Chapter 9 Chapter 7 Uncertainty

one Our history has come to this point, it is time to look back at the journey we have traveled.We have seen how the magnificent classical physics building suddenly collapsed, and we have seen how Planck's quantum hypothesis ignited the spark of a new revolution with the black body problem as the guide.After that, Einstein's light quantum theory endowed the newborn quantum with substantial power, allowing it to stand up for the first time to stand out from the crowd, and Bohr's atomic theory created a new world with the help of its infinite energy. Come. We have also talked about how the two theories of particles and waves have been in constant confrontation about the nature of light since 300 years ago.Starting from de Broglie, this essential contradiction has become the basic problem of physics, and Heisenberg created his matrix mechanics from discontinuity, and Schrödinger also discovered his wave along another continuous path equation.Although these two theories have been proved to be equivalent by mathematics, their physical meaning has aroused widespread debate. Bonn's probability explanation has pushed the determinism of hundreds of years onto the stage of doubt and has become the focus of the wave. .On the other hand, the war between fluctuations and particles has now reached the most critical time.

Next, some really weird things are going to happen in physics.It will transform people's philosophy into a specious madness, and turn physics itself into a maelstrom. The most famous debate of the 20th century was about to unfold, with repercussions that continue to this day.We've come a long way, we're all exhausted and weary, but we can't turn around.Looking back, the white clouds blocked the way home, and it was impossible to return to the warm comfort of the classical theory. Before our eyes, there was only a long and rugged road leading to a distant and unknown place.Now, let us muster up the greatest courage and follow the physicists to go on and see what kind of scene is hidden at the end of this road.

We are back to February 1927, that magical winter.The past few months have been a nightmare for Heisenberg, as more and more people turn to Schrödinger and his damned wave theory, forgetting about his matrix.Heisenberg's original excellent papers are now being rewritten into alternative forms of the wave equation, which makes him especially intolerable.He later wrote to Pauli: "For every paper on matrices, people rewrite it in 'conjugated' wave form, which annoys me. I think they'd better learn both ways. " But what saddened him the most was undoubtedly that Bohr also turned to his opposite.Bohr, the Bohr who he regarded as a strict teacher, loving father, and good friend, the Bohr whom they called "the Pope of Quantum Theory" behind his back, the commander-in-chief and spiritual leader of the Copenhagen Legion, actually opposed him now!This made Heisenberg feel extremely wronged and sad.Later, when Bohr criticized his theory again, Heisenberg actually cried tears.For Heisenberg, Bohr's position in his mind was unique. Without his support, Heisenberg felt like a child swimming in a river without an adult's arms, feeling isolated and helpless.

However, now that Bohr has gone to Norway for vacation, he is probably skiing?Heisenberg, remembering Bohr's poor skiing ability, couldn't help smiling.Bohr could no longer provide any help, and now he and Klein huddled together, concentrating on studying relativistic fluctuations.fluctuation!Heisenberg snorted, even if he killed him, he would not admit it. Electrons should be interpreted as fluctuations.But things weren't so bad, he still had at least a few comrades in arms: his old friend Pauli, Jordan of Göttingen, and Dirac, who was also visiting Copenhagen now. Not long ago, Dirac and Jordan developed a transformation theory respectively, which made it easy for Heisenberg to use matrices to deal with some probability problems that had been dealt with by Schrödinger's equation.To Heisenberg's delight, discontinuity was taken as a basis in Dirac's theory, which further convinced him that Schrödinger's explanation was dubious.However, if discontinuity is the premise, some variables in this system are difficult to explain. For example, the trajectory of an electron is always continuous, right?

Heisenberg tried his best to recall the history of the creation of matrix mechanics, trying to see where the problem was.We still remember that Heisenberg's assumption at that time was: the entire physical theory can only be premised on observable quantities, and only these variables are deterministic and can form the basis of any system.But Heisenberg also remembered that Einstein didn't quite agree with this. He was too heavily influenced by classical philosophy and was a hopelessly transcendentalist. "You don't really believe that only observable quantities qualify for physics?" Einstein once asked him.

"Why not?" Heisenberg said in surprise, "When you created the theory of relativity, didn't you just abandon it because 'absolute time' was unobservable?" Einstein laughed: "A good trick can't be played twice. You know that in principle it's wrong to try to build a theory based on observable quantities alone. It's just the opposite: it's the theory that determines what we can observe." .” Yeah?Theory determines what we observe?So how does theory explain the trajectory of an electron in a cloud chamber?In Schrödinger's view, this is a superposition of a series of eigenstates, but forget

him!Heisenberg said to himself, let's explain it in terms of our more orthodox matrix.However, the matrix is ​​discontinuous, but the trajectory is continuous, and the so-called "trajectory" has long been discarded as an unobservable quantity when the matrix was created... The night was quiet outside the window, and Heisenberg was thinking hard but couldn't figure it out.He was full of worries, tossing and turning, and decided to get up and go for a walk in Faelled Park, not far from the Bohr Institute.The park was empty in the middle of the night, and the evening wind was still bitter and cold on the face, but it made people sober.Heisenberg's mind was full of matrices, large and small, and he remembered the strange multiplication rules of matrices:

p×q ≠ q×p Theory determines what we observe?The theory says, p×q ≠ q×p, does it determine what we observe? What does I×II mean?Take Line I first and then transfer to Line II.So, what does p×q mean? p is momentum, q is position, it doesn't mean... It seemed that a flash of lightning flashed across the night sky, and Heisenberg's mind suddenly became clear and clear. p×q ≠ q×p, doesn’t this mean that observing the momentum p first, and then observing the position q, is the result different from observing q first and then p? Wait, what does this mean?Suppose we have a small ball moving forward, so at every moment, aren't its momentum and position two definite variables?Why are the results different just because of the difference in the order of observation?Heisenberg's palms were sweating, he knew that there was an extremely important secret hidden here.How is this possible?If we want to measure the length and width of a rectangle, isn't it the same thing to measure the length first or the width first?

unless…… Unless the action of measuring the momentum p itself affects the value of q.In turn, the act of measuring q also affects the value of p.But, kidding, what if I measure p and q at the same time? Heisenberg suddenly seemed to have seen a divine revelation, and he suddenly became enlightened. p×q ≠ q×p, does our equation tell us that it is impossible to observe p and q at the same time?Theory not only determines what we can observe, it also determines what we cannot observe! However, I'm confused, what does it mean that p and q cannot be observed at the same time?Observation p affects q?Observation q affects p?What the hell are we talking about?If I say that a small ball is at time t, its position coordinates are 10 meters, and its speed is 5 meters per second, is there any problem?

"There is a problem, there is a big problem." Heisenberg clapped his hands and said. "How can you know that at time t, the position of a certain ball is 10 meters, and the speed is 5 meters per second? How do you know?" "What? Needless to say? Observe, measure." "Here is the key! Measurement!" Heisenberg said, beating his head, "I understand now that the problem lies in the behavior of measurement. The length and width of a rectangle are fixed, and you measure it At the same time, its width will never change because of it, and vice versa. How do you measure its position for the classic small ball? You have to see it, or use some kind of instrument to detect it, anyway , you have to touch it in some way, otherwise how do you know its position? Take 'seeing' for example, how can you 'see' the position of a small ball? There must be some photon from The light source goes off, hits this ball, and bounces into your eye, right? The point is, a classical small ball is a giant, and a photon hitting it is like an ant hitting an elephant, and the impact on it is negligible, It will never affect its speed. Because of this, after measuring its position, we can measure its speed calmly with negligible error.

"But we're talking about electrons now! It's so small and light that the impact of a photon on it must be negligible. Measuring the position of an electron? Well, we send a photon on a mission, how does it come back?" What about the report? Yes, I touched the electron, but it gave me a hard bump and went off somewhere, and I can't say anything about its current speed. See, to measure its position, We drastically change its velocity, which is its momentum. We can't know exactly where an electron is and exactly what its momentum is at the same time." Heisenberg hurried back to the research institute, immersed himself in calculations, and finally came up with a formula: △p×△q > h/2π Δp and Δq are the errors of measuring p and measuring q respectively, and h is Planck's constant.Heisenberg found that the product of the error in measuring p and measuring q must be greater than a certain constant.If we measure p very precisely, that is to say, △p is very small, then correspondingly, △q must become very large, that is to say, our knowledge about q will become very vague and uncertain.Conversely, if we measure the position q very accurately, p will become wobbly, and the error will increase sharply. If we measure p with 100% accuracy, that is, △p=0, then △q will become infinite.That is to say, if we know all the information about the momentum p of an electron, then we lose all the information about its position q at the same time, we don’t know where it is at all, no matter how we arrange the experiment, we can’t do it better.You can't have both, either we know p precisely and let go of q, or we know q precisely and give up all knowledge of p, or we compromise and obtain a relatively vague p and a relatively vague q at the same time . p and q are like a pair of enemies in the previous life, they don't meet each other in life, they move like participating in a business, and they are in a state of having you but not me.Whenever we draw close to one, we simultaneously and dramatically alienate the other.This kind of strange quantity is called "conjugate quantity", and we will see later that there are many such quantities. This principle of Heisenberg was published in the "Journal of Physics" on March 23, 1927, and it is called the Uncertainty Principle.When it was first translated into Chinese, it was adorably translated as "uncertainty principle", but most of it is now changed to the more general "uncertainty principle". *********** Quantum character sketch Schrödinger: Heisenberg: Bohr: two The Uncertainty Principle... Not sure?Once again we have come across this nasty word.Again, this term is frowned upon in physics.If physics can't determine anything, what do we need it for?Born's probabilistic explanation was annoying enough—even given all the conditions, it was impossible to predict the outcome.Now Heisenberg is doing even better, given all the conditions?This premise itself is impossible. Given some of the conditions, the other part of the conditions will become vague and undetermined.Given p, then we say goodbye to q. This is not pretty, there must be something wrong.We can't measure q if we measure p?I don't give up, I have to come and try to see if it works.Well, Heisenberg takes over, remember the Wilson cloud chamber?Didn't you worry about this problem in the first place?Through the cloud chamber we can see the trajectory of the electron movement, so of course we can calculate its instantaneous velocity by continuously measuring its position, so can we know its momentum at the same time? "This problem," Heisenberg said with a smile, "I finally figured it out. What the electrons leave in the cloud chamber is not a fine 'track' as we understand it, in fact it is just a series of condensed water droplets. You put When it is zoomed in, it is discontinuous, a bunch of 'dotted lines', it is impossible to accurately obtain the concept of position, let alone violate the uncertainty principle." "Oh? That's right. Then let's be more careful and find out the fine trajectories of the electrons? We can use a larger microscope to do this job, isn't it theoretically impossible?" "By the way, the microscope!" Heisenberg said enthusiastically, "I was just about to talk about the microscope. Let's do a thought experiment (Gedanken-experiment), imagine that we have an extremely powerful microscope. But No matter how powerful the microscope is, it also has its basic principles. You must know, no matter what, if we use a wave to observe things smaller than its wavelength, it will not be accurate at all, just like using a coarse It’s like a pen can’t draw a thin line. If we want to observe something as small as an electron, we must use light with a very short wavelength. Ordinary light can’t do it, we need ultraviolet rays, X-rays, or even gamma rays.” "Well, since thought experiments don't cost money anyway, let's just assume that the higher-ups allocated huge sums of money for the first time and built us a state-of-the-art gamma-ray microscope. Then, now we can see electrons accurately. location?" "But," Heisenberg pointed out, "have you forgotten? Any wave that detects an electron necessarily disturbs the electron itself. The shorter the wave, the higher the frequency, right? Everyone remembers that Planck's formula E = hν, the higher the frequency, the higher the energy will be correspondingly, so the disturbance to the electron will be stronger, and at the same time we will be unable to understand its momentum even more.You see, this satisfies the uncertainty principle perfectly. " "You are sophistry. Well, let's accept the fact that every time we use a photon to detect the position of an electron, it will cause a strong disturbance to it, causing it to change direction and speed, and fly in another direction. However, we still We can use some clever, roundabout methods to achieve our goal. For example, we can measure the direction velocity of the bounced photon, so as to deduce how it affects the electron, and then derive the direction velocity of the electron itself. How , doesn't this break your trick?" "Still not possible." Heisenberg shook his head and said, "In order to achieve such a high sensitivity, our microscope must have a lens with a large diameter. You know, the lens gathers the light from all directions to a focal point, Then we can't tell where the bounced photons came from. If we reduce the diameter of the lens to ensure that the photons are not focused, then the sensitivity of the microscope will be too poor to do the job. So your cleverness still doesn't work .” "That's a hell of a thing. So how about looking at the bounce of the microscope itself?" "In the same way, to observe such a subtle effect, you need to use light with a short wavelength, so its energy is large, and it causes disturbance to the microscope itself that erases everything..." Wait, we don't give up.Well, we admit that our observation equipment is very rough, our fingers are clumsy, our civilization is only a few thousand years old, and modern science has only been established for less than 300 years.We admit that with our current state of technology, we cannot simultaneously observe the position and momentum of a tiny electron, because our instruments are stupid and clumsy.However, this does not mean that electrons do not have position and momentum at the same time. Maybe in the future, even in the distant future, we will develop a cutting-edge technology, and we will invent extremely sophisticated instruments to accurately measure the position of electrons. And what about momentum?You can't deny the possibility. "That's not what you say." Heisenberg said thoughtfully. "The problem here is that the theory limits what we can observe, not the error caused by the experiment. Measuring the exact momentum and position at the same time is in principle It is impossible in the world, no matter how advanced the technology is. Just like you can never build a perpetual motion machine, you can never build a microscope that can detect p and q at the same time. No matter what theories we create in the future, they All must obey the uncertainty principle, which is a basic principle, and all subsequent theories must be under its supervision to gain legitimacy." Isn't Heisenberg's conclusion too overbearing?Moreover, wouldn't physicists lose all face in this way?Imagine the public: what, you're a physicist?Oh, I'm so sorry for you, you don't even know the momentum and position of an electron!At least our Tommy knows how to handle his ball. However, we still have to present the facts, reason, and convince others with virtue.One thought experiment after another has been proposed, but we just can't precisely measure the electron's momentum and at the same time get its position precisely.The product of the errors of the two must be greater than that constant, that is, h divided by 2π.Fortunately, we all remember that h is very small, only 6.626×10^-34 joule seconds, so if △p and △q are of similar magnitude, they are both on the order of 10^-17.We can now reassure the uninformed masses that things are not so bad, and the effect only becomes apparent at the scale of electrons and photons.For Tommy's ball, 10^-17 is so insignificant that it can't be felt at all.Tommy could shoot his ball without worrying about losing it because he couldn't figure out where it was. But in the electronic-scale world, that's very different.At the end of the last chapter, we imagined that we were reduced to the size of electrons to explore the mysteries of atoms. At that time, our height was only 10^-23 meters.Now, Mom, worried about our naughty behavior, wants to measure where we are, but they are doomed to be disappointed: the measurement is off by 10^-17 meters, which is 1 million times our own height! What does the error of 1 million times mean? If we are usually 1.75 meters tall, the error will reach 1.75 million meters, which is 1750 kilometers. Mothers have to look for us everywhere along the entire Beijing-Shanghai Railway. "Uncertainty" has become worthy of the name. At all times, nature stubbornly sticks to this bottom line, never giving us any chance to get accurate values ​​​​of position and momentum at the same time.No matter how many tricks we can do, it will always be better than us, and it will beat our cleverness every time.Can't measure the electron's position and momentum?Let's design a very small and very small container, which can only accommodate one electron without leaving any extra space. How about this?Electronics can't move around, right?However, first of all, this kind of container cannot be manufactured, because it must also be composed of electrons, so it must have a position that fluctuates, causing the internal space to fluctuate.Taking a step back, even if it is possible, in this case, the electrons will mysteriously permeate through the container wall and appear outside the container, like the legendary Laoshan Taoist who passed through the wall.The uncertainty principle endows it with this magical ability to break through all constraints.Another way is to cool down.We all know that atoms are constantly vibrating, and temperature is the macroscopic manifestation of this vibration. When the temperature drops to absolute zero, the atoms are theoretically completely still.At that time, the momentum is determined to be zero, so we only need to measure the position, right?Unfortunately, absolute zero cannot be reached. No matter how hard we try, the atom still desperately retains the last bit of internal energy to prevent us from measuring its momentum.No matter who it is, it is impossible to make atoms completely still, and neither can the legendary saints—they cannot overcome the uncertainty principle. Momentum p and position q, they are really "incompatible".Whenever one quantity appears in the universe, the other mysteriously disappears.Or, both appear in an indistinct guise.Heisenberg soon discovered another pair of similar enemies, energy E and time t.As long as the energy E is measured more accurately, the time t becomes more blurred; conversely, the more accurately the time t is measured, the energy E begins to fluctuate on a large scale.Moreover, their relationship obeys the same uncertainty rules: △E×△t > h/2π Ladies and gentlemen, our universe has become very strange.All kinds of physical quantities follow Heisenberg's uncertainty principle, one after another, like bubbles rising and bursting in the mysterious sea.In the eyes of the ancients, "emptiness" means nothingness.But later people learned that there are countless molecules in the invisible air, and "empty" should refer to the vacuum that evacuates the air.Later, people felt that all kinds of fields, from gravitational field to electromagnetic field, should also be excluded from the concept of "empty", which should only refer to space itself. But now, the concept is getting muddled again.First of all, Einstein's theory of relativity tells us that space itself can also be warped and deformed. In fact, gravity is just its curvature.And Heisenberg's uncertainty principle presents a more exotic scenario: we know that the more accurately t is measured, the more uncertain E becomes.So for a very, very short instant, a very definite instant, there can be huge fluctuations in energy even in a vacuum.This kind of energy appears out of nowhere completely relying on uncertainty, and it really violates the law of energy conservation!But this moment is very short, before people have time to discover it, it disappears mysteriously, making the law of energy conservation as a whole maintained.The shorter the interval, the more certain t is, the more uncertain E is, and the greater the energy that can appear out of thin air. Therefore, our vacuum is actually boiling all the time, and mysterious energies are produced and disappeared everywhere.Einstein told us that energy and matter can be converted into each other, so in the vacuum, there are actually some "ghost" matter constantly appearing, but they disappeared in another world before we caught them .Vacuum itself is the best medium to provide this fluctuation. Now if we talk about "emptiness", we should say it clearly: there is no matter, no energy, no time, and no space.This is nothing, it is not imaginable at all (can you imagine what it would be like to have no space?).But many people say that this is not "empty", because space and time themselves seem to be created from nothing through some mechanism. I am really going crazy, so what exactly is "empty"? *********** Gossip after dinner: out of thin air Once upon a time, all scientists believed that it was absolutely impossible to create something out of nothing.Matter cannot be created out of thin air, nor can energy be created out of thin air, let alone space-time itself.But the emergence of the uncertainty principle shattered all these old concepts. Heisenberg told us that in a very small space and a very short time, anything is possible, because we are very certain about time, so in turn, we are very uncertain about energy.Energetic matter can escape the shackles of the laws of physics, appearing and disappearing freely.However, the price of this kind of freedom is that it can only be limited to a very short period of time. When the time comes, Cinderella will show her original shape, and these mysterious material energies will disappear, in order to maintain the law of conservation of mass and energy. Not destroyed on a large scale. However, at the end of the 1960s, someone thought of a possibility: the energy of gravity is a negative number (because gravity is suction, assuming that the potential energy at infinity is 0, then when the object approaches, the gravitational work makes its potential energy negative), Therefore, the material energy generated out of thin air in a short period of time can form a gravitational field between them, and the negative energy produced by it just offsets itself, so that the total energy remains 0, and the law of conservation is not violated.In this way matter is literally created from nothing. Many people believe that our universe itself arose through this mechanism.Quantum effects make a small piece of space-time suddenly arise from no space-time at all, and then due to the action of various forces, it suddenly expands exponentially, expanding to the scale of the entire universe in an instant. MIT scientist Alan Guth (Alan Guth, based on this idea, created the "inflation theory" of the universe (Inflation).In the very early days of the creation of the universe, each piece of space exploded at an unimaginably astonishing speed, which caused the total volume of the universe to increase many, many times.This can explain why its structure looks uniform in all directions today. There have been many versions of the theory of inflation since its inception, but it is difficult to confirm whether this theory is correct, because the universe is not like our laboratory, which can be observed and studied at will.But most physicists still prefer it as a promising theory. In 1998, Gus also published a popular book on inflation. His favorite sentence is: "The universe itself is a free lunch." It means that the universe came from nothing. However, if it is harsher, this cannot be regarded as a strict "creation out of nothing".Because even if there is no matter, no time and space, we still have a premise: the existence of physical laws!How did the various rules of relativity and quantum theory, such as the uncertainty principle itself, emerge from nothing?Or are they self-evident?We're getting more and more mysterious, so let's stop here. three When Heisenberg completed his uncertainty principle, he immediately wrote to Pauli and Bohr in Norway to tell them his thoughts.After receiving Heisenberg's letter, Bohr immediately set off from Norway and returned to Copenhagen, ready to have an in-depth discussion with Heisenberg on this issue.Heisenberg probably thought that such a great discovery would surely move Bohr's heart and make him agree with his consistent ideas on quantum mechanics.However, he was very wrong. In Norway, Bohr thought about the wave-particle problem while skiing, and the new idea gradually took shape in his mind.When he saw Heisenberg's paper, he naturally used this idea to confirm the whole conclusion.He asked Heisenberg whether this uncertainty comes from the nature of particles or from the nature of waves?Heisenberg was taken aback for a moment, he didn't think about any waves at all.Of course it is a particle, since the photon hits the electron, the uncertainty of position and momentum is caused, isn't it obvious? Bohr shook his head seriously. He used the giant microscope imagined by Heisenberg to prove that the uncertainty to a large extent is not only caused by the discontinuous particle nature, but also by the wave nature.We discussed earlier the de Broglie wavelength formula λ= h/mv, mv is the momentum p, so p= h/λ, for every momentum p, there is always a concept of wavelength accompanying it.For the Et relation, E= hν, there is still the fluctuation concept of frequency ν in it.Heisenberg refused this outright, and it was not easy for him to accept volatility. Bohr was obviously impatient with Heisenberg's stubbornness, and he clearly said to Heisenberg: "Your microscope experiment It's not right," Heisenberg cried out in anger.The two had a big quarrel, and of course Klein helped Bohr, which made the atmosphere in Copenhagen very sharp.What started out as a matter of physics turned into an almost personal misunderstanding, to the point that Heisenberg had to send Pauli's letter back for clarification.In the end, Pauli himself went to Denmark, which finally calmed down the aftermath of the incident. Unfortunately for Heisenberg, he was wrong about the microscope.Heisenberg probably suffered from some kind of "microscopic phobia" from birth, and he became dizzy when he touched a microscope.Back then, he couldn't figure out the most basic microscope resolution problem during his doctoral dissertation defense, and almost didn't get his degree.This time Bohr finally made him realize that uncertainty is based on the double basis of waves and particles, which is actually a kind of swing between waves and particles: the more you know about the properties of waves, the more The properties of the particles are less known.Heisenberg finally accepted Bohr's criticism and added a footnote to his paper stating that uncertainty is actually built on both continuity and discontinuity at the same time, and thanked Bohr for pointing this out. Bohr also gained something from this debate. He found that the general significance of the uncertainty principle was greater than he imagined.He thought that this was just a partial principle, but now he realizes that this principle is one of the core cornerstones of quantum theory.In a letter to Einstein, Bohr praised Heisenberg's theory, saying that he had shown "in a very beautiful way" how uncertainty could be applied to quantum theory.After the long Easter holiday, both parties took a step back, and the situation finally brightened.In his letter to Pauli, Heisenberg regained his good mood, saying that "again we can simply discuss physics problems and forget everything else".Indeed, brothers are fighting against the wall, and they must also defend themselves. The Copenhagen faction is now united like a solid rock. They will soon face greater challenges together and engrave the name of Copenhagen in the history of physics. glorious history. But then again.Volatility, granularity, these two words have haunted us from the very beginning of our history until now.Well, uncertainty is built on volatility and granularity at the same time...but isn't that just nonsense?Our patience is limited, why don't we open the skylight and tell the truth, is this damn electron a particle or a wave? Particles or waves, it is really a topic with a lot of emotion.This is a 300-year saga, full of ups and downs, interspersed with the greatest names in the history of physics: Newton, Hooke, Huygens, Young, Fresnel, Foucault, Maxwell, Hertz, Thomson, Einstein, Compton, De Broglie... Who can explain the kindness and resentment?We are in a dilemma. On the one hand, the double-slit experiment and Maxwell's theory unambiguously reveal the wave nature of light, and on the other hand, the photoelectric effect and the Compton effect also clearly show that it is a particle.As far as electrons are concerned, Bohr's transition, the spectrum in atoms, and Heisenberg's matrix all emphasize its discontinuous side. It seems that the particle nature has the upper hand, but Schrödinger's equation exaggerates its continuity, even Put all the labels of fluctuations on its face. No matter how you look at it, there is no way that an electron is not a particle; no matter how you look at it, there is no way that an electron is not a wave. How should this be done? When encountering difficult problems, the best way is to ask our idol, Mr. Sherlock Holmes who is omnipotent.He said: "My method is based on the assumption that when you eliminate all impossible conclusions, what remains, no matter how bizarre, must be the truth." ("New Detective? A soldier with white skin") What a wise saying.Then, it is impossible for the electron not to be a particle, and it is also impossible for it not to be a wave.Then the only possibility left is... It is both a particle and a wave at the same time! But wait, is this too much?It's totally unacceptable.What is "being both a particle and a wave at the same time"?These two images are clearly mutually exclusive.Is it possible for a person to be both male and female (eunuchs and the like do not count)?Isn't this statement contradictory? However, if you want to believe in Holmes, you must also believe in Bohr, because Bohr thinks so.Undoubtedly, an electron must be interpreted from both particle and wave perspectives, and any unilateral description is incomplete.Only when the two concepts of particle and wave are organically combined, can an electron become a flesh and blood electron, and truly become a complete image.The electron without particle is blind, and the electron without wave is lame. This still doesn't convince us, is it both a particle and a wave?It's hard to imagine, is the electron like a ghost, emitting a strange wave around the particle at the same time, making itself a superposition of these two states?Has anyone ever witnessed such a nightmarish scenario?Come out to testify? "No, you get it wrong." Bohr shook his head and said, "Anytime we observe an electron, of course it can only exhibit one property, either a particle or a wave. Anyone who claims to see a particle-wave mixed superposition is either老花眼，要么是纯粹在胡说八道。但是，作为电子这个整体概念来说，它却表现出一种波-粒的二像性来，它可以展现出粒子的一面，也可以展现出波的一面，这完全取决于我们如何去观察它。我们想看到一个粒子？那好，让它打到荧光屏上变成一个小点。看，粒子！我们想看到一个波？也行，让它通过双缝组成干涉图样。看，波！” 奇怪，似乎有哪里不对，却说不出来……好吧，电子有时候变成电子的模样，有时候变成波的模样，嗯，不错的变脸把戏。可是，撕下它的面具，它本来的真身究竟是个什么呢？ “这就是关键！这就是你我的分歧所在了。”玻尔意味深长地说，“电子的'真身'？或者换几个词，电子的原型？电子的本来面目？电子的终极理念？这些都是毫无意义的单词，对于我们来说，唯一知道的只是每次我们看到的电子是什么。我们看到电子呈现出粒子性，又看到电子呈现出波动性，那么当然我们就假设它是粒子和波的混合体。我一点都不关心电子'本来'是什么，我觉得那是没有意义的。事实上我也不关心大自然'本来'是什么，我只关心我们能够'观测'到大自然是什么。电子又是个粒子又是个波，但每次我们观察它，它只展现出其中的一面，这里的关键是我们'如何'观察它，而不是它'究竟'是什么。” 玻尔的话也许太玄妙了，我们来通俗地理解一下。现在流行手机换彩壳，我昨天心情好，就配一个shining的亮银色，今天心情不好，换一个比较有忧郁感的蓝色。咦奇怪了，为什么我的手机昨天是银色的，今天变成蓝色了呢？这两种颜色不是互相排斥的吗？我的手机怎么可能又是银色，又是蓝色呢？很显然，这并不是说我的手机同时展现出银色和蓝色，变成某种稀奇的“银蓝”色，它是银色还是蓝色，完全取决于我如何搭配它的外壳。我昨天决定这样装配它，它就呈现出银色，而今天改一种方式，它就变成蓝色。它是什么颜色，取决于我如何装配它！ 但是，如果你一定要打破砂锅地问：我的手机“本来”是什么颜色？那可就糊涂了。假如你指的是它原装出厂时配着什么外壳，我倒可以告诉你。不过要是你强调是哲学意义上的“本来”，或者“理念中手机的颜色”到底是什么，我会觉得你不可理喻。真要我说，我觉得它“本来”没什么颜色，只有我们给它装上某种外壳并观察它，它才展现出某种颜色来。它是什么颜色，取决于我们如何观察它，而不是取决于它“本来”是什么颜色。我觉得，讨论它“本来的颜色”是痴人说梦。 再举个例子，大家都知道“白马非马”的诡辩，不过我们不讨论这个。我们问：这匹马到底是什么颜色呢？你当然会说：白色啊。可是，也许你身边有个色盲，他会争辩说：不对，是红色！大家指的是同一匹马，它怎么可能又是白色又是红色呢？你当然要说，那个人在感觉颜色上有缺陷，他说的不是马本来的颜色，可是，谁又知道你看到的就一定是正确的颜色呢？假如世上有一半色盲，谁来分辨哪一半说的是“真相”呢？不说色盲，我们戴上一副红色眼镜，这下看出去的马也变成了红色吧？它怎么刚刚是白色，现在是红色呢？哦，因为你改变了观察方式，戴上了眼镜。那么哪一种方式看到的是真实呢？天晓得，庄周做梦变成了蝴蝶还是蝴蝶做梦变成了庄周？你戴上眼镜看到的是真实还是脱下眼镜看到的是真实？ 我们的结论是，讨论哪个是“真实”毫无意义。我们唯一能说的，是在某种观察方式确定的前提下，它呈现出什么样子来。我们可以说，在我们运用肉眼的观察方式下，马呈现出白色。同样我们也可以说，在戴上眼镜的观察方式下，马呈现出红色。色盲也可以声称，在他那种特殊构造的感光方式观察下，马是红色。至于马“本来”是什么色，完全没有意义。甚至我们可以说，马“本来的颜色”是子虚乌有的。我们大多数人说马是白色，只不过我们大多数人采用了一种类似的观察方式罢了，这并不指向一种终极真理。 电子也是一样。电子是粒子还是波？那要看你怎么观察它。如果采用光电效应的观察方式，那么它无疑是个粒子；要是用双缝来观察，那么它无疑是个波。它本来到底是个粒子还是波呢？又来了，没有什么“本来”，所有的属性都是同观察联系在一起的，让“本来”见鬼去吧。 但是，一旦观察方式确定了，电子就要选择一种表现形式，它得作为一个波或者粒子出现，而不能再暧昧地混杂在一起。这就像我们可怜的马，不管谁用什么方式观察，它只能在某一时刻展现出一种颜色。从来没有人有过这样奇妙的体验：这匹马同时又是白色，又是红色。波和粒子在同一时刻是互斥的，但它们却在一个更高的层次上统一在一起，作为电子的两面被纳入一个整体概念中。这就是玻尔的“互补原理”（Complementary Principle），它连同波恩的概率解释，海森堡的不确定性，三者共同构成了量子论“哥本哈根解释”的核心，至今仍然深刻地影响我们对于整个宇宙的终极认识。 “第三次波粒战争”便以这样一种戏剧化的方式收场。而量子世界的这种奇妙结合，就是大名鼎鼎的“波粒二象性”。 Four 三百年硝烟散尽，波和粒子以这样一种奇怪的方式达成了妥协：两者原来是不可分割的一个整体。就像漫画中教皇善与恶的两面，虽然在每个确定的时刻，只有一面能够体现出来，但它们确实集中在一个人的身上。波和粒子是一对孪生兄弟，它们如此苦苦争斗，却原来是演出了一场物理学中的绝代双骄故事，这教人拍案惊奇，唏嘘不已。 现在我们再回到上一章的最后，重温一下波和粒子在双缝前遇到的困境：电子选择左边的狭缝，还是右边的狭缝呢？现在我们知道，假如我们采用任其自然的观测方式，它波动的一面就占了上风。这个电子于是以某种方式同时穿过了两道狭缝，自身与自身发生干涉，它的波函数ψ按照严格的干涉图形花样发展。但是，当它撞上感应屏的一刹那，观测方式发生了变化！我们现在在试图探测电子的实际位置了，于是突然间，粒子性接管了一切，这个电子凝聚成一点，按照ψ的概率随机地出现在屏幕的某个地方。 假使我们在某个狭缝上安装仪器，试图测出电子究竟通过了哪一边，注意，这是另一种完全不同的观测方式！ ! !我们试图探测电子在通过狭缝时的实际位置，可是只有粒子才有实际的位置。这实际上是我们施加的一种暗示，让电子早早地展现出粒子性。事实上，的确只有一边的仪器将记录下它的踪影，但同时，干涉条纹也被消灭，因为波动性随着粒子性的唤起而消失了。我们终于明白，电子如何表现，完全取决于我们如何观测它。种瓜得瓜，种豆得豆，想记录它的位置？好，那是粒子的属性，电子善解人意，便表现出粒子性来，同时也就没有干涉。不作这样的企图，电子就表现出波动性来，穿过两道狭缝并形成熟悉的干涉条纹。 量子派物理学家现在终于逐渐领悟到了事情的真相：我们的结论和我们的观测行为本身大有联系。这就像那匹马是白的还是红的，这个结论和我们用什么样的方法去观察它有关系。有些看官可能还不服气：结论只有一个，亲眼看见的才是唯一的真实。色盲是视力缺陷，眼镜是外部装备，这些怎么能够说是看到“真实”呢？其实没什么分别，它们不外乎是两种不同的观测方式罢了，我们的论点是，根本不存在所谓“真实”。 好吧，现在我视力良好，也不戴任何装置，看到马是白色的。那么，它当真是白色的吗？其实我说这话前，已经隐含了一个前提：“用人类正常的肉眼，在普通光线下看来，马呈现出白色。”再技术化一点，人眼只能感受可见光，波长在400－760纳米左右，这些频段的光混合在一起才形成我们印象中的白色。所以我们论断的前提就是，在400－760纳米的光谱区感受马，它是白色的。 许多昆虫，比如蜜蜂，它的复眼所感受的光谱是大大不同的。蜜蜂看不见波长比黄光还长的光，却对紫外线很敏感。在它看来，这匹马大概是一种蓝紫色，甚至它可能绘声绘色地向你描绘一种难以想象的“紫外色”。现在你和蜜蜂吵起来了，你坚持这马是白色的，而蜜蜂一口咬定是蓝紫色。你和蜜蜂谁对谁错呢？其实都对。那么，马怎么可能又是白色又是紫色呢？其实是你们的观测手段不同罢了。对于蜜蜂来说，它也是“亲眼”见到，人并不比蜜蜂拥有更多的正确性，离“真相”更近一点。话说回来，色盲只是对于某些频段的光有盲点，眼镜只不过加上一个滤镜而已，本质上也是一样的，也没理由说它们看到的就是“虚假”。 事实上，没有什么“客观真相”。讨论马本质上“到底是什么颜色”，正如我们已经指出过的，是很无聊的行为。根本不存在一个绝对的所谓“本色”，除非你先定义观测的方式。 玻尔也好，海森堡也好，现在终于都明白：谈论任何物理量都是没有意义的，除非你首先描述你测量这个物理量的方式。一个电子的动量是什么？我不知道，一个电子没有什么绝对的动量，不过假如你告诉我你打算怎么去测量，我倒可以告诉你测量结果会是什么。根据测量方式的不同，这个动量可以从十分精确一直到万分模糊，这些结果都是可能的，也都是正确的。一个电子的动量，只有当你测量时，才有意义。假如这不好理解，想象有人在纸上画了两横夹一竖，问你这是什么字。嗯，这是一个“工”字，但也可能是横过来的“H”，在他没告诉你怎么看之前，这个问题是没有定论的。现在，你被告知：“这个图案的看法应该是横过来看。”这下我们明确了：这是一个大写字母H。只有观测手段明确之后，答案才有意义。 测量！在经典理论中，这不是一个被考虑的问题。测量一块石头的重量，我用天平，用弹簧秤，用磅秤，或者用电子秤来做，理论上是没有什么区别的。在经典理论看来，石头是处在一个绝对的，客观的外部世界中，而我——观测者——对这个世界是没有影响的，至少，这种影响是微小得可以忽略不计的。你测得的数据是多少，石头的“客观重量”就是多少。但量子世界就不同了，我们已经看到，我们测量的对象都是如此微小，以致我们的介入对其产生了致命的干预。我们本身的扰动使得我们的测量中充满了不确定性，从原则上都无法克服。采取不同的手段，往往会得到不同的答案，它们随着不确定性原理摇摇摆摆，你根本不能说有一个客观确定的答案在那里。在量子论中没有外部世界和我之分，我们和客观世界天人合一，融和成为一体，我们和观测物互相影响，使得测量行为成为一种难以把握的手段。在量子世界，一个电子并没有什么“客观动量”，我们能谈论的，只有它的“测量动量”，而这又和我们的测量手段密切相关。 各位，我们已经身陷量子论那奇怪的沼泽中了，我只希望大家不要过于头昏脑涨，因为接下来还有无数更稀奇古怪的东西，错过了未免可惜。我很抱歉，这几节我们似乎沉浸于一种玄奥的哲学讨论，而且似乎还要继续讨论下去。这是因为量子革命牵涉到我们世界观的根本变革，以及我们对于宇宙的认识方法。量子论的背后有一些非常形而上的东西，它使得我们的理性战战兢兢，汗流浃背。但是，为了理解量子论的伟大力量，我们又无法绕开这些而自欺欺人地盲目前进。如果你从史话的一开始跟着我一起走到了现在，我至少对你的勇气和毅力表示赞赏，但我也无法给你更多的帮助。假如你感到困惑彷徨，那么玻尔的名言“如果谁不为量子论而感到困惑，那他就是没有理解量子论”或许可以给你一些安慰。而且，正如我们以后即将描述的那样，你也许应该感到非常自豪，因为爱因斯坦和你是一个处境。 但现在，我们必须走得更远。上面一段文字只是给大家一个小小的喘息机会，我们这就继续出发了。 如果不定义一个测量动量的方式，那么我们谈论电子动量就是没有意义的？这听上去似乎是一种唯心主义的说法。难道我们无法测量电子，它就没有动量了吗？让我们非常惊讶和尴尬的是，玻尔和海森堡两个人对此大点其头。一点也不错，假如一个物理概念是无法测量的，它就是没有意义的。我们要时时刻刻注意，在量子论中观测者是和外部宇宙结合在一起的，它们之间现在已经没有明确的分界线，是一个整体。在经典理论中，我们脱离一个绝对客观的外部世界而存在，我们也许不了解这个世界的某些因素，但这不影响其客观性。可如今我们自己也已经融入这个世界了，对于这个物我合一的世界来说，任何东西都应该是可以测量和感知的。只有可观测的量才是存在的！ 卡尔?萨根（Karl Sagan）曾经举过一个很有意思的例子，虽然不是直接关于量子论的，但颇能说明问题。 “我的车库里有一条喷火的龙！”他这样声称。 “太稀罕了！”他的朋友连忙跑到车库中，但没有看见龙。“龙在哪里？” “哦，”萨根说，“我忘了说明，这是一条隐身的龙。” 朋友有些狐疑，不过他建议，可以撒一些粉末在地上，看看龙的爪印是不是会出现。但是萨根又声称，这龙是飘在空中的。 “那既然这条龙在喷火，我们用红外线检测仪做一个热扫描？” “也不行。”萨根说，“隐形的火也没有温度。” “要么对这条龙喷漆让它现形？”——“这条龙是非物质的，滑不溜手，油漆无处可粘。” 反正没有一种物理方法可以检测到这条龙的存在。萨根最后问：“这样一条看不见摸不着，没有实体的，飘在空中喷着没有热度的火的龙，一条任何仪器都无法探测的龙，和'根本没有龙'之间又有什么差别呢？” 现在，玻尔和海森堡也以这种苛刻的怀疑主义态度去对待物理量。不确定性原理说，不可能同时测准电子的动量p和位置q，任何精密的仪器也不行。许多人或许会认为，好吧，就算这是理论上的限制，和我们实验的笨拙无关，我们仍然可以安慰自己，说一个电子实际上是同时具有准确的位置和动量的，只不过我们出于某种限制无法得知罢了。 但哥本哈根派开始严厉地打击这种观点：一个具有准确p和q的经典电子？这恐怕是自欺欺人吧。有任何仪器可以探测到这样的一个电子吗？——没有，理论上也不可能有。那么，同样道理，一个在臆想的世界中生存的，完全探测不到的电子，和根本没有这样一个电子之间又有什么区别呢？ 事实上，同时具有p和q的电子是不存在的！p和q也像波和微粒一样，在不确定原理和互补原理的统治下以一种此长彼消的方式生存。对于一些测量手段来说，电子呈现出一个准确的p，对于另一些测量手段来说，电子呈现出准确的q。我们能够测量到的电子才是唯一的实在，这后面不存在一个“客观”的，或者“实际上”的电子！ 换言之，不存在一个客观的，绝对的世界。唯一存在的，就是我们能够观测到的世界。物理学的全部意义，不在于它能够揭示出自然“是什么”，而在于它能够明确，关于自然我们能“说什么”。没有一个脱离于观测而存在的绝对自然，只有我们和那些复杂的测量关系，熙熙攘攘纵横交错，构成了这个令人心醉的宇宙的全部。测量是新物理学的核心，测量行为创造了整个世界。 *********** 饭后闲话：奥卡姆剃刀 同时具有p和q的电子是不存在的。有人或许感到不理解，探测不到的就不是实在吗？ 我们来问自己，“这个世界究竟是什么”和“我们在最大程度上能够探测到这个世界是什么”两个命题，其实质到底有多大的不同？我们探测能力所达的那个世界，是不是就是全部实在的世界？比如说，我们不管怎样，每次只能探测到电子是个粒子或者是个波，那么，是不是有一个“实在”的世界，在那里电子以波-粒子的奇妙方式共存，我们每次探测，只不过探测到了这个终极实在于我们感观中的一部分投影？同样，在这个“实在世界”中还有同时具备p和q的电子，只不过我们与它缘悭一面，每次测量都只有半面之交，没法窥得它的真面目？ 假设宇宙在创生初期膨胀得足够快，以致它的某些区域对我们来说是如此遥远，甚至从创生的一刹那以光速出发，至今也无法与它建立起任何沟通。宇宙年龄大概有150亿岁，任何信号传播最远的距离也不过150亿光年，那么，在距离我们150亿光年之外，有没有另一些“实在”的宇宙，虽然它们不可能和我们的宇宙之间有任何因果联系？ 在那个实在世界里，是不是有我们看不见的喷火的龙，是不是有一匹具有“实在”颜色的马，而我们每次观察只不过是这种“实在颜色”的肤浅表现而已。我跟你争论说，地球“其实”是方的，只不过它在我们观察的时候，表现出圆形而已。但是在那个“实在”世界里，它是方的，而这个实在世界我们是观察不到的，但不表明它不存在。 如果我们运用“奥卡姆剃刀原理”（Occams Razor），这些观测不到的“实在世界”全都是子虚乌有的，至少是无意义的。这个原理是14世纪的一个修道士威廉所创立的，奥卡姆是他出生的地方。这位奥卡姆的威廉还有一句名言，那是他对巴伐利亚的路易四世说的：“你用剑来保卫我，我用笔来保卫你。” 剃刀原理是说，当两种说法都能解释相同的事实时，应该相信假设少的那个。比如，地球“本来”是方的，但观测时显现出圆形。这和地球“本来就是圆的”说明的是同一件事。但前者引入了一个莫名其妙的不必要的假设，所以前者是胡说。同样，“电子本来有准确的p和q，但是观测时只有1个能显示”，这和“只存在具有p或者具有q的电子”说明的也是同一回事，但前者多了一个假设，我们应当相信后者。“存在但观测不到”，这和“不存在”根本就是一码事。 同样道理，没有粒子-波混合的电子，没有看不见的喷火的龙，没有“绝对颜色”的马，没有150亿光年外的宇宙（150亿光年这个距离称作“视界”），没有隔着1厘米四维尺度观察我们的四维人，没有绝对的外部世界。史蒂芬?霍金在中说：“我们仍然可以想像，对于一些超自然的生物，存在一组完全地决定事件的定律，它们能够观测宇宙现在的状态而不必干扰它。然而，我们人类对于这样的宇宙模型并没有太大的兴趣。看来，最好是采用奥卡姆剃刀原理，将理论中不能被观测到的所有特征都割除掉。” 你也许对这种实证主义感到反感，反驳说：“一片无人观察的荒漠，难道就不存在吗？”以后我们会从另一个角度来讨论这片无人观察的荒漠，这里只想指出，“无人的荒漠”并不是原则上不可观察的。 Fives 正如我们的史话在前面一再提醒各位的那样，量子论革命的破坏力是相当惊人的。在概率解释，不确定性原理和互补原理这三大核心原理中，前两者摧毁了经典世界的因果性，互补原理和不确定原理又合力捣毁了世界的客观性和实在性。新的量子图景展现出一个前所未有的世界，它是如此奇特，难以想象，和人们的日常生活格格不入，甚至违背我们的理性本身。但是，它却能够解释量子世界一切不可思议的现象。这种主流解释被称为量子论的“哥本哈根”解释，它是以玻尔为首的一帮科学家作出的，他们大多数曾在哥本哈根工作过，许多是量子论本身的创立者。哥本哈根派的人物除了玻尔，自然还有海森堡、波恩、泡利、狄拉克、克莱默、约尔当，也包括后来的魏扎克和盖莫夫等等，这个解释一直被当作是量子论的正统，被写进各种教科书中。 当然，因为它太过奇特，太教常人困惑，近80年来没有一天它不受到来自各方面的置疑、指责、攻击。也有一些别的解释被纷纷提出，这里面包括德布罗意-玻姆的隐函数理论，埃弗莱特的多重宇宙解释，约翰泰勒的系综解释、Ghirardi-Rimini-Weber的“自发定域”（Spontaneous Localization），Griffiths-Omnes-GellMann-Hartle的“脱散历史态”（Decoherent Histories, or Consistent Histories），等等，等等。我们的史话以后会逐一地去看看这些理论，但是公平地说，至今没有一个理论能取代哥本哈根解释的地位，也没有人能证明哥本哈根解释实际上“错了”（当然，可能有人争辩说它“不完备”）。隐函数理论曾被认为相当有希望，可惜它的胜利直到今天还仍然停留在口头上。因此，我们的史话仍将以哥本哈根解释为主线来叙述，对于读者来说，他当然可以自行判断，并得出他自己的独特看法。 哥本哈根解释的基本内容，全都围绕着三大核心原理而展开。我们在前面已经说到，首先，不确定性原理限制了我们对微观事物认识的极限，而这个极限也就是具有物理意义的一切。其次，因为存在着观测者对于被观测物的不可避免的扰动，现在主体和客体世界必须被理解成一个不可分割的整体。没有一个孤立地存在于客观世界的“事物”（being），事实上一个纯粹的客观世界是没有的，任何事物都只有结合一个特定的观测手段，才谈得上具体意义。对象所表现出的形态，很大程度上取决于我们的观察方法。对同一个对象来说，这些表现形态可能是互相排斥的，但必须被同时用于这个对象的描述中，也就是互补原理。 最后，因为我们的观测给事物带来各种原则上不可预测的扰动，量子世界的本质是“随机性”。传统观念中的严格因果关系在量子世界是不存在的，必须以一种统计性的解释来取而代之，波函数ψ就是一种统计，它的平方代表了粒子在某处出现的概率。当我们说“电子出现在x处”时，我们并不知道这个事件的“原因”是什么，它是一个完全随机的过程，没有因果关系。 有些人可能觉得非常糟糕：又是不确定又是没有因果关系，这个世界不是乱套了吗？物理学家既然什么都不知道，那他们还好意思呆在大学里领薪水，或者在电视节目上欺世盗名？然而事情并没有想象的那么坏，虽然我们对单个电子的行为只能预测其概率，但我们都知道，当样本数量变得非常非常大时，概率论就很有用了。我们没法知道一个电子在屏幕上出现在什么位置，但我们很有把握，当数以万亿记的电子穿过双缝，它们会形成干涉图案。这就好比保险公司没法预测一个客户会在什么时候死去，但它对一个城市的总体死亡率是清楚的，所以保险公司一定是赚钱的！ 传统的电视或者电脑屏幕，它后面都有一把电子枪，不断地逐行把电子打到屏幕上形成画面。对于单个电子来说，我并不知道它将出现在屏幕上的哪个点，只有概率而已。不过大量电子叠在一起，组成稳定的画面是确定无疑的。看，就算本质是随机性，但科学家仍然能够造出一些有用的东西。如果你家电视画面老是有雪花，不要怀疑到量子论头上来，先去检查一下天线。 当然时代在进步，俺的电脑屏幕现在变成了薄薄的液晶型，那是另一回事了。 至于令人迷惑的波粒二象性，那也只是量子微观世界的奇特性质罢了。我们已经谈到德布罗意方程λ= h/p，改写一下就是λp=h，波长和动量的乘积等于普朗克常数h。对于微观粒子来说，它的动量非常小，所以相应的波长便不能忽略。但对于日常事物来说，它们质量之大相比h简直是个天文数字，所以对于生活中的一个足球，它所伴随的德布罗意波微乎其微，根本感觉不到。我们一点都用不着担心，在世界杯决赛中，眼看要入门的那个球会突然化为一缕波，消失得杳然无踪。 但是，我们还是觉得不太满意，因为对“观测行为”，我们似乎还没有作出合理的解释。一个电子以奇特的分身术穿过双缝，它的波函数自身与自身发生了干涉，在空间中严格地，确定地发展。在这个阶段，因为没有进行观测，说电子在什么地方是没有什么意义的，只有它的概率在空间中展开。物理学家们常常摆弄玄虚说：“电子无处不在，而又无处在”，指的就是这个意思。然而在那以后，当我们把一块感光屏放在它面前以测量它的位置的时候，事情突然发生了变化！电子突然按照波函数的概率分布而随机地作出了一个选择，并以一个小点的形式出现在了某处。这时候，电子确定地存在于某点，自然这个点的概率变成了100％，而别的地方的概率都变成了0。也就是说，它的波函数突然从空间中收缩，聚集到了这一个点上面，在这个点出现了强度为1的高峰。而其他地方的波函数都瞬间降为0。 哦，上帝，发生了什么事？为什