Chapter 10 Chapter 9 Measurement Problems

one We have met Feng at the Cuomo meeting.John Von Neumann, one of the founders of modern computers, is the most outstanding mathematician of the twentieth century.All kinds of legends about him are like long-lasting legends in the scientific world, spreading more and more widely and becoming more and more mysterious: it is said that he could multiply eight-digit numbers in his head at the age of six, calculus at the age of eight, and calculus at the age of twelve. He was proficient in functional analysis at the age of 19, and some people said that he had a photographic memory and was proficient in history. Some people cited all kinds of unimaginable examples to illustrate how amazing his mental arithmetic ability is.Some say he knew five languages ​​by the age of ten and could write hilarious doggerel in each, a number that turns out to be seven in others.In any case, everyone admits that this guy is a rare genius in a century.

It would take a lot of time to enumerate his outstanding achievements: from set theory to research on the foundations of mathematics; from operator rings to ergodic theory; from game theory to numerical analysis; You can write a lot about it.But here we only focus on his contribution to quantum theory, which alone is enough to give him a place in our history. As we have mentioned above, Dirac published the famous "Principles of Quantum Mechanics" textbook in 1930, completing the universal synthesis of quantum mechanics.But from a purely mathematical point of view, quantum theory still lacks a common and rigorous foundation, and this deficiency was made up by von Neumann.In 1926, he came to Göttingen and served as the assistant of the famous Hilbert. The two of them, together with Nordheim, soon jointly published the paper "Fundamentals of Quantum Mechanics", which incorporated Hilbert's The operator theory is introduced into the quantum theory, which makes this physical system mathematically rigorous.In 1932, von Neumann developed this work again and published the famous book "The Mathematical Foundations of Quantum Mechanics".This book was published in English by Princeton in 1955, and it is still a classic textbook.We have no intention of getting too deep into the mathematics, but von Neumann proved several interesting results, especially about our measurement behavior, which deeply influenced the way a generation of physicists thought about the collapse of the wave function.

We still remember the measurement problem that plagued us in the last chapter: whenever we observe, the wave function of the system collapses, and a practical result jumps out according to the probability. If we don’t observe, it develops strictly according to the equation .These are two completely different processes. The latter is continuous, mathematically reversible, and completely deterministic, while the former is a collapse, which is random and irreversible. It is still unclear what the internal mechanism is.How are these two processes converted?What triggers this drastic change in the wave function?Is it observation?But when we speak in this way, the language we use is everyday, ambiguous, and ambiguous.We have been using the word observation for granted without giving it a precise definition.What kind of behavior counts as an observation?If seeing with eyes open is considered an observation, what about touching with hands when eyes are closed?What about poking with a stick?What about recording with an instrument?If people can be regarded as observers, what about cats?What about a computer?What about a Geiger counter?

Feng.Neumann astutely pointed out that the instruments we use to measure objects are themselves composed of indeterminate particles, which have their own wave functions.When we use an instrument to observe, this will only involve the instrument itself into this fuzzy superposition state.Well, if we want to measure whether an electron has passed through the left or the right slit, we use an instrument to measure it and report this result in the direction the indicator wobbles.However, what makes people laugh and cry is that because this instrument itself also has its own wave function, if we do not observe the instrument itself, its wave function will also fall into a fuzzy superposition state!Neumann's mathematical model shows that when the instrument measures the electron, the electron's wave function collapses, but the left/right superposition is just transferred to the instrument.Now our instrument is in the superposition state of the indicator pointing left or right!If we use instrument B to measure that instrument A again, well, now the wave function of A collapses again, and its state becomes definite, but B falls into ambiguity again. In a word, when we use instrument to measure instrument, the whole chain The last instrument of is always in an indeterminate state, which is called infinite regression.From another point of view, if we add the measuring instruments to the whole system, the wave function of this large system has never completely collapsed!

However, we are fairly certain that the process is over when we see the results reported by the instrument.We ourselves will not be in some absurd superposition state.When our brain receives the measured information, the game is over, and the wave function is no longer messed up. Could it be that the participation of human consciousness is the reason for the collapse of the wave function?It is only when the result of the random choice of electrons is realized that it truly becomes reality, emerging from the wave function into the world.And as long as it is not conscious, the wave function remains indeterminate, merely shifting from one place to the last measuring instrument.In Neumann's view, the wave function can be regarded as a vector in Hilbert space, and the collapse is its projection in a certain direction.But what causes this projection?Is it our sense of freedom?

In other words, since an instrument cannot be aware of whether its pointer is pointing left or right, it must be caught in a left/right mix.A cat cannot be aware of whether it is alive or dead, so it can be stuck in a dead/alive hybrid state.However, you and I can realize whether the electron is left or right, whether we are alive or dead, so the wave function finally completely collapses here, and the world finally becomes reality, so as not to confuse our consciousness. crazy?Irrational?Nonsense?incredible?Perhaps everyone has this feeling of shock.Natural science, the proudest aristocrat, the lawgiver of the universe, the tireless explorer of the ultimate mysteries of nature, the judge who always claims to be the most objective, the strictest, the most meticulous, and the least tolerant of subjective consciousness, now unexpectedly Put the human consciousness, or in other words, the soul, at the center of the universe!Copernicus expelled man from the center of the universe, and now they come back in a different form?That's enough to make every scientist shudder.

No, this must be nonsense, and the person who said it must be crazy, or a physics idiot.Does physics require consciousness?This is the biggest joke of the century!But wait a minute, the person who said this may be much smarter than you, maybe a Nobel Prize winner in physics? Eugene.Eugene Wigner was born on November 17, 1902 in Budapest, Hungary.He met von Neumann, who was his junior, while attending a Lutheran secondary school.One of the two is better at mathematics and the other is better at physics. It has been a fairly complementary combination for a long time.Wigner is one of the most important physicists of the twentieth century. He applied group theory to quantum mechanics and played a vital role in the establishment of the atomic nucleus model.He became the founder of quantum field theory together with Dirac, Jordan and others. By the way, his sister married Dirac and thus became the latter's brother-in-law.He participated in the Manhattan Project and made outstanding contributions to the theory of nuclear reactions.In 1963, he was awarded the Nobel Prize in Physics.

Regarding the observation problem in quantum theory, Wigner's opinion is: Consciousness undoubtedly plays an important role in triggering the wave function.While people were still arguing about Schrödinger's unlucky cat, Wigner came out and poked a bigger hornet's nest, which is the so-called friend of Wigner. Wigner's friend is some imaginary acquaintance (whose model, I guess, is either Dirac or von Neumann!) and who wears a gas-proof Mask also stayed in the box to observe the cat.Wigner himself withdrew from the room to observe what was going on in the box.Now, for Wigner, who knows nothing about the situation in the room, can he assume that the box is in a mixed state of (live cat happy friend) AND (dead cat sad friend)?However, when he asked that friend afterwards, the latter would definitely deny this superposition state.Wigner concludes that superposition does not apply when the friend's consciousness is included in the overall system.Even though he himself is outside the door, the wave function in the box is constantly being touched by the observations of his friends, so there are only two pure states of a live cat or a dead cat.

Wigner argued that it is not surprising that consciousness can act on the external world, causing the wave function to collapse.Because changes in the external world can cause changes in our consciousness, according to Newton's third law, the principle of action and reaction, consciousness should also be able to act on the external world in reverse.He titled the paper "Remarks on the mind-body question" (Remarks on the mind-body question), and collected it in his 1967 collection of essays. Has quantum theory gone too far?Is consciousness, this ethereal concept, really going to occupy the sacred realm of physics and become a core of our theory?People always reject this horrible idea deep in their hearts. Peter Coveney and Roger Highfield wrote a book called "The Arrow of Time" (The arrow of time), which talks about dimension Garner's claim.But in the Chinese version of this book, the translator specially added a reader's note, saying that this consciousness-based explanation is far-fetched, and it claims that observations can be made by a set of measuring instruments, so they are completely objective.But this argument is obviously untenable, because the instrument only adds a link to von Neumann's infinite receding chain. Without observing the instrument, it is still in the superimposed wave function.

But the question is, what exactly is consciousness?This poses far more problems than our wave function itself, and is a strategy that does not pay off.Is consciousness independent of matter?Does it obey the laws of physics?Can consciousness exist in lower animals?Can it exist in a machine?A flood of more problems engulfing us helpless is not much better than worrying about how the wave function collapses. In fact, only idle philosophers talk about this kind of problem, and real brain scientists and neuroscientists are often dismissive or indifferent to it.When the problem of consciousness was drawn into the explanation of quantum theory, many books introducing physics presented a cross-sectional diagram of the brain, explaining the various divisions of the cortex, the connection of neural knots, and the hippocampus. This is indeed an interesting sight. !Next, we might as well make a few simple discussions on this problem of consciousness, but we don't want to spend too much time on it, because our history will continue to move forward, and there are still some novel things waiting for us.

At the end of this section, it should be specially stated that the effect of consciousness on the external world is only a possible statement.This does not mean that all kinds of so-called supernatural powers, telepathy, telekinesis, bending spoons at a distance, etc. have a theoretical basis.For these things, it's best to stick to the principle that particularly outlandish claims need to be backed by particularly strong evidence, requiring rigorous, reproducible, double-blind experiments on each individual case.As far as I know, no example of a psychic function has passed a similar test. Gossip after dinner: Heisenberg and the German atomic bomb program (6) Calculating the size of the critical mass is essentially a statistical problem.In order to ensure that enough uranium-235 molecules get split before too many neutrons escape and stop the chain reaction, it should be able to ensure that at least 2^80 molecules (about a mole) react, which is to maintain eighty splits .How big is this range?This is equivalent to asking approximately what radius a person (molecule) will stay in after randomly going forward and back eighty times.This is a very famous drunken walking problem, and if you read Gamow's old popular science book "From One to Infinity", maybe you still have a little impression of it.Heisenberg calculated a distance: 54 centimeters, which is equivalent to 13 tons of uranium-235, and it was unimaginable to separate so much at that time. However, the figure of 54 centimeters is an upper limit, that is to say, only uranium 235 with a radius of 54 centimeters is needed in the worst case.In fact, many specific cases such as the absorption of neutrons, or in far fewer cases, chain reactions can be ignored in the calculation, and there are various important constraints that Heisenberg was too clever to ignore.Heisenberg's oversimplification of a rather complicated problem, and his lack of a thorough understanding of fast neutron reactions, as can be seen from his calculations, all led him to treat several tons of uranium-235 as a The lower limit, that is, the minimum required quality, and carried this view until after the bombing of Hiroshima (unbeknownst to him, Perls had already made the correct result in 1939!). Such a mistake, not to mention a first-class physicist like Heisenberg, even an ordinary physics student should not make it.And no one has ever refuted his results!This inevitably makes some people think that Heisenberg specially concocted such a mistake to deceive his superiors and prevent the manufacture of the atomic bomb.Unfortunately, judging from all the circumstances, Heisenberg himself was convinced of this. On August 6, 1945, the German scientists imprisoned in Farm Hall were shocked by the news of Hiroshima.Heisenberg commented at the beginning: I do not believe the news of the atomic bomb at all, of course I may be wrong.I thought they (the allies) might have ten tons of enriched uranium, but didn't expect them to have ten tons of pure uranium 235!Heisenberg still believed that several tons of uranium-235 were needed for a nuclear bomb.Hahn was shocked by this comment because he thought it would take very little uranium to make a bomb (this is what Heisenberg said before, but it was referring to a reactor bomb, where the reactor becomes unstable and becomes explosive, Hahn was clearly mistaken).Heisenberg corrected this view, then speculated that the Allies might have found a way to efficiently separate the isotopes (he still thought the Allies had separated that much uranium-235, not that his own estimates were wrong!). At nine o'clock sharp, everyone listened to the BBC news together, and then had a lively discussion.Heisenberg made some correct analyses, but came up with the 54cm estimate.The next day, everyone began to draft a memorandum.On the third day, Heisenberg and Woz discussed the possibility of uranium bombs. Heisenberg felt that uranium might be easier to split than imagined (he learned from newspapers that atomic bombs were not big), but he had no information because Germany has no reactors to produce uranium.Until this time, Heisenberg still thought that the quality of the uranium bomb needed to be several tons. (This topic will end with one more section, ha ha.) two Consciousness collapses the wave function?But what is consciousness?It's one of the most-discussed questions by philosophers, but the response in the scientific community has been relatively lukewarm.In the field of psychology, the behaviorist school represented by John B. Watson and BF Skinner is usually willing to decompose mental events into stimuli and responses for research, while ignoring the consciousness itself that cannot be confirmed by experiments .Indeed, even giving a precise definition of consciousness is difficult. Where it arises, where it works, and how it acts on our bodies is still a mystery.People can generally reach a consensus that not all activities of the brain are conscious. In fact, many activities of the brain are unconscious to us. process.When the "Ninth Symphony" sounded in my ears, my childhood in middle school suddenly appeared before my eyes, but I didn't know how my brain completed this process step by step. It was done subconsciously!Sometimes I even wonder: why do I think so?In addition, many people also admit that consciousness seems to be closely related to our attention, and it also requires a certain memory ability to complete coherent actions. To be sure, consciousness is not a concrete physical reality.No one has ever found any tangible consciousness inside a skull during brain surgery.Is it the function of a part of the brain?It would seem so, but which part is responsible for consciousness is a matter of debate.Some people say it is the brain, because the brain has various complex communication functions, and the cerebellum, which controls the body, looks more like an automatic machine.When we learn to swim or ride a bicycle, we always have to be cautious at the beginning, pay attention to the control of every posture of the body, and think carefully before every movement.But once proficient, the cerebellum takes over the movement of the body, turning it into an instinctive behavior.For example, a person who is used to riding a bicycle does not need to be aware of his every movement all the time.In fact, the reaction of our consciousness is quite slow (experiments report that there is a delay of half a second). When a pianist plays skillfully, he often does it in one go without thinking. It can't be called a fully conscious behavior, as we usually say: it's so familiar that you don't even think about it.And it's worth noting that such acquired physical skills can often remain unforgotten for a long time. It is also said that the brain does not have consciousness, but only directs the actions of the body.In one experiment, we stimulated a certain area of ​​the brain to move the subject's right hand, but the subject didn't want to move it!Then, when we consciously want to move our right hand, somewhere the desire must be generated by consciousness, which is then transmitted to a specific cortex by electrical signals, and finally leads to the movement itself.The experimenters believe that the midbrain and thalamus are the seat of this free consciousness.But others think it's the reticulum, or the hippocampus.Many people also believe that the left hemisphere of the brain can be called conscious, while the right hemisphere is an automaton. Putting these specific arguments aside, let's look at the question from a higher level: what is consciousness in essence?Is it some mysterious immaterial ghost that exists completely out of our bodies and brains, and we only gain this consciousness when it possesses us?Obviously, most scientists will not agree with this statement. A tacit view is that consciousness is a structural model that exists entirely based on a material basis (our brain), but requires a higher level of law to understand it. explain it.This is the so-called Holism explanation. What is consciousness?This is like asking: what is information?A message is a kind of information, but its carrier itself is not the information, but the content it contains.Let me tell you: The Lakers lost today. These eight characters are not information in themselves, but the real information is the fact that the Lakers lost.The same information can be expressed in another carrier, such as writing a line to tell you, or sending you an E-Mail, or making a gesture.Therefore, the research carrier itself cannot draw useful conclusions about the relevant information. Even if I break down these eight characters into strokes and study them thoroughly, it will not help me understand the significance of the Lakers' loss.Information does not exist in each character, but in the combination of these eight characters, and its description requires a higher level of language and rules than a single character. What is Beethoven's Ninth Symphony?It is nothing more than a string of notes.But the notes themselves are not the symphony, if we want to describe this great piece, we are dealing with the pattern of the notes!What is Hemingway's The Old Man and the Sea?It is nothing more than a string of letters.But the letters themselves are not fiction, their patterns are!In order to better understand that letters are not novels, but combination patterns are the concept of novels, we assume that the simplest encoding method is used to encrypt the work "The Old Man and the Sea", that is, to replace each letter with a corresponding symbol.For example, A is replaced by a circle, B is replaced by a square, C is replaced by a triangle, and so on.Now that we have a book full of weird symbols in our hands, I ask you: Is this still The Old Man and the Sea?Most people should admit: still.Because there is no loss of information in the original book, its combination mode is still there intact, but it is just changed to a different expression at the basic level, and it can be decompiled back.This encrypted version of "The Old Man and the Sea" is completely equivalent to the original "The Old Man and the Sea"! Back to our question: what is consciousness?Consciousness is a pattern of composition of the groups of atoms that make up the brain!The material basis of our brain is no different from a rock, made up of the same atoms of carbon, hydrogen, and oxygen.The electrons that make up our brains are exactly the same as those that make up a rock, and even if they were swapped, it wouldn't turn our head into a rock.Our consciousness is entirely based on the structural patterns of our brains!As long as a bunch of atoms are arranged in a certain way, it can form our consciousness, just as a bunch of letters can be arranged in a certain way to form "The Old Man and the Sea".It doesn't take some immaterial spirit to possess it here, just as you wouldn't believe it, only when Hemingway's spirit is attached to a pile of letters can it become The Old Man and the Sea.A single brain cell obviously cannot be conscious of anything, but many brain cells are combined in a specific pattern, and it is in the combination that consciousness arises. Well, at this point, most people should be satisfied with this rather materialistic statement.But just a few more reasonable steps down, many people may feel a cold sweat on their backs.If consciousness depends entirely on the way atoms are assembled, the first corollary is that it can be replicated.Publishers print thousands of copies of The Old Man and the Sea, why can't atoms be copied?If our technology develops to a certain level and can scan the position and state of every atom in your body, and recombine them in another place, is this new person you?Will he have the same consciousness as you?Or simply, is he the same person as you?If we admit that consciousness is entirely based on atomic arrangement patterns, our answer is undoubtedly YES!This is two different concepts from human cloning. A human clone only inherits your genes, but this replicant has your consciousness, your memory, your feelings, everything about you. He is yourself! In recent years, we have made great breakthroughs in quantum communication.It is already possible to transmit an unknown quantum state to a second one intact, and indeed many concrete protocols have been proposed.Although reassuringly, there is a principle called the no cloning theorem (Wootters, Zurek and Dieks proposed in 1982) that stipulates that the original original must be destroyed while transmitting the quantum state.In other words, the quantum state can only be cut and paste, but not copy paste, which prevents two you from appearing.But the question is, if you are destroyed and then rebuilt in another place, do you think this is the original you? Another inference is that the combination mode itself does not require a specific material basis to appear.We have seen that we can completely rewrite "The Old Man and the Sea" with another set of symbols, which does not make a substantial difference.For a movie, I can record it on film, or on videotape, VCD, LD or DVD.Of course, some people will raise objections, saying that the compression actually caused the loss of information. The VCD version of Matrix is ​​no longer the movie version of Matrix. Use other expression systems such as CMY, HSI, YUV or YIQ to express.For another example, any sequence can be compressed using some reversible compression techniques such as Huffman coding, letters can also be replaced by Morse code, and songs can be recorded with numbered notation or staves. Although they look very different, the information contained in them is different. Are the same!If you are interested, use the white stones in Go to represent 0, and the black stones to represent 1. You can undoubtedly copy a VCD with Go chess that covers the entire Tiananmen Square, which is completely equivalent! Then, as long as there is some kind of complex system that can contain the main information of our conscious mode or is equivalent to it, obviously we should think that consciousness does not have to depend on the physical body of our biological organism to exist!Assuming that all the information of our brain is scanned and stored in a computer, this computer calculates the reactions of these molecules to various stimuli strictly according to the laws of physics and finally obtains the corresponding results to respond, then theoretically speaking, This computer behaves exactly like us!Can we say that this computer actually has our consciousness? For many positivists, the criteria for judging consciousness or thinking follow strictly the method of this model structure theory.Consciousness is nothing more than some complex pattern structure, or some complex algorithm between input and output.Any system that can emulate this algorithm can reasonably be considered conscious.and Feng.Alan Neumann is also the founder of modern computers.In 1950, Alan Turin proposed a standard for judging whether a computer can actually think like a human, which is the famous Turing test.He envisions a supercomputer and a human hiding behind the scenes to answer questions from the interrogator, while the interrogator tries to tell which is the human and which is the computer.Turing argued that if the computer is so well disguised that no one can actually tell it apart from a real person, then we can claim that the computer is capable of thinking, or consciousness, like a human being. (His original word was wisdom).Modern computers can already beat chess grandmasters (poor Kasparov!), but it is not known how long it will be until the day of truly fooling a tester is here. Let us guess for ourselves. People who hold the view that computers can actually become conscious once they are complex enough are often called strong artificial intelligence.In their view, the human brain is essentially an extremely complex computer, but it is not composed of transistors or integrated circuits, but biological cells.But cells also work on tiny electrical currents, and even if we don't fully understand how, there's no reason to think there's something supernatural about it.Like Schrödinger's analogy in his famous pamphlet "What is Life", a steam engineer who sees an electric motor for the first time will be surprised to find that this machine is very different from the thermodynamic machine he knows, But he'd reasonably assume it was working on some principle he didn't understand, and wouldn't make a fuss about the ghosts driving everything. You may ask, how complex is an algorithm to qualify as consciousness?This does have practical benefits for our understanding of when the wave function collapses!But this is likely to be another problem, like the famous paradox: one grain of sand landed is not a sand pile, two grains of sand landed is not a sand pile, but a hundred thousand grains of sand will definitely be a sand pile.So, which grain of sand will form a sand pile when it hits the ground?Scientists usually don't bother to answer this kind of ambiguity. Just like arguing whether cats or E. coli are conscious, we are still at a loss about wave functions! Of course, there are also some more extreme views that any system that executes some kind of algorithm can be regarded as having some degree of consciousness!Take the compass, for example, it will be argued that it likes to point south, and when it is set out of order, it tries to avoid this state out of disgust, and returns to the state it likes.In this rather pantheistic view, everything is conscious, in varying degrees.Consciousness, to put it simply, is a systematic algorithm that likes those outputs with high probability and hates those with low probability.An amoeba with phototaxis is also conscious, but the complexity of its consciousness is many times lower than ours. You may not believe this statement, but once you admit that consciousness is just an arrangement pattern on the basis of matter, it is difficult for you to deny some of the strange properties we mentioned.Even to the dreaded question of whether it is possible for consciousness to persist after death, our answer should be, in principle, yes!That's like asking, does the Ninth Symphony live on after the concert?Obviously, as long as we keep the arrangement information, we can use different methods to reproduce it concretely at any time (there is no shortage of carbon atoms or hydrogen atoms at any time).Of course, before our technical ability is not yet able to obtain all the combined information and retain them (maybe we will never have this technology), people will naturally lose consciousness after death, just like burning all the music scores after a concert, This piece of music is naturally lost. You may have been dumbfounded, but our statement bases consciousness on a completely objective and materialistic basis, and it is actually the least pretentiously mysterious one!Consciousness is not an independent existence, but an objective property manifested when the system is complex to a certain extent.Although it is a combination mechanism, it cannot be manifested without a specific substance (for the time being, the physical body is the only possibility).Just as software cannot run without hardware, the embodiment of consciousness cannot be separated from matter.If we were forced to search for a consciousness independent of matter, we would go too far. Of course, trying to convince a dualistic public that the soul or consciousness is just an arrangement and collective behavior of a large number of neurons will come as a surprise.It is also a difficult task for thorough materialists to try to convince them that consciousness as a specific arrangement of information can be preserved for a long time and reproduced on different platforms.Psychologist and neuroscientist Francis Crick has to call this claim the astonishing hypothesis (see "The Astonishing Hypothesis: A Scientific Quest for the Soul").But for most scientists, this is perhaps a natural inference.Of course, some people think that consciousness or soul is not an objective by-product created by complexity, it may not be able to be compared with algorithms, and it does have some kind of active effect!This includes Roger of Oxford University.Roger Penrose, if you are interested in understanding his views, you can read his book "The Emperor's New Mind". three What do we gain from our dizzying circle back at the problem of consciousness?Have we figured out when the cat's quantum state collapses?Have we figured out exactly how consciousness acts on the wave function?There seems to be none, but there are more questions: If consciousness is just a manifestation of the complexity of the brain, how does this delicate structure specifically affect the wave function?Can we already assume that a sufficiently complex computer also has the ability to collapse the wave function?What confuses us instead is that it seems like this is a dead end.The wave function of the electron is a physical law of nature at a most fundamental level, and as we have already discussed, consciousness The rule followed is the overall effect that can only be manifested by a combination of a large number of atoms, and it is likely to be at a very high level.Just as you cannot use the grammatical rules of words and sentences to deal with the plot of a novel, using wave functions and consciousness to connect each other seems to be a level of confusion, just like someone trying to use Newton's laws to explain the rules of economics. If consciousness makes everything break away from the quantum superposition state and become a real reality, then we can't help but ask a natural question: what is the state of intelligent life before it has evolved and there is no consciousness in this universe? Woolen cloth?Could it be that the appearance of the first conscious creature made the history of the universe from creation to that moment a reality in an instant?難道說智慧的參與可以在那一刻改變過去，而這個過去甚至包含了它自身的演化歷史？ 一九七九年是愛因斯坦誕辰一百周年，在他生前工作的普林斯頓召開了一次紀念他的討論會。在會上，愛因斯坦的同事，也是玻爾的密切合作者之一約翰．惠勒（John Wheeler）提出了一個相當令人吃驚的構想，也就是所謂的延遲實驗（delayed choice experiment）。在前面的章節裡，我們已經對電子的雙縫干涉非常熟悉了，根據哥本哈根解釋，當我們不去探究電子到底通過了哪條縫，它就同時通過雙縫而產生干涉，反之，它就確實地通過一條縫而順便消滅干涉圖紋。惠勒通過一個戲劇化的思維實驗指出，我們可以延遲電子的這一決定，使得它在已經實際通過了雙縫螢幕之後，再來選擇究竟是通過了一條縫還是兩條！ 這個實驗的基本思路是，用塗著半鍍銀的反射鏡來代替雙縫。一個光子有一半可能通過反射鏡，一半可能被反射，這是一個量子隨機過程，跟它選擇雙縫還是單縫本質上是一樣的。把反射鏡和光子入射途徑擺成四十五度角，那麼它一半可能直飛，另一半可能被反射成九十度角。但是，我們可以通過另外的全反射鏡，把這兩條分開的岔路再交匯到一起。在終點觀察光子飛來的方向，我們可以確定它究竟是沿著哪一條道路飛來的。 但是，我們也可以在終點處再插入一塊呈四十五度角的半鍍銀反射鏡，這又會造成光子的自我干涉。如果我們仔細安排位相，我們完全可以使得在一個方向上的光子呈反相而相互抵消，而在一個確定的方向輸出。這樣的話我們每次都得到一個確定的結果（就像每次都得到一個特定的干涉條紋一樣），根據量子派的說法，此時光子必定同時沿著兩條途徑而來！ 總而言之，如果我們不在終點處插入半反射鏡，光子就沿著某一條道路而來，反之它就同時經過兩條道路。現在的問題是，是不是要在終點處插入反射鏡，這可以在光子實際通過了第一塊反射鏡，已經快要到達終點時才決定。我們可以在事情發生後再來決定它應該怎樣發生！如果說我們是這齣好戲的導演的話，那麼我們的光子在其中究竟扮演了什麼角色，這可以等電影拍完以後再由我們決定！ 雖然聽上去古怪，但這卻是哥本哈根派的一個正統推論！惠勒後來引玻爾的話說，任何一種基本量子現象只在其被記錄之後才是一種現象，我們是在光子上路之前還是途中來做出決定，這在量子實驗中是沒有區別的。歷史不是確定和實在的除非它已經被記錄下來。更精確地說，光子在通過第一塊透鏡到我們插入第二塊透鏡這之間到底在哪裡，是個什麼，是一個無意義的問題，我們沒有權利去談論它，它不是一個客觀真實！惠勒用那幅著名的龍圖來說明這一點，龍的頭和尾巴（輸入輸出）都是確定的清晰的，但它的身體（路徑）卻是一團迷霧，沒有人可以說清。 在惠勒的構想提出五年後，馬里蘭大學的卡洛爾．阿雷（Carroll O Alley）和其同事當真做了一個延遲實驗，其結果真的證明，我們何時選擇光子的模式，這對於實驗結果是無影響的（和玻爾預言的一樣，和愛因斯坦的相反！），與此同時慕尼克大學的一個小組也作出了類似的結果。 這樣稀奇古怪的事情說明了什麼呢？ 這說明，宇宙的歷史，可以在它實際發生後才被決定究竟是怎樣發生的！在薛定諤的貓實驗裡，如果我們也能設計某種延遲實驗，我們就能在實驗結束後再來決定貓是死是活！比如說，原子在一點鐘要麼衰變毒死貓，要麼就斷開裝置使貓存活。但如果有某個延遲裝置能夠讓我們在二點鐘來延遲決定原子衰變與否，我們就可以在二點鐘這個未來去實際決定貓在一點鐘的死活！ 這樣一來，宇宙本身由一個有意識的觀測者創造出來也不是什麼不可能的事情。雖然宇宙的行為在道理上講已經演化了幾百億年，但某種延遲使得它直到被一個高級生物所觀察才成為確定。我們的觀測行為本身參與了宇宙的創造過程！這就是所謂的參與性宇宙模型（The Prticipatory Universe）。宇宙本身沒有一個確定的答案，而其中的生物參與了這個謎題答案的構建本身！ 這實際上是某種增強版的人擇原理（anthropic principle）。人擇原理是說，我們存在這個事實本身，決定了宇宙的某些性質為什麼是這樣的而不是那樣的。也就是說，我們討論所有問題的前提是：事實上已經存在了一些像我們這樣的智慧生物來討論這些問題。我們回憶一下笛卡兒的第一原理：不管我懷疑什麼也好，有一點我是不能懷疑的，那就是我在懷疑本身。我思故我在！類似的原則也適用於人擇原理：不管這個宇宙有什麼樣的性質也好，它必須要使得智慧生物可能存在於其中，不然就沒有人來問宇宙為什麼是這樣的？這個問題了。隨便什麼問題也好，你首先得保證有一個人來問問題，不然就沒有意義了。 舉個例子，目前宇宙似乎是在以一個恰到好處的速度在膨脹。只要它膨脹得稍稍快一點，當初的物質就會四散飛開，而無法凝聚成星系和行星。反過來，如果稍微慢一點點，引力就會把所有的物質都吸到一起，變成一團具有驚人的密度和溫度的大雜燴。而我們正好處在一個臨界速度上，這才使得宇宙中的各種複雜結構和生命的誕生成為可能。這個速度要準確到什麼程度呢？大約是10^55分之一，這是什麼概念？你從宇宙的一端瞄準並打中在另一端的一隻蒼蠅（相隔三百億光年），所需準確性也不過10^30分之一。類似的驚人準確的宇宙常數，我們還可以舉出幾十個。 我們問：為什麼宇宙以這樣一個速度膨脹？人擇原理的回答是：宇宙必須以這樣一個速度膨脹，不然就沒有你來問這個問題了。因為只有以這樣一個速度膨脹，生命和智慧才可能誕生，從而使問題的提出成為可能！顯然不會有人問：為什麼宇宙以一米／秒的速度膨脹？因為以這個速度膨脹的宇宙是一團火球，不會有人在那裡存在。 參與性宇宙是增強的人擇原理，它不僅表明我們的存在影響了宇宙的性質，更甚，我們的存在創造了宇宙和它的歷史本身！可以想像這樣一種情形：各種宇宙常數首先是一個不確定的疊加，只有被觀測者觀察後才變成確定。但這樣一來它們又必須保持在某些精確的範圍內，以便創造一個好的環境，令觀測者有可能在宇宙中存在並觀察它們！這似乎是一個邏輯迴圈：我們選擇了宇宙，宇宙又創造了我們。這件怪事叫做自指或者自啟動（self-exciting），意識的存在反過來又創造了它自身的過去！ 請各位讀者確信，我寫到這裡已經和你們一樣頭大如鬥，嗡嗡作響不已。這個理論的古怪差不多已經超出了我們可以承受的心理極限，我們在意識這裡已經筋疲力盡，無力繼續前進了。對此感到不可接受的也絕不僅僅是我們這些門外漢，當時已經大大有名的約翰．貝爾（John Bell，我們很快就要講到他）就嘟囔道：難道億萬年來，宇宙波函數一直在等一個單細胞生物的出現，然後才坍縮？還是它還得多等一會兒，直到出現了一個有資格的，有博士學位的觀測者？要是愛因斯坦在天有靈，看到有人在他的誕辰紀念上發表這樣古怪的，違反因果律的模型，不知作何感想？ 就算從哥本哈根解釋本身而言，意識似乎也走得太遠了。大多數主流的物理學家仍然小心謹慎地對待這一問題，持有一種更為正統的哥本哈根觀點。然而所謂正統觀念其實是一種鴕鳥政策，它實際上就是把這個問題拋在一邊，簡單地假設波函數一觀測就坍縮，而對它如何坍縮，何時坍縮，為什麼會坍縮不聞不問。量子論只要在實際中管用就行了，我們更為關心的是一些實際問題，而不是這種玄之又玄的闡述！ 但是，無論如何，當新物理學觸及到這樣一個困擾了人類千百年的本體問題核心後，這無疑也激起了許多物理學家們的熱情和好奇心。的確有科學家沿著維格納的方向繼續探索，並論證意識在量子論解釋中所扮演的地位。這裡面的代表人物是伯克利勞倫斯國家物理實驗室的美國物理學家亨利．斯塔普（Henry Stapp），他自一九九三年出版了著作《精神，物質和量子力學》（Mind, Matter, and Quantum Mechanics）之後，便一直與別的物理學家為此辯論至今（大家如果有興趣，可以去他的網頁http:／／www-physics.lbl.gov／~stapp／stappfiles.html看看他的文章）。這種說法也獲得了某些人的支持，去年，也就是二○○三年，還有人（阿姆斯特丹大學的Dick J. Bierman）宣稱用實驗證明了人類意識的確使波函數坍縮。不過這一派的支持者也始終無法就意識建立起有說服力的模型來，對於他們的宣稱，我們在心懷懼意的情況下最好還是採取略為審慎的保守態度，看看將來的發展如何再說。 我們沿著哥本哈根派開拓的道路走來，但或許是走得過頭了，誤入歧途，結果發現在盡頭藏著一隻叫做意識的怪獸讓我們驚恐不已。這已經不是玻爾和哥本哈根派的本意，我們還是退回到大多數人站著的地方，看看還有沒有別的道路可以前進。嗯，我們發現的確還有幾條小路通向未知的盡頭，讓我們試著換幾條道路走走，看看它是不是會把我們引向光明的康莊大道。不過讓我們先在原來的那條路上做好記號，醒目地寫下意識怪獸的字樣並打上驚嘆號以警醒後人。好，現在我們出發去另一條道路探險，這條小道看上去籠罩在一片濃霧繚繞中，並且好像在遠處分裂成無限條岔路。我似乎已經有不太美妙的預感，不過還是讓我們擦擦汗，壯著膽子前去看看吧。 飯後閒話：海森堡和德國原子彈計畫（七） 海森堡不久便從報上得知了炸彈的實際重量：二百千克，核心爆炸物只有幾千克。他顯得煩躁不已，對自己的估計錯在何處感到非常納悶。他對哈特克說：他們是怎麼做到的？如果我們這些曾經幹過同樣工作的教授們連他們（理論上）是怎麼做到的都搞不懂，我感到很丟臉。德國人討論了多種可能性，但一直到十四號，事情才起了決定性的轉變。 到了八月十四號，海森堡終於意識到了正確的計算方法（也不是全部的），他在別的科學家面前進行了一次講授，並且大體上得到了相對正確的結果。他的結論是六.二釐米半徑十六千克！而在他授課時，別的科學家對此表現出一無所知，他們的提問往往幼稚可笑。德國人為他們的驕傲自大付出了最終的代價。 對此事的進一步分析可以在一九九八年出版的《海森堡與納粹原子彈計畫》（Paul Rose）和二○○○年出版的《希特勒的鈾俱樂部》（Jeremy Bernstein）二書中找到非常詳盡的資料。大體上說，近幾年來已經比較少有認真的歷史學家對此事表示異議，至少在英語世界是如此。 關於一九四一年海森堡和玻爾在哥本哈根的會面，也就是《哥本哈根》一劇中所探尋的那個場景，我們也已經有了突破性的進展。關於這場會面的討論是如此之多之熱烈，以致玻爾的家屬提前十年（原定保密五十年）公佈了他的一些未寄出的信件，其中談到了一九四一年的會面（我們知道，玻爾生前幾乎從不談起這些），為的是不讓人們再誤解它們的內容。這些信件於二○○二年二月六日在玻爾的官方網站（http:／／www.nbi.dk ）上公佈，引起一陣熱潮，使這個網站的日點擊率從五十左右猛漲至一萬五千。 在這些首次被披露的信件中，我們可以看到玻爾對海森堡來訪的態度。這些信件中主要的一封是在玻爾拿到Robert Jungk的新書《比一千個太陽更明亮》之後準備寄給海森堡的，我們在前面已經說到，這本書讚揚了德國人在原子彈問題上表現出的科學道德（基於對海森堡本人的採訪！）。玻爾明確地說，他清楚地記得當年的每一句談話，他和妻子瑪格麗特都留下了強烈的印象：海森堡和魏紮克努力地試圖說服玻爾他們，德國的最終勝利不可避免，因此採取不合作態度是不明智的。玻爾說，海森堡談到原子彈計畫時，給他留下的唯一感覺就是在海森堡的領導下，德國正在按部就班地完成一切。他強調說，他保持沉默，不是海森堡後來宣稱的因為對原子彈的可行性感到震驚，而是因為德國在致力於製造原子彈！玻爾顯然對海森堡的以及Jungk的書造成的誤導感到不滿。在別的信件中，他也提到，海森堡等人對別的丹麥科學家解釋說，他們對德國的態度是不明智的，因為德國的勝利十分明顯。玻爾似乎曾經多次想和海森堡私下談一次，以澄清關於這段歷史的誤解，但最終他的信件都沒有發出，想必是思量再三，還是覺得恩恩怨怨就這樣讓它去吧。 這些檔可以在http:／／www.nbi.dk／NBA／papers／docs／cover.html 找到。 容易理解，為什麼多年後玻爾夫人再次看到海森堡和魏紮克時，憤怒地對旁人說：不管別人怎麼說，那不是一次友好的訪問！ 這些檔也部分支援了海森堡的傳記作者Cassidy在二○○○年的Physics Today雜誌上的文章（這篇文章是針對《哥本哈根》一劇而寫的）。Cassidy認為海森堡當年去哥本哈根是為了說服玻爾德國佔領歐洲並不是最壞的事（至少比蘇聯佔領歐洲好），並希望玻爾運用他的影響來說服盟國的科學家不要製造原子彈。 當然仍然有為海森堡辯護的人，主要代表是他的一個學生Klaus Gottstein，當年一起同行的魏紮克也仍然認定，是玻爾犯了一個可怕的記憶錯誤。 不管事實怎樣也好，海森堡的真實形象也許也就是一個普通人毫無準備地被捲入戰爭歲月裡去的普通德國人。他不是英雄，也不是惡棍，他對於納粹的不認同態度有目共睹，他或許也只是身不由己地做著一切戰爭年代無奈的事情。儘管歷史學家的意見逐漸在達成一致，但科學界的態度反而更趨於對他的同情。Rice大學的Duck和Texas大學的Sudarshan說：再偉大的人也只有十％的時候是偉大的重要的只是他們曾經做出過原創的，很重要，很重要的貢獻所以海森堡在他的後半生是不是一個完人對我們來說不重要，重要的是他創立了量子力學。 在科學史上，海森堡的形象也許一直還將是那個在赫爾格蘭島日出時分為物理學帶來了黎明的大男孩吧？ (end) Four 吃一塹，長一智，我們總結一下教訓。之所以前頭會碰到意識這樣的可怕東西，關鍵在於我們無法準確地定義一個觀測者！一個人和一台照相機之間有什麼分別，大家都說不清道不明，於是給意識乘隙而入。而把我們逼到不得不去定義什麼是觀測者這一步的，則是那該死的坍縮。一個觀測者使得波函數坍縮？這似乎就賦予了所謂的觀測者一種在宇宙中至高無上的地位，他們享有某種超越基本物理定律的特權，可以創造一些真正奇妙的事情出來。 真的，追本朔源，罪魁禍首就在曖昧的波函數坍縮那裡了。這似乎像是哥本哈根派的一個魔咒，至今仍然把我們陷在其中不得動彈，而物理學的未來也在它的詛咒下顯得一片黯淡。拿康奈爾大學的物理學家科特．戈特弗雷德（Kurt Gottfried）的話來說，這個坍縮就像是一個美麗理論上的一道醜陋疤痕，它雲遮霧繞，似是而非，模糊不清，每個人都各持己見，為此吵嚷不休。怎樣在觀測者和非觀測者之間劃定界限？薛定諤貓的波函數是在我們打開箱子的那一剎那坍縮？還是它要等到光子進入我們的眼睛並在視網膜上激起電脈衝信號？或者它還要再等一會兒，一直到這信號傳輸到大腦皮層的某處並最終成為一種精神活動時才真正坍縮？如果我們在這上面大鑽牛角尖的話，前途似乎不太美妙。 那麼，有沒有辦法繞過這所謂的坍縮和觀測者，把智慧生物的介入從物理學中一腳踢開，使它重新回到我們所熟悉和熱愛的軌道上來呢？讓我們重溫那個經典的雙縫困境：電子是穿過左邊的狹縫呢，還是右邊的？按照哥本哈根解釋，當我們未觀測時，它的波函數呈現兩種可能的線性疊加。而一旦觀測，則在一邊出現峰值，波函數坍縮了，隨機地選擇通過了左邊或者右邊的一條縫。量子世界的隨機性在坍縮中得到了最好的體現。 要擺脫這一困境，不承認坍縮，那麼只有承認波函數從未選擇左還是右，它始終保持在一個線性疊加的狀態，不管是不是進行了觀測。可是這又明顯與我們的實際經驗不符，因為從未有人在現實中觀察到同時穿過左和右兩條縫的電子，也沒有人看見過同時又死又活的貓（半死不活，奄奄一息的倒有不少）。事到如今，我們已經是騎虎難下，進退維谷，哥本哈根的魔咒已經纏住了我們，如果我們不鼓起勇氣，作出最驚世駭俗的假設，我們將註定困頓不前。 如果波函數沒有坍縮，則它必定保持線性疊加。電子必定是左／右的疊加，但在現實世界中從未觀測到這種現象。 有一個狂想可以解除這個可憎的詛咒，雖然它聽上去真的很瘋狂，但慌不擇路，我們已經是nothing to lose。失去的只是桎梏，但說不定贏得的是整個世界呢？ Yes!電子即使在觀測後仍然處在左／右的疊加，但是，我們的世界也只不過是疊加的一部分！當電子穿過雙縫後，處於疊加態的不僅僅是電子，還包括我們整個的世界！也就是說，當電子經過雙縫後，出現了兩個疊加在一起的世界，在其中的一個世界裡電子穿過了左邊的狹縫，而在另一個裡，電子則通過了右邊！ 波函數無需坍縮，去隨機選擇左還是右，事實上兩種可能都發生了！只不過它表現為整個世界的疊加：生活在一個世界中的人們發現在他們那裡電子通過了左邊的狹縫，而在另一個世界中，人們觀察到的電子則在右邊！量子過程造成了兩個世界！這就是量子論的多世界解釋（Many Worlds Interpretation，簡稱MWI）。 要更好地瞭解MWI，不得不從它的創始人，一生頗有傳奇色彩的休．埃弗萊特（Hugh Everett III，他的祖父和父親也都叫Hugh Everett，因此他其實是埃弗萊特三世）講起。一九三○年十一月九日，愛因斯坦在《紐約時報雜誌》上發表了他著名的文章《論科學與宗教》，他的那句名言至今仍然在我們耳邊迴響：沒有宗教的科學是跛足的，沒有科學的宗教是盲目的。兩天后，小埃弗萊特就在華盛頓出生了。 埃弗萊特對愛因斯坦懷有深深的崇敬，在他只有十二歲的時候，他就寫信問在普林斯頓的愛因斯坦一些關於宇宙的問題，而愛因斯坦還真的覆信回答了他。當他拿到化學工程的本科學位之後，他也進入了普林斯頓攻讀。一開始他進的是數學系，但他很快想方設法轉投物理。五十年代正是量子論方興未艾，而哥本哈根解釋如日中天，一統天下的時候。埃弗萊特認識了許多在這方面的物理學生，其中包括玻爾的助手Aage Peterson，後者和他討論了量子論中的觀測難題，這激起了埃弗萊特極大的興趣。他很快接觸了約翰．惠勒，惠勒鼓勵了他在這方面的思考，到了一九五四年，埃弗萊特向惠勒提交了兩篇論文，多世界理論（有時也被稱作埃弗萊特主義-Everettism）第一次亮相了。 按照埃弗萊特的看法，波函數從未坍縮，而只是世界和觀測者本身進入了疊加狀態。當電子穿過雙縫後，整個世界，包括我們本身成為了兩個獨立的疊加，在每一個世界裡，電子以一種可能出現。但不幸的是，埃弗萊特用了一個容易誤導和引起歧義的詞分裂（splitting），他打了一個比方，說宇宙像一個阿米巴變形蟲，當電子通過雙縫後，這個蟲子自我裂變，繁殖成為兩個幾乎一模一樣的變形蟲。唯一的不同是，一個蟲子記得電子從左而過，另一個蟲子記得電子從右而過。 惠勒也許意識到了這個用詞的不妥，他在論文的空白裡寫道：分裂？最好換個詞。但大多數物理學家並不知道他的意見。也許，惠勒應該搞得戲劇化一點，比如寫上我想到了一個絕妙的用詞，可惜空白太小，寫不下。在很長的一段時間裡，埃弗萊特的理論被人們理解成：當電子通過雙縫的時候，宇宙神奇地分裂成了兩個獨立的宇宙，在一個裡面電子通過左縫，另一個相反。這樣一來，宇宙的歷史就像一條岔路，每進行一次觀測，它就分岔成若干小路，每條路對應於一個可能的結果。而每一條岔路又隨著繼續觀察而進一步分裂，直至無窮。但每一條路都是實在的，只不過它們之間無法相互溝通而已。 假設我們觀測雙縫實驗，發現電子通過了左縫。其實當我們觀測的一瞬間，宇宙已經不知不覺地分裂了，變成了幾乎相同的兩個。我們現在處於的這個叫做左宇宙，另外還有一個右宇宙，在那裡我們將發現電子通過了右縫，但除此之外一切都和我們這個宇宙完全一樣。你也許要問：為什麼我在左宇宙裡，而不是在右宇宙裡？這種問題顯然沒什麼意義，因為在另一個宇宙中，另一個你或許也在問：為什麼我在右宇宙，而不是左宇宙裡？觀測者的地位不再重要，因為無論如何宇宙都會分裂，實際上所有的結果都會出現，量子過程所產生的一切可能都對應於相應的一個宇宙，只不過在大多數蠻荒宇宙中，沒有智慧生物來提出問題罷了。 這樣一來，薛定諤的貓也不必再為死活問題困擾。只不過是宇宙分裂成了兩個，一個有活貓，一個有死貓罷了。對於那個活貓的宇宙，貓是一直活著的，不存在死活疊加的問題。對於死貓的宇宙，貓在分裂的那一刻就實實在在地死了，不要等人們打開箱子才坍縮，從而蓋棺定論。 從宇宙誕生以來，已經進行過無數次這樣的分裂，它的數量以幾何級數增長，很快趨於無窮。我們現在處於的這個宇宙只不過是其中的一個，在它之外，還有非常多的其他的宇宙。有些和我們很接近，那是在家譜樹上最近剛剛分離出來的，而那些從遙遠的古代就同我們分道揚鑣的宇宙則可能非常不同。也許在某個宇宙中，小行星並未撞擊地球，恐龍仍是世界主宰。在某個宇宙中，埃及豔后克婁派特拉的鼻子稍短了一點，沒有教愷撒和安東尼怦然心動。那些反對歷史決定論的鼻子派歷史學家一定會對後來的發展大感興趣，看看是不是真的存在歷史蝴蝶效應。在某個宇宙中，格魯希沒有在滑鐵盧遲到，而希特勒沒有在敦克爾克前下達停止進攻的命令。而在更多的宇宙裡，因為物理常數的不適合，根本就沒有生命和行星的存在。 嚴格地說，歷史和將來一切可能發生的事情，都已經實際上發生了，或者將要發生。只不過它們在另外一些宇宙裡，和我們所在的這個沒有任何物理接觸。這些宇宙和我們的世界互相平行，沒有聯繫，根據奧卡姆剃刀原理，這些奇妙的宇宙對我們都是沒有意義的。多世界理論有時也稱為平行宇宙（Parallel Universes）理論，就是因為這個道理。 宇宙的分裂其實應該算是一種誤解，不過直到現在，大多數人，包括許多物理學家仍然是這樣理解埃弗萊特的！這樣一來，這個理論就顯得太大驚小怪了，為了一個小小的電子從左邊還是右邊通過的問題，我們竟然要興師動眾地牽涉整個宇宙的分裂！許多人對此的評論是殺雞用牛刀。愛因斯坦曾經有一次說：我不能相信，僅僅是因為看了它一眼，一隻老鼠就使得宇宙發生劇烈的改變。這話他本來是對著哥本哈根派說的，不過的確代表了許多人的想法：用犧牲宇宙的代價來迎合電子的隨機選擇，未免太不經濟廉價，還產生了那麼多不可觀察的平行宇宙的廢料。MWI後來最為積極的鼓吹者之一，德克薩斯大學的布萊斯．德威特（Bryce S. DeWitt）在描述他第一次聽說MWI的時候說：我仍然清晰地記得，當我第一次遇到多世界概念時所受到的震動。一百個略有缺陷的自我拷貝，都在不停地分裂成進一步的拷貝，而最後面目全非。這個想法是很難符合常識的。這是一種徹頭徹尾的精神分裂症對於我們來說，也許接受意識，還要比相信宇宙分裂來得容易一些！ 不難想像，埃弗萊特的MWI在一九五七年作為博士論文發表後，雖然有惠勒的推薦和修改，在物理界仍然反應冷淡。埃弗萊特曾經在一九五九年特地飛去哥本哈根見到玻爾，但玻爾根本就不想討論任何對於量子論新的解釋，也不想對此作什麼評論，這使他心灰意冷。作為玻爾來說，他當然一生都堅定地維護著哥本哈根理論，對於五十年代興起的一些別的解釋，比如玻姆的隱函數理論（我們後面要談到），他的評論是這就好比我們希望以後能證明2×2＝5一樣。在玻爾臨死前的最後的訪談中，他還在批評一些哲學家，聲稱：他們不知道它（互補原理）是一種客觀描述，而且是唯一可能的客觀描述。 受到冷落的埃弗萊特逐漸退出物理界，他先供職於國防部，後來又成為著名的Lambda公司的創建人之一和主席，這使他很快成為百萬富翁。但他的見解後來被人稱為二十世紀隱藏得最深的秘密之一的卻長期不為人們所重視。直到七十年代，德威特重新發掘了他的多世界解釋並在物理學家中大力宣傳，MWI才開始為人所知，並迅速成為熱門的話題之一。如今，這種解釋已經擁有大量支持者，坐穩哥本哈根解釋之後的第二把交椅，並大有後來居上之勢。為此，埃弗萊特本人曾計畫復出，重返物理界去做一些量子力學方面的研究工作，但他不幸在一九八二年因為心臟病去世了。 在惠勒和德威特所在的德州大學，埃弗萊特是最受尊崇的人之一。當他應邀去做量子論的演講時，因為他的煙癮很重，被特別允許吸煙。這是那個禮堂有史以來唯一的一次例外。 five 針對人們對MWI普遍存在的誤解，近來一些科學家也試圖為其正名，澄清這種稀奇古怪的宇宙分裂並非MWI和埃弗萊特的本意（如Tegmark一九九八），我們在這裡也不妨稍微講一講。當然要準確地描述它需要用到非常複雜的數學工具和數學表達，我們的史話還是以史為本，在理論上儘量淺顯一點。這裡只是和諸位進行一點最膚淺的探討，用到的數學保證不超過中學水準，希望各位看官也不要望而卻步。 首先我們要談談所謂相空間的概念。每個讀過中學數學的人應該都建立過二維的笛卡兒平面：畫一條x軸和一條與其垂直的y軸，並加上箭頭和刻度。在這樣一個平面系統裡，每一個點都可以用一個包含兩個變數的座標（x,y）來表示，例如（1,2），或者（4.3,5.4），這兩個數字分別表示該點在x軸和y軸上的投影。當然，並不一定要使用直角坐標系統，也可以用極座標或者其他坐標系統來描述一個點，但不管怎樣，對於二維平面來說，用兩個數字就可以唯一地指明一個點了。如果要描述三維空間中的一個點，那麼我們的座標裡就要有三個數字，比如（1,2,3），這三個數字分別代表該點在三個互相垂直的維度方向的投影。 讓我們擴展一下思維：假如有一個四維空