Chapter 14 Chapter 10 Inequality-1

one This trip in Wonderland of the Many Worlds may confuse everyone, but like the long obscure poem Jabberwocky that Alice reads in the mirror, it should undoubtedly leave a strong impression.Indeed, imagine ourselves splitting over time into projections in multiple worlds, and these doubles grow geometrically to infinity.Such a wonderful scene really adds a bit of irony to the universe in which we live.Some people may think that there is nothing more lovely than "consciousness" in such a model. What do Everett and those scientists who support many worlds value in it? However, the benefits of MWI are also obvious. Its greatest feat is to kick the "observer", which is in the way, out of physics.Now the entire universe just evolves strictly according to the wave function, and there is no need to humbly ask for help from the "observer" or the choice of "intelligent creatures".Physicists no longer have to worry about the miraculous "collapse" and put ugly patches on the beautiful theoretical framework to explain the mechanism of the R process.Our poor Schrödinger cat finally got rid of the torment of being dead and alive, and instead lived happily (one dead and one alive) in two different worlds.

The important thing is that nature can make its own decisions again. It doesn't have to linger in the shadow of the "observer" until a master with "consciousness" appreciates an "observation" before it can become a reality, otherwise it has to Buried a lifetime in the superposition of probability waves.In MWI, the universe itself becomes the sole master again, and any observer is a part of it, which is split and projected into various worlds as it evolves.The splitting of the universe only depends on the introduction of the environment and the irreversible amplification process. Such an objective picture is still in line with the traditional taste of most scientists. At least it will not drive people crazy like the Copenhagen School, so that they can't sleep well.

A by-product of MWI is that it falls back on the determinism of classical theory.Because as far as the Schrödinger equation itself is concerned, it is decisive, that is to say, given the state at a certain time t, we can deduce it from both positive and negative directions to obtain the state of the system at any time.In this sense, the "passage" of time is nothing but an illusion!In addition, since there is no "collapse" or R process, but only a definite U process, "randomness" will no longer be messed around with each other.In this sense, God does not play dice anymore. He stands at a high angle and has a bird’s-eye view of the wave function of the entire universe, so everything is still under control: the universe as a whole is still strictly evolving according to the definite Schrödinger equation.Nor does the electron have to roll a dice and make a random choice to go through a slit: it just goes through a slit in each of the two worlds at the same time.However, for us ordinary people, because we are entangled in the world of mortals, our inherent limitations confuse our eyes, so that we can only see the shadow of a certain world.And in this projection, reality is random, jumpy, surprising.

(* By the way, let me clarify the wording problem here. For MWI, people generally like to call the multiple branches "World" (World), and their sum as "Universe" (Universe). In this way, there is only one universe. The Schrödinger equation develops, and the "worlds" are many, splitting apart over time.But some people like to call each branch "universe" and their sum as "multiverse", such as the famous multi-universe physicist David Deutsch.This is just a matter of name, multi-world or multi-universe, they refer to the same meaning. ) However, although MWI can also be justified, in any case, there are many universes in reality, which sounds too weird to ordinary people.Even for philosophically elegant reasons (especially Occam's razor), people feel that MWI should be taken with caution: it's not very admirable to drag the entire universe down for the sake of a small electron.But among cosmologists, the MWI is a popular and well-received idea.In particular, it does not require the special status of "observer", but attributes the history and evolution of the universe to itself, which makes cosmologists who suffer from the Copenhagen interpretation and the curse of participatory models feel very sympathetic .Generally speaking, physicists who are engaged in quantum gravity (such as superstring) and cosmology prefer MWI, and if the scope is expanded to general "scientists", the proportion of people who think it is weird and unacceptable is greatly Increase.Among the supporters of many worlds, there are Feynman, Weinberg, and Hawking that we are familiar with. Some people also include Murray Gell-Mann, the founder of the quark model and the winner of the Nobel Prize in Physics in 1969. , but as one of the founders of the "consistent history" interpretation of quantum theory, we still leave him to the corresponding chapter of the history, although this interpretation can actually be regarded as an enhanced version of MWI.

Those who expressed direct opposition to MWI include Bell, Stein, Kent, and Penrose.Some of them, such as Penrose, are also engaged in gravity, which can be regarded as very unique. However, for the readers of our history, maybe you don’t need to pay attention to the different philosophical tastes of cosmologists or other scientists. The important thing is that now we have a Copenhagen explanation and a multi-universe explanation. Only then can we know, which one should we believe?It is normal for people to have different aesthetic viewpoints in life. For example, you like Beethoven and I like Mozart, you like Li Bai and I like Du Fu. It is not surprising, but science, especially natural science, is different.Isn't science great because it can become the unique law of the universe without being influenced by subjective will?Economists may fight each other for various models, but the ultimate goal of physics is not to be practical, but to explore the deep hidden mysteries of nature.It must treat all kinds of assumptions with the strictest attitude, pick out those unqualified and remove them from its own system, so as to maintain its immortal vitality forever.The history of science should be a process of constantly examining oneself, constantly taking practice as the only criterion, and constantly climbing towards that Platonic ideal.For this, it must provide a screening mechanism to kick out those theories that look beautiful but do not conform to the facts. This has become an important sign that it is different from philosophy or religion.

Perhaps we can accept the opinion of the famous and controversial philosopher of science, Karl Popper, and draw the dividing line between science and metaphysics at "falsifiability".That is, a scientific claim must be falsified.For example, I said: "There are no white crows in the world." This is a statement that conforms to the "scientific method", because as long as you really find a white crow, you can prove my mistake and overthrow my theory.But, as in the example we gave earlier, if I claim, "I have an invisible flying dragon in my garage," that's not a scientific claim, because you can't prove me wrong anyway.If we accept these unprovable assertions as science, then there will be many funny things in "science": in addition to flying dragons, there will also be three-headed dogs, eight-legged donkeys, Chinese-speaking monkeys... everything is amazing up.Anyway, you can't prove that a three-headed dog "doesn't exist", can you?

If Hertz hadn't discovered sparks caused by electromagnetic waves in his 1887 experiment, Maxwell's theory would have been disproved.If Eddington hadn't detected the displacement of those stars during the 1919 eclipse, then Einstein's theory of relativity would have been disproved (although the experiment is not without its problems today).If Wu Jianxiong and others did not find the expected effect in the experiment in 1956-1957, then Yang and Li's assumption of parity violation under weak action would be falsified.No matter at that time or in the future, you can design some experiments. If the result is so-and-so, you can prove that the theory is incorrect. This is the falsifiability of science.Of course, some concepts have been falsified, such as the flat earth theory, phlogiston, and light ether, but no matter what, we can at least say that the expressions they adopt conform to the "scientific" method.

Others, such as "God", are hard to say. There is no experiment that can prove that God "does not exist" (it is not necessary to prove that it does not exist, but there is no such possibility).So we might as well kick it out of the realm of science and leave it to religious buffs to ponder. Going back to the history, in order to make our two explanations conform to Popper's principle, can we design an experiment to identify which one is credible and which one is false?Copenhagen explained that the observer caused the wave function to collapse, and MWI said that the universe split, but, for us in reality, there is no observable difference!Anyway, the fact must be that the electrons appear somewhere on the screen "seemingly" randomly according to the probability of the wave function, doesn't it?Even if we observe 1 million times, we still can't tell which one is wrong, Copenhagen or many worlds!

Since the 1970s, the theory of decoherence (decoherence) proposed, developed, and popularized by Dieter Zeh, Wojciech H Zurek, Gell-Mann and others seems to have a huge impact on Everett’s multiverse explanation. s help.As we have discussed a little earlier, this theory explains how an object transitions from a microscopic superposition state to a macroscopic definite state: it mainly involves the macroscopic nature of objects such as detectors or cats, that is, compared to electrons The number of degrees of freedom is much greater, and their interaction with the environment.This theory is a duck to water in MWI. It explains why the world does not show superposition on a large scale, and explains how the world "splits", which were not explained by MWI before.Broadly speaking, when an instrument observes a system, it also becomes entangled with its environment, causing the instrument's superposition state to rapidly degenerate into a classical correlation.We say this very roughly, and it can in fact be proved mathematically.If we use the system's so-called "density matrix" (Desity Matrix) to represent it, then the elements on the diagonal of this matrix represent the classical probability states, and other places represent the correlation between these states.We will see that when decoherence occurs, the density matrix of the instrument or cat rapidly diagonalizes, making the quantum superposition property gone forever (see attached picture).This process is so fast that we don't notice it at all.

However, although decoherence theory is a powerful supplement to MWI, it cannot prove that MWI is the only explanation.Decoherence can explain why in a universe full of quantum superposition and uncertainty, the world still seems classical and "objective" when we look at the world on a daily large scale, but it cannot answer whether the wave function has always been developing normally, or whether it is Will jump from time to time.In fact, we can also use decoherence in the Copenhagen interpretation to determine the boundary between "observers" and "non-observers" - according to their respective size, or number of degrees of freedom!Those that are prone to decoherence may be more qualified to appear as observers, and the so-called observation may be just an irreversible amplification process.But in the final analysis, we are still not sure whether it is Copenhagen or multiverse!

In Popper's later years (he died in 1994), I imagine he had mixed feelings.On the one hand, some of his conclusions back then were correct. For example, quantum mechanics itself did not exclude deterministic factors (nor did it exclude indeterminism).Regarding the principle of complementarity, he was almost completely convinced by Bohr in Copenhagen, but now he can still reconsider other alternatives.On the other hand, we will also be very interested to know what Popper thinks about the status quo in which various interpretations in the field of quantum theory are side by side and can hardly be distinguished by practice. But let’s describe some interesting experiments that “strongly support” MWI, including the crazy “quantum suicide” and the currently hot quantum computer that claims to “use multiple parallel worlds to work together”. *********** After-dinner gossip: falsification and confirmation Regarding the definition of "science", the two factions of verification and falsification have been arguing endlessly. This topic is too big, and we are not interested in participating. Here are just a few casual remarks on the issue of verification and falsification. How can a proposition be stated as scientific?According to the falsificationists, it must be possible to be proven false.For example, "all crows are black", then you can prove the error of this proposition as long as you find a crow that is not black, so there is no problem with this proposition.On the contrary, if you have to "prove" to accept this assertion, it will be difficult, and in fact it is impossible!Unless you have caught all the crows, how can you know that you have caught all the crows in the world? For scientific theories, "confirmation" is almost impossible.For example, we say "the law of the universe is F=ma", what is being said here is a kind of universality, but how do you prove it?You can only "prove" this point unless you have observed all phenomena in every corner of the universe since ancient times and found no exceptions.Even so, there is no guarantee that this rule will still work in the future.In fact, almost no scientific theory can be "proven", as long as it can be proved "wrong" but has not been proved "wrong" (according to Popper, with a positive attitude towards falsification), We tentatively accept it as a sound theory.It has been admitted since Hume that a limited number of instances (no matter how many) alone can form a basis for verification. However, according to empiricists like Locke, the basis of all our knowledge comes from our experience, and the establishment of science is a kind of inductivism on experience.For example, we see the sun rising from the east every day, and it has been like this every day for thousands of years, then we should be able to "reasonably" deduce a rule from it: the sun rises from the east every day.And use it to predict that the sun will still rise from the east tomorrow.If we fall into Hume's agnosticism, then we can't talk about any "knowledge" at all, because everything tomorrow is uncertain anyway. According to inductivism, we induce a law from past phenomena, and when this phenomenon is repeated, each time it becomes another "confirmation" of this law.For example, every time the sun rises again, the certainty of the proposition "the sun rises in the east every day" is slightly confirmed again.Every time we see a black crow, the truth of the proposition "all crows are black" increases slightly again, until we encounter a crow that is not black. Most of us probably think so, but this kind of empiricism leads to very interesting results.Let's do such a reasoning. Everyone knows that the inverse of a proposition is equivalent to itself.For example, "all crows are black" can be changed to the equivalent proposition "everything that is not black is not a crow".Now if we meet a white cat, this phenomenon undoubtedly confirms the statement "everything that is not black is not a crow" (a white cat is not black, and a white cat is not a crow), so likewise, it also slightly confirms that "crows are not crows". is black" the original proposition. All in all, "meet a white cat" slightly increases the probability of "all crows are black".Interesting, right? This paradox was proposed by the famous German logical positivist Carl G Hempel, who also studied mathematics with Hilbert in his youth.If you accept this conclusion, then the next time your instructor asks you to go to the field to prove a proposition such as "Insects have six legs", you don't have to go out in the wind and rain.Just by sitting at home and observing numerous instances of "anything without six legs is not an insect" (like a table, a chair, a lamp, yourself...), you can contribute as much to the proposition as actually observing insects in the wild! Our understanding of the theory of knowledge is still very superficial. two The creepy and ridiculous "quantum suicide" experiment was proposed by Hans Moravec, Bruno Marchal et al. in the late 1980s, and was developed and reproduced in 1998 by cosmologist Max Tegmark in his well-known paper promoting MWI. carry.This is actually a live-action version of Schrödinger's cat.Everyone knows that in the cat experiment, if the atom decays, the cat will be poisoned to death, otherwise it will survive.In this regard, the explanation of the Copenhagen school is: before we observe it, the cat is "dead and alive", but after the observation, the wave function of the cat collapses, and the cat is either dead or alive. MWI claims that each experiment must produce a live cat and a dead cat at the same time, but they exist in two parallel worlds. What is the real difference between the two?The key point is that the Copenhagen School believes that there is always only one cat, and it starts to be in a superposition state. After the collapse, there is a 50% possibility of death and a 50% possibility of life.However, the multiverse believes that cats are not superimposed, but "split" into two, one dead and one alive, there must be a live cat! Now if there is a benevolent man who has the courage to dedicate himself to science, he volunteers to replace that hapless cat.Out of humanitarianism, in order to save him from suffering, we changed the gas bottle into a gun.If the atom decays (or utilizes some other quantum mechanism, such as a photon passing through the half-silvering), the gun goes "bang" and sends our friend on his way.On the contrary, the gun only made a "click" sound. Now comes the key question, when a photon reaches a half-coated mirror, according to the Copenhagen school, half of you may hear a "click" and be safe, and the other half is not so wonderful, you hear a "pop" and nothing happens. I no longer know.And according to the multiverse, there must be one you hear "click", and another you hear "bang" in another world.But the problem is that the person who heard the "bang" died immediately, and he lost all feeling, and this world has no meaning for "you".The only world that makes sense to you is the one you live in. So, in terms of the anthropic principle (which we discussed earlier), the only "existences" that make sense to you are those worlds in which you live.You will always just hear "click" and live on!Because the multiverse is different from Copenhagen, there will always be one of you living in a certain world! Let's fire a photon every second to the half-coated mirror to activate the mechanism.At this time, Copenhagen predicts that even if you are very lucky, you will hear several "clicks" at most and eventually die.But the prophecy of the multiverse is: there will always be a "you" alive, and his world is the only meaningful existence for "you".As long as you sit in front of the gun, from your own perspective, you will only ever hear the click every second, and you will never die (although in a surprising number of other worlds, you will never die. Dead bodies have been strewn about, but those worlds mean nothing to you)! But as soon as you move away from the gun, you hear the "pop" again, because these worlds regain meaning to you, and you can live to witness them.All in all, the multiverse prophecy is this: as long as you're in front of the gun, it never fires (for you), and as soon as you move away, it starts randomly "popping" again. So, for the tester himself, if he keeps hearing “click” and lives well, he can be sure to a large extent that the multiverse explanation is correct.If he is dead, then the Copenhagen interpretation is correct.But this is meaningless to him, everyone is dead. You may be confused by the anthropic principle here.In any case, the gun keeps "clicking" is a very small probability, isn't it (if n times, the probability is 1/2^n)?How can you say that for you the gun "must" behave this way?But the problem is that the premise of "for you" is that "you" must exist! Let's take this example: If you are a male, you will definitely find such an "interesting" fact: your father has a son, your grandfather has a son, your great-grandfather has a son... all the way back to any n generations of ancestors, regardless of history Frozen glaciers, floods, wild beasts, turmoil, hunger and barrenness, not only can they survive, but they will continue to have offspring, and there will always be a son. This is a very small probability (if you are a woman, you can push the way to your natal family).But if you say with emotion that your existence is a once-in-a-century "miracle", it will be very ridiculous.Obviously, the prerequisite for you to be able to feel emotion is your existence itself!In fact, speaking "objectively", the probability of a family having sons in n generations is extremely small, but for you and me, it is "must" and the probability is 100%!In the same way, some people lament the ingenuity of the universe, and the probability of its creation is so low, but according to the anthropic principle, the universe must be like this!In Quantum Suicide, the gun has to be 100% non-firing for you as long as you are always present! But it is a pity: even if you find that the multiverse explanation is correct, it is only knowledge for you alone.As far as we onlookers are concerned, the facts are always the same: you are shot dead after a few clicks.All we can do is argue around your dead body, whether according to Copenhagen, you have disappeared from the universe forever, or according to MWI, you are still alive and well in some world.We "outsiders" are projected into the world you live in. This probability is extremely low and can almost be ignored, but for you "personally", it is 100% necessary for you to exist in that world!And, since the worlds can't interfere with each other, you can never come to us from that world and tell us that the multiverse is true! In fact, Tegmark and others don’t need to bother to design any “quantum suicide” experiments. According to their thinking, if the multiverse explanation is correct, then for someone, no matter how he tries to commit suicide, he will not die!If he wiped his neck with a knife, then because the knife is made up of a group of particles conforming to the Schrödinger wave equation, there is always a very, very small, but definitely non-zero possibility that these particles have quantum tunneling at that moment. Somehow it penetrated the man's neck without any damage, thus keeping the man alive!Of course, this probability is extremely small, but according to MWI, everything that could happen has actually happened, so this phenomenon will always happen in a certain world!From an "objective" point of view, this person is dead in 99.99999...99% of the world, but from his "subjective point of view", he is still alive!It doesn't matter what the method is, whether it's jumping off a building, lying on a rail, or hanging himself, there are always some worlds that keep him alive.From the person's own point of view, no matter how he dies, he won't die! This is the strange theory derived from the quantum suicide thought experiment, euphemistically called "quantum immortality".As far as the subjective point of view is concerned, not only can a person never complete suicide, but in fact once he begins to exist, he will never disappear!There is always some quantum effect that keeps a person from aging, and according to the MWI, these very low probabilities always correspond to some actual world!If the multiverse theory is correct, then we have the corollary that once a "consciousness" begins to exist, it must be immortal from its own perspective! (Gosh, how did we talk about "consciousness" again!) This is the strongest version of the anthropic principle, also known as the "ultimate anthropic principle". It is conceivable that supporters of multiverse theory such as Tegmark felt dumbfounded when their proposal was interpreted into such a strange theory.The cosmologist at the University of Pennsylvania had to come out and say that "immortality" is not the orthodox inference of MWI.He said that a person has experienced some kind of non-quantization process "before death", so that the so-called consciousness cannot be continuously transitioned and maintained forever.Unfortunately, few people believed his defense. This question will no doubt be of interest to scientists and philosophers alike.Those who support MWI will also criticize that the death of "human" in a large sample of the universe cannot be simply ignored, because we still know almost nothing about "consciousness", how it "continuously exists", and there is no Not checked.Some biased opinions will think that if "consciousness" must exist continuously in some branches of the universe, then we should conclude that it not only exists always, but also "continuously" forever, that is, we should not have "loss of consciousness". ” (e.g. sleeping or unconscious).But maybe there are some worlds where we never sleep, who knows?Besides, falling asleep for a while and then waking up again does not seem to be considered "meaningless" for "consciousness".And more importantly, maybe it is still a question of how to define what "you" in many worlds is.In short, there are endless logical circles here, and there is almost nothing that can be tested in practice, all empty-to-empty.I don't think Popper would be happy with that! Regarding the suicide experiment itself, I don't think anyone would actually try it just to test Copenhagen and MWI!Because no matter what, only you know the result of the experiment, and you cannot tell it to the masses.And if the Copenhagen Interpretation is unfortunately correct, you're out of luck.Although it is said that "when you hear the Tao, you can die at night", generally speaking, after hearing the Tao, it is better to use it to do something more meaningful.Also, even if you really don't die at gunpoint, you can't really tell if that's the result of a multi-world prophecy, or if it's just your luck being very, very, very good.The most you can say is: "I declare with 99.999999..99% confidence that many worlds are correct." That's it. According to Shikhovtsev's latest biography, Everett himself somehow believes that his "consciousness" continues along some branch of the universe that does not lead to death (of course he is unaware of suicide experiments).But the tragedy and irony is that his family believed in parallel universes so much that his daughter Liz, in her suicide note, said she went to meet him in "another parallel world" (of course, she did not kill herself to test this theory).Maybe the Everett family actually met in a world, but at least in this world we are in now (and most other worlds), we see that people cannot be resurrected after death.So, at least in consideration of the feelings of family and friends in most worlds, I strongly advise readers not to attempt this with scientific zeal. We've been on the many-worlds road long enough, and, as we did with the Copenhagen School, our quests have gotten weirder and weirder in the end, rough and weedy and exhausting, and in the end There will be metaphysical things like "consciousness" and "immortality" again (what the hell)!We still retreat in spite of the difficulties, return to the original fork in the road, and see if there are other different options.But before we leave this path, there is one more thing worth mentioning, and that is the so-called "quantum computer". In 1977, Everett accepted the invitation of Wheeler and DeWitt to give lectures at the University of Texas. During lunch, DeWitt specially arranged for one of Wheeler's students to sit next to Everett. Asked about Hilbert spaces.The student was David Deutsch. three The invention of the computer is one of the most important events in the 20th century. The emergence of this new thing has fundamentally changed the human society, making our ability break through the limit and reach an unimaginable level.Today, computers have penetrated into every corner of our lives, and we can barely move without it.Among other things, the history you are reading was typed and edited on my laptop, although using a modern PC for word processing would be overkill, or using Ian Stewart "It's like driving a Rolls-Royce to deliver milk," but thanks to the progress of the times, this luxury has entered thousands of households after all.Moreover, in today's information business society, its replacement is so fast that people have to worry about upgrading their "old" computers every two or three years, and it is not without heartache to pay the capitalists The silver that has been accumulated with great difficulty. Looking back at the history of computer development, people often lament the rapid development of science and technology.Usually we regard the ENIAC of the University of Pennsylvania in 1946 as the world's first electronic computer, but of course, with different definitions of the concept of "computer", people often refer to the German Konrad Zuse in 1941 The Z3 built in 1999, the ABC (Atanasoff-Berry Computer) built by Iowa State University during World War II, or the Collosus built by the Turing team to break the German code.In any case, these were big, unwieldy things that could fill an entire room, some crammed with unsightly tubes, some trailing long wires, input and output by punched paper or tape, and modern It's like the difference between beauty and the beast compared to a light and delicate home computer.However, if we mathematically idealize these two seemingly very different, Beauty and the Beast are essentially the same!Regardless of whether it is a huge early computer or the PC we use today, they can actually be simplified into such a machine: it reads an input each time, and depending on its internal state at the time, according to a pre-compiled rule table Make corresponding operations: this operation can be writing output, or changing the internal state, or simply doing nothing or even shutting down.The key here is that the input and output of our machine can be infinite, but its internal state and rule table must be finite.This model is actually the prototype of all "computers". It was proposed by Alan Turing, one of the founders of modern computers, and is also called "The Turing Machine".In Turing's original paper, it was described as a sort of box with an infinitely long tape running through it, with input at one end and output at the other.Information is recorded on the tape, generally a sequence of 0s and 1s.The machine moves the tape as needed, reads data from one end, performs operations according to a programmed table of rules, and finally outputs the results of calculations on the other end. The computers we use today, no matter how sophisticated and complex they may appear to be, are essentially Turing machines.It reads in a stream of data, processes it according to a specific algorithm, and outputs the result on the other end.In this sense, the difference between the Pentium 4 and the 286 is that the former is faster and more efficient, but they are also Turing machines, and they can actually do the same amount of things!I mean, the 286 can do what the Pentium can do if given enough time and output space (to record temporary storage data). 286 is already too advanced. Even if it degenerates into the most primitive form of Turing machine, that is, the machine that can only move the tape left or right and act accordingly, they can solve as many things, but It's just a question of speed and efficiency. At the most basic level, the information a computer processes is a binary code, in other words, a sequential stream of 0s and 1s.Friends who are a little familiar with computers know that we call each "bit" of information a "bit" (bit, actually binary digit), for example, information 1010 contains 4 bits. 8 bits are equal to 1 byte, 1024 bytes are 1K, 1024K=1M, 1024M=1G, everyone must be very clear. For traditional computers, 1 bit is the smallest unit of information.It is either 0 or 1, corresponding to the circuit being on or off.If a computer reads 10 bits of information, it is equivalent to saying that it reads a 10-digit binary number (for example, 1010101010), and each bit of this number is a definite 0 or 1.This seems to be taken for granted in people's eyes. 但是，接下来就让我们进入神奇的量子世界。一个bit是信息流中的最小单位，这看起来正如一个量子！我们回忆一下走过的路上所见到的那些奇怪景象，量子论最叫人困惑的是什么呢？是不确定性。我们无法肯定地指出一个电子究竟在哪里，我们不知道它是通过了左缝还是右缝，我们不知道薛定谔的猫是死了还是活着。根据量子论的基本方程，所有的可能性都是线性叠加在一起的！电子同时通过了左和右两条缝，薛定谔的猫同时活着和死了。只有当实际观测它的时候，上帝才随机地掷一下骰子，告诉我们一个确定的结果，或者他老人家不掷骰子，而是把我们投影到两个不同的宇宙中去。 大家不要忘记，我们的电脑也是由微观的原子组成的，它当然也服从量子定律（事实上所有的机器肯定都是服从量子论的，只不过对于传统的机器来说，它们的工作原理并不主要建立在量子效应上）。假如我们的信息由一个个电子来传输，我们规定，当一个电子是“左旋”的时候，它代表了0，当它是“右旋”的时候，则代表1（通常我们会以“上”和“下”来表示自旋方向，不过可能有读者会对“上旋”感到困惑，我们换个称呼，这无所谓）。现在问题来了，当我们的电子到达时，它是处于量子叠加态的。这岂不是说，它同时代表了0和1？ 这就对了，在我们的量子计算机里，一个bit不仅只有0或者1的可能性，它更可以表示一个0和1的叠加！一个“比特”可以同时记录0和1，我们把它称作一个“量子比特”（qubit）。假如我们的量子计算机读入了一个10bits的信息，所得到的就不仅仅是一个10位的二进制数了，事实上，因为每个bit都处在0和1的叠加态，我们的计算机所处理的是2^10个10位数的叠加！ 换句话说，同样是读入10bits的信息，传统的计算机只能处理1个10位的二进制数，而如果是量子计算机，则可以同时处理2^10个这样的数！ 利用量子演化来进行某种图灵机式的计算早在70年代和80年代初便由Bennett，Benioff等人进行了初步的讨论。到了1982年，那位极富传奇色彩的美国物理学家理查德?费因曼（Richard Feynman）注意到，当我们试图使用计算机来模拟某些物理过程，例如量子叠加的时候，计算量会随着模拟对象的增加而指数式地增长，以致使得传统的模拟很快变得不可能。费因曼并未因此感到气馁，相反，他敏锐地想到，也许我们的计算机可以使用实际的量子过程来模拟物理现象！如果说模拟一个“叠加”需要很大的计算量的话，为什么不用叠加本身去模拟它呢？每一个叠加都是一个不同的计算，当所有这些计算都最终完成之后，我们再对它进行某种幺正运算，把一个最终我们需要的答案投影到输出中去。费因曼猜想，这在理论上是可行的，而他的确猜对了！ 1985年，我们那位在埃弗莱特的谆谆教导和多宇宙论的熏陶下成长起来的大卫?德义奇闪亮登场了。他仿照图灵当年走的老路子，成功地证明了，一台普适的量子计算机是可能的。所谓“普适机”（universal machine）的概念可能对大家有点陌生以及令人困惑，它可以回到图灵那里，其基本思想是，存在某种图灵机，把一段指令编成合适的编码对其输入，可以令这台机器模拟任何图灵机的行为。我无意在这里过于深入细节，因为那是相当费脑筋的事情，虽然其中的数学一点也不复杂。如果各位有兴趣深入探索的话可以参阅一些介绍图灵工作的文章（我个人还是比较推荐彭罗斯的《皇帝新脑》），在这里各位所需要了解的无非是：我们聪明睿智的德义奇先生证明了一件事，那就是我们理论上可以建造一种机器，它可以模拟任何特殊量子计算机的过程，从而使得一切形式的量子计算成为可能。传统的电脑处理信息流的时候用到的是所谓的“布尔逻辑门”（Boolean Logic Gate），比如AND，OR，NOT，XOR等等。在量子计算机中只需把它们换成相应的量子逻辑门即可。 说了那么多，一台量子计算机有什么好处呢？ 德义奇证明，量子计算机无法实现超越算法的任务，也就是说，它无法比普通的图灵机做得更多。从某种确定的意义上来说，量子计算机也是一种图灵机。但和传统的机器不同，它的内态是不确定的，它同时可以执行多个指向下一阶段的操作。如果把传统的计算机称为决定性的图灵机（Deterministic Turing Machine, DTM），量子计算机则是非决定性的图灵机（NDTM）。德义奇同时证明，它将具有比传统的计算机大得多的效率。用术语来讲，执行同一任务时它所要求的复杂性（complexity）要低得多。理由是显而易见的，量子计算机执行的是一种并行计算，正如我们前面举的例子，当一个10bits的信息被处理时，量子计算机实际上操作了2^10个态！ 在如今这个信息时代，网上交易和电子商务的浪潮正席卷全球，从政府至平民百姓，都越来越依赖于电脑和网络系统。与此同时，电子安全的问题也显得越来越严峻，谁都不想黑客们大摇大摆地破解你的密码，侵入你的系统篡改你的资料，然后把你银行里的存款提得精光，这就需要我们对私隐资料执行严格的加密保护。目前流行的加密算法不少，很多都是依赖于这样一个靠山，也即所谓的“大数不可分解性”。大家中学里都苦练过因式分解，也做过质因数分解的练习，比如把15这个数字分解成它的质因数的乘积，我们就会得到15=5×3这样一个唯一的答案。 问题是，分解15看起来很简单，但如果要分解一个很大很大的数，我们所遭遇到的困难就变得几乎不可克服了。比如，把10949769651859分解成它的质因数的乘积，我们该怎么做呢？糟糕的是，在解决这种问题上，我们还没有发现一种有效的算法。一种笨办法就是用所有已知的质数去一个一个地试，最后我们会发现10949769651859＝4220851×2594209（数字取自德义奇的著作The Fabric of Reality），但这是异常低效的。更遗憾的是，随着数字的加大，这种方法所费的时间呈现出几何式的增长！每当它增加一位数，我们就要多费3倍多的时间来分解它，很快我们就会发现，就算计算时间超过宇宙的年龄，我们也无法完成这个任务。当然我们可以改进我们的算法，但目前所知最好的算法（我想应该是GNFS）所需的复杂性也只不过比指数性的增长稍好，仍未达到多项式的要求（所谓多项式，指的是当处理数字的位数n增大时，算法所费时间按照多项式的形式，也就是n^k的速度增长）。 所以，如果我们用一个大数来保护我们的秘密，只有当这个大数被成功分解时才会泄密，我们应当是可以感觉非常安全的。因为从上面的分析可以看出，想使用“暴力”方法，也就是穷举法来破解这样的密码几乎是不可能的。虽然我们的处理器速度每隔18个月就翻倍，但也远远追不上安全性的增长：只要给我们的大数增加一两位数，就可以保好几十年的平安。目前最流行的一些加密术，比如公钥的RSA算法正是建筑在这个基础之上。 但量子计算机实现的可能使得所有的这些算法在瞬间人人自危。量子计算机的并行机制使得它可以同时处理多个计算，这使得大数不再成为障碍！1994年，贝尔实验室的彼得?肖（Peter Shor）创造了一种利用量子计算机的算法，可以有效地分解大数（复杂性符合多项式！）。比如我们要分解一个250位的数字，如果用传统计算机的话，就算我们利用最有效的算法，把全世界所有的计算机都联网到一起联合工作，也要花上几百万年的漫长时间。但如果用量子计算机的话，只需几分钟！一台量子计算机在分解250位数的时候，同时处理了10^500个不同的计算！ 更糟的事情接踵而来。在肖发明了他的算法之后，1996年贝尔实验室的另一位科学家洛弗?格鲁弗（Lov Grover）很快发现了另一种算法，可以有效地搜索未排序的数据库。如果我们想从一个有n个记录但未排序的数据库中找出一个特定的记录的话，大概只好靠随机地碰运气，平均试n/2次才会得到结果，但如果用格鲁弗的算法，复杂性则下降到根号n次。这使得另一种著名的非公钥系统加密算法，DES面临崩溃。现在几乎所有的人都开始关注量子计算，更多的量子算法肯定会接连不断地被创造出来，如果真的能够造出量子计算机，那么对于现在所有的加密算法，不管是RSA，DES，或者别的什么椭圆曲线，都可以看成是末日的来临。最可怕的是，因为量子并行运算内在的机制，即使我们不断增加密码的位数，也只不过给破解者增加很小的代价罢了，这些加密术实际上都破产了！ 2001年，IBM的一个小组演示了肖的算法，他们利用7个量子比特把15分解成了3和5的乘积。当然，这只是非常初步的进展，我们还不知道，是否真的可以造出有实际价值的量子计算机，量子态的纠缠非常容易退相干，这使得我们面临着技术上的严重困难。虽然2002年，斯坦弗和日本的科学家声称，一台硅量子计算机是可以利用现在的技术实现的，2003年，马里兰大学的科学家们成功地实现了相距0.7毫米的两个量子比特的互相纠缠，一切都在向好的方向发展，但也许量子计算机真正的运用还要过好几十年才会实现。这个项目是目前最为热门的话题之一，让我们且拭目以待。