Chapter 5 Chapter 3 Bolide

one Things weren't significantly better for physics in those early quantum days.Abandoned by his master, this rebellious elf has to wander the wilderness, gathering strength for the day that will shock the world.During this bleak period of more than four years, people used Planck's formula with an ostrich mentality, but they did not pursue the meaning behind the formula as if they were stealing their ears.However, above their heads, the thick dark clouds are still lingering, but they are becoming more and more menacing. After all, a torrential rain that will wash away the world is inevitable.

And what heralds the arrival of this great change, as usual, is a lightning that splits the world.In the chaos, the electric spark wiped out a dazzling light, representing eternal hope.The entanglement of light and electricity, two powers that even the gods fear, opened up a whole new era in an instant. Having said that, we still have to take the trouble to go back to the beginning of the first chapter, and take another look at Hertz's extraordinary experiment.As we have already mentioned, the explosion of electric sparks on the Hertzian receiver confirmed the existence of electromagnetic waves, but he also found that the sparks appeared more easily once light fell on the gap.

Hertz described this phenomenon in the paper, but did not delve into the reasons for it.There was too much to do in that exciting and great age, and with Hertz's untimely death, he did not have the leisure to pursue every problem that came his way.However, others have carried out in-depth research in this area, and soon the facts became very clear. It turned out to be like this: when light shines on a metal, electrons will be ejected from its surface.For unknown reasons, the electrons that were originally bound in the atoms on the metal surface, when exposed to a certain amount of light, fled away like frightened birds, like a family of vampires who couldn't see the light.For this interesting phenomenon between light and electricity, people have given it a name called "The Photoelectric Effect".

Soon, a series of experiments on the photoelectric effect were made in various laboratories.Although these experiments were very rough and primitive at the time, the results still showed some basic properties of the phenomenon between light and electricity.Two basic facts were soon known: First, whether light can knock electrons from the surface of a particular metal depends only on the frequency of the light.Light with high frequency (such as ultraviolet light) can eject electrons with higher energy, while light with low frequency (such as red light and yellow light) cannot eject a single electron.Secondly, whether electrons can be knocked out has nothing to do with the intensity of light.No matter how weak the ultraviolet light is, it can knock out the electrons on the metal surface, but no matter how strong the red light is, it cannot do this.By increasing the intensity of the light, all you can do is increase the number of electrons knocked out.For example, strong violet light can knock out more electrons from the metal surface than weak violet light.

All in all, for a specific metal, whether electrons can be ejected depends on the frequency of light.How many electrons are ejected depends on the intensity of the light. But scientists soon discovered that they were caught in a huge puzzle.Because... this phenomenon doesn't make sense, it doesn't seem like it should be like this. We all already know that light is a wave.For waves, the strength of the wave represents its energy.It is easy for us to understand that electrons are bound inside the metal by some kind of energy. If the energy given by the outside is not enough, it will not be enough to knock the electrons out.However, logically speaking, if we increase the intensity of the light wave, we will increase its energy. Why, for red light, no matter how intense the light is, it cannot hit even an electron?And frequency, what is frequency?It is nothing more than the frequency of the wave vibration.If the frequency is high, it means that the wave vibrates more frequently, so it stands to reason that light waves that vibrate frequently should strike more electrons.However, all experiments point in the opposite direction: the intensity of light determines the number of electrons, and the frequency of light determines whether electrons can be ejected.Isn't this a joke?

Imagine a hunter going to hunt rabbits. Rabbits hide in holes in the ground and refuse to come out easily.Hunters know that for a cunning rabbit, it may not be enough to scare it out by beating gongs and drums alone, but must use tricks such as flooding it.That is to say, the method used determines whether the rabbit can be driven out.Assuming that there are a thousand rabbit holes in the local area, how many assistants the hunter has and how many holes he can act at the same time determine how many rabbits he can scare.However, in the actual hunting, the hunter suddenly discovered that the failure of the rabbit to come out is not due to the method used, but how many assistants start at the same time.If you only act on one rabbit hole, no rabbit will come out even if there is a thunderstorm.On the contrary, how many rabbits are driven out has nothing to do with our number, but with the methods used.Even if I have a thousand people beating gongs and drums on a thousand rabbit holes at the same time, at most only one rabbit will jump out.And as long as I fill a rabbit hole with water, a thousand rabbits will scurry around.If it were a manga, there would be a big sweat bead on the hunter's head.

Scientists have found that they face the same embarrassing situation as hunters when it comes to the photoelectric effect.Maxwell's electromagnetism theory seems to be at a loss in terms of optoelectronics, and he doesn't know what to do.The facts revealed by the experiment are simple and clear, and repeated repetitions only further confirm this basic fact, but this fact is just the opposite of the theory.So, what is the problem?Is the theory wrong, or are our eyes playing tricks on us? The problem goes far beyond that.All indications indicate that there is a close relationship between the frequency of light and the energy of electrons.For each specific frequency of light, the energy of the electrons it emits has a corresponding upper limit.For example, if ultraviolet light can excite electrons with an energy of 20 electron volts, changing to purple light may only have a maximum of 10 electron volts.From the perspective of volatility, this is very incredible.Moreover, according to Maxwell's theory, if the ejection of an electron is based on energy absorption, it should be a continuous process, and this energy can be accumulated.That is, if a metal is shone with very weak light, it must take a certain amount of time for the electrons to absorb before reaching enough energy to jump out of the surface.In this case, there should be a time lag between the time when the light is illuminated and when the electrons fly out.However, experiments have shown that the jumping out of electrons is instantaneous. As soon as the light hits the metal, electrons will fly out immediately, even if the light is dim. The difference is only in the number of electrons flying out.

Odd thing. For the poor physicists, everything always goes their way.It is not easy to have a basically perfect theory, but experiments always produce some strange things to disturb people's good dreams.This goddamn photoelectric effect is a frustrating and disappointing thing.The elegant and noble Maxwell's theory faced great difficulties in front of this small mud pond. How to cross it without soiling its gorgeous clothes is really a nerve-wracking thing. However, what is even more unfortunate is that people always underestimate the difficulties in front of them.Clean freak physicists still pondering how to incorporate photoelectric phenomena into Maxwell's theory without compromising its perfection, don't know that this matter is much more serious than they imagined.Soon people will find that this is not a problem of dirty robes at all, but a fundamental difficulty involving the foundation of the entire physical system.But at the time it was impossible to see this without the most genius, boldest, and sharpest vision.

But then again, the most genius, boldest and most vigorous figure in the history of science lived precisely in that era. In 1905, at the Bern Patent Office in Switzerland, a 26-year-old civil servant with a third-class technician title and a young man with a disheveled hair stopped his eyes on the photoelectric effect for a while.This man's name is Albert Einstein. So in an instant, lightning pierced the night sky. The storm is finally coming. two The Swiss Patent Office in Bern is today an efficient and modern institution providing patent and trademark application and search services.The beautiful architecture and perfect network system make it present a typical modern style like some other big companies.As a pure scientist, generally, he seldom deals with the patent office, because science knows no borders, and there are no patents to apply for.The door of science is, after all, open to the whole world.

For the scientific community, however, Bern's patent office means a lot.Its significance in the history of modern science is no different from the city of Mecca in Islamic culture, with a rather sacred brilliance in it.This is all because 100 years ago, the patent office "very discerning" hired a small staff, and his name was Albert Einstein.This story once again tells us that there are sometimes big monks in small temples. In 1905, for Einstein, the bad days were almost over.The era of wandering around for work and livelihood is over, and there is no need to feel sorry for yourself for nothing.The Patent Office provided him with a stable position and income. Although he was only a third-class technician—and he applied for a second class—at least he was still an official civil servant.Einstein was devastated by his father's death three years ago, but he quickly found comfort and compensation from his wife.The Serbian girl Mileva Marec agreed to marry this often absent-minded daredevil in the second year (1903), and the two soon had a son named Hans.

Now, Einstein works 8 hours a day in his office, fiddling with the pile of patent drawings of all kinds, and then he rushes home and walks on the road in Bern with his baby carriage.When he was free, he met with friends, and everyone discussed Hume, Spinoza, and Lessing with great interest.On a whim, Einstein took out his violin to perform or accompany everyone.Of course, most of the time, he still delved into the physics issues he was most interested in, and when he was deep in thought, he often forgot to eat or sleep. 1905 is a rather mysterious year.In this year, the geniuses of human beings gushed out like rivers, rolling up the most shocking and beautiful waves.So much so that when we look back today, we can't help but be amazed and excited, and we can't stop talking about such a miracle.In terms of human wisdom, this year is really an extreme peak. The wonderful scientific melody composed in those days still makes us ecstatic until today, without knowing the taste of meat.And the creator of all these masterworks, this man who has climbed to the pinnacle of genius, is our little civil servant in the Bern patent office. Let's get back to business. On March 18, 1905, Einstein published a paper in the "Annalen der Physik" (Annalen der Physik) magazine titled "A Heuristic Viewpoint on the Generation and Transformation of Light" ( A Heuristic Interpretation of the Radiation and Transformation of Light), as the beginning of a series of miracles in 1905.This article is the sixth official paper Einstein published in his lifetime (the first was on capillarity in 1901, which was, in his own words, "worthless"), and it will Bringing him a Nobel Prize also ushered in a new era of quantum theory. Einstein started from Planck's quantum hypothesis.Everyone still remembers that Planck assumed that when a black body absorbs and emits energy, it is not continuous, but divided into "pieces", and there is a basic energy unit there.This unit, he called "quantum", its size is described by Planck's constant h.If we start from Planck's equation, we can easily deduce how much energy is contained in a "quantum" of a specific radiation frequency. The final formula is simple and clear: E = hν where E is energy, h is Planck's constant, and ν is frequency.Even elementary school students can use this simple formula to do some calculations.For example, for the radiation whose frequency is 10 to the 15th power, what is the corresponding quantum energy?Then simply multiply 10^15 by h=6.6×10^-34, which equals 6.6×10^-19 joules.This value is very small, so we usually don't notice the existence of discontinuity. Einstein read Planck's papers that had long been ignored by most authorities and himself, and he was deeply moved by the idea of ​​quantization.With a deep intuition, he felt that quantization is also an inevitable choice for light.Although there is a god-like Maxwell theory aloft, Einstein rebelled against everything and did not stop for it.On the contrary, he thinks that Maxwell's theory is only valid for an average situation, and Maxwell contradicts the experiment for issues such as the emission and absorption of instantaneous energy.It can already be seen from the photoelectric effect. Let us revisit the incongruity between the photoelectric effect and electromagnetic theory: Electromagnetic theory believes that light is a kind of wave, and its intensity represents its energy. Increasing the intensity of light should be able to hit electrons with higher energy.But experiments have shown that increasing the intensity of the light only knocks out a greater number of electrons, not their energy.To knock out higher-energy electrons, the frequency of the irradiated light must be increased. Raise the frequency, raise the frequency.Einstein suddenly had a flash of inspiration, E = hν, increasing the frequency, isn’t it just increasing the energy of a single quantum?Higher-energy quanta can knock out higher-energy electrons, and increasing the intensity of light just increases the number of quanta, so the corresponding result is to knock out more electrons.All of a sudden, everything seemed logical. Einstein wrote: "...according to this supposition, the energy of a ray of light emanating from a point is not distributed continuously as it propagates through an expanding space, but consists of a finite number of It is composed of "energy quanta" at a certain location. These energy quanta are indivisible, they can only be absorbed or emitted in whole." The smallest basic unit of energy that makes up light, Einstein later called them "light quanta".It was not until 1926 that American physicist Lewis (GNLewis) replaced it with the term commonly used today, called "photon" (photon). From the perspective of light quantum, everything becomes very concise and easy to understand.Light with a higher frequency, such as ultraviolet light, has a single quantum of light with higher energy (E = hν) than light with a lower frequency, so when its quantum acts on the metal surface, it can excite more The kinetic energy of the electrons comes.The energy of the quantum has nothing to do with the intensity of the light. The strong light only contains a larger number of photons, so it can excite a larger number of electrons.But for low-frequency light, every quantum of it is not enough to excite electrons, so no matter how many light quanta it contains, it will not help. We imagine the photoelectric effect as an auction with a high entry fee.Each quantum is a customer, and it carries as much energy as a person has in funds.To enter the auction site, everyone must first pay a certain amount of admission fee, and in the venue, a person can only buy one item. When a light quantum hits the metal surface, if it brings enough money (high enough energy), it is eligible to enter the auction site (can hit electrons).As for how good it can buy (how high-energy electrons it excites), it depends on how much money it has left after paying the admission fee (how much energy it has left).The higher the frequency, the more money a person has. Big money like ultraviolet light can easily buy very expensive goods after paying the entrance fee, while light with a lower frequency is not so luxurious. However, how much money a person has has nothing to do with how many items a "delegation" can buy.How many things can be bought is only related to the number of "delegates" (intensity of light), but not to how much money each person has (frequency of light).If I have a delegation of 500 people, everyone has enough money to enter, then I can buy 500 items back, and no matter how rich you are alone, you can only buy one thing (because one person You can only buy one item, that's the rule).How good the stuff you get is another matter.Then again, if everyone in your delegation has too little money to pay the entrance fee, no matter how many people you have, you won't be able to buy anything, because the rule is that you can only buy it as an individual. There is no continuity and accumulation, and everyone's money cannot be used together. The equation derived by Einstein has the same meaning as our auction: 1/2 mv^2 = hν– P 1/2 mv^2 is the maximum kinetic energy that excites electrons, which is what we say, "how good" goods can be bought. hν is the energy of a single quantum, which is how much money you have in total. P is the minimum energy required to excite electrons, which is the "entry fee".So what this equation tells us is actually quite simple: How good of an item you can buy depends on your total bankroll minus the entry fee. The key assumption here is that light absorbs energy in the form of quanta, which has no continuity and cannot be accumulated.A quantum excites a corresponding electron.So the problem of the instantaneousness of the effect revealed by the experiment is also easily solved: the quantum effect is originally an instantaneous effect, and there is no such thing as accumulation. But, did you smell something from it?Quantum of light, photon, what exactly is light?Haven't we already clearly concluded that light is a fluctuation?What is the concept of light quantum? As if by fate, history returned to the starting point after a big circle.With regard to the nature of light, the fight is on again, and the "third microwave war" is about to break out.But this time, the result is a full-scale world war, the world is turned upside down, and everything is reborn after being destroyed. *********** After-dinner gossip: The Miracle Year If you look at history from a relatively high perspective, everything follows a specific trajectory, there is no reason for nothing, and there is no unreasonable development.The heroes who are on the cusp of the era are actually only suitable for the basic requirements of that era, and only then have they obtained the supreme glory that belongs to them. However, if we stand in Lushan Mountain and cast our eyes on the specific scene, we can also understand the glory and progress brought by a great man to the times.Although it cannot be said that without these great figures, the development of mankind will go astray, but it cannot be denied that heroes and geniuses have made great contributions to the world. It is even more so in the history of science.The entire history of science can be said to be a splendid galaxy embellished with the names of geniuses, and there are a few particularly bright stars, the light emitted by them travels through the entire universe and reaches the end of time and space.Their wisdom exudes such gorgeous brilliance in a certain period, which is amazing.To this day, we have not been able to find a more suitable word to describe it, but can only name it "miracle". There are two years in the history of science that fit the title of "miracle", and they are closely connected with the names of two geniuses.These two years were 1666 and 1905, and those two geniuses were Newton and Einstein. In 1666, 23-year-old Newton returned to his hometown in the countryside for vacation in order to avoid the plague.During those days, he independently completed several pioneering works, including the invention of calculus (flow number), the completion of the experimental analysis of light decomposition, and the pioneering work of universal gravitation.In that year he laid the foundations of mathematics, mechanics, and optics, any one of which would place him among the greatest scientists of all time.It's hard to imagine how a person's mind can produce so many inspirations in such a short period of time. People can only use a Latin annus mirabilis to express this year, which is the "miracle year" (of course, some people will Arguing that 1667 was also the year of the miracle). So did Einstein in 1905.Living in the patent office, he published 6 papers this year. On March 18, it was the article on the photoelectric effect we mentioned above, which became one of the cornerstones of quantum theory. On April 30, a paper on measuring molecular size was published, which earned him a Ph.D. On May 11 and later on December 19, two papers on Brownian motion became milestones in molecular theory. On June 30, he published a paper entitled "On the Electrodynamics of Moving Objects". This unremarkable topic was later given a thunderous name called "Special Relativity". I don't need to say more about its significance. On September 27th, regarding the relationship between object inertia and energy, this is a further explanation of the special theory of relativity, and the famous mass-energy equation E=mc2 is proposed in it. This year's work alone deserves at least three Nobel Prizes.Whether the significance of the theory of relativity can be evaluated by the Nobel Prize is hard to say.And all this was done by one person with paper and pen in the office of the Patent Office.It is indeed hard to imagine whether such a miracle will happen again, because it is too incredible.In today's highly detailed science, it is unimaginable that one person can make such a huge contribution in such a short period of time. Poincaré 100 years ago has been called the "last all-rounder" in mathematics, and Einstein's theory of relativity may also be the last theory full of personal heroism and legend, right?Is this our luck, or is it our misfortune? three As mentioned last time, Einstein put forward the hypothesis of light quantum, which is used to explain the phenomenon in the photoelectric effect that cannot be explained by electromagnetic theory. However, the concept of light quantum is very confusing to other scientists.Hasn’t the problem of light already been characterized?Isn't light already included in Maxwell's theory, clearly described as a type of electromagnetic wave?What about this light quantum? In fact, light quantum is a very bold assumption, which is directly challenging the classical physical system.Einstein himself was aware of this, and it seemed to him that this was his most rebellious paper.In a letter to his friend Habicht (C. Habicht), Einstein described his four epoch-making papers. Only on the light quantum, he used the word "very revolutionary", and not even the theory of relativity such a description. The light quantum is incompatible with the traditional electromagnetic wave image, and it is actually a version of the particle theory in the past, assuming that light is discrete and composed of small basic units.One hundred years have passed since the era of Thomas Young, and the law of heaven has been reincarnated in the dark. The overlord who was defeated in the past reappeared on the stage with a rebellious attitude, challenging the wave theory that had already occupied the throne.These two destined opponents will finally have a final decisive battle, so as to realize the ultimate meaning of their respective existence: if there is no you, why am I standing here alone? However, the situation of Quantum of Light is as difficult and unacceptable as the fluctuations of the uprising back then.The position occupied by fluctuations today is even far greater than that of the particle dynasty shrouded in Newton's halo 100 years ago.The fluctuating throne is appointed by Maxwell, and has the entire Electromagnetic Kingdom as an ally.From the very beginning, this decisive battle is no longer limited to the domain of light, but is a matter of the nature of the entire electromagnetic spectrum.And we will soon see that more than ten years later, the war will be expanded, and the entire physical world will be involved, thus forming a veritable world war. At that time, even Einstein himself was very cautious about the attitude of light quantum, let alone those respectable old-school scientific gentlemen.On the one hand, this is incompatible with the classical electromagnetic image; on the other hand, none of the experiments on the photoelectric effect at that time could very clearly confirm the correctness of the photon.The Jedi counterattack of the particles did not really attract people's attention until 1915, and the cause was also very ironic: American Millikan (RAMillikan) wanted to use experiments to prove that the light quantum image was wrong, but repeated experiments repeatedly. Afterwards, he discovered ironically that he had largely confirmed the correctness of Einstein's equations.Experimental data show quite convincingly that in all cases the photoelectric phenomenon exhibits a quantized character and not the other way around. If Millikan’s experiment is just a successful anti-encirclement and suppression by the particle revolutionary army, and its significance is not enough to convince all physicists, then in 1923, Compton (AH Compton) led the army to achieve a decisive victory. Victory, showing their hidden amazing power at a glance.After this battle, no one doubted that it turned out to be a regular army of comparable strength that stood up against the classic wave empire. The battlefield of this battle is the land of X-Ray.When Compton was studying X-rays scattered by free electrons, he discovered a strange phenomenon: the scattered X-rays were divided into two parts, one part had the same wavelength as the original incident ray, while the other part was longer than the original ray wavelength , there is a functional relationship between the specific size and the scattering angle. If the usual wave theory is used, scattering should not change the wavelength of the incident light.But how to explain the extra rays with longer wavelengths?Compton thought hard, trying to find the answer from the classical theory, but he was hit hard.Finally one day, he made a desperate decision, introduced the assumption of light quantum, and regarded X-ray as a collection of photon beams with energy hν.This assumption immediately allowed him to see the dawn, and it suddenly became clear: the part of the rays with longer wavelengths was caused by the collision between photons and electrons.Like ordinary balls, photon not only has energy, but also has momentum. When it collides with electrons, it will exchange part of its energy to electrons.In this way, the energy of the photon decreases, according to the formula E = hν, the decrease of E leads to the decrease of ν, and the frequency becomes smaller, that is, the wavelength becomes larger, over. On the basis of particles, the relationship between wavelength change and scattering angle is derived, which is in good agreement with the experiment.This was an extremely beautiful battle of annihilation, and the wave power was disarmed without any chance of counterattack.Compton concludes: "There is now little doubt that Roentgen rays are a quantum phenomenon...Experiments have convincingly shown that radiation quanta have not only energy but also an impulse in a certain direction. " God made light, Einstein pointed out what light is, and Compton was the first to "see" this light in a real sense. The "Third Microwave War" broke out in an all-round way.The comeback army of particles is equipped with the most advanced weapons: photoelectric effect and Compton effect.These two cannons were so powerful that it was difficult for the wave defenders to resist and retreat steadily.However, the positions that the Volatile Army has painstakingly managed for nearly a hundred years are not so easy to break through. The strong backing of Maxwell's theory and the entire classical physics system makes them still invincible.It soon became clear to the supporters of volatility that there was no going back, because Moscow was behind them!The complete failure of wave theory will mean the collapse of Maxwell's electromagnetic system, but at least for now, the ambitious plan of particles is still difficult to realize. After Unstable stabilized his position, he quickly reassessed his strength.Although it can't do anything about the photoelectric issue, the ace weapons it relied on to build the country at the beginning are still not rusted or invalid, and still have a strong lethality.Although Mote's revival came swiftly, it lacked depth after all, and it even had to rely on the ammunition seized from Waves to fight.For example, the photoelectric effect we have seen, the verification of the light quantum theory involves the measurement of frequency and wavelength, but this still depends on the interference phenomenon of light to achieve.Thomas Young, the founding father of Unwavering, has such a great spirit that the banner of Unwavering is still shining for a hundred years behind him, deterring all opposing forces.In every middle school laboratory, the light passing through the two slits still persists in displaying light and dark interference fringes, undeniably showing his volatility to the world.Although Fresnel's paper has been covered with dust in the library, anyone who is interested can still repeat his experiment to confirm the existence of Poisson bright spots.Maxwell's youthful equations are still giving predictions every day, and electromagnetic waves are still meekly moving at a speed of 300,000 kilometers per second according to his predictions, neither faster nor slower. The battle situation soon fell into a stalemate, both sides stationed troops in their own handy positions, and no one was able to occupy the other side's territory.Once photons fall into the swamp of interference, they appear clumsy and unable to extricate themselves; as soon as light waves enter the jungle of optoelectronics, they also become confused and at a loss.Particles or waves?In the 20th century, when human civilization reached its peak, it was helpless to deal with the oldest phenomenon in the universe. Here, however, we have to divide our words.Let the two armies of particles and waves confront each other for a while, let's jump out of the world of light and electromagnetic waves, and look back at how quantum theory affects real matter - atomic nuclei and electrons.The prince from Denmark appeared on the stage. Above his head, a big bolide streaked across the cloudy sky. Although it was only fleeting, it ignited a prairie fire on the ground, illuminating the boundless darkness. Four In September 1911, 26-year-old Niels Bohr crossed the English Channel and set foot on the land of the British Isles.The young Bohr would never have imagined that 32 years later, he would come to this island again, but he would be hiding in the magazine of a mosquito bomber, braving the test of high-altitude hypoxia and being thrown into the island at any time. The risk in the sea, the destination was reached after a narrow escape.At that time, it was Prime Minister Churchill who personally signed the order to transfer the Taishan Beidou in the field of atomic physics from the hands of the Nazis, so that the Allied forces successfully weakened Germany's advantage in the competition for the atomic bomb.This has also become the most legendary and well-told story in Bohr's life. Of course, in 1911, Bohr was just a young man with lofty aspirations and dreams, but he was unknown.He walked on the campus of Cambridge, imagining how Newton and Maxwell walked here in those days, rejoicing like a child.After settling down hastily, the first thing Bohr did was to visit the famous JJ Thomson (Joseph John Thomson), who was a well-known physicist at the time, the head of the Cavendish Laboratory, and discoverer and Nobel Prize winner. JJ received Bohr very warmly. Although Bohr's English was not good, the two talked for a long time. JJ accepted Bohr's paper and put it on his desk. All seemed to be going well, but poor Niels didn't know that Thomson was "notorious" for disregarding students' papers.In fact, Bohr's papers have been lying on the table, JJ did not read a word.Cambridge was really not an exciting place for Bohr, and his project did not go very smoothly.All in all, apart from showing off in a football team, there seemed to be nothing that Bohr thought worth mentioning during his Cambridge days.Disappointed, Bohr decided to seek some change, and he set his sights on Manchester.Manchester's polluted skies may seem unappealing compared to Cambridge, but to a physics student there is a name that shines in gold: Ernest Rutherford. Speaking of which, Rutherford was also a student of JJ Thomson.The scientist who was born on a farm in New Zealand maintains the thrifty and simple style of a farmer. He is always so enthusiastic and caring for his assistants and students, and provides all the help he can.Besides, the timing chosen by Bohr could not have been more appropriate. In 1912, it was the year when the dawn of dawn was approaching and a new page of science was about to be written.People have already stood on the threshold leading to the mysterious inner world of the atom, just waiting for Bohr to take this decisive step. 这个故事还要从前一个世纪说起。1897年，JJ汤姆逊在研究阴极射线的时候，发现了原子中电子的存在。这打破了从古希腊人那里流传下来的“原子不可分割”的理念，明确地向人们展示：原子是可以继续分割的，它有着自己的内部结构。那么，这个结构是怎么样的呢？汤姆逊那时完全缺乏实验证据，他于是展开自己的想象，勾勒出这样的图景：原子呈球状，带正电荷。而带负电荷的电子则一粒粒地“镶嵌”在这个圆球上。这样的一幅画面，也就是史称的“葡萄干布丁”模型，电子就像布丁上的葡萄干一样。 但是，1910年，卢瑟福和学生们在他的实验室里进行了一次名留青史的实验。他们用α粒子（带正电的氦核）来轰击一张极薄的金箔，想通过散射来确认那个“葡萄干布丁”的大小和性质。但是，极为不可思议的情况出现了：有少数α粒子的散射角度是如此之大，以致超过90度。对于这个情况，卢瑟福自己描述得非常形象：“这就像你用十五英寸的炮弹向一张纸轰击，结果这炮弹却被反弹了回来，反而击中了你自己一样”。 卢瑟福发扬了亚里士多德前辈“吾爱吾师，但吾更爱真理”的优良品格，决定修改汤姆逊的葡萄干布丁模型。他认识到，α粒子被反弹回来，必定是因为它们和金箔原子中某种极为坚硬密实的核心发生了碰撞。这个核心应该是带正电，而且集中了原子的大部分质量。但是，从α粒子只有很少一部分出现大角度散射这一情况来看，那核心占据的地方是很小的，不到原子半径的万分之一。 于是，卢瑟福在次年（1911）发表了他的这个新模型。在他描述的原子图象中，有一个占据了绝大部分质量的“原子核”在原子的中心。而在这原子核的四周，带负电的电子则沿着特定的轨道绕着它运行。这很像一个行星系统（比如太阳系），所以这个模型被理所当然地称为“行星系统”模型。在这里，原子核就像是我们的太阳，而电子则是围绕太阳运行的行星们。 但是，这个看来完美的模型却有着自身难以克服的严重困难。因为物理学家们很快就指出，带负电的电子绕着带正电的原子核运转，这个体系是不稳定的。两者之间会放射出强烈的电磁辐射，从而导致电子一点点地失去自己的能量。作为代价，它便不得不逐渐缩小运行半径，直到最终“坠毁”在原子核上为止，整个过程用时不过一眨眼的工夫。换句话说，就算世界如同卢瑟福描述的那样，也会在转瞬之间因为原子自身的坍缩而毁于一旦。原子核和电子将不可避免地放出辐射并互相中和，然后把卢瑟福和他的实验室，乃至整个英格兰，整个地球，整个宇宙都变成一团混沌。 不过，当然了，虽然理论家们发出如此阴森恐怖的预言，太阳仍然每天按时升起，大家都活得好好的。电子依然快乐地围绕原子打转，没有一点失去能量的预兆。而丹麦的年轻人尼尔斯?玻尔照样安安全全地抵达了曼彻斯特，并开始谱写物理史上属于他的华彩篇章。 玻尔没有因为卢瑟福模型的困难而放弃这一理论，毕竟它有着α粒子散射实验的强力支持。相反，玻尔对电磁理论能否作用于原子这一人们从未涉足过的层面，倒是抱有相当的怀疑成分。曼彻斯特的生活显然要比剑桥令玻尔舒心许多，虽然他和卢瑟福两个人的性格是如此不同，后者是个急性子，永远精力旺盛，而他玻尔则像个害羞的大男孩，说一句话都显得口齿不清。但他们显然是绝妙的一个团队，玻尔的天才在卢瑟福这个老板的领导下被充分地激发出来，很快就在历史上激起壮观的波澜。 1912年7月，玻尔完成了他在原子结构方面的第一篇论文，历史学家们后来常常把它称作“曼彻斯特备忘录”。玻尔在其中已经开始试图把量子的概念结合到卢瑟福模型中去，以解决经典电磁力学所无法解释的难题。但是，一切都只不过是刚刚开始而已，在那片还没有前人涉足的处女地上，玻尔只能一步步地摸索前进。没有人告诉他方向应该在哪里，而他的动力也不过是对于卢瑟福模型的坚信和年轻人特有的巨大热情。玻尔当时对原子光谱的问题一无所知，当然也看不到它后来对于原子研究的决定性意义，不过，革命的方向已经确定，已经没有什么能够改变量子论即将崭露头角这个事实了。 在浓云密布的天空中，出现了一线微光。虽然后来证明，那只是一颗流星，但是这光芒无疑给已经僵硬而老化的物理世界注入了一种新的生机，一种有着新鲜气息和希望的活力。这光芒点燃了人们手中的火炬，引导他们去寻找真正的永恒的光明。 终于，7月24日，玻尔完成了他在英国的学习，动身返回祖国丹麦。在那里，他可爱的未婚妻玛格丽特正在焦急地等待着他，而物理学的未来也即将要向他敞开心扉。在临走前，玻尔把他的论文交给卢瑟福过目，并得到了热切的鼓励。只是，卢瑟福有没有想到，这个青年将在怎样的一个程度上，改变人们对世界的终极看法呢？ 是的，是的，时机已到。伟大的三部曲即将问世，而真正属于量子的时代，也终于到来。 *********** 饭后闲话：诺贝尔奖得主的幼儿园 卢瑟福本人是一位伟大的物理学家，这是无需置疑的。但他同时更是一位伟大的物理导师，他以敏锐的眼光去发现人们的天才，又以伟大的人格去关怀他们，把他们的潜力挖掘出来。在卢瑟福身边的那些助手和学生们，后来绝大多数都出落得非常出色，其中更包括了为数众多的科学大师们。 我们熟悉的尼尔斯·玻尔，20世纪最伟大的物理学家之一，1922年诺贝尔物理奖得主，量子论的奠基人和象征。在曼彻斯特跟随过卢瑟福。 保罗·狄拉克（Paul Dirac），量子论的创始人之一，同样伟大的科学家，1933年诺贝尔物理奖得主。他的主要成就都是在剑桥卡文迪许实验室做出的（那时卢瑟福接替了JJ汤姆逊成为这个实验室的主任）。狄拉克获奖的时候才31岁，他对卢瑟福说他不想领这个奖，因为他讨厌在公众中的名声。卢瑟福劝道，如果不领奖的话，那么这个名声可就更响了。 中子的发现者，詹姆斯·查德威克（James Chadwick）在曼彻斯特花了两年时间在卢瑟福的实验室里。他于1935年获得诺贝尔物理奖。 布莱克特（Patrick MS Blackett）在一次大战后辞去了海军上尉的职务，进入剑桥跟随卢瑟福学习物理。他后来改进了威尔逊云室，并在宇宙线和核物理方面作出了巨大的贡献，为此获得了1948年的诺贝尔物理奖。 1932年，沃尔顿（ETS Walton）和考克劳夫特（John Cockcroft）在卢瑟福的卡文迪许实验室里建造了强大的加速器，并以此来研究原子核的内部结构。这两位卢瑟福的弟子在1951年分享了诺贝尔物理奖金。 这个名单可以继续开下去，一直到长得令人无法忍受为止：英国人索迪（Frederick Soddy），1921年诺贝尔化学奖。瑞典人赫维西（Georg von Hevesy），1943年诺贝尔化学奖。德国人哈恩（Otto Hahn），1944年诺贝尔化学奖。英国人鲍威尔（Cecil Frank Powell），1950年诺贝尔物理奖。美国人贝特（Hans Bethe），1967年诺贝尔物理奖。苏联人卡皮查（PLKapitsa），1978年诺贝尔化学奖。 除去一些稍微疏远一点的case，卢瑟福一生至少培养了10位诺贝尔奖得主（还不算他自己本人）。当然，在他的学生中还有一些没有得到诺奖，但同样出色的名字，比如汉斯·盖革（Hans Geiger，他后来以发明了盖革计数器而著名）、亨利·莫斯里（Henry Mosley，一个被誉为有着无限天才的年轻人，可惜死在了一战的战场上）、恩内斯特?马斯登（Ernest Marsden，他和盖革一起做了α粒子散射实验，后来被封为爵士）……等等，等等。 卢瑟福的实验室被后人称为“诺贝尔奖得主的幼儿园”。他的头像出现在新西兰货币的最大面值——100元上面，作为国家对他最崇高的敬意和纪念。 Fives 1912年8月1日，玻尔和玛格丽特在离哥本哈根不远的一个小镇上结婚，随后他们前往英国展开蜜月。当然，有一个人是万万不能忘记拜访的，那就是玻尔家最好的朋友之一，卢瑟福教授。 虽然是在蜜月期，原子和量子的图景仍然没有从玻尔的脑海中消失。他和卢瑟福就此再一次认真地交换了看法，并加深了自己的信念。回到丹麦后，他便以百分之二百的热情投入到这一工作中去。揭开原子内部的奥秘，这一梦想具有太大的诱惑力，令玻尔完全无法抗拒。 为了能使大家跟得上我们史话的步伐，我们还是再次描述一下当时玻尔面临的处境。卢瑟福的实验展示了一个全新的原子面貌：有一个致密的核心处在原子的中央，而电子则绕着这个中心运行，像是围绕着太阳的行星。然而，这个模型面临着严重的理论困难，因为经典电磁理论预言，这样的体系将会无可避免地释放出辐射能量，并最终导致体系的崩溃。换句话说，卢瑟福的原子是不可能稳定存在超过1秒钟的。 玻尔面临着选择，要么放弃卢瑟福模型，要么放弃麦克斯韦和他的伟大理论。玻尔勇气十足地选择了放弃后者。他以一种深刻的洞察力预见到，在原子这样小的层次上，经典理论将不再成立，新的革命性思想必须被引入，这个思想就是普朗克的量子以及他的h常数。 应当说这是一个相当困难的任务。如何推翻麦氏理论还在其次，关键是新理论要能够完美地解释原子的一切行为。玻尔在哥本哈根埋头苦干的那个年头，门捷列夫的元素周期律已经被发现了很久，化学键理论也已经被牢固地建立。种种迹象都表明在原子内部，有一种潜在的规律支配着它们的行为，并形成某种特定的模式。原子世界像一座蕴藏了无穷财宝的金字塔，但如何找到进入其内部的通道，却是一个让人挠头不已的难题。 然而，像当年的贝尔佐尼一样，玻尔也有着一个探险家所具备的最宝贵的素质：洞察力和直觉，这使得他能够抓住那个不起眼，但却是唯一的，稍纵即逝的线索，从而打开那扇通往全新世界的大门。1913年初，年轻的丹麦人汉森（Hans Marius Hansen）请教玻尔，在他那量子化的原子模型里如何解释原子的光谱线问题。对于这个问题，玻尔之前并没有太多地考虑过，原子光谱对他来说是陌生和复杂的，成千条谱线和种种奇怪的效应在他看来太杂乱无章，似乎不能从中得出什么有用的信息。然而汉森告诉玻尔，这里面其实是有规律的，比如巴尔末公式就是。他敦促玻尔关心一下巴尔末的工作。 突然间，就像伊翁（Ion）发现了藏在箱子里的绘着戈耳工的麻布，一切都豁然开朗。Mountain darkly, vista.在谁也没有想到的地方，量子得到了决定性的突破。 1954年，玻尔回忆道：当我一看见巴尔末的公式，一切就都清楚不过了。 要从头回顾光谱学的发展，又得从伟大的本生和基尔霍夫说起，而那势必又是一篇规模宏大的文字。鉴于篇幅，我们只需要简单地了解一下这方面的背景知识，因为本史话原来也没有打算把方方面面都事无巨细地描述完全。概括来说，当时的人们已经知道，任何元素在被加热时都会释放出含有特定波长的光线，比如我们从中学的焰色实验中知道，钠盐放射出明亮的黄光，钾盐则呈紫色，锂是红色，铜是绿色……等等。将这些光线通过分光镜投射到屏幕上，便得到光谱线。各种元素在光谱里一览无余：钠总是表现为一对黄线，锂产生一条明亮的红线和一条较暗的橙线，钾则是一条紫线。总而言之，任何元素都产生特定的唯一谱线。 但是，这些谱线呈现什么规律以及为什么会有这些规律，却是一个大难题。拿氢原子的谱线来说吧，这是最简单的原子谱线了。它就呈现为一组线段，每一条线都代表了一个特定的波长。比如在可见光区间内，氢原子的光谱线依次为：656，484，434，410，397，388，383，380……纳米。这些数据无疑不是杂乱无章的，1885年，瑞士的一位数学教师巴尔末（Johann Balmer）发现了其中的规律，并总结了一个公式来表示这些波长之间的关系，这就是著名的巴尔末公式。将它的原始形式稍微变换一下，用波长的倒数来表示，则显得更加简单明了： ν＝R（1/2^2 - 1/n^2） 其中的R是一个常数，称为里德伯（Rydberg）常数，n是大于2的正整数（3，4，5……等等）。 在很长一段时间里，这是一个十分有用的经验公式。但没有人可以说明，这个公式背后的意义是什么，以及如何从基本理论将它推导出来。但是在玻尔眼里，这无疑是一个晴天霹雳，它像一个火花，瞬间点燃了玻尔的灵感，所有的疑惑在那一刻变得顺理成章了，玻尔知道，隐藏在原子里的秘密，终于向他嫣然展开笑颜。 我们来看一下巴耳末公式，这里面用到了一个变量n，那是大于2的任何正整数。n可以等于3，可以等于4，但不能等于3.5，这无疑是一种量子化的表述。玻尔深呼了一口气，他的大脑在急速地运转，原子只能放射出波长符合某种量子规律的辐射，这说明了什么呢？我们回忆一下从普朗克引出的那个经典量子公式：E = hν。频率（波长）是能量的量度，原子只释放特定波长的辐射，说明在原子内部，它只能以特定的量吸收或发射能量。而原子怎么会吸收或者释放能量的呢？这在当时已经有了一定的认识，比如斯塔克（J.Stark）就提出，光谱的谱线是由电子在不同势能的位置之间移动而放射出来的，英国人尼科尔森（JWNicholson）也有着类似的想法。玻尔对这些工作无疑都是了解的。 一个大胆的想法在玻尔的脑中浮现出来：原子内部只能释放特定量的能量，说明电子只能在特定的“势能位置”之间转换。也就是说，电子只能按照某些“确定的”轨道运行，这些轨道，必须符合一定的势能条件，从而使得电子在这些轨道间跃迁时，只能释放出符合巴耳末公式的能量来。 我们可以这样来打比方。如果你在中学里好好地听讲过物理课，你应该知道势能的转化。一个体重100公斤的人从1米高的台阶上跳下来，他/她会获得1000焦耳的能量，当然，这些能量会转化为落下时的动能。但如果情况是这样的，我们通过某种方法得知，一个体重100公斤的人跳下了若干级高度相同的台阶后，总共释放出了1000焦耳的能量，那么我们关于每一级台阶的高度可以说些什么呢？ 明显而直接的计算就是，这个人总共下落了1米，这就为我们台阶的高度加上了一个严格的限制。如果在平时，我们会承认，一个台阶可以有任意的高度，完全看建造者的兴趣而已。但如果加上了我们的这个条件，每一级台阶的高度就不再是任意的了。我们可以假设，总共只有一级台阶，那么它的高度就是1米。或者这个人总共跳了两级台阶，那么每级台阶的高度是0.5米。如果跳了3次，那么每级就是1/3米。如果你是间谍片的爱好者，那么大概你会推测每级台阶高1/39米。但是无论如何，我们不可能得到这样的结论，即每级台阶高0.6米。道理是明显的：高0.6米的台阶不符合我们的观测（总共释放了1000焦耳能量）。如果只有一级这样的台阶，那么它带来的能量就不够，如果有两级，那么总高度就达到了1.2米，导致释放的能量超过了观测值。如果要符合我们的观测，那么必须假定总共有一又三分之二级台阶，而这无疑是荒谬的，因为小孩子都知道，台阶只能有整数级。 在这里，台阶数“必须”是整数，就是我们的量子化条件。这个条件就限制了每级台阶的高度只能是1米，或者1/2米，而不能是这其间的任何一个数字。 原子和电子的故事在道理上基本和这个差不多。我们还记得，在卢瑟福模型里，电子像行星一样绕着原子核打转。当电子离核最近的时候，它的能量最低，可以看成是在“平地”上的状态。但是，一旦电子获得了特定的能量，它就获得了动力，向上“攀登”一个或几个台阶，到达一个新的轨道。当然，如果没有了能量的补充，它又将从那个高处的轨道上掉落下来，一直回到“平地”状态为止，同时把当初的能量再次以辐射的形式释放出来。 关键是，我们现在知道，在这一过程中，电子只能释放或吸收特定的能量（由光谱的巴尔末公式给出），而不是连续不断的。玻尔做出了合理的推断：这说明电子所攀登的“台阶”，它们必须符合一定的高度条件，而不能像经典理论所假设的那样，是连续而任意的。连续性被破坏，量子化条件必须成为原子理论的主宰。 我们不得不再一次用到量子公式E = hν，还请各位多多包涵。史蒂芬?霍金在他那畅销书的Acknowledgements里面说，插入任何一个数学公式都会使作品的销量减半，所以他考虑再三，只用了一个公式E = mc2。我们的史话本是戏作，也不考虑那么多，但就算列出公式，也不强求各位看客理解其数学意义。唯有这个E = hν，笔者觉得还是有必要清楚它的含义，这对于整部史话的理解也是有好处的，从科学意义上来说，它也决不亚于爱因斯坦的那个E = mc2。所以还是不厌其烦地重复一下这个方程的描述：E代表能量，h是普朗克常数，ν是频率。 回到正题，玻尔现在清楚了，氢原子的光谱线代表了电子从一个特定的台阶跳跃到另外一个台阶所释放的能量。因为观测到的光谱线是量子化的，所以电子的“台阶”（或者轨道）必定也是量子化的，它不能连续而取任意值，而必须分成“底楼”，“一楼”，“二楼”等，在两层“楼”之间，是电子的禁区，它不可能出现在那里。正如一个人不能悬在两级台阶之间漂浮一样。如果现在电子在“三楼”，它的能量用W3表示，那么当这个电子突发奇想，决定跳到“一楼”（能量W1）的期间，它便释放出了W3-W1的能量。我们要求大家记住的那个公式再一次发挥作用，W3-W1 = hν。所以这一举动的直接结果就是，一条频率为ν的谱线出现在该原子的光谱上。 玻尔所有的这些思想，转化成理论推导和数学表达，并以三篇论文的形式最终发表。这三篇论文（或者也可以说，一篇大论文的三个部分），分别题名为《论原子和分子的构造》（On the Constitution of Atoms and Molecules），《单原子核体系》（Systems Containing Only a Single Nucleus）和《多原子核体系》（Systems Containing Several Nuclei），于1913年3月到9月陆续寄给了远在曼彻斯特的卢瑟福，并由后者推荐发表在《哲学杂志》（Philosophical Magazine）上。这就是在量子物理历史上划时代的文献，亦即伟大的“三部曲”。 这确确实实是一个新时代的到来。如果把量子力学的发展史分为三部分，1900年的普朗克宣告了量子的诞生，那么1913年的玻尔则宣告了它进入了青年时代。一个完整的关于量子的理论体系第一次被建造起来，虽然我们将会看到，这个体系还留有浓重的旧世界的痕迹，但它的意义却是无论如何不能低估的。量子第一次使全世界震惊于它的力量，虽然它的意识还有一半仍在沉睡中，虽然它自己仍然置身于旧的物理大厦之内，但它的怒吼已经无疑地使整个旧世界摇摇欲坠，并动摇了延绵几百年的经典物理根基。神话中的巨人已经开始苏醒，那些藏在古老城堡里的贵族们，颤抖吧！