Chapter 6 Chapter 4 Deep in the Clouds

one It should be said that Bohr's new theory of atomic structure was not very popular with physicists after it was introduced.In the eyes of some people, this theory actually has the arrogant intention to overthrow Maxwell's system, which itself is outrageous.Sir Rayleigh (one of the discoverers of the Rayleigh-Jeans line we mentioned earlier) showed complete disinterest, and JJ Thomson, Bohr's tutor at Cambridge, declined to comment.Others, less venerable, were more blunt, such as a physicist declaring in class: "If this is going to be explained by quantum mechanics, then I'd rather not explain it." Others claimed that if If the quantum model is actually true, they will withdraw from the physics community.Even open-minded people, such as Einstein and Born, initially found the theory too reluctant to fully accept.

But quantum power is beyond anyone's imagination.The victory came so quickly and swiftly that Bohr himself was almost at a loss and at a loss.First of all, Bohr's derivation is completely in line with the hydrogen atomic spectrum line described by Balmer's formula, and from W2-W1 = hν This formula, we can calculate the expression of ν in reverse, so as to compare with Balmer's original formula ν=R (1/2^2 - 1/n^2), and calculate the theoretical value of Rydberg constant R Come.In fact, the difference between the predicted value of Bohr's theory and the experimental value is only one-thousandth, which undoubtedly makes his theory have a solid foundation immediately.

Not only that, Bohr's model predicted the existence of some new spectral lines, and these predictions were quickly confirmed by experimental physicists.In the so-called "Pickering line series" (Pickering line series) debate, Bohr even achieved a decisive victory with strong evidence.His atomic system explained the spectra of some helium ions with remarkable accuracy, which was astonishingly accurate compared to the older equations.The work of Henry Moseley (the young genius we mentioned earlier, who unfortunately died on the battlefield) on X-rays further confirmed the correctness of the atom-nucleus model.It is now known that the chemical properties of an atom depend on its nuclear charge, rather than the traditional atomic weight.The electron shell model based on Bohr's theory was also developed step by step.There were only a few minor difficulties to be solved, such as the discovery that the spectrum of the hydrogen atom was not one line but could be split into many lines.These effects become more strange and obvious with the participation of electromagnetic fields (about these phenomena, people use the so-called "Stark effect" and "Zeman effect" to describe).But the Bohr system quickly gave a strong counterattack. Under the conditions of winning the allies of Einstein's theory of relativity and assuming that electrons have more degrees of freedom (quantum numbers), Bohr and some other scientists tried to A. Sommerfeld proved that all these phenomena can be smoothly included in Bohr's quantum system.Although the brutal world war had broken out, it did not stop the great progress of science in that period.

Every day, new reports and experimental evidence arrived on Bohr's desk like snowflakes.And almost every report is further confirming the correctness of the Borna quantum model.Of course, along with these reports, congratulations from all walks of life, social invitations and letters of appointment from various universities came overwhelmingly.Bohr seemed to have become a leader in atomic physics.Out of a sense of responsibility to the motherland, he rejected the position in Manchester introduced by Rutherford, although it was undoubtedly a better choice both financially and academically.Bohr is now a professor at the University of Copenhagen and decided to build a special institute for further research in theoretical physics.This institute, as we will see later, will become an eye-catching pearl in Europe. Its brilliance will attract the most outstanding young people from all over Europe to gather here and emit more brilliant brilliance of thought.

Here, we might as well review some basic features of the Bohr model.It is basically a continuation of Rutherford's planetary model, but in the Bohr model, a series of quantization conditions are introduced, so that this system has distinct quantization characteristics. First, Bohr postulated that electrons could only be in certain "certain" energy states when orbiting the nucleus.These energy states are discontinuous and are called stationary states.You can have E1, you can have E2, but you cannot take any value between E1 and E2.As we have already described, electrons can only be in one steady state, there is no buffer zone between the two steady states, there is a forbidden area for electrons, and electrons cannot appear there.

However, Bohr allowed electrons to switch, or transition, between different energy states.When electrons transition from the high-energy E2 state to the E1 state, the energy of E2-E1 is emitted, and the energy is released in the form of radiation. According to our basic formula, we know that the frequency of this radiation is ν, so that E2-E1 = hν.Conversely, when an electron absorbs energy, it can also climb from a low-energy state to a higher-energy state, and the relationship still conforms to our formula.We must note that this energy transition is a quantized behavior. If an electron transitions from E2 to E1, it does not mean that the electron has experienced any state between the two energies of E2 and E1 during this process.If you're still confused, the specter of continuity is still haunting your mind.In fact, Quantum is like a superb magician. It appeared at one end of the stage smiling and waving its hat, and then appeared on the other side of the stage in a blink of an eye.And at no point did it pass center stage!

Every possible energy level represents the orbit of an electron, just like a satellite 500 kilometers above the ground and a satellite 800 kilometers above the ground represent different potential energies.When an electron neither emits nor absorbs energy, it moves steadily in an orbit.When it absorbs a certain amount of energy, it disappears from the original orbit, and mysteriously appears on a higher-energy orbit farther from the nucleus.Conversely, as it falls desperately toward the nucleus, it emits the energy it scavenged in its high-energy orbit. It was soon discovered that the chemical properties of an atom mainly depend on the number of electrons in its outermost shell, and thus exhibit regular periodicity.But people have also been very puzzled, that is, for heavy elements with many electrons, why some of its electrons can occupy the outer electron orbit for a long time without losing energy and falling to the lower orbit near the nucleus.This question was answered by the young Pauli in 1925: he discovered that no two electrons can share the same state, and that a layer of orbitals can accommodate a finite number of different states, that is, a Orbits have a certain capacity.When electrons fill up an orbital, no other electrons can join that orbital.

An atom is like a dormitory, each room has a four-digit house number.There are only two rooms on the ground floor, 1001 and 1002.There are 8 rooms on the second floor, and the house numbers are 2001, 2002, 2101, 2102, 2111, 2112, 2121 and 2122.The higher the building, the more rooms it has.Pauli, the grumpy administrator, puts up a notice at the gate announcing that no two e-tenants can stay in the same house.So the electrons rushed into this building, the first two occupied the two cheap and good-quality rooms on the ground floor, and the latecomers had to settle for the next best thing because the ground floor was full, and began to fill the second floor s room.After the second floor was full, it was the turn of the third and fourth floors... until the sixth, seventh, and eighth floors where the rent was outrageous.Unfortunately, although the electronic living in the high place cannot make ends meet, there is no way to do it, because the downstairs is full of people and cannot move out.They complained and called Pauli's outrageous rule "the exclusion principle".

However, this measure can indeed help people better understand some basic codes of conduct of the "chemical society".For example, gregarious Cyborgs always try to fill every room on a floor with tenants.We imagine a "sodium mansion", on its third floor, there is only one lone tenant living in Room 3001.On the third floor of the adjacent "Chlorine Building", there happened to be only one vacant room (3122).Out of electronic yearning for excitement, the lonely man in the sodium building decided to move to the chlorine building to fill the empty room, and he was warmly welcomed by the tenants there.This move also contributed to the association of the two buildings, forming a "salt community".And in some high-rise buildings, because there are too many empty rooms, it is impossible to find enough solitary people to fill a floor, so even if only one wing is filled, the electrons are satisfied.

All of this, of course, is a figurative and general statement.The actual situation is much more complicated. For example, the rooms on each floor are divided into several levels due to different facilities.It is not a general principle that the taller the more expensive, for example, a presidential suite on the sixth floor is likely to be much more expensive than an ordinary room on the seventh floor.But this is not a problem. The key point is that Bohr's electron orbital model explained the nature and behavior of atoms very convincingly, and its predictions and experimental results are basically in perfect agreement.In less than two years, Bohr's theory achieved a brilliant victory, and physicists all over the world began to accept the Bohr model.Even our diehard—Planck, who refused to recognize the practicality of quantum—has begun to re-examine his original great discovery.

The achievement of Bohr's theory is huge and deeply rooted in the hearts of the people. He himself won the Nobel Prize in 1922 for this.However, this still does not resolve the deep contradiction between it and the old system.Regardless of whether the Bohr orbit is successful or not, Maxwell's equation still has to say that an electron moving around the nucleus must release electromagnetic radiation.Bohr also felt deeply helpless about this. He did not have the ability to overthrow the entire classical electromagnetic system. To use a popular saying, "the remnants of feudalism are still very strong."As a compromise, Bohr turned around and tried to reconcile his atomic system with Maxwellian theory and establish a connection between the two theories.He tried to prove to the world that both systems are correct, but they can only be established within the scope of their respective applications.When our vision gradually expands from the scope of atoms to the ordinary world, the quantum effect will gradually disappear, and the classical electromagnetism can replace the h constant again as the master of the world.In this process, at any time, there is a definite corresponding state between the two systems.This is what he called the "correspondence principle" published in 1918. The principle of correspondence itself has rich meanings, and it still has reference significance for us today.But it is also undeniable that this "ambiguous" relationship with the classical system is a fatal congenital deficiency of Bohr's theory.What he led was an incomplete revolution. Although he appeared as a revolutionist, he ultimately relied on the support of traditional forces.Bohr's quantum can only act on the strength of the classical system, and its self-awareness is still in a deep sleep and has not awakened.Of course, despite this, its achievements have amazed the world, but this cannot prevent it from falling to the other side of the horizon with a long tail light in the near future, becoming a fleeting meteor . Of course, such a short lifespan for a theory of such great significance only shows one thing: science was advancing at a pace beyond our imagination in those days.It was a period of time that cannot be met, the golden age of theoretical physics.Looking back now, only the bright moon and the clear breeze accompany the river to the east. *********** After-dinner gossip: Atoms and galaxies As soon as Rutherford's model was born, it was called the "planetary model" or "solar system model".This is of course a figurative name, but it is undeniable that there are indeed many similarities between the tiny system of the atom and the huge system of the solar system.Both have a core that occupies an insignificant volume (compared to the entire system) but concentrates more than 99% of its mass and angular momentum.People can't help thinking, is the atom itself a "small universe"?Or, our universe is composed of thousands of "small universes", which in turn form a larger "universe" with thousands of other universes?This brings to mind the famous little poem by William Blake: To see a world in a grain of sand. *Seeing the world from a grain of sand And a heaven in a wild flower *I know Tianchen from a flower Hold infinity in the palm of your hand *hold infinity in the palm of your hand And eternity in an hour *Use a moment to keep eternity Can we "see the world from a grain of sand"?The analogy between atoms and the solar system does not give us much enlightenment, because the actual distance between planets is much farther than that of electrons (proportionally speaking, of course).However, some scientists have recently proposed that the universe does have an astonishingly repetitive structure on different scales.For example, the analogy between atoms and galaxies, and the analogy between atoms and neutron stars, they all show very similarities in various aspects—such as radius, period, vibration, etc.If you magnify an atom by a factor of 10^17, it behaves like a white dwarf.If it is magnified 10^30 times, it is believed that it is equivalent to a Milky Way.Of course, equivalent does not mean completely equal, I mean, if the atomic system is enlarged by 10^30 times, its various mechanical and structural constants are very close to the Milky Way we observe.It has also been suggested that atoms should be analogous to the solar system at high energies.That is to say, the atom must be in a very high excited state (approximately hundreds of principal quantum numbers), at that time, its various structures are quite close to our solar system. This view, that the universe exhibits a similar structure at all levels, is known as the "fractal universe" model.In its view, even an atom contains some information of the entire universe, and it is a "holographic embryo" of the universe.So-called "fractals", an intriguing subject of research in chaotic dynamics, show us how complex structures repeat over and over at different levels.Whether the evolution of the universe also obeys some kind of chaotic dynamics principle is still unknown, and the so-called "fractal universe" is just a family's opinion.Here is an interesting story, just for everyone to laugh. two Once upon a time, the rise of Bohr's theory brought brilliant light to the entire dark physical sky, making people think that they saw the beauty of the paradise.Unfortunately, this false bubble boom did not last long.Although the old physical world has become full of scars under various impacts, the magnificent palace of the Bohr atomic model failed to withstand the more violent revolutionary impact, and was burned in chaos, leaving only some broken tiles and ruins. For our condolences today.The initial rainstorm has passed, the land is bleak, and the sky is still thick with clouds.The setting sun was like blood, casting an afterglow in the sky, dyeing the ruins golden and red, setting off a heavier atmosphere and heralding the coming of a bigger storm. The decline of the Bohr dynasty seems to be doomed on the day it was born.Although this theory borrows the infinite power of the newborn quantum, its foundation is still built on the fragile old foundation.The idea of ​​quantization is just a mercenary in Bohr's theory. It is more like being forced to add, rather than the starting point and foundation of the whole theory.For example, Bohr assumed that electrons can only have quantized energy levels and orbits, but why?Why do electrons have to be quantized?What is its theoretical basis?Bohr was vague on this, talking about him left and right.Of course, a harsh empiricist would argue that electrons are quantized because experiments have observed them to be, and no other reason is needed.But in any case, if the basic postulates of a theory feel insecure, the prospects for the theory are not so promising.In their attitude towards Bohr's quantum hypothesis, scientists undoubtedly think of Euclid's fifth postulate (this axiom says that there can only be one straight line parallel to a known straight line passing through a point outside the line. People later proved that this axiom is not not very reliable).Undoubtedly, it is better to be derived from some more basic axioms. These more basic axioms should become the cornerstone of the whole theory, not just a gorgeous decoration. When later historians commented on Bohr's theory, they always used words such as "semi-classical and half-quantum", or "new wine in old bottles".It is like a face-changing master. When an electron revolves around a single orbit, it shows the face of classical mechanics. Once the orbit changes, it immediately turns into a quantized appearance.This duplicity, although backed by the skillful principle of correspondence, is also questionable.However, these issues are not the key point. The key point is that after a series of major victories, Bohr's army finally found that it had reached the end of its strength, and there were some strong fortresses that could not be attacked anyway. For example, we already know the problem of splitting atomic spectral lines. Although under the efforts of Sommerfeld and others, the Bohr model explained the Zeeman effect under the magnetic field and the Stark effect under the electric field.However, there are always endless changes in nature, which is a headache.Scientists soon discovered a complex splitting of spectral lines under weak magnetic fields, called the "anomalous Zeeman effect."This phenomenon requires the introduction of a quantum number with a value of 1/2, and Bohr's theory has nothing to do with it, sighing.This problem puzzles many scientists, and it makes them sleepless.It is said that when Pauli visited Bohr's home, he once responded to Mrs. Bohr's greetings with a grumpy complaint: "Of course I am not good! I can't understand the abnormal Zeeman effect!" This question has been raised until Pauli asked him After the incompatibility principle, it is finally resolved. In addition, the Bohr theory found to its dismay that its power was limited to a model of the atom with only one electron.For hydrogen atoms, deuterium atoms, or ionized helium atoms, it gives convincing arguments.But for ordinary helium atoms with only two extranuclear electrons, it is powerless.Even for an electron atom, what Bohr can say clearly is only the frequency of the spectral line. As for the intensity, width or polarization of the spectral line, Bohr still can only shrug his shoulders and use his big tongue Say sorry for the accent. On the battlefield of hydrogen molecules, Bohr's theory was also defeated. In order to solve all these difficulties, Bohr, Lande, Pauli, Kramers, etc. made a lot of efforts, introduced one new assumption after another, established one new model after another , and some even violated Bohr and Sommerfeld's theory itself.By 1923, although the bleak Bohr theory could barely solve the problem and gained people's general acceptance, it was already like a robe full of patches, and it needed to be completely reformed fundamentally.The energetic young people in Göttingen began to reject this patchy system, hoping to seek a more powerful and perfect theory, so as to root the idea of ​​quantum into physics in essence, so as to end the Such a rough sojourn life. The decline of the Bohr system was as rapid as its prosperity.More and more people began to pay attention to the atomic world, and made more experimental observations.Every day, people can get new information, stimulate their enthusiasm, and uncover the face of this mysterious kingdom.In Copenhagen and Göttingen, physics geniuses talked about atomic nuclei, electrons and quantum with great enthusiasm. Pages of manuscripts filled with formulas and letters carried inspiration and creativity, interweaving into a prelude to the arrival of a great era.The green mountains can't cover it, after all, it flows eastward.The pace of the times is so fast that the faltering Bohr atom is finally powerless, withdraws from the stage of history, and disappears into the vast yellow dust, leaving only one name for us to recall from time to time. If the pioneering work of Heisenberg (Werner Heisenberg) and Schrödinger (Erwin Schrodinger) in 1925-1926 is regarded as the end of Bohr's system, the theory flourished for about 13 years in total.It allows people to see the great significance of quantum in the physical world, and for the first time uses its power to uncover the mystery inside the atom.However, as we have seen, Bohr's revolution was an incomplete revolution, and the quantum hypothesis did not gain a fundamental position in his system, but seemed to be only a vassal to reconcile the contradiction between classical theory and reality.Bohr's theory can't explain why electrons have discrete energy levels and quantized behavior. It only knows what it is, but not why.Bohr took an eclectic route between quantum theory and classical theory, which made his atoms always have a half-new color, and eventually collapsed due to insurmountable difficulties.Bohr's orbital atom is like a dazzling bolide, which emits such a strong light, but crosses the night sky in a blink of an eye, and falls into darkness and chaos again.It comes and goes in such a hurry that people don't even have time to tie a knot on the belt and make some beautiful wishes. However, its great significance has not faded in any way because of its short life.It was it that unearthed quantum power and paved the way for future pioneers.It is a link between the past and the future, which has effectively promoted the pace of the entire physics.The Bohr model is still a fairly good approximation, and some of its ideas are still used for reference and learning by people today.Although the atomic picture it depicts is outdated, it is so vivid and vivid that it is still the standard style in the hearts of the public until today, and even represents the image of science.For example, we should be able to recall that until the end of the 1980s, the figure representing "science" could still be seen everywhere on the streets of China: three electrons orbiting the nucleus along an elliptical orbit.This pattern finally disappeared in the 1990s, and someone finally realized the problem. In the Bohr system, there is already a contradiction between randomness and determinism.As far as Bohr's theory is concerned, it is impossible to judge when and where an electron automatically transitions, it is more like a random process. In 1919, at the invitation of Max Planck, Bohr visited post-war Berlin.There, Planck and Einstein received him warmly, and the three giants of quantum mechanics discussed several physical issues.Bohr believed that the transition of electrons between orbits seems to be unpredictable, and it is a spontaneous random process. At least theoretically, there is no way to calculate the specific transition conditions of an electron.Einstein shook his head, thinking that any physical process is deterministic and predictable.This has planted the seeds of the protracted dispute between the two in the future. Of course, our venerable Mr. Niels Bohr will not withdraw from the physics stage because of the collapse of the old quantum theory.On the contrary, the wonderful story about him has just begun.He will also fight on the front line of physics for a long time until he dies. In September 1921, Bohr's research institute in Copenhagen was finally completed, and the 36-year-old Bohr became the director of the institute.His personality charm soon attracted talented young people from all over the world like a magnetic field, and soon turned it into an academic center throughout Europe.Georg von Hevesy, Otto Frisch, Pauli, Heisenberg, Nevill Mott, Landau, George Gamov... people Come here, fully feel the free atmosphere here and Bohr's care, and form an academic spirit full of passion, vitality, optimism and enterprising spirit, which is the "Copenhagen spirit" praised by later generations.In the tiny country of Denmark, there is a sacred place in the eyes of the physics community. This place will profoundly affect the future of quantum mechanics, as well as our fundamental worldview and way of thinking. three When Bohr's atoms were still mired in the quagmire and unable to extricate themselves, a new revolution was already brewing.This time, the revolutionaries came not from the poor proletarian masses, but from a prominent aristocratic family.Prince Louis Victor Pierre Raymond de Broglie will add a new dimension to his glorious family history. The title of "Prince" (Prince, also translated as "son") is not what we usually understand, it is the son of the king.In fact, it doesn't rank very high in the knighthood table, and it doesn't seem to be seen in the English-speaking world.Generally speaking, its status is slightly lower than that of "Viscount" and slightly higher than that of "Baron".But this is only because Louis is not the boss in the family. The De Broglie family has a long history. Many generals, marshals, and ministers have emerged from his ancestors. Liu's subordinates served.They participated in the War of the Polish Succession (1733-1735), the War of the Austrian Succession (1740-1748), the Seven Years' War (1756-1763), the American War of Independence (1775-1782), the French Revolution (1789), the February Revolution (1848), accepted by Francis II II, Holy Roman Emperor, later abdicated to become Emperor Francis I of Austria) and Louis Philippe (Louis Philippe, King of France, historically known as the Duke of Orleans), the family inherited the highest hereditary title: Duke Duc, equivalent to Duke in English).Louis de Broglie's elder brother, Maurice de Broglie (Maurice de Broglie), is the sixth Duke of de Broglie. In 1960, when Maurice passed away, Louis finally inherited the title from his brother, becoming the seventh duc de Broglie. Of course, before that, Louis still carried the title of prince.Little Louis showed a strong interest in history. His grandfather, Jacques Victor Albert, duc de Broglie, was not only a politician, but also an outstanding historian when he was Prime Minister of France from 1873 to 1874. , especially proficient in the history of late Rome, wrote the book "Histoire de leglise et de lempire romain" (Histoire de leglise et de lempire romain).Under the influence of his grandfather, little Louis decided to enter the University of Paris to study history. At the age of 18 (1910), he graduated from university, but did not pursue further studies in the field of history, because his interests had turned strongly to physics.His elder brother, Maurice de Broglie (the sixth Duke of De Broglie) is a famous ray physicist. Louis followed his elder brother to participate in the Brussels Physics Conference in 1911, and his enthusiasm for science was completely overwhelmed. inspired, and determined to dedicate his life to this exciting cause. Soon after switching to physics, World War I broke out.De Broglie enlisted in the army and was assigned a job as a radio technician.He was much luckier than poor Henry Moseley, and was able to survive the war unscathed and go on to college to study his physics.His doctoral supervisor is the famous Paul Langevin (Paul Langevin). At this point I need to pause for a moment to make a statement.Our storytelling so far has looked back at some exciting revolutions and eye-opening new ideas (at least I hope so), but generally still hovers in the realm of the classic world.And according to my impression, so far, our topics have generally not exceeded the scope of middle school physics textbooks and college entrance examinations.For ordinary readers, the only thing that is slightly unfamiliar may be the quantum leap thought.And accepting this idea is not a very difficult and unwilling thing. After that, however, we're in a whole world of fantasy.This world is bizarre, completely different from the one we usually perceive and identify with.In this new world, all the images and concepts appear crazy and irrational, more like the wonderland in Alice's dream than the down-to-earth land.Many nouns are so odd that their true meaning can only be grasped with the aid of mathematical tools.Of course, the author will, as always, try to express them in the simplest language, but it is still necessary to remind everyone to be mentally prepared.For the convenience of expression, I will try my best to state one thing completely, and then change the topic.Although in history, all of these are overwhelming, they are mixed together, turbulent, and people can't tell the clues.In the following narration, we may have to jump between years from time to time, and readers who want to grasp the sense of time should pay attention to the exact year. We are already on the cusp of a great moment.The new quantum mechanics will be created soon, and this time, its power will be fully deployed, so that all old things, including Bohr's half-new system, will be completely destroyed. do.It will soon unveil a new world for us, a new world that, even a glimpse into it, is enough to make people dizzy and heart-shattering.However, since we are already standing here, we can only move forward without hesitation.So follow me, countless exciting things are waiting for us ahead. Our topic returns to De Broglie.He has been thinking about a problem, that is, how to naturally introduce a concept of period into Bohr's atomic model to conform to the observed reality.Originally, this condition was a quantization mode imposed on electrons. Under Bohr's rigid rules, although electrons were obedient, they always felt a little unwilling.It's time, de Brogue figured, to unleash the electrons and let them make their own decisions. How to endow electrons with a basic property so that they can consciously exhibit various periodic and quantized phenomena?De Bro was aware of Einstein and his theory of relativity.He began to reason like this: According to Einstein's famous equation, if an electron has a mass m, then it must have an intrinsic energy E = mc^2.Well, let's recall again the fundamental quantum equation that I said was very useful, E = hν, that is to say, corresponding to this energy, electrons must have an intrinsic frequency.The calculation of this frequency is simple, since mc^2 = E = hν, so ν = mc^2/h. it is good.Electrons have an intrinsic frequency.So what is the frequency?It is a cycle of some kind of vibration.Then we conclude that there is something vibrating inside the electron.What is it that is vibrating?With the help of the theory of relativity, de Broglie started his calculations, and found that... when an electron moves forward with a speed of v0, it must be accompanied by a wave with a speed of c^2/v0... Oh, you heard me right.When electrons are moving forward, they are always accompanied by a wave.Careful readers may have doubts, because they find that the wave speed c^2/v0 will be much faster than the speed of light, but this is not a problem.De Broglie proved that such waves cannot carry actual energy or information, and therefore do not violate relativity.Einstein just said that no energy signal can be transmitted faster than the speed of light, and he turned a blind eye to de Broglie's waves. De Broglie called this wave "phase wave", and later generations also called it "de Broglie wave" in memory of him.Calculating the wavelength of this wave is easy, simply divide the velocity obtained above by its frequency, then we get: λ = (c^2/v0 ) / (mc^2/h) = h/mv0.This is called the de Broglie wavelength formula. But wait, we don't seem to have caught up yet.We're talking about a "wave"!But we were clearly discussing the problem of electrons first, why did a wave suddenly emerge from the electrons?Where did it come from?I hope you haven't forgotten our poor armies of waves and particles, which have been struggling and stalemate during the prosperity and decline of the Bohr atom. In 1923, before de Broglie found out his phase wave, it happened that Compton explained the Compton effect with the theory of photons, and it was not long after he led the counterattack of particles.The unlucky particles had to give up their all-out attack because they suddenly discovered that there were fluctuating spies in the rear of the electrons!And no matter how hard you drive them, you can't drive them away. Electrons are actually a wave!This is unbelievable.In front of these avant-garde and rebellious young people, the respectable gentleman Planck could only shake his head and sigh, unable to speak.If there was only one person in the world who supported De Broglie at that time, it was Einstein.德布罗意的导师朗之万对自己弟子的大胆见解无可奈何，出于挽救失足青年的良好愿望，他把论文交给爱因斯坦点评。谁料爱因斯坦马上予以了高度评价，称德布罗意“揭开了大幕的一角”。整个物理学界在听到爱因斯坦的评论后大吃一惊，这才开始全面关注德布罗意的工作。 证据，我们需要证据。所有的人都在异口同声地说。如果电子是一个波，那么就让我们看到它是一个波的样子。把它的衍射实验做出来给我们看，把干涉图纹放在我们的眼前。德布罗意有礼貌地回敬道：是的，先生们，我会给你们看到证据的。我预言，电子在通过一个小孔的时候，会像光波那样，产生一个可观测的衍射现象。 1925年4月，在美国纽约的贝尔电话实验室，戴维逊（CJDavisson）和革末（LH Germer）在做一个有关电子的实验。这个实验的目的是什么我们不得而知，但它牵涉到用一束电子流轰击一块金属镍（nickel）。实验要求金属的表面绝对纯净，所以戴维逊和革末把金属放在一个真空的容器中，以确保没有杂志混入其中。 不幸的是，发生了一件意外。这个真空容器因为某种原因发生了爆炸，空气一拥而入，迅速地氧化了镍的表面。戴维逊和革末非常懊丧，不过他们并不因此放弃实验，他们决定，重新净化金属表面，把实验从头来过。当时，去除氧化层的好办法就是对金属进行高热加温，这正是戴维逊所做的。 两人并不知道，正如雅典娜暗中助推着阿尔戈英雄们的船只，幸运女神正在这个时候站在他俩的身后。容器里的金属，在高温下发生了不知不觉的变化：原本它是由许许多多块小晶体组成的，而在加热之后，整块镍融合成了一块大晶体。虽然在表面看来，两者并没有太大的不同，但是内部的剧变已经足够改变物理学的历史。 当电子通过镍块后，戴维逊和革末瞠目结舌，久久说不出话来。他们看到了再熟悉不过的景象：X射线衍射图案！可是并没有X射线，只有电子，人们终于发现，在某种情况下，电子表现出如X射线般的纯粹波动性质来。电子，无疑地是一种波。 更多的证据接踵而来。1927年，GP汤姆逊，著名的JJ汤姆逊的儿子，在剑桥通过实验进一步证明了电子的波动性。他利用实验数据算出的电子行为，和德布罗意所预言的吻合得天衣无缝。 命中注定，戴维逊和汤姆逊将分享1937年的诺贝尔奖金，而德布罗意将先于他们8年获得这一荣誉。有意思的是，GP汤姆逊的父亲，JJ汤姆逊因为发现了电子这一粒子而获得诺贝尔奖，他却因为证明电子是波而获得同样的荣誉。历史有时候，实在富有太多的趣味性。 *********** 饭后闲话：父子诺贝尔 俗话说，将门无犬子，大科学家的后代往往也会取得不亚于前辈的骄人成绩。JJ汤姆逊的儿子GP汤姆逊推翻了老爸电子是粒子的观点，证明电子的波动性，同样获得诺贝尔奖。这样的世袭科学豪门，似乎还不是绝无仅有。 居里夫人和她的丈夫皮埃尔?居里于1903年分享诺贝尔奖（居里夫人在1911年又得了一个化学奖）。他们的女儿约里奥?居里（Irene Joliot-Curie）也在1935年和她丈夫一起分享了诺贝尔化学奖。居里夫人的另一个女婿，美国外交家Henry R. Labouisse，在1965年代表联合国儿童基金会（UNICEF）获得了诺贝尔和平奖。 1915年，William Henry Bragg和William Lawrence Bragg父子因为利用X射线对晶体结构做出了突出贡献，分享了诺贝尔物理奖金。 我们大名鼎鼎的尼尔斯?玻尔获得了1922年的诺贝尔物理奖。他的小儿子，埃格?玻尔（Aage Bohr）于1975年在同样的领域获奖。 卡尔?塞班（Karl Siegbahn）和凯伊?塞班（Kai Siegbahn）父子分别于1924和1981年获得诺贝尔物理奖。 假如俺的老爸是大科学家，俺又会怎样呢？不过恐怕还是如现在这般浪荡江湖，寻求无拘无束的生活吧，呵呵。 Four “电子居然是个波！”这个爆炸性新闻很快就传遍了波动和微粒双方各自的阵营。刚刚还在康普顿战役中焦头烂额的波动一方这下扬眉吐气，终于可以狠狠地嘲笑一下死对头微粒。《波动日报》发表社论，宣称自己取得了决定性的胜利。“微粒的反叛势力终将遭遇到他们应有的可耻结局——电子的下场就是明证。”光子的反击，在波动的眼中突然变得不值一提了，连电子这个老大哥都搞定了，还怕小小的光子？ 不过这次，波动的乐观态度未免太一厢情愿，它高兴得过早了。微粒方面的宣传舆论工具也没闲着，《微粒新闻》的记者采访了德布罗意，结果德布罗意说，当今的辐射物理被分成粒子和波两种观点，这两种观点应当以某种方式统一，而不是始终地尖锐对立——这不利于理论的发展前景。对于微粒来说，讲和的提议自然是无法接受的，但至少让它高兴的是，德布罗意没有明确地偏向波动一方。微粒的技术人员也随即展开反击，光究竟是粒子还是波都还没说清，谁敢那样大胆地断言电子是个波？让我们看看电子在威尔逊云室里的表现吧。 威尔逊云室是英国科学家威尔逊（CTRWilson）在1911年发明的一种仪器。水蒸气在尘埃或者离子通过的时候，会以它们为中心凝结成一串水珠，从而在粒子通过之处形成一条清晰可辨的轨迹，就像天空中喷气式飞机身后留下的白雾。利用威尔逊云室，我们可以研究电子和其他粒子碰撞的情况，结果它们的表现完全符合经典粒子的规律。在过去，这或许是理所当然的事情，但现在对于粒子军来说，这个证据是宝贵的。威尔逊因为发明云室在1927年和康普顿分享了诺贝尔奖金。如果说1937年戴维逊和汤姆逊的获奖标志着波动的狂欢，那10年的这次诺贝尔颁奖礼无疑是微粒方面的一次盛典。不过那个时候，战局已经出乎人们的意料，有了微妙的变化。Of course, this is all for later. 捕捉电子位置的仪器也早就有了，电子在感应屏上，总是激发出一个小亮点。Hey，微粒的将军们说，波动怎么解释这个呢？哪怕是电子组成衍射图案，它还是一个一个亮点这样堆积起来的。如果电子是波的话，那么理论上单个电子就能构成整个图案，只不过非常黯淡而已。可是情况显然不是这样，单个电子只能构成单个亮点，只有大量电子的出现，才逐渐显示出衍射图案来。 微粒的还击且不去说他，更糟糕的是，无论微粒还是波动，都没能在“德布罗意事变”中捞到实质性的好处。波动的嘲笑再尖刻，它还是对光电效应、康普顿效应等等现象束手无策，而微粒也还是无法解释双缝干涉。双方很快就发现，战线还是那条战线，谁都没能前进一步，只不过战场被扩大了而已。电子现在也被拉进有关光本性的这场战争，这使得战争全面地被升级。现在的问题，已经不再仅仅是光到底是粒子还是波，现在的问题，是电子到底是粒子还是波，你和我到底是粒子还是波，这整个物质世界到底是粒子还是波。 事实上，波动这次对电子的攻击只有更加激发了粒子们的同仇敌忾之心。现在，光子、电子、α粒子、还有更多的基本粒子，他们都决定联合起来，为了“大粒子王国”的神圣保卫战而并肩奋斗。这场波粒战争，已经远远超出了光的范围，整个物理体系如今都陷于这个争论中，从而形成了一次名副其实的世界大战。玻尔在1924年曾试图给这两支军队调停，他和克莱默（Kramers）还有斯雷特（Slater）发表了一个理论（称作BSK理论），尝试同时从波和粒子的角度去解释能量转换，但双方正打得眼红，这次调停成了外交上的彻底失败，不久就被实验所否决。战火熊熊，燃遍物理学的每一寸土地，同时也把它的未来炙烤得焦糊不清。 物理学已经走到了一个十字路口。它迷茫而又困惑，不知道前途何去何从。昔日的经典辉煌已经变成断瓦残垣，一切回头路都被断绝。如今的天空浓云密布，不见阳光，在大地上投下一片阴影。人们在量子这个精灵的带领下一路走来，沿途如行山阴道上，精彩目不暇接，但现在却突然发现自己已经身在白云深处，彷徨而不知归路。放眼望去，到处是雾茫茫一片，不辨东南西北，叫人心中没底。玻尔建立的大厦虽然看起来还是顶天立地，但稍微了解一点内情的工程师们都知道它已经几经裱糊，伤筋动骨，摇摇欲坠，只是仍然在苦苦支撑而已。更何况，这个大厦还凭借着对应原理的天桥，依附在麦克斯韦的旧楼上，这就教人更不敢对它的前途抱有任何希望。在另一边，微粒和波动打得烽火连天，谁也奈何不了谁，长期的战争已经使物理学的基础处在崩溃边缘，它甚至不知道自己是建立在什么东西之上。 不过，我们也不必过多地为一种悲观情绪所困扰。在大时代的黎明到来之前，总是要经历这样的深深的黑暗，那是一个伟大理论诞生前的阵痛。当大风扬起，吹散一切岚雾的时候，人们会惊喜地发现，原来他们已经站在高高的山峰之上，极目望去，满眼风光。 那个带领我们穿越迷雾的人，后来回忆说：“1924到1925年，我们在原子物理方面虽然进入了一个浓云密布的领域，但是已经可以从中看见微光，并展望出一个令人激动的远景。” 说这话的是一个来自德国的年轻人，他就是维尔纳?海森堡（Werner Heisenberg）。 在本史话第二章的最后，我们已经知道，海森堡于1901年出生于维尔兹堡（Wurzburg），他的父亲后来成为了一位有名的希腊文教授。小海森堡9岁那年，他们全家搬到了慕尼黑，他的祖父在那里的一间学校（叫做Maximilians Gymnasium的）当校长，而海森堡也自然进了这间学校学习。虽然属于“高干子弟”，但小海森堡显然不用凭借这种关系来取得成绩，他的天才很快就开始让人吃惊，特别是数学和物理方面的，但是他同时也对宗教、文学和哲学表现出强烈兴趣。这样的多才多艺预示着他以后不仅仅将成为一个划时代的物理学家，同时也将成为一为重要的哲学家。 1919年，海森堡参予了镇压巴伐利亚苏维埃共和国的军事行动，当然那时候他还只是个大男孩，把这当成一件好玩的事情而已。对他来说，更严肃的是在大学里选择一条怎样的道路。当他进入慕尼黑大学后，这种选择便很现实地摆在他面前：是跟着林德曼（Ferdinand von Lindemann），一位著名的数学家学习数论呢，还是跟着索末非学习物理？海森堡终于选择了后者，从而迈出了一个科学巨人的第一步。 1922年，玻尔应邀到哥廷根进行学术访问，引起轰动，甚至后来被称为哥廷根的“玻尔节”。海森堡也赶到哥廷根去听玻尔的演讲，才三年级的他竟然向玻尔提出一些学术观点上的异议，使得玻尔对他刮目相看。事实上，玻尔此行最大的收获可能就是遇到了海森堡和泡利，两个天才无限的年轻人。而这两人之后都会远赴哥本哈根，在玻尔的研究室和他一起工作一段日子。 到了1925年，海森堡——他现在是博士了——已经充分成长为一个既朝气蓬勃又不乏成熟的物理学家。他在慕尼黑、哥廷根和哥本哈根的经历使得他得以师从当时最好的几位物理大师。而按他自己的说法，他从索末非那里学到了乐观态度，在哥廷根从波恩，弗兰克还有希尔伯特那里学到了数学，而从玻尔那里，他学到了物理（索末非似乎很没有面子，呵呵）。 现在，该轮到海森堡自己上场了。物理学的天空终将云开雾散，露出璀璨的星光让我们目眩神迷。在那其中有几颗特别明亮的星星，它们的光辉照亮了整个夜空，组成了最华丽的星座。不用费力分辩，你应该能认出其中的一颗，它就叫维尔纳?海森堡。作为量子力学的奠基人之一，这个名字将永远镌刻在时空和历史中。 *********** 饭后闲话：被误解的名言 这个闲话和今天的正文无关，不过既然这几日讨论牛顿，不妨多披露一些关于牛顿的历史事实。 牛顿最为人熟知的一句名言是这样说的：“如果我看得更远的话，那是因为我站在巨人的肩膀上”（If I have seen further it is by standing on ye shoulders of Giants）。这句话通常被用来赞叹牛顿的谦逊，但是从历史上来看，这句话本身似乎没有任何可以理解为谦逊的理由。 首先这句话不是原创。早在12世纪，伯纳德（Bernard of Chartres，他是中世纪的哲学家，著名的法国沙特尔学校的校长）就说过：“Nos esse quasi nanos gigantium humeris insidientes”。这句拉丁文的意思就是说，我们都像坐在巨人肩膀上的矮子。这句话，如今还能在沙特尔市那著名的哥特式大教堂的窗户上找到。从伯纳德以来，至少有二三十个人在牛顿之前说过类似的话。 牛顿说这话是在1676年给胡克的一封信中。当时他已经和胡克在光的问题上吵得昏天黑地，争论已经持续多年（可以参见我们的史话）。在这封信里，牛顿认为胡克把他（牛顿自己）的能力看得太高了，然后就是这句著名的话：“如果我看得更远的话，那是因为我站在巨人的肩膀上”。 这里面的意思无非两种：牛顿说的巨人如果指胡克的话，那是一次很明显的妥协：我没有抄袭你的观念，我只不过在你工作的基础上继续发展——这才比你看得高那么一点点。牛顿想通过这种方式委婉地平息胡克的怒火，大家就此罢手。但如果要说大度或者谦逊，似乎很难谈得上。牛顿为此一生记恨胡克，哪怕几十年后，胡克早就墓木已拱，他还是不能平心静气地提到这个名字，这句话最多是试图息事宁人的外交词令而已。另一种可能，巨人不指胡克，那就更明显了：我的工作就算不完全是自己的，也是站在前辈巨人们的肩上——没你胡克的事。 更多的历史学家认为，这句话是一次恶意的挪揄和讽刺——胡克身材矮小，用“巨人”似乎暗含不怀好意。持这种观点的甚至还包括著名的史蒂芬?霍金，正是他如今坐在当年牛顿卢卡萨教授的位子上。 牛顿还有一句有名的话，大意说他是海边的一个小孩子，捡起贝壳玩玩，但还没有发现真理的大海。这句话也不是他的原创，最早可以追溯到Joseph Spence。但牛顿最可能是从约翰?米尔顿的《复乐园》中引用（牛顿有一本米尔顿的作品集）。这显然也是精心准备的说辞，牛顿本人从未见过大海，更别提在海滩行走了。他一生中见过的最大的河也就是泰晤士河，很难想象大海的意象如何能自然地从他的头脑中跳出来。 我谈这些，完全没有诋毁谁的意思。我只想说，历史有时候被赋予了太多的光圈和晕轮，但还历史的真相，是每一个人的责任，不论那真相究竟是什么。同时，这也丝毫不影响牛顿科学上的成就——他是有史以来最伟大的科学家。