Chapter 4 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 dismal 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 that exists between light and electricity, people have given it a name called the photoelectric effect (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 ten 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 transient. 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.Physicists with a cleanliness are still thinking hard about how to incorporate the photoelectric phenomenon into Maxwell's theory without compromising its perfection, but they 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 Patent Office in Bern, 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. one time.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 meant 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 a hundred years ago, the patent office hired a small clerk with great foresight, 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 job, 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.Serbian girl Mileva.In the second year (1903) Mileva Marec agreed to marry this often absent-minded daredevil, and the two soon had a son named Hans.

Now, Einstein worked eight hours a day in his office, fiddling with the assorted pile of patent drawings, and then he rushed home, pushing the stroller for a walk on the road in Bern.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 was 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 masterpieces, this man who has climbed to the pinnacle of genius, is our little civil servant in the patent office in Bern. Let's get back to business. On March 18, 1905, Einstein published a paper in the "Annalen der Physik" (Annalen der Physik) titled "A Heuristic on the Generation and Transformation of Light." A Heuristic Interpretation of the Radiation and Transformation of Light, the beginning of a series of miracles in 1905.This article is the sixth official paper published by Einstein in his lifetime (the first one was published in 1901 on capillarity, which, in his own words, is worthless), and this paper It will bring him a Nobel Prize and also usher 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, which he called a quantum, was 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 travels through an ever-expanding space, but is composed of a finite number of composed of energy quanta.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 the American physicist GN Lewis replaced it with the term commonly used today, called photon. From the perspective of light quantum, everything becomes very concise and easy to understand.For light with higher frequency, such as ultraviolet light, its single quantum contains higher energy (E = hν) than light with low 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.The amount of things that can be bought is only related to the number of delegations (the intensity of the light), and has nothing to do with how much money each person has (the frequency of the light).If I have a delegation of 500 people, and 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 a person can only buy one thing. You can buy the same item, the rules are like this).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 on your own. Admission by identity has no continuity and accumulation, and everyone's money cannot be used together. The equation derived by Einstein has the same meaning as our auction: One/2mv^2=hν-P 1/2mv^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 transient nature of the effect revealed by the experiment is also easily solved: the quantum effect is originally a transient 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, wars are fought 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 a miracle. There are two years in the history of science, which are suitable for 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 generate so many inspirations in such a short period of time. People can only use a Latin word annus mirabilis to represent this year, which is the miracle year (of course, some people will argue that a 667 was actually a miracle year). The same is true of Einstein in 1905.Living in the patent office, he published six 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, and 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.A hundred years ago, Poincaré was already known as 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 very revolutionary words, and even the theory of relativity has no such describe. The light quantum is incompatible with the traditional electromagnetic wave image, and it is actually a replica of the particle theory in the past, assuming that light is discrete and composed of small basic units.From Thomas.Another hundred years have passed since Yang's era, and the heavens are in a circle. 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 a hundred 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 particles did not really attract people's attention until 1915, and the cause was also very ironic: the American RA Millikan wanted to use experiments to prove that the light quantum image was wrong, but many After repeated experiments, he found out ironically that he had confirmed the correctness of Einstein's equations to a large extent.Experimental data show quite convincingly that in all cases photoelectric phenomena exhibit a quantized character and not the other way around. If it is said that Millikan's experiment was 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 the victory. A decisive victory, revealing the amazing power hidden in them 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 concluded: Now, there is little doubt that Roentgen rays (Note: X-rays) are a quantum phenomenon. Experiments have convincingly shown that radiation quanta not only have energy, but also have an impulse in a certain direction. God made light, Einstein pointed out what light is, and Compton was the first to see it in a real sense. The third microwave war broke out in full swing.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 project 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.The unsteady founding father Thomas.Yang, his spirit is so great that a hundred years behind him still shines with a fluctuating battle flag, 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 twentieth century, when human civilization reached its peak, it was powerless to deal with the oldest phenomena in the universe. Here, however, we have to divide our words.Let the two armies of particles and waves fight against 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 the real material nucleus and electrons.The prince from Denmark appeared on the stage. Above his head, a big bolide streaked across the dark clouded sky. Although it was only fleeting, it ignited a prairie fire on the ground, illuminating the boundless darkness. Four In September 1911, twenty-six-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 thirty-two years later, he would come to this island again, but he was hiding in the magazine of a mosquito bomber, braving the test of high-altitude hypoxia and being thrown away at any time. The risk of entering the sea, and only reached the destination 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 hastily settled down, the first thing Bohr did was to visit the famous JJ Thomson (Joseph John Thomson). Discoverer, Nobel laureate. 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 did not 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.Compared with Cambridge, Manchester's polluted skies may seem unattractive, but to a physics student, there is a shining name there: Ernest.Rutherford (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 Bohr chose 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.人們已經站在了通向原子神秘內部世界的門檻上，只等玻爾來邁出這決定性的一步了。 這個故事還要從前一個世紀說起。一八九七年，JJ湯姆遜在研究陰極射線的時候，發現了原子中電子的存在。這打破了從古希臘人那裡流傳下來的原子不可分割的理念，明確地向人們展示：原子是可以繼續分割的，它有著自己的內部結構。那麼，這個結構是怎麼樣的呢？湯姆遜那時完全缺乏實驗證據，他於是展開自己的想像，勾勒出這樣的圖景：原子呈球狀，帶正電荷。而帶負電荷的電子則一粒粒地鑲嵌在這個圓球上。這樣的一幅畫面，也就是史稱的葡萄乾布丁模型，電子就像布丁上的葡萄乾一樣。 但是，一九一○年，盧瑟福和學生們在他的實驗室裡進行了一次名留青史的實驗。他們用α粒子（帶正電的氦核）來轟擊一張極薄的金箔，想通過散射來確認那個葡萄乾布丁的大小和性質。但是，極為不可思議的情況出現了：有少數α粒子的散射角度是如此之大，以致超過九十度。對於這個情況，盧瑟福自己描述得非常形象：這就像你用十五英寸的炮彈向一張紙轟擊，結果這炮彈卻被反彈了回來，反而擊中了你自己一樣。 盧瑟福發揚了亞里斯多德前輩吾愛吾師，但吾更愛真理的優良品格，決定修改湯姆遜的葡萄乾布丁模型。他認識到，α粒子被反彈回來，必定是因為它們和金箔原子中某種極為堅硬密實的核心發生了碰撞。這個核心應該是帶正電，而且集中了原子的大部分品質。但是，從α粒子只有很少一部分出現大角度散射這一情況來看，那核心佔據的地方是很小的，不到原子半徑的萬分之一。 於是，盧瑟福在次年（一九一一）發表了他的這個新模型。在他描述的原子圖像中，有一個佔據了絕大部分品質的原子核在原子的中心。而在這原子核的四周，帶負電的電子則沿著特定的軌道繞著它運行。這很像一個行星系統（比如太陽系），所以這個模型被理所當然地稱為行星系統模型。在這裡，原子核就像是我們的太陽，而電子則是圍繞太陽運行的行星們。 但是，這個看來完美的模型卻有著自身難以克服的嚴重困難。因為物理學家們很快就指出，帶負電的電子繞著帶正電的原子核運轉，這個體系是不穩定的。兩者之間會放射出強烈的電磁輻射，從而導致電子一點點地失去自己的能量。作為代價，它便不得不逐漸縮小運行半徑，直到最終墜毀在原子核上為止，整個過程用時不過一眨眼的工夫。換句話說，就算世界如同盧瑟福描述的那樣，也會在轉瞬之間因為原子自身的坍縮而毀於一旦。原子核和電子將不可避免地放出輻射並互相中和，然後把盧瑟福和他的實驗室，乃至整個英格蘭，整個地球，整個宇宙都變成一團混沌。不過，當然了，雖然理論家們發出如此陰森恐怖的預言，太陽仍然每天按時升起，大家都活得好好的。電子依然快樂地圍繞原子打轉，沒有一點失去能量的預兆。而丹麥的年輕人尼爾斯．玻爾照樣安安全全地抵達了曼徹斯特，並開始譜寫物理史上屬於他的華彩篇章。 玻爾沒有因為盧瑟福模型的困難而放棄這一理論，畢竟它有著α粒子散射實驗的強力支援。相反，玻爾對電磁理論能否作用於原子這一人們從未涉足過的層面，倒是抱有相當的懷疑成分。曼徹斯特的生活顯然要比劍橋令玻爾舒心許多，雖然他和盧瑟福兩個人的性格是如此不同，後者是個急性子，永遠精力旺盛，而他玻爾則像個害羞的大男孩，說一句話都顯得口齒不清。但他們顯然是絕妙的一個團隊，玻爾的天才在盧瑟福這個老闆的領導下被充分地激發出來，很快就在歷史上激起壯觀的波瀾。 一九一二年七月，玻爾完成了他在原子結構方面的第一篇論文，歷史學家們後來常常把它稱作曼徹斯特備忘錄。玻爾在其中已經開始試圖把量子的概念結合到盧瑟福模型中去，以解決經典電磁力學所無法解釋的難題。但是，一切都只不過是剛剛開始而已，在那片還沒有前人涉足的處女地上，玻爾只能一步步地摸索前進。沒有人告訴他方向應該在哪裡，而他的動力也不過是對於盧瑟福模型的堅信和年輕人特有的巨大熱情。玻爾當時對原子光譜的問題一無所知，當然也看不到它後來對於原子研究的決定性意義，不過，革命的方向已經確定，已經沒有什麼能夠改變量子論即將嶄露頭角這個事實了。 在濃雲密佈的天空中，出現了一線微光。雖然後來證明，那只是一顆流星，但是這光芒無疑給已經僵硬而老化的物理世界注入了一種新的生機，一種有著新鮮氣息和希望的活力。這光芒點燃了人們手中的火炬，引導他們去尋找真正的永恆的光明。 終於，七月二十四日，玻爾完成了他在英國的學習，動身返回祖國丹麥。在那裡，他可愛的未婚妻瑪格麗特正在焦急地等待著他，而物理學的未來也即將要向他敞開心扉。在臨走前，玻爾把他的論文交給盧瑟福過目，並得到了熱切的鼓勵。只是，盧瑟福有沒有想到，這個青年將在怎樣的一個程度上，改變人們對世界的終極看法呢？ 是的，是的，時機已到。偉大的三部曲即將問世，而真正屬於量子的時代，也終於到來。 飯後閒話：諾貝爾獎得主的幼稚園 盧瑟福本人是一位偉大的物理學家，這是無需置疑的。但他同時更是一位偉大的物理導師，他以敏銳的眼光去發現人們的天才，又以偉大的人格去關懷他們，把他們的潛力挖掘出來。在盧瑟福身邊的那些助手和學生們，後來絕大多數都出落得非常出色，其中更包括了為數眾多的科學大師們。 我們熟悉的尼爾斯．玻爾，二十世紀最偉大的物理學家之一，一九二二年諾貝爾物理獎得主，量子論的奠基人和象徵。在曼徹斯特跟隨過盧瑟福。 Paul.狄拉克（Paul Dirac），量子論的創始人之一，同樣偉大的科學家，一九三三年諾貝爾物理獎得主。他的主要成就都是在劍橋卡文迪許實驗室做出的（那時盧瑟福接替了JJ湯姆遜成為這個實驗室的主任）。狄拉克獲獎的時候才三十一歲，他對盧瑟福說他不想領這個獎，因為他討厭在公眾中的名聲。盧瑟福勸道，如果不領獎的話，那麼這個名聲可就更響了。 中子的發現者，詹姆斯．查德威克（James Chadwick）在曼徹斯特花了兩年時間在盧瑟福的實驗室裡。他於一九三五年獲得諾貝爾物理獎。 布萊克特（Patrick MS Blackett）在一次大戰後辭去了海軍上尉的職務，進入劍橋跟隨盧瑟福學習物理。他後來改進了威爾遜雲室，並在宇宙線和核子物理方面作出了巨大的貢獻，為此獲得了一九四八年的諾貝爾物理獎。 一九三二年，沃爾頓（ETS Walton）和考克勞夫特（John Cockcroft）在盧瑟福的卡文迪許實驗室裡建造了強大的加速器，並以此來研究原子核的內部結構。這兩位盧瑟福的弟子在一九五一年分享了諾貝爾物理獎金。 這個名單可以繼續開下去，一直到長得令人無法忍受為止：英國人索迪（Frederick Soddy），一九二一年諾貝爾化學獎。瑞典人赫維西（Georg von Hevesy），一九四三年諾貝爾化學獎。德國人哈恩（Otto Hahn），一九四四年諾貝爾化學獎。英國人鮑威爾（Cecil Frank Powell），一九五○年諾貝爾物理獎。美國人貝特（Hans Bethe），一九六七年諾貝爾物理獎。蘇聯人卡皮查（PL Kapitsa），一九七八年諾貝爾化學獎。 除去一些稍微疏遠一點的case，盧瑟福一生至少培養了十位諾貝爾獎得主（還不算他自己本人）。當然，在他的學生中還有一些沒有得到諾獎，但同樣出色的名字，比如漢斯．蓋革（Hans Geiger，他後來以發明了蓋革計數器而著名）、亨利．莫斯里（Henry Mosley，一個被譽為有著無限天才的年輕人，可惜死在了一戰的戰場上）、恩內斯特．馬斯登（Ernest Marsden，他和蓋革一起做了α粒子散射實驗，後來被封為爵士）等等，等等。 盧瑟福的實驗室被後人稱為諾貝爾獎得主的幼稚園。他的頭像出現在新西蘭貨幣的最大面值一百元上面，作為國家對他最崇高的敬意和紀念。 five 一九一二年八月一日，玻爾和瑪格麗特在離哥本哈根不遠的一個小鎮上結婚，隨後他們前往英國展開蜜月。當然，有一個人是萬萬不能忘記拜訪的，那就是玻爾家最好的朋友之一，盧瑟福教授。 雖然是在蜜月期，原子和量子的圖景仍然沒有從玻爾的腦海中消失。他和盧瑟福就此再一次認真地交換了看法，並加深了自己的信念。回到丹麥後，他便以百分之二百的熱情投入到這一工作中去。揭開原子內部的奧秘，這一夢想具有太大的誘惑力，令玻爾完全無法抗拒。 為了能使大家跟得上我們史話的步伐，我們還是再次描述一下當時玻爾面臨的處境。盧瑟福的實驗展示了一個全新的原子面貌：有一個緻密的核心處在原子的中央，而電子則繞著這個中心運行，像是圍繞著太陽的行星。然而，這個模型面臨著嚴重的理論困難，因為經典電磁理論預言，這樣的體系將會無可避免地釋放出輻射能量，並最終導致體系的崩潰。換句話說，盧瑟福的原子是不可能穩定存在超過一秒鐘的。 玻爾面臨著選擇，要麼放棄盧瑟福模型，要麼放棄麥克斯韋和他的偉大理論。玻爾勇氣十足地選擇了放棄後者。他以一種深刻的洞察力預見到，在原子這樣小的層次上，經典理論將不再成立，新的革命性思想必須被引入，這個思想就是普朗克的量子以及他的h常數。 應當說這是一個相當困難的任務。如何推翻麥氏理論還在其次，關鍵是新理論要能夠完美地解釋原子的一切行為。玻爾在哥本哈根埋頭苦幹的那個年頭，門捷列夫的元素週期律已經被發現了很久，化學鍵理論也已經被牢固地建立。種種跡象都表明在原子內部，有一種潛在的規律支配著它們的行為，並形成某種特定的模式。原子世界像一座蘊藏了無窮財寶的金字塔，但如何找到進入其內部的通道，卻是一個讓人撓頭不已的難題。 然而，像當年的貝爾佐尼一樣，玻爾也有著一個探險家所具備的最寶貴的素質：洞察力和直覺，這使得他能夠抓住那個不起眼，但卻是唯一的，稍縱即逝的線索，從而打開那扇通往全新世界的大門。一九一三年初，年輕的丹麥人漢森（Hans Marius Hansen）請教玻爾，在他那量子化的原子模型裡如何解釋原子的光譜線問題。對於這個問題，玻爾之前並沒有太多地考慮過，原子光譜對他來說是陌生和複雜的，成千條譜線和種種奇怪的效應在他看來太雜亂無章，似乎不能從中得出什麼有用的資訊。然而漢森告訴玻爾，這裡面其實是有規律的，比如巴爾末公式就是。他敦促玻爾關心一下巴爾末的工作。 突然間，就像伊翁（Ion）發現了藏在箱子裡的繪著戈耳工的麻布，一切都豁然開朗。山重水複疑無路，柳暗花明又一村。在誰也沒有想到的地方，量子得到了決定性的突破。一九五四年，玻爾回憶道：當我一看見巴爾末的公式，一切就都清楚不過了。 要從頭回顧光譜學的發展，又得從偉大的本生和基爾霍夫說起，而那勢必又是一篇規模宏大的文字。鑒於篇幅，我們只需要簡單地瞭解一下這方面的背景知識，因為本史話原來也沒有打算把方方面面都事無巨細地描述完全。概括來說，當時的人們已經知道，任何元素在被加熱時都會釋放出含有特定波長的光線，比如我們從中學的焰色實驗中知道，鈉鹽放射出明亮的黃光，鉀鹽則呈紫色，鋰是紅色，銅是綠色等等。將這些光線通過分光鏡投射到螢幕上，便得到光譜線。各種元素在光譜裡一覽無餘：鈉總是表現為一對黃線，鋰產生一條明亮的紅線和一條較暗的橙線，鉀則是一條紫線。總而言之，任何元素都產生特定的唯一譜線。 但是，這些譜線呈現什麼規律以及為什麼會有這些規律，卻是一個大難題。拿氫原子的譜線來說吧，這是最簡單的原子譜線了。它就呈現為一組線段，每一條線都代表了一個特定的波長。比如在可見光區間內，氫原子的光譜線依次為：656,484,434,410,397,388,383,380納米。這些資料無疑不是雜亂無章的，一八八五年，瑞士的一位數學教師巴爾末（Johann Balmer）發現了其中的規律，並總結了一個公式來表示這些波長之間的關係，這就是著名的巴爾末公式。將它的原始形式稍微變換一下，用波長的倒數來表示，則顯得更加簡單明瞭： ν＝R（1／2^2-1／n^2） 其中的R是一個常數，稱為里德伯（Rydberg）常數，n是大於二的正整數（三，四，五等等）。 在很長一段時間裡，這是一個十分有用的經驗公式。但沒有人可以說明，這個公式背後的意義是什麼，以及如何從基本理論將它推導出來。但是在玻爾眼裡，這無疑是一個晴天霹靂，它像一個火花，瞬間點燃了玻爾的靈感，所有的疑惑在那一刻變得順理成章了，玻爾知道，隱藏在原子裡的秘密，終於向他嫣然展開笑顏。 我們來看一下巴爾末公式，這裡面用到了一個變數n，那是大於二的任何正整數。n可以等於三，可以等於四，但不能等於三．五，這無疑是一種量子化的表述。玻爾深呼了一口氣，他的大腦在急速地運轉，原子只能放射出波長符合某種量子規律的輻射，這說明了什麼呢？我們回憶一下從普朗克引出的那個經典量子公式：E＝hν。頻率（波長）是能量的量度，原子只釋放特定波長的輻射，說明在原子內部，它只能以特定的量吸收或發射能量。而原子怎麼會吸收或者釋放能量的呢？這在當時已經有了一定的認識，比如斯塔克（J. Stark）就提出，光譜的譜線是由電子在不同勢能的位置之間移動而放射出來的，英國人尼科爾森（JW Nicholson）也有著類似的想法。玻爾對這些工作無疑都是瞭解的。 一個大膽的想法在玻爾的腦中浮現出來：原子內部只能釋放特定量的能量，說明電子只能在特定的勢能位置之間轉換。也就是說，電子只能按照某些確定的軌道運行，這些軌道，必須符合一定的勢能條件，從而使得電子在這些軌道間躍遷時，只能釋放出符合巴爾末公式的能量來。 我們可以這樣來打比方。如果你在中學裡好好地聽講過物理課，你應該知道勢能的轉化。一個體重一百公斤的人從一米高的臺階上跳下來，他／她會獲得一千焦耳的能量，當然，這些能量會轉化為落下時的動能。但如果情況是這樣的，我們通過某種方法得知，一個體重一百公斤的人跳下了若干級高度相同的臺階後，總共釋放出了一千焦耳的能量，那麼我們關於每一級臺階的高度可以說些什麼呢？ 明顯而直接的計算就是，這個人總共下落了一米，這就為我們臺階的高度加上了一個嚴格的限制。如果在平時，我們會承認，一個臺階可以有任意的高度，完全看建造者的興趣而已。但如果加上了我們的這個條件，每一級臺階的高度就不再是任意的了。我們可以假設，總共只有一級臺階，那麼它的高度就是一米。或者這個人總共跳了兩級臺階，那麼每級臺階的高度是0.5米。如果跳了三次，那麼每級就是1/3米。如果你是間諜片的愛好者，那麼大概你會推測每級臺階高1/39米。但是無論如何，我們不可能得到這樣的結論，即每級臺階高0.6米。道理是明顯的：高0.6米的臺階不符合我們的觀測（總共釋放了一千焦耳能量）。如果只有一級這樣的臺階，那麼它帶來的能量就不夠，如果有兩級，那麼總高度就達到了1.2米，導致釋放的能量超過了觀測值。如果要符合我們的觀測，那麼必須假定總共有一又三分之二級臺階，而這無疑是荒謬的，因為小孩子都知道，臺階只能有整數級。 在這裡，臺階數必須是整數，就是我們的量子化條件。這個條件就限制了每級臺階的高度只能是一米，或者1/2米，而不能是這其間的任何一個數字。 原子和電子的故事在道理上基本和這個差不多。我們還記得，在盧瑟福模型裡，電子像行星一樣繞著原子核打轉。當電子離核最近的時候，它的能量最低，可以看成是在平地上的狀態。但是，一旦電子獲得了特定的能量，它就獲得了動力，向上攀登一個或幾個臺階，到達一個新的軌道。當然，如果沒有了能量的補充，它又將從那個高處的軌道上掉落下來，一直回到平地狀態為止，同時把當初的能量再次以輻射的形式釋放出來。 關鍵是，我們現在知道，在這一過程中，電子只能釋放或吸收特定的能量（由光譜的巴爾末公式給出），而不是連續不斷的。玻爾做出了合理的推斷：這說明電子所攀登的臺階，它們必須符合一定的高度條件，而不能像經典理論所假設的那樣，是連續而任意的。連續性被破壞，量子化條件必須成為原子理論的主宰。 我們不得不再一次用到量子公式E＝hν，還請各位多多包涵。Stephen.霍金在他那暢銷書《時間簡史》的Acknowledgements裡面說，插入任何一個數學公式都會使作品的銷量減半，所以他考慮再三，只用了一個公式E＝mc二。我們的史話本是戲作，也不考慮那麼多，但就算列出公式，也不強求各位看客理解其數學意義。唯有這個E ＝hν，筆者覺得還是有必要清楚它的含義，這對於整部史話的理解也是有好處的，從科學意義上來說，它也決不亞於愛因斯坦的那個E ＝mc二。所以還是不厭其煩地重複一下這個方程的描述：E代表能量，h是普朗克常數，ν是頻率。 回到正題，玻爾現在清楚了，氫原子的光譜線代表了電子從一個特定的臺階跳躍到另外一個臺階所釋放的能量。因為觀測到的光譜線是量子化的，所以電子的臺階（或者軌道）必定也是量子化的，它不能連續而取任意值，而必須分成底樓，一樓，二樓等，在兩層樓之間，是電子的禁區，它不可能出現在那裡。正如一個人不能懸在兩級臺階之間漂浮一樣。如果現在電子在三樓，它的能量用W3表示，那麼當這個電子突發奇想，決定跳到一樓（能量W一）的期間，它便釋放出了W3-W1的能量。我們要求大家記住的那個公式再一次發揮作用，W3-W1＝hν。所以這一舉動的直接結果就是，一條頻率為ν的譜線出現在該原子的光譜上。 玻爾所有的這些思想，轉化成理論推導和數學表達，並以三篇論文的形式最終發表。這三篇論文（或者也可以說，一篇大論文的三個部分），分別題名為《論原子和分子的構造》（On the Constitution of Atoms and Molecules），《單原子核體系》（Systems Containing Only a Single Nucleus）和《多原子核體系》（Systems Containing Several Nuclei），於一九一三年三月到九月陸續寄給了遠在曼徹斯特的盧瑟福，並由後者推薦發表在《哲學雜誌》（Philosophical Magazine）上。這就是在量子物理歷史上劃時代的文獻，亦即偉大的三部曲。 這確確實實是一個新時代的到來。如果把量子力學的發展史分為三部分，一九○○年的普朗克宣告了量子的誕生，那麼一九一三年的玻爾則宣告了它進入了青年時代。一個完整的關於量子的理論體系第一次被建造起來，雖然我們將會看到，這個體系還留有濃重的舊世界的痕跡，但它的意義卻是無論如何不能低估的。量子第一次使全世界震驚於它的力量，雖然它的意識還有一半仍在沉睡中，雖然它自己仍然置身於舊的物理大廈之內，但它的怒吼已經無疑地使整個舊世界搖搖欲墜，並動搖了延綿幾百年的經典物理根基。神話中的巨人已經開始蘇醒，那些藏在古老城堡裡的貴族們，顫抖吧！