Chapter 5 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 can only be explained by quantum mechanics, then I prefer not to explain it.Others claim they will quit physics if the quantum model turns out to be true.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 the formula W2-W1=hν, we can calculate the expression of ν in reverse, so that it is consistent with Balmer's original formula ν=R(1 /2^2-1/n^2) to calculate the theoretical value of the Rydberg constant R.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 debate over the so-called Pickering line series, Bohr 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.And Henry.The work of Mosley (the young genius we mentioned earlier, who unfortunately died on the battlefield) on X-rays further confirmed the correctness of the atomic nuclei 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 weird and obvious with the participation of electromagnetic fields (about these phenomena, people use the so-called Stark effect and Zeeman 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 assumed that electrons could only be in 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 the number of different states that one orbital can accommodate is limited, that is to say , a track has 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 eight 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 does help people better understand some basic behavioral principles of chemical society.For example, gregarious Cyborgs always try to fill every room on a floor with tenants.We imagine a sodium mansion with only one lone tenant living in room 3001 on the third floor.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 led 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 die-hard Planck, who refuses to admit that quantum is practical, began to re-examine his original great discovery.

The achievements of Bohr's theory are huge and deeply rooted in the hearts of the people, for which he himself won the Nobel Prize in 1922.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, and 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 does not 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 the 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, which 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 made up of thousands of small universes, which in turn form a larger universe with thousands of other universes?This reminds me of William.That 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 *Knowing Tianchen from a flower Hold infinity in the palm of your hand *Grasp infinity with one 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 about the entire universe, and it is a holographic embryo of the universe.So-called fractals, an intriguing subject of study in chaotic dynamics, show us how complex structures repeat themselves over and over at different levels.Whether the evolution of the universe also obeys some chaotic dynamics principle is still unknown, and the so-called fractal universe is just a family 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, projecting the 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 best to derive 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 semi-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, known as 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 anomalous Zeeman effect!This problem was not finally resolved until Pauli proposed his exclusion principle. 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 poorly managed Bohr theory was barely able to solve the problem and gained general acceptance, it was already like a patched robe that needed a radical overhaul. up.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, this theory has flourished for about thirteen 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 postwar 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 Niels.Mr. 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, Lev D. Landau, George Gamov people here 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.Louis.Victor.Pires.Raymond.De.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.Roughly speaking, its status is slightly lower than Viscount (Viscount) and slightly higher than Baron (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. Sixteen's subordinates served.They participated in the War of Polish Succession (1733︱1735), the War of Austrian Succession (1740︱1748), the Seven Years War (1756︱173), American War of Independence (1775︱1782), French Revolution (1789), February Revolution (1848), accepted Francis II (Holy Roman Emperor) , later abdicated to become Emperor Francis I of Austria) and Louis.The canonization of Philip (Louis Philippe, King of France, known as the Duke of Orleans in history), the family inherits the title of the highest hereditary status: Duke (French Duc, equivalent to English Duke).Louis.De Broglie's brother, Maurice.Maurice de Broglie is the sixth Duke of De Broglie.In 1960, when Maurice passed away, Louis finally inherited the honorary title from his brother, becoming the seventh duc de Broglie. Of course, before that, Louis still bore 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 served as Prime Minister of France from 1873 to 1874. An excellent historian, especially of late Roman history, who wrote the Histoire de l'e'glise et de l'empire romain (History of the Holy See).Under the influence of his grandfather, little Louis decided to enter the University of Paris to study history.At the age of eighteen (1910), he graduated from university, but did not pursue further studies in the field of history, because his interest had turned strongly to physics.His brother, Morris.De Broglie (the sixth Duke of De Broglie) is a famous ray physicist. Louis followed his brother to attend the Brussels Physics Conference in 1911, and his enthusiasm for science was fully stimulated , 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 is better than poor Henry.Mosley was much more fortunate to be able to survive the war unscathed and continue to study physics at university.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 seem 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 narrative, 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 us recall again the very useful fundamental quantum equation I said, E = hν, that is to say, corresponding to this energy, electrons must have an intrinsic frequency.The calculation of this frequency is very simple, because mc^2=E=hν, so ν=mc^2/h. 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?De Broglie started his calculation with the help of the theory of relativity, 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 and information, and therefore do not violate the theory of 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 a phase wave, and later generations also called it a de Broglie wave in memory of him.Calculating the wavelength of this wave is easy, simply divide the speed obtained above by its frequency, then we get: λ=(c^2/v)/(mc^2/h)=h/mv .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 his phase wave, it happened that Compton explained the Compton effect with the photon theory, and it was not long after he led the particle counterattack.The unlucky particles had no choice but 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.德布羅意的導師朗之萬對自己弟子的大膽見解無可奈何，出於挽救失足青年的良好願望，他把論文交給愛因斯坦點評。誰料愛因斯坦馬上予以了高度評價，稱德布羅意揭開了大幕的一角。整個物理學界在聽到愛因斯坦的評論後大吃一驚，這才開始全面關注德布羅意的工作。 證據，我們需要證據。所有的人都在異口同聲地說。如果電子是一個波，那麼就讓我們看到它是一個波的樣子。把它的衍射實驗做出來給我們看，把干涉圖紋放在我們的眼前。德布羅意有禮貌地回敬道：是的，先生們，我會給你們看到證據的。我預言，電子在通過一個小孔的時候，會像光波那樣，產生一個可觀測的衍射現象。 一九二五年四月，在美國紐約的貝爾電話實驗室，大衛遜（CJ Davisson）和革末（LH Germer）在做一個有關電子的實驗。這個實驗的目的是什麼我們不得而知，但它牽涉到用一束電子流轟擊一塊金屬鎳（nickel）。實驗要求金屬的表面絕對純淨，所以大衛遜和革末把金屬放在一個真空的容器中，以確保沒有雜質混入其中。 不幸的是，發生了一件意外。這個真空容器因為某種原因發生了爆炸，空氣一擁而入，迅速地氧化了鎳的表面。大衛遜和革末非常懊喪，不過他們並不因此放棄實驗，他們決定，重新淨化金屬表面，把實驗從頭來過。當時，去除氧化層的好辦法就是對金屬進行高熱加溫，這正是大衛遜所做的。 兩人並不知道，正如雅典娜暗中助推著阿爾戈英雄們的船隻，幸運女神正在這個時候站在他倆的身後。容器裡的金屬，在高溫下發生了不知不覺的變化：原本它是由許許多多塊小晶體組成的，而在加熱之後，整塊鎳融合成了一塊大晶體。雖然在表面看來，兩者並沒有太大的不同，但是內部的劇變已經足夠改變物理學的歷史。 當電子通過鎳塊後，大衛遜和革末瞠目結舌，久久說不出話來。他們看到了再熟悉不過的景象：X射線衍射圖案！可是並沒有X射線，只有電子，人們終於發現，在某種情況下，電子表現出如X射線般的純粹波動性質來。電子，無疑地是一種波。 更多的證據接踵而來。一九二七年，GP湯姆遜，著名的JJ湯姆遜的兒子，在劍橋通過實驗進一步證明了電子的波動性。他利用實驗資料算出的電子行為，和德布羅意所預言的吻合得天衣無縫。 命中註定，大衛遜和湯姆遜將分享一九三七年的諾貝爾獎金，而德布羅意將先於他們八年獲得這一榮譽。有意思的是，GP湯姆遜的父親，JJ湯姆遜因為發現了電子這一粒子而獲得諾貝爾獎，他卻因為證明電子是波而獲得同樣的榮譽。歷史有時候，實在富有太多的趣味性。 飯後閒話：父子諾貝爾 俗話說，將門無犬子，大科學家的後代往往也會取得不亞於前輩的驕人成績。JJ湯姆遜的兒子GP湯姆遜推翻了老爸電子是粒子的觀點，證明電子的波動性，同樣獲得諾貝爾獎。這樣的世襲科學豪門，似乎還不是絕無僅有。 居里夫人和她的丈夫皮埃爾．居里於一九○三年分享諾貝爾獎（居里夫人在一九一一年又得了一個化學獎）。他們的女兒約里奧．居里（Irene Joliot-Curie）也在一九三五年和她丈夫一起分享了諾貝爾化學獎。居里夫人的另一個女婿，美國外交家Henry R.Labouisse，在一九六五年代表聯合國兒童基金會（UNICEF）獲得了諾貝爾和平獎。 一九一五年，William Henry Bragg和William Lawrence Bragg父子因為利用X射線對晶體結構做出了突出貢獻，分享了諾貝爾物理獎金。 我們大名鼎鼎的尼爾斯．玻爾獲得了一九二二年的諾貝爾物理獎。他的小兒子，埃格．玻爾（Aage Bohr）於一九七五年在同樣的領域獲獎。 Carl.塞班（Karl Siegbahn）和凱伊．塞班（Kai Siegbahn）父子分別於一九二四和一九八一年獲得諾貝爾物理獎。 假如俺的老爸是大科學家，俺又會怎樣呢？不過恐怕還是如現在這般浪蕩江湖，尋求無拘無束的生活吧，呵呵。 Four 電子居然是個波！這個爆炸性新聞很快就傳遍了波動和微粒雙方各自的陣營。剛剛還在康普頓戰役中焦頭爛額的波動一方這下揚眉吐氣，終於可以狠狠地嘲笑一下死對頭微粒。《波動日報》發表社論，宣稱自己取得了決定性的勝利。微粒的反叛勢力終將遭遇到他們應有的可恥結局電子的下場就是明證。光子的反擊，在波動的眼中突然變得不值一提了，連電子這個老大哥都搞定了，還怕小小的光子？ 不過這次，波動的樂觀態度未免太一廂情願，它高興得過早了。微粒方面的宣傳輿論工具也沒閒著，《微粒新聞》的記者採訪了德布羅意，結果德布羅意說，當今的輻射物理被分成粒子和波兩種觀點，這兩種觀點應當以某種方式統一，而不是始終地尖銳對立這不利於理論的發展前景。對於微粒來說，講和的提議自然是無法接受的，但至少讓它高興的是，德布羅意沒有明確地偏向波動一方。微粒的技術人員也隨即展開反擊，光究竟是粒子還是波都還沒說清，誰敢那樣大膽地斷言電子是個波？讓我們看看電子在威爾遜雲室裡的表現吧。 威爾遜雲室是英國科學家威爾遜（CTR Wilson）在一九一一年發明的一種儀器。水蒸氣在塵埃或者離子通過的時候，會以它們為中心凝結成一串水珠，從而在粒子通過之處形成一條清晰可辨的軌跡，就像天空中噴氣式飛機身後留下的白霧。利用威爾遜雲室，我們可以研究電子和其他粒子碰撞的情況，結果它們的表現完全符合經典粒子的規律。在過去，這或許是理所當然的事情，但現在對於粒子軍來說，這個證據是寶貴的。威爾遜因為發明雲室在一九二七年和康普頓分享了諾貝爾獎金。如果說一九三七年大衛遜和湯姆遜的獲獎標誌著波動的狂歡，那十年的這次諾貝爾頒獎禮無疑是微粒方面的一次盛典。不過那個時候，戰局已經出乎人們的意料，有了微妙的變化。當然這都是後話了。 捕捉電子位置的儀器也早就有了，電子在感應屏上，總是激發出一個小亮點。Hey，微粒的將軍們說，波動怎麼解釋這個呢？哪怕是電子組成衍射圖案，它還是一個一個亮點這樣堆積起來的。如果電子是波的話，那麼理論上單個電子就能構成整個圖案，只不過非常黯淡而已。可是情況顯然不是這樣，單個電子只能構成單個亮點，只有大量電子的出現，才逐漸顯示出衍射圖案來。 微粒的還擊且不去說他，更糟糕的是，無論微粒還是波動，都沒能在德布羅意事變中撈到實質性的好處。波動的嘲笑再尖刻，它還是對光電效應、康普頓效應等等現象束手無策，而微粒也還是無法解釋雙縫干涉。雙方很快就發現，戰線還是那條戰線，誰都沒能前進一步，只不過戰場被擴大了而已。電子現在也被拉進有關光本性的這場戰爭，這使得戰爭全面地被升級。現在的問題，已經不再僅僅是光到底是粒子還是波，現在的問題，是電子到底是粒子還是波，你和我到底是粒子還是波，這整個物質世界到底是粒子還是波。 事實上，波動這次對電子的攻擊只有更加激發了粒子們的同仇敵愾之心。現在，光子、電子、α粒子、還有更多的基本粒子，他們都決定聯合起來，為了大粒子王國的神聖保衛戰而並肩奮鬥。這場波粒戰爭，已經遠遠超出了光的範圍，整個物理體系如今都陷於這個爭論中，從而形成了一次名副其實的世界大戰。玻爾在一九二四年曾試圖給這兩支軍隊調停，他和克萊默（Kramers）還有斯雷特（Slater）發表了一個理論（稱作BSK理論），嘗試同時從波和粒子的角度去解釋能量轉換，但雙方正打得眼紅，這次調停成了外交上的徹底失敗，不久就被實驗所否決。戰火熊熊，燃遍物理學的每一寸土地，同時也把它的未來炙烤得焦糊不清。 物理學已經走到了一個十字路口。它迷茫而又困惑，不知道前途何去何從。昔日的經典輝煌已經變成斷瓦殘垣，一切回頭路都被斷絕。如今的天空濃雲密佈，不見陽光，在大地上投下一片陰影。人們在量子這個精靈的帶領下一路走來，沿途如行山陰道上，精采目不暇接，但現在卻突然發現自己已經身在白雲深處，彷徨而不知歸路。放眼望去，到處是霧茫茫一片，不辨東南西北，叫人心中沒底。玻爾建立的大廈雖然看起來還是頂天立地，但稍微瞭解一點內情的工程師們都知道它已經幾經裱糊，傷筋動骨，搖搖欲墜，只是仍然在苦苦支撐而已。更何況，這個大廈還憑藉著對應原理的天橋，依附在麥克斯韋的舊樓上，這就教人更不敢對它的前途抱有任何希望。在另一邊，微粒和波動打得烽火連天，誰也奈何不了誰，長期的戰爭已經使物理學的基礎處在崩潰邊緣，它甚至不知道自己是建立在什麼東西之上。 不過，我們也不必過多地為一種悲觀情緒所困擾。在大時代的黎明到來之前，總是要經歷這樣的深深的黑暗，那是一個偉大理論誕生前的陣痛。當大風揚起，吹散一切嵐霧的時候，人們會驚喜地發現，原來他們已經站在高高的山峰之上，極目望去，滿眼風光。 那個帶領我們穿越迷霧的人，後來回憶說：一九二四到一九二五年，我們在原子物理方面雖然進入了一個濃雲密佈的領域，但是已經可以從中看見微光，並展望出一個令人激動的遠景。 說這話的是一個來自德國的年輕人，他就是維爾納．海森堡（Werner Heisenberg）。 在本史話第二章的最後，我們已經知道，海森堡於一九○一年出生於維爾茲堡（Wrzburg），他的父親後來成為了一位有名的希臘文教授。小海森堡九歲那年，他們全家搬到了慕尼克，他的祖父在那裡的一間學校（叫做Maximilians Gymnasium的）當校長，而海森堡也自然進了這間學校學習。雖然屬於高幹子弟，但小海森堡顯然不用憑藉這種關係來取得成績，他的天才很快就開始讓人吃驚，特別是數學和物理方面的，但是他同時也對宗教、文學和哲學表現出強烈興趣。這樣的多才多藝預示著他以後不僅僅將成為一個劃時代的物理學家，同時也將成為一為重要的哲學家。 一九一九年，海森堡參與了鎮壓巴伐利亞蘇維埃共和國的軍事行動，當然那時候他還只是個大男孩，把這當成一件好玩的事情而已。對他來說，更嚴肅的是在大學裡選擇一條怎樣的道路。當他進入慕尼克大學後，這種選擇便很現實地擺在他面前：是跟著林德曼（Ferdinand von Lindemann），一位著名的數學家學習數論呢，還是跟著索末非學習物理？海森堡終於選擇了後者，從而邁出了一個科學巨人的第一步。 一九二二年，玻爾應邀到哥廷根進行學術訪問，引起轟動，甚至後來被稱為哥廷根的玻爾節。海森堡也趕到哥廷根去聽玻爾的演講，才三年級的他竟然向玻爾提出一些學術觀點上的異議，使得玻爾對他刮目相看。事實上，玻爾此行最大的收穫可能就是遇到了海森堡和泡利，兩個天才無限的年輕人。而這兩人之後都會遠赴哥本哈根，在玻爾的研究室和他一起工作一段日子。 到了一九二五年，海森堡他現在是博士了已經充分成長為一個既朝氣蓬勃又不乏成熟的物理學家。他在慕尼克、哥廷根和哥本哈根的經歷使得他得以師從當時最好的幾位物理大師。而按他自己的說法，他從索末非那裡學到了樂觀態度，在哥廷根從波恩，弗蘭克還有希爾伯特那裡學到了數學，而從玻爾那裡，他學到了物理（索末非似乎很沒有面子，呵呵）。 現在，該輪到海森堡自己上場了。物理學的天空終將雲開霧散，露出璀璨的星光讓我們目眩神迷。在那其中有幾顆特別明亮的星星，它們的光輝照亮了整個夜空，組成了最華麗的星座。不用費力分辨，你應該能認出其中的一顆，它就叫維爾納．海森堡。作為量子力學的奠基人之一，這個名字將永遠鐫刻在時空和歷史中。 飯後閒話：被誤解的名言 這個閒話和今天的正文無關，不過既然這幾日討論牛頓，不妨多披露一些關於牛頓的歷史事實。 牛頓最為人熟知的一句名言是這樣說的：如果我看得更遠的話，那是因為我站在巨人的肩膀上（If I have seen further it is by standing on the shoulders of Giants）。這句話通常被用來讚歎牛頓的謙遜，但是從歷史上來看，這句話本身似乎沒有任何可以理解為謙遜的理由。 首先這句話不是原創。早在十二世紀，伯納德（Bernard of Chartres，他是中世紀的哲學家，著名的法國沙特爾學校的校長）就說過：Nos esse quasi nanos gigantium humeris insidientes。這句拉丁文的意思就是說，我們都像坐在巨人肩膀上的矮子。這句話，如今還能在沙特爾市那著名的哥特式大教堂的窗戶上找到。從伯納德以來，至少有二三十個人在牛頓之前說過類似的話。 牛頓說這話是在一六七六年給胡克的一封信中。當時他已經和胡克在光的問題上吵得昏天黑地，爭論已經持續多年（可以參見我們的史話）。在這封信裡，牛頓認為胡克把他（牛頓自己）的能力看得太高了，然後就是這句著名的話：如果我看得更遠的話，那是因為我站在巨人的肩膀上。 這裡面的意思無非兩種：牛頓說的巨人如果指胡克的話，那是一次很明顯的妥協：我沒有抄襲你的觀念，我只不過在你工作的基礎上繼續發展這才比你看得高那麼一點點。牛頓想通過這種方式委婉地平息胡克的怒火，大家就此罷手。但如果要說大度或者謙遜，似乎很難談得上。牛頓為此一生記恨胡克，哪怕幾十年後，胡克早就墓木已拱，他還是不能平心靜氣地提到這個名字，這句話最多是試圖息事寧人的外交詞令而已。另一種可能，巨人不指胡克，那就更明顯了：我的工作就算不完全是自己的，也是站在前輩巨人們的肩上沒你胡克的事。 更多的歷史學家認為，這句話是一次惡意的揶揄和諷刺胡克身材矮小，用巨人似乎暗含不懷好意。持這種觀點的甚至還包括著名的史蒂芬．霍金，正是他如今坐在當年牛頓盧卡薩教授的位子上。 牛頓還有一句有名的話，大意說他是海邊的一個小孩子，撿起貝殼玩玩，但還沒有發現真理的大海。這句話也不是他的原創，最早可以追溯到Joseph Spence。但牛頓最可能是從約翰．密爾頓的《復樂園》中引用（牛頓有一本密爾頓的作品集）。這顯然也是精心準備的說辭，牛頓本人從未見過大海，更別提在海灘行走了。他一生中見過的最大的河也就是泰晤士河，很難想像大海的意象如何能自然地從他的頭腦中跳出來。 我談這些，完全沒有詆毀誰的意思。我只想說，歷史有時候被賦予了太多的光圈和暈輪，但還歷史的真相，是每一個人的責任，不論那真相究竟是什麼。同時，這也絲毫不影響牛頓科學上的成就他是有史以來最偉大的科學家。