Chapter 3 Chapter Two Dark Clouds

one On April 27, 1900, the weather in London was still a bit cold.In the coffee shop by the side of the road, people were chatting enthusiastically 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 high society seems to have put their enthusiasm for science in Humphrey.Sir Humphry Davy poured so much into it that he remained extraordinarily 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 old man, Lord Kelvin, who was famous for his stubbornness. Kelvin's lecture was entitled "Nineteenth-Century Dark Clouds Over the Dynamic Theory of Heat and Light".Already seventy-six years old at the time, the gray-haired man began his speech with his characteristic Irish accent. His first sentence was as follows:

Kinetic theory asserts that both heat and light are modes of motion.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 cited 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 turned into 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 on black body radiation.

The purpose of the Michelson︱Morley experiment is to detect the drifting speed of light ether for the earth.In people's minds at the time, 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 on its face.Michelson conducted an experiment in 1881 to measure this relative velocity, but the results were not very satisfactory.So he cooperated with another physicist, Morey, and arranged 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.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 of the ether wind caused by the four seasons of the earth's orbit around the sun. The painting was also 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 glorious peak, would collapse inexplicably, so people still proposed many compromise methods. Irish physicist Fitzgerald Fitzgerald (George FitzGerald) 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 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 significance, because it is difficult to imagine how much of a hypothetical physical quantity that only has theoretical significance is necessary.Kelvin's first dark cloud was proposed in this sense, but he believed that the hypothesis of length contraction had gotten people out of the woods anyway, and all that had to be done was to modify the existing theory to better make the ether and matter The interaction is self-consistent.

As for the second dark cloud, it refers to the inconsistency between black body radiation experiment and theory.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 Six 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.Using the word accident means 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, and the results of this experiment were so shocking that its experimenters could not believe the correctness of their results for quite a period of time.But it is 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.People at that time generally believed that objects burned because phlogiston left the object.But one day in 1774, Lavoisier decided to measure the exact 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 also began 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 remains should be pure nitrogen.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.It was suggested that fluorescent substances could produce X-rays when exposed to sunlight, so Becquerel conducted research on this. He chose a uranium oxide as a fluorescent substance, exposed it to the sun, and found that it did make black The negative film in the paper 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 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 research of black body radiation. Our story is finally on the right track, and it all starts 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.Physically defined black bodies refer 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 that hits the object from the small hole cannot be reflected, the small hole looks absolutely black, which is what we define as a blackbody. At the end of the nineteenth century, people began to be interested in the problem of thermal radiation 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 giants and blue giants, the former is dark red and has a lower temperature, and usually belongs to old stars; while the latter has extremely high temperature and is a young star. stellar model). 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 Gustav Robert Kirchhoff and 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, all this is when William.When Wilhelm Wien was going to theoretically derive the black body radiation formula, some basic backgrounds in the physics community on this topic. Wayne, 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 and became a member of the Helmholtz Laboratory main researcher.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, Winn assumed that 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 -fifth 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 on mathematics and physics can read it and ignore it. its specific meaning). This is the well-known formula of the Wien distribution.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, Wayne'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 a black body was heated to a high temperature of more than 1,000 K, the measured curves in the short wavelength range and Wien The formula fit well, but at long wavelengths, experiment and theory diverged.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 temperature.In the last few years of the nineteenth century, the PTR, an institution founded by Siemens and Helmholtz, seemed to be the most prominent place in the field of thermodynamics. The group of theoretical and experimental physicists here seemed to be 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 zero, 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 name that is very suitable for appearing in science fiction, called the ultraviolet catastrophe.Obviously, the Rayleigh︱Jins formula cannot give the correct distribution of black body radiation. 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's formula suitable for short waves.If it is 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 the 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 German with a mustache and a little bald head, 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 twentieth 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. let go.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 performance has achieved one of the biggest breakthroughs in physics, 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 absolute law embodied in Wien's formula, which 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 the Wien 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 spent six years on the problem (in 1894, before he had learned of Wein's work, he had begun investigating the field) , but all efforts seem 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 Wayne's formula disappear as far as possible in the range of long waves, and be exclusively exerted in short waves.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 and 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 the time, I had been wrestling with radiation and matter for six years, to no avail.But I know that this problem is crucial to the whole of physics, and I have found the formula for determining the energy distribution.So, whatever the cost, I had to 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. Gossip after dinner: 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 seventeenth and eighteenth 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.Yang is one of the world's leading scientists.But soon, the center shifted to France.The rise of France started with Bernoulli (Daniel Bernoulli), D'Alembert (JRd'Alembert), Lavoisier, Lamarck, etc., and then went to Ampere (Andre Marie Ampere), Fresnel, Nicolas Carnot (Nicolas Carnot), Rapp The era of Lars, Foucault, Poisson, and Lagrange has already dominated Europe.However, in the second half of the nineteenth century, Germany began to catch up, and a large number of geniuses emerged, such as Gauss, Ohm, Humboldt, Friedrich Wohler, Helmholtz, Clausius, Boltzmann, Hertz Even though Great Britain has even produced such great men as Faraday, Maxwell, and Darwin, it is 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 for 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 chewed on the meaning of the new formula over and over again, realizing its connection and difference with the original two formulas.我們已經看到了，如果從玻爾茲曼運動粒子的角度來推導輻射定律，就得到威恩的形式，要是從純麥克斯韋電磁輻射的角度來推導，就得到瑞利︱金斯的形式。那麼，新的公式，它究竟是建立在粒子的角度上，還是建立在波的角度上呢？ 作為一個傳統的保守的物理學家，普朗克總是盡可能試圖在理論內部解決問題，而不是顛覆這個理論以求得突破。更何況，他面對的還是有史以來最偉大的麥克斯韋電磁理論。但是，在種種嘗試都失敗了以後，普朗克發現，他必須接受他一直不喜歡的統計力學立場，從玻爾茲曼的角度來看問題，把熵和機率引入到這個系統裡來。 那段日子，是普朗克一生中最忙碌，卻又最光輝的日子。二十年後，一九二○年，他在諾貝爾得獎演說中這樣回憶道： 經過一生中最緊張的幾個禮拜的工作，我終於看見了黎明的曙光。一個完全意想不到的景象在我面前呈現出來。（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） 什麼是完全意想不到的景象呢？原來普朗克發現，僅僅引入分子運動理論還是不夠的，在處理熵和機率的關係時，如果要使得我們的新方程成立，就必須做一個假定，假設能量在發射和吸收的時候，不是連續不斷，而是分成一份一份的。 為了引起各位聽眾足夠的注意力，我想我應該把上面這段話重複再寫一遍。事實上我很想用初號的黑體字來寫這段話，但可惜論壇不給我這個功能。 必須假定，能量在發射和吸收的時候，不是連續不斷，而是分成一份一份的。 在瞭解它的具體意義之前，不妨先瞭解一個事實：正是這個假定，推翻了自牛頓以來二百多年，曾經被認為是堅固不可摧毀的經典世界。這個假定以及它所衍生出的意義，徹底改變了自古以來人們對世界的最根本的認識。極盛一時的帝國，在這句話面前轟然土崩瓦解，倒坍之快之徹底，就像愛倫．坡筆下厄舍家那間不祥的莊園。 好，回到我們的故事中來。能量不是連續不斷的，這有什麼了不起呢？ very impressive.因為它和有史以來一切物理學家的觀念截然相反（可能某些偽科學家除外，呵呵）。自從伽利略和牛頓用數學規則馴服了大自然之後，一切自然的過程就都被當成是連續不間斷的。如果你的中學物理老師告訴你，一輛小車沿直線從A點行駛到B點，卻不經過兩點中間的C點，你一定會覺得不可思議，甚至開始懷疑該教師是不是和校長有什麼裙帶關係。自然的連續性是如此地不容置疑，以致幾乎很少有人會去懷疑這一點。當預報說氣溫將從二十度上升到三十度，你會毫不猶豫地判定，在這個過程中間氣溫將在某個時刻到達二十五度，到達二十八度，到達二十九又一／二度，到達二十九又三／四度，到達二十九又九／十度總之，一切在二十度到三十度之間的值，無論有理的還是無理的，只要它在那段區間內，氣溫肯定會在某個時刻，精確地等於那個值。 對於能量來說，也是這樣。當我們說，這個化學反應總共釋放出了一百焦耳的能量的時候，我們每個人都會潛意識地推斷出，在反應期間，曾經有某個時刻，總體系釋放的能量等於50焦耳，等於32.233焦耳，等於3.14159焦耳。總之，能量的釋放是連續的，它總可以在某個時刻達到範圍內的任何可能的值。這個觀念是如此直接地植入我們的內心深處，顯得天經地義一般。 這種連續性，平滑性的假設，是微積分的根本基礎。牛頓、麥克斯韋那龐大的體系，便建築在這個地基之上，度過了百年的風雨。當物理遇到困難的時候，人們縱有懷疑的目光，也最多盯著那巍巍大廈，追問它是不是在建築結構上有問題，卻從未有絲毫懷疑它腳下的土地是否堅實。而現在，普朗克的假設引發了一場大地震，物理學所賴以建立的根本基礎開始動搖了。 普朗克的方程倔強地要求，能量必須只有有限個可能態，它不能是無限連續的。在發射的時候，它必須分成有限的一份份，必須有個最小的單位。這就像一個吝嗇鬼無比心痛地付帳，雖然他盡可能地試圖一次少付點錢，但無論如何，他每次最少也得付上一個penny，因為沒有比這個更加小的單位了。這個付錢的過程，就是一個不連續的過程。我們無法找到任何時刻，使得付帳者正好處於付了1.0001元這個狀態，因為最小的單位就是0.01元，付的帳只能這樣一份一份地發出。我們可以找到他付了一元的時候，也可以找到他付了一.零一元的時候，但在這兩個狀態中間，不存在別的狀態，雖然從理論上說，一元和1.01元之間，還存在著無限多個數字。 普朗克發現，能量的傳輸也必須遵照這種貨幣式的方法，一次至少要傳輸一個確定的量，而不可以無限地細分下去。能量的傳輸，也必須有一個最小的基本單位。能量只能以這個單位為基礎一份份地發出，而不能出現半個單位或者四分之一單位這種情況。在兩個單位之間，是能量的禁區，我們永遠也不會發現，能量的計量會出現小數點以後的數字。 一九○○年十二月十四日，人們還在忙活著準備歡度耶誕節。這一天，普朗克在德國物理學會上發表了他的大膽假設。他宣讀了那篇名留青史的《黑體光譜中的能量分佈》的論文，其中改變歷史的是這段話： 為了找出N個振子具有總能量Un的可能性，我們必須假設Un是不可連續分割的，它只能是一些相同部件的有限總和（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） 這個基本部件，普朗克把它稱作能量子（Energieelement），但隨後很快，在另一篇論文裡，他就改稱為量子（Elementarquantum），英語就是quantum。這個字來自拉丁文quantus，本來的意思就是多少，量。量子就是能量的最小單位，就是能量裡的一美分。一切能量的傳輸，都只能以這個量為單位來進行，它可以傳輸一個量子，兩個量子，任意整數個量子，但卻不能傳輸1又1/2個量子，那個狀態是不允許的，就像你不能用現錢支付1又1/2美分一樣。 那麼，這個最小單位究竟是多少呢？從普朗克的方程裡可以容易地推算出這個常數的大小，它約等於6.55×10^-27爾格*秒，換算成焦耳，就是6.626×20^-34焦耳*秒。這個單位相當的小，也就是說量子非常的小，非常精細。因此由它們組成的能量自然也十分細密，以至於我們通常看起來，它就好像是連續的一樣。這個值，現在已經成為了自然科學中最為重要的常數之一，以它的發現者命名，稱為普朗克常數，用h來表示。 請記住一九○○年十二月十四日這個日子，這一天就是量子力學的誕辰。量子的幽靈從普朗克的方程中脫胎出來，開始在歐洲上空遊蕩。幾年以後，它將爆發出令人咋舌的力量，把一切舊的體系徹底打破，並與聯合起來的保守派們進行一場驚天動地的決鬥。我們將在以後的章節裡看到，這個幽靈是如此地具有革命性和毀壞性，以致於它所過之處，最富麗堂皇的宮殿都在瞬間變成了斷瓦殘垣。物理學構築起來的精密體系被毫不留情地砸成廢鐵，千百年來亙古不變的公理被扔進垃圾箱中不得翻身。它所帶來的震撼力和衝擊力是如此地大，以致於後來它的那些偉大的開創者們都驚嚇不已，紛紛站到了它的對立面。當然，它也決不僅僅是一個破壞者，它更是一個前所未有的建設者，科學史上最傑出的天才們參與了它成長中的每一步，賦予了它華麗的性格和無可比擬的力量。人類理性最偉大的構建終將在它的手中誕生。 一場前所未有的革命已經到來，一場最為反叛和徹底的革命，也是最具有傳奇和史詩色彩的革命。暴風雨的種子已經在烏雲的中心釀成，只等適合的時候，便要催動起史無前例的雷電和風暴，向世人昭示它的存在。而這一切，都是從那個叫做馬克斯？普朗克的男人那裡開始的。 飯後閒話：連續性和悖論 古希臘有個學派叫做愛利亞派，其創建人名叫巴門尼德（Parmenides）。這位哲人對運動充滿了好奇，但在他看來，運動是一種自相矛盾的行為，它不可能是真實的，而一定是一個假相。why?因為巴門尼德認為世界上只有一個唯一的存在，既然是唯一的存在，它就不可能有運動。因為除了存在就是非存在，存在怎麼可能移動到非存在裡面去呢？所以他認為存在是絕對靜止的，而運動是荒謬的，我們所理解的運動只是假相而已。 巴門尼德有個學生，就是大名鼎鼎的芝諾（Zeno）。他為了為他的老師辯護，證明運動是不可能的，編了好幾個著名的悖論來說明運動的荒謬性。我們在這裡談談最有名的一個，也就是阿喀琉斯追龜辯，這裡面便牽涉到時間和空間的連續性問題。 阿喀琉斯是史詩《伊利亞特》裡的希臘大英雄。有一天他碰到一隻烏龜，烏龜嘲笑他說：別人都說你厲害，但我看你如果跟我賽跑，還追不上我。 阿喀琉斯大笑說：這怎麼可能。我就算跑得再慢，速度也有你的十倍，哪會追不上你？ 烏龜說：好，那我們假設一下。你離我有一百米，你的速度是我的十倍。現在你來追我了，但當你跑到我現在這個位置，也就是跑了一百米的時候，我也已經又向前跑了十米。當你再追到這個位置的時候，我又向前跑了一米，你再追一米，我又跑了1/10米總之，你只能無限地接近我，但你永遠也不能追上我。 阿喀琉斯怎麼聽怎麼有道理，一時丈二和尚摸不著頭腦。 這個故事便是有著世界性聲名的芝諾悖論（之一），哲學家們曾經從各種角度多方面地闡述過這個命題。這個命題令人困擾的地方，就在於它採用了一種無限分割空間的辦法，使得我們無法跳過這個無限去談問題。雖然從數學上，我們可以知道無限次相加可以限制在有限的值裡面，但是數學從本質上只能告訴我們怎麼做，而不能告訴我們能不能做到。 但是，自從量子革命以來，學者們越來越多地認識到，空間不一定能夠這樣無限分割下去。量子效應使得空間和時間的連續性喪失了，芝諾所連續無限次分割的假設並不能夠成立。這樣一來，芝諾悖論便不攻自破了。量子論告訴我們，無限分割的概念是一種數學上的理想，而不可能在現實中實現。一切都是不連續的，連續性的美好藍圖，其實不過是我們的一種想像。 five 我們的故事說到這裡，如果給大家留下這麼一個印象，就是量子論天生有著救世主的氣質，它一出世就像閃電劃破夜空，引起眾人的驚歎及歡呼，並摧枯拉朽般地打破舊世界的體系。如果是這樣的話，那麼筆者表示抱歉，因為事實遠遠並非如此。 我們再回過頭來看看物理史上的偉大理論：牛頓的體系閃耀著神聖不可侵犯的光輝，從誕生的那刻起便有著一種天上地下唯我獨尊的氣魄。麥克斯韋的方程組簡潔深刻，傾倒眾生，被譽為上帝譜寫的詩歌。愛因斯坦的相對論雖然是平民出身，但骨子卻繼承著經典體系的貴族優雅氣質，它的光芒稍經發掘後便立即照亮了整個時代。這些理論，它們的成功都是近乎壓倒性的，天命所歸，不可抗拒。而偉人們的個人天才和魅力，則更加為其抹上了高貴而驕傲的色彩。但量子論卻不同，量子論的成長史，更像是一部艱難的探索史，其中的每一步，都充滿了陷阱、荊棘和迷霧。量子的誕生伴隨著巨大的陣痛，它的命運註定了將要起伏而多舛。量子論的思想是如此反叛和躁動，以至於它與生俱來地有著一種對抗權貴的平民風格；而它顯示出來的潛在力量又是如此地巨大而近乎無法控制，這一切都使得所有的人都對它懷有深深的懼意。 而在這些懷有戒心的人們中間，最有諷刺意味的就要算量子的創始人：普朗克自己了。作為一個老派的傳統物理學家，普朗克的思想是保守的。雖然在那個決定命運的一九○○年，他鼓起了最大的勇氣做出了量子的革命性假設，但隨後他便為這個離經叛道的思想而深深困擾。在黑體問題上，普朗克孤注一擲想要得到一個積極的結果，但最後匯出的能量不連續性的圖像卻使得他大為吃驚和猶豫，變得畏縮不前起來。 如果能量是量子化的，那麼麥克斯韋的理論便首當其衝站在應當受置疑的地位，這在普朗克看來是不可思議，不可想像的。事實上，普朗克從來不把這當做一個問題，在他看來，量子的假設並不是一個物理真實，而純粹是一個為了方便而引入的假設而已。普朗克壓根也沒有想到，自己的理論在歷史上將會有著多麼大的意義，當後來的一系列事件把這個意義逐漸揭露給他看時，他簡直都不敢相信自己的眼睛，並為此惶恐不安。有人戲稱，普朗克就像是童話裡的那個漁夫，他親手把魔鬼從封印的瓶子裡放了出來，自己卻反而被這個魔鬼嚇了個半死。 有十幾年的時間，量子被自己的創造者所拋棄，不得不流浪四方。普朗克不斷地告誡人們，在引用普朗克常數h的時候，要儘量小心謹慎，不到萬不得已千萬不要胡思亂想。這個思想，一直要到一九一五年，當玻爾的模型取得了空前的成功後，才在普朗克的腦海中扭轉過來。量子論就像神話中的英雄海格力斯（Hercules），一出生就被拋棄在荒野裡，命運更為他安排了重重枷鎖。他的所有榮耀，都要靠自己那非凡的力量和一系列艱難的鬥爭來爭取。作為普朗克本人來說，他從一個革命的創始者而最終走到了時代的反面，沒能在這段振奮人心的歷史中起到更多的積極作用，這無疑是十分遺憾的。在他去世前出版的《科學自傳》中，普朗克曾回憶過他那企圖調和量子與經典理論的徒勞努力，並承認量子的意義要比那時他所能想像的重要得多。 不過，我們並不能因此而否認普朗克在量子論所做出的偉大而決定性的貢獻。有一些觀點可能會認為普朗克只是憑藉了一個巧合般的猜測，一種胡亂的拼湊，一個純粹的運氣才發現了他的黑體方程，進而假設了量子的理論。他只是一個幸運兒，碰巧猜到了那個正確的答案而已。而這個答案究竟意味著什麼，這個答案的內在價值卻不是他能夠回答和挖掘的。但是，幾乎所有的關於普朗克的傳記和研究都會告訴我們，雖然普朗克的公式在很大程度上是經驗主義的，但是一切證據都表明，他已經充分地對這個答案做好了準備。一九○○年，普朗克在黑體研究方面已經浸淫了六年，做好了理論上突破的一切準備工作。其實在當時，他自己已經很清楚，經典的電磁理論已經無法解釋實驗結果，必須引入熱力學解釋。而這樣一來，輻射能量的不連續性已經是一個不可避免的結果。這個概念其實早已在他的腦海中成形，雖然可能普朗克本人沒有清楚地意識到這一點，或者不肯承認這一點，但這個思想在他的潛意識中其實已經相當成熟，呼之欲出了。正因為如此，他才能在匯出方程後的短短時間裡，以最敏銳的直覺指出蘊含在其中的那個無價的假設。普朗克以一種那個時代非常難得的開創性態度來對待黑體的難題，他為後來的人打開了一扇通往全新未知世界的大門。無論從哪個角度來看，這樣的偉大工作，其意義都是不能低估的。 而普朗克的保守態度也並不是偶然的。實在是量子的思想太驚人，太過於革命。從量子論的成長歷史來看，有著這樣一個怪圈：科學巨人們參與了推動它的工作，卻終於因為不能接受它驚世駭俗的解釋而紛紛站到了保守的一方去。在這個名單上，除了普朗克，更有閃閃發光的瑞利、湯姆遜、愛因斯坦、德布羅意，乃至薛定諤。這些不僅是物理史上最偉大的名字，好多更是量子論本身的開創者和關鍵人物。量子就在同它自身創建者的鬥爭中成長起來，每一步都邁得艱難而痛苦不堪。我們會在以後的章節中，詳細地去觀察這些激烈的思想衝擊和觀念碰撞。不過，正是這樣的磨礪，才使得一部量子史話顯得如此波瀾壯闊，激動人心，也使得量子論本身更加顯出它的不朽光輝來。量子論不像牛頓力學或者愛因斯坦相對論，它的身上沒有天才的個人標籤，相反，整整一代精英共同促成了它的光榮。 作為老派科學家的代表，普朗克的科學精神和人格力量無疑是可敬的。在納粹統治期間，正是普朗克的努力，才使得許多猶太裔的科學家得到保護，得以繼續工作。但是，量子論這個精靈蹦跳在時代的最前緣，它需要最有銳氣的頭腦和最富有創見的思想來啟動它的靈氣。二十世紀初，物理的天空中已是黑雲壓城，每一升空氣似乎都在激烈地對流和振盪。一個偉大的時代需要偉大的人物，有史以來最出色和最富激情的一代物理學家便在這亂世的前夕成長起來。 一九○○年十二月十四日，普朗克在柏林宣讀了他關於黑體輻射的論文，宣告了量子的誕生。那一年他四十二歲。 就在那一年，一個名叫阿爾伯特．愛因斯坦（Albert Einstein）的青年從蘇黎世聯邦工業大學（ETH）畢業，正在為將來的生活發愁。他在大學裡曠了無窮多的課，以致他的教授閔可夫斯基（Minkowski）憤憤地罵他是懶狗。沒有一個人肯留他在校做理論或者實驗方面的工作，一個失業的黯淡前途正等待著這位不修邊幅的年輕人。 在丹麥，十五歲的尼爾斯．玻爾（Niels Bohr）正在哥本哈根的中學裡讀書。玻爾有著好動的性格，每次打架或爭論，總是少不了他。學習方面，他在數學和科學方面顯示出了非凡的天才，但是他的笨拙的口齒和慘不忍睹的作文卻是全校有名的笑柄。特別是作文最後的總結（conclusion），往往使得玻爾頭痛半天，在他看來，這種總結是無意義的重複而已。有一次他寫一篇關於金屬的論文，最後總結道：In conclusion，I would like to mention uranium（總而言之，我想說的是鈾）。 埃爾文．薛定諤（Erwin Schrodinger）比玻爾小兩歲，當時在維也納的一間著名的高級中學Akademisches Gymnasium上學。這間中學也是物理前輩玻爾茲曼，著名劇作家施尼茨勒（Arthur Schnitzler）和齊威格（Stefanie Zweig）的母校。對於剛入校的學生來說，拉丁文是最重要的功課，每週要占八個小時，而數學和物理只用三個小時。不過對薛定諤來說一切都是小菜一碟，他熱愛古文、戲劇和歷史，每次在班上都是第一。小埃爾文長得非常帥氣，穿上禮服和緊身褲，儼然一個翩翩小公子，這也使得他非常受到歡迎。 馬克斯．波恩（Max Born）和薛定諤有著相似的教育背景，經過了家庭教育，高級中學的過程進入了佈雷斯勞大學（這也是當時德國和奧地利中上層家庭的普遍做法）。不過相比薛定諤來說，波恩並不怎麼喜歡拉丁文，甚至不怎麼喜歡代數，儘管他對數學的看法後來在大學裡得到了改變。他那時瘋狂地喜歡上了天文，夢想著將來成為一個天文學家。 Louis.德布羅意（Louis de Broglie）當時八歲，正在他那顯赫的貴族家庭裡接受良好的幼年教育。他對歷史表現出濃厚的興趣，並樂意把自己的時間花在這上面。 沃爾夫岡．Ernst.泡利（Wolfgang Ernst Pauli）才出生八個月，可憐的小傢伙似乎一出世就和科學結緣。他的middle name，Ernst，就是因為他父親崇拜著名的科學家恩斯特．馬赫（Ernst Mach）才給他取的。 而再過十二個月，維爾茲堡（Wurzberg）的一位著名希臘文獻教授就要喜滋滋地看著他的寶貝兒子小海森堡（Werner Karl Heisenberg）呱呱墜地。稍早前，羅馬的一位公務員把他的孩子命名為恩里科．費米（Enrico Fermi）。二十個月後，保羅．狄拉克（Paul Dirac）也將出生在英國的布里斯托爾港。 好，演員到齊。那麼，好戲也該上演了。