做出的伟大而决定性的贡献。有一些观点可能会认为普朗克只是凭借了一个巧合般的猜测，一种胡乱的拼凑，一个纯粹的运气才发现了他的黑体方程，进而假设了量子的理论。他只是一个幸运儿，碰巧猜到了那个正确的答案而已。而这个答案究竟意味着什么，这个答案的内在价值却不是他能够回答和挖掘的。但是，几乎所有的关于普朗克的传记和研究都会告诉我们，虽然普朗克的公式在很大程度上是经验主义的，但是一切证据都表明，他已经充分地对这个答案做好了准备。1900年，普朗克在黑体研究方面已经浸淫了6年，做好了理论上突破的一切准备工作。其实在当时，他自己已经很清楚，经典的电磁理论已经无法解释实验结果，必须引入热力学解释。而这样一来，辐射能量的不连续性已经是一个不可避免的结果。这个概念其实早已在他的脑海中成形，虽然可能普朗克本人没有清楚地意识到这一点，或者不肯承认这一点，但这个思想在他的潜意识中其实已经相当成熟，呼之欲出了。正因为如此，他才能在导出方程后的短短时间里，以最敏锐的直觉指出蕴含在其中的那个无价的假设。普朗克以一种那个时代非常难得的开创性态度来对待黑体的难题，他为后来的人打开了一扇通往全新未知世界的大门。无论从哪个角度来看，这样的伟大工作，其意义都是不能低估的。 而普朗克的保守态度也并不是偶然的。实在是量子的思想太惊人，太过于革命。从量子论的成长历史来看，有着这样一个怪圈：科学巨人们参予了推动它的工作，却终于因为不能接受它惊世骇俗的解释而纷纷站到了保守的一方去。在这个名单上，除了普朗克，更有闪闪发光的瑞利、汤姆逊、爱因斯坦、德布罗意，乃至薛定谔。这些不仅是物理史上最伟大的名字，好多更是量子论本身的开创者和关键人物。量子就在同它自身创建者的斗争中成长起来，每一步都迈得艰难而痛苦不堪。我们会在以后的章节中，详细地去观察这些激烈的思想冲击和观念碰撞。不过，正是这样的磨砺，才使得一部量子史话显得如此波澜壮阔，激动人心，也使得量子论本身更加显出它的不朽光辉来。量子论不像牛顿力学或者爱因斯坦相对论，它的身上没有天才的个人标签，相反，整整一代精英共同促成了它的光荣。 作为老派科学家的代表，普朗克的科学精神和人格力量无疑是可敬的。在纳粹统治期间，正是普朗克的努力，才使得许多犹太裔的科学家得到保护，得以继续工作。但是，量子论这个精灵蹦跳在时代的最前缘，它需要最有锐气的头脑和最富有创见的思想来激活它的灵气。20世纪初，物理的天空中已是黑云压城，每一升空气似乎都在激烈地对流和振荡。一个伟大的时代需要伟大的人物，有史以来最出色和最富激情的一代物理学家便在这乱世的前夕成长起来。 1900年12月14日，普朗克在柏林宣读了他关于黑体辐射的论文，宣告了量子的诞生。那一年他42岁。 就在那一年，一个名叫阿尔伯特·爱因斯坦（Albert Einstein）的青年从苏黎世联邦工业大学（ETH）毕业，正在为将来的生活发愁。他在大学里旷了无穷多的课，以致他的教授闵可夫斯基（Minkowski）愤愤地骂他是“懒狗”。没有一个人肯留他在校做理论或者实验方面的工作，一个失业的黯淡前途正等待着这位不修边幅的年轻人。 在丹麦，15岁的尼尔斯·玻尔（Niels Bohr）正在哥本哈根的中学里读书。玻尔有着好动的性格，每次打架或争论，总是少不了他。学习方面，他在数学和科学方面显示出了非凡的天才，但是他的笨拙的口齿和惨不忍睹的作文却是全校有名的笑柄。特别是作文最后的总结（conclusion），往往使得玻尔头痛半天，在他看来，这种总结是无意义的重复而已。有一次他写一篇关于金属的论文，最后总结道：In conclusion， I would like to mention uranium（总而言之，我想说的是铀）。 埃尔文·薛定谔（Erwin Schrodinger）比玻尔小两岁，当时在维也纳的一间著名的高级中学Akademisches Gymnasium上学。这间中学也是物理前辈玻尔兹曼，著名剧作家施尼茨勒（Arthur Schnitzler）和齐威格（Stefanie Zweig）的母校。对于刚入校的学生来说，拉丁文是最重要的功课，每周要占8个小时，而数学和物理只用3个小时。不过对薛定谔来说一切都是小菜一碟，他热爱古文、戏剧和历史，每次在班上都是第一。小埃尔文长得非常帅气，穿上礼服和紧身裤，俨然一个翩翩小公子，这也使得他非常受到欢迎。 马克斯·波恩（Max Born）和薛定谔有着相似的教育背景，经过了家庭教育，高级中学的过程进入了布雷斯劳大学（这也是当时德国和奥地利中上层家庭的普遍做法）。不过相比薛定谔来说，波恩并不怎么喜欢拉丁文，甚至不怎么喜欢代数，尽管他对数学的看法后来在大学里得到了改变。他那时疯狂地喜欢上了天文，梦想着将来成为一个天文学家。 路易斯·德布罗意（Louis de Broglie）当时8岁，正在他那显赫的贵族家庭里接受良好的幼年教育。他对历史表现出浓厚的兴趣，并乐意把自己的时间花在这上面。 沃尔夫冈·恩斯特·泡利（Wolfgang Ernst Pauli）才出生8个月，可怜的小家伙似乎一出世就和科学结缘。他的middle name，Ernst，就是因为他父亲崇拜著名的科学家恩斯特·马赫（Ernst Mach）才给他取的。 而再过12个月，维尔兹堡（Wurzberg）的一位著名希腊文献教授就要喜滋滋地看着他的宝贝儿子小海森堡（Werner Karl Heisenberg）呱呱坠地。稍早前，罗马的一位公务员把他的孩子命名为恩里科·费米（Enrico Fermi）。20个月后，保罗·狄拉克（Paul Dirac）也将出生在英国的布里斯托尔港。 好，演员到齐。那么，好戏也该上演了。