Chapter 17 Chapter 12 New Expedition-1

one In 1953, the young but accomplished physicist Murray Gell-Mann left Princeton to become a lecturer at the University of Chicago.At that time, Chicago was still shrouded in the brilliance of Enrico Fermi. It has been nearly 16 years since this scientific giant won the Nobel Prize in 1938 for his outstanding contribution to nuclear physics theory.Gell-Mann may not have imagined that in another 16 years, the same honor would fall on him. Although already successful and famous, Fermi still has a generous and easy-going attitude, willing to discuss scientific issues with everyone.In the era of rapid development of nuclear physics, quantum theory, as its basis, has been regarded as a sacred and inviolable classic, but Fermi was always full of doubts. He asked Gell-Mann more than once:

Since quantum theory is correct, superposition must be a universal phenomenon.But why does Mars have a definite orbit instead of spreading out from the orbit? Naturally, the answer was within the Copenhagenist's bag: the reason why Mars didn't disperse was because someone was "observing" it, or someone was looking at it.Every time you look at it, its wave function collapses.But both Fermi and Gell-Mann felt that this answer was too boring and stupid, and there must be a better explanation. It's a pity that during Fermi's lifetime, he couldn't get a better answer.He died soon in 1954, and Gell-Mann switched to Caltech the following year, where he started his great career.Caltech has a steady stream of good students, Hartle (James

B Hartle) is one of them. In the 1960s, he studied for a Ph.D. under Gell-Mann, conducted sufficient research and thinking on quantum cosmology, and gradually formed an idea in his mind.At that time, Feynman's path integral method had been established for more than 20 years, and in the 1970s, as we mentioned earlier in the history, a new theory - decoherence theory was developed in Zurek and Zeh et al. It has also been established under the efforts ofIn the 1980s, Everett's multi-universe explanation revived in the physics community, and quickly aroused everyone's interest... All external conditions gradually matured, and in 1984, Griffith (Robert Griffith)

Griffiths published his paper, the decoherence history (abbreviated as DH) interpretation was officially established. We remember Everett's MWI: the universe is projected into multiple "worlds" in the evolution of the Schrödinger equation, producing different outcomes in each world.In this way, more and more "worlds" are gradually produced in the development history of the universe.There is only one history, but there are many worlds! When Hartl and Gell-Mann read Griffith's paper on "history," they had a sudden epiphany.They began to shout: "No! The facts are just the opposite of Everett's assumption: there is only one world, but many histories!"

When the word "History" is mentioned, the first thing that comes to our minds is probably concepts such as ancient Egypt, Babylon, Greece and Rome, Tang, Song, Yuan, Ming and Qing Dynasties.History is the study of the past.But in physics, the past, present, and future are not clearly distinguished, at least in theory, there are no features that allow us to clearly distinguish these states.Talking about "history" from a physical point of view, we only define it as a period of time that a system has experienced and the state changes it has experienced during this period.For example, if we discuss the "history" of a bunch of particles closed in a box, we can predict that they will gradually spread out according to the second law of thermodynamics, and finally reach the maximum thermal radiation equilibrium state.Of course, it is also possible that a black hole will form in it and be in equilibrium with the remaining thermal radiation. Due to quantum fluctuations and Hawking evaporation, it is very likely that the system will constantly swing between these two equilibrium states, but anyway , corresponding to a specific moment, our system will have a specific state, and connecting them is what we call the "history" of the system.

We have to keep in mind that in quantum mechanics everything is discrete and not continuous, so when we talk about "a period of time" we are really talking about a collection of all moments, starting from t0, t1, t2, all the way to tn.So what we call "history" actually means that corresponding to the time tk, the system has a corresponding state Ak. We still use metaphors that the broad masses of the people like to see and hear to illustrate the problem.Imagine a football team participating in a certain league, and the league will have n rounds in total.Then, the "history" of this team is nothing more than: corresponding to the kth round of the league (moment k), if we observe, we will get the result Ak of ​​this game (Ak can be 1:0, 2:1, 3 :3...etc).If the "history" of this team is written out completely, it will probably look like this:

1:2, 2:3, 1:1, 4:1, 2:0, 0:0, 1:3... For the sake of brevity, we only examine the situation of one game now.The total number of all possible "history" of a game is theoretically infinite. Of course, in reality, the score is generally not too high.If the game has not been played, or at least we do not know its outcome, then for each "history" we can only estimate the probability of its occurrence.In practice, even probabilities are often difficult to calculate (although referring to bookmaker odds or browsing some poker sites may help, they can sometimes be quite misleading), but the is a theoretical problem, so we assume that by calculation, we can get an accurate probability for any kind of history.For example, the probability of a "history" such as a 1:0 win is 10%, a 1:2 loss is 20% ... and so on.

Having said so much, what is the use of these?Don't be impatient, we will see the outcome soon. So far, since we have been dealing with classical probabilities, they are "additive"!That is to say, if we have two histories a and b, and their occurrence probabilities are Pa and Pb respectively, then the probability of "a or b" occurring is Pa+Pb.Taking our example, if we want to ask: "What is the probability of winning by 2 goals?", then it must be equal to the sum of all historical probabilities of winning by 2 goals, which is P(2:0) ＋P(3:1)＋P(4:2)＋... This seems to be a matter of course.

But let's go back to quantum theory.Curiously, in quantum theory such additions are not always possible!Take the experiment we have discussed so dryly, if "the electron goes through the left slit" is one kind of history, and "the electron goes through the right slit" is another kind of history, then "the electron goes through the left slit or goes through the right slit" How likely is it?We have to put it into the so-called "density matrix" D to calculate, arrange them in a table! In this table, the value staying on the coordinates (left, left) is the probability of "passing the left seam" history.Staying on (right, right) is undoubtedly the probability of "passing the right slit".But wait, we still have two extras, D(left,right) and D(right,left)!What are these two things?They are not any probabilities, but indicate a cross-interference between the "left" and "right" histories!What's terrible is that the calculation results often show that these interference terms are not zero.

In other words, the two histories of "passing the left slit" and "passing the right slit" are not independent, but entangled with each other, and there are interference terms between them.When we calculate the situation of "the electron passes through the left slit or through the right slit", what we get is not a traditional probability. To put it simply, such a "joint history" has no probability!This is why in the double slit experiment, we cannot say "the electron either passes through the left slit or the right slit", it must pass through the double slit at the same time, because the two histories are "coherent"!

Going back to our football analogy, in a "quantum league", all possible histories are coherent, and a history like 1:0 and a history like 2:0 interfere with each other, so their probabilities are not additive!That is, if the probability of 1:0 is 10% and the probability of 2:0 is 15%, then the probability of "1:0 or 2:0" is not 25%, but something vague , it cannot be assigned a probability! That doesn't sound very good, but if these probabilities don't add up, people who gamble on football or buy football lottery tickets must be overwhelmed and unable to invest their money reasonably.If the probability cannot be calculated, So what else can we do?But don't worry, because something wonderful is about to happen: although we can't predict the probability of "1:0 or 2:0", we can indeed predict the probability of "winning or drawing"!This is all because of the existence of the "decoherence" mechanism! Here is the magic secret: When we don't care about the specific score of a game, but only care about the relationship between winning and losing, we actually ignore a lot of information.For example, when we discuss a history as "win, win, draw, lose, win, lose..." instead of specific scores, we actually construct a "rough" history.In each round of the league, the states Ak we observe contain an infinite number of more refined states.For example, when we say that the team "wins" in the second round, it includes 1:0, 2:1, 2:0, 3:1...all the specific results that can be summed up as "wins".In terminology, we call each specific possible score "fine-grained history" (fine-grained history), and the history like "win" and "lose" is called "coarse-grained history" (coarse-grained history). grained history). Again, for the sake of brevity, we only examine the case of one game.For a single game, its "coarse-grained history" is nothing more than three types: win, draw, and loss.If the probability of "winning" is 30% and the probability of "drawing" is 40%, what is the probability of "either winning or drawing", that is, "undefeated"?Everyone still remembers our discussion above, and may start to worry, because quantum theory may not be able to give a classical probability, but this time it is different!This time, quantum theory gave an answer similar to classical probability: the probability of "undefeated" = 30 + 40 = 70%! Why is this?It turns out that when we calculated the relationship between "win" and "draw", we actually calculated the relationship between all the "grain histories" contained in them!If we put "win" and "draw" into the matrix to calculate, we will indeed get interference items such as (win, draw), but what is this interference item?It is the sum of the interference of all the fine-grained histories that make up the two kinds of coarse-grained histories!That is to say, it includes "interference between 1:0 and 0:0", "interference between 1:0 and 1:1", "interference between 2:0 and 1:1"... etc.In short, every possible pair of interferences was accounted for, and we were surprised to find that all these interferences added together exactly canceled out.When the final result comes out, the interference term between "win" and "draw" has become small enough to be ignored, if not completely disappeared. The two coarse-grained histories of "victory" and "peace" are no longer relevant, they are "decoherent"! In quantum mechanics, we can specifically use the so-called "path integral" method to construct a "decoherence function" to calculate all these histories.We mentioned the path integral a little earlier in our history. It is a quantum calculation method published by the famous American physicist Feynman in 1942. Feynman himself later shared with others the 1965 Nobel Prize in Physics.Path integral is a method of summing the entire time and space. When a particle moves from A to B, we express its trajectory as the superposition of all possible spaces and all possible times!We only care about its initial state and final state, and ignore its intermediate state. For these states that we don't care about, we traverse and sum it on every possible path. The subtlety is that these paths are often will cancel itself out. The same thing happens on the Quantum Football Field: We only care about the outcome of the game, not the more subtle things such as the specific score.When we ignore the specific score, in fact, the traversal summation is performed for each possible score (history).When all the fine grain histories are summed up, their interference tends to cancel out completely, or at least, nearly cancel out.At this time, classical probability is back on the table, the probability of two coarse-grained histories becomes additive again, and quantum theory can finally work again!We may not be able to tell whether a game is 1:0 or 2:0, but we can undoubtedly tell whether a game is won or tied!Because the two histories are no longer relevant! The key is that we must construct a sufficiently "coarse-grained" history.It's like I send you two digital photos, a close-up of Jennifer Lopez and Jennifer Aniston, and ask you, who do you think is prettier.If you enlarge these photos to the maximum size, you may see only some color blocks of different colors, and the two photos seem to be no big difference to you.Only when the resolution is lowered enough or you step back far enough to blur the color blocks can you see the entire composition and effectively distinguish the difference between the two photos and make comparisons.In short, two pictures can only be distinguished if they are sufficiently "coarse-grained", and so is our "history"!If the "grains" of two histories are so fine that they interfere with each other, we cannot distinguish them, for example, we cannot distinguish between "electron passed through the left slit" and "electron passed through the right slit" two histories , they happen simultaneously!But if the particles of history are "coarse" enough, then we can effectively separate the two histories, and they are decoherent! When we observe the behavior of electrons and get the final result, we actually construct a "coarse-grained history".We can boil it down to two things: "We observe the particle on the left" and "We observe the particle on the right".Why do we say they are coarse-grained histories?Because there are so many things we ignore.Now we only care about where the electrons are when we observe them, not where we stand in the laboratory, whether we ate ramen, burgers or sushi today, and we don’t even care how much dust is in the air when we make observations. On us, how many photons came in through the window and interacted with us... In theory, each different situation should correspond to a specific history, such as "We who ate ramen noodles observed that electrons in Left" and "we who ate hamburgers observed that the electrons are on the left" are actually two different histories. "Observing that the electron is on the left and being hit by 100 million photons at the same time" and "observing that the electron is on the left and being hit by 100 million and 1 photons at the same time" are also two different histories, but we don't care about these, and Just degenerate them into the category of "we observe electrons on the left", so we actually construct a very coarse-grained history. Now, when we compute the interference between the two histories "We observed the electron to the left" and "We observed the electron to the right", we're actually doing a traversal summation over too many things.We traversed the different fates of "you who ate hamburgers", "you who ate sushi", "you who ate ramen".We have traversed every photon that hit you during this period, and we have traversed the interaction between you and every electron at the end of the universe... If we say "we observe the position of the electron" is a system, the components that make up this system There are n particles, and among them, the state of m particles actually determines whether we observe electrons on the left or on the right.Then, except the m particles, the fate of every particle has been added up in the calculation.In terms of time, except for the moment of actual observation, at every moment—whether in the past or in the future—the states of all particles are added.After all these calculations are done, the interferences in each direction will be almost equal and they will be canceled out from the result.Finally, the two coarse-grained histories of "we observe electrons on the left" and "we observe electrons on the right" are decoherent, and they are no longer related to each other, and we can only feel one of them! You may think this sounds like a magical story, but this is indeed an interpretation of quantum theory that has become very popular recently! In 1984 Griffith opened the way for it, and soon in 1991, Hartle began to expand and perfect it.Soon Gell-Mann and Omnes (Roland Omnes) joined the ranks, and these eminent physicists quickly turned it into an eloquent system.It is still necessary for us to investigate this idea further, so as to gain a deeper understanding of the connotation of quantum theory. two According to the explanation of decoherence history (DH), if we divide the history of the universe finely enough, then in fact, there are many fine particle histories "occurring at the same time" (coherent) every moment.For example, when there is no observation, the electron obviously experiences two histories of "passing through the left slit" and "passing through the right slit" at the same time.But generally speaking, we are not interested in overly fine-grained history, we only care about the coarse-grained history that we can observe.Because of mutual decoherence (decoherence), these histories have lost their connection, and only one can be felt by us. According to the thickness of history grains, we can create a "history tree".Or take our Quantum League as an example, how rough can a team's history in the league be divided?Maybe we can just divide it into two categories: "winning the league championship" and "not winning the league championship".At this very coarse level, we only care specifically about winning the championship, and nothing else, they will all be added in the calculation.But we can also continue to be "precise". For example, in the branch of "winning the championship", we can continue to divide it into two branches according to the winning percentage: "winning the championship with a winning rate of more than 50%" and "winning the championship but not exceeding 50%".In a similar way, we can continue to divide the points, down to the total number of games won, the specific outcome of each game... until the detailed score of each game.Of course, in reality, we can still continue to "fine-grain", such as who scored the goal, how many spectators came to the stadium, how many of them wore red clothes, and how many grasses grew on the stadium.But here we assume that the most detailed information of a game is the specific score, and there is no more detailed information.In this way, our history tree cannot be further divided when it reaches a specific score. The bottom layer is the "leaves", also known as "the most fine-grained history" (maximally fine-grained histories). For two leaves, they are usually related to each other.We cannot clearly distinguish between 1-0 wins and 2-0 wins, and therefore cannot calculate them using traditional probabilities.But we can construct those histories that conform to common sense through appropriate coarse-graining. For example, we can distinguish the three categories of history of "win", "draw" and "lose", because they have lost interference and decoherence .This allows us to compute these histories using traditional classical probabilities, which form a "family" of decoherent histories, only within the same family can we use the usual rational logic to deal with the probability relationship between them.Sometimes, we don't say "decoherence", but call it "consistent histories". Griffith, one of the founders of DH, loves to use this word, so "decoherence history" is also often used. It is called the "consistent history" explanation, and more popularly, it can also be called the "many histories" theory. In general, the closer you are to the root (up) in the history tree, the more coarse-grained and less intrusive it is.Of course, not all coarse-grained histories are free from interference and can be assigned traditional probabilities, specifically, certain "consistency conditions" must be met, and these conditions can be rigorously derived mathematically. Now let's consider the case of Schrödinger's cat: when that fateful atom decays, the atom itself does go through the two possible seminal histories of decay/non-decay.Atoms themselves are just individual particles, and there's not much we ignore.But once the cat is dragged into this plot, our historical script is replaced by cat dead/cat alive, the situation is different!Both "the cat is dead" and "the cat is alive" are very vague statements. To describe a cat, it takes 10^27 particles. When we say "the cat is alive", we ignore the relationship between the cat and the outside world. Everything about it, such as how it breathes, how it exchanges matter and energy with the outside world... and so on.Even if the "cat dies", the n particles on it still have to interact with the outside world.In other words, "cat alive" and "cat dead" are actually the sum of two types of history, just like "win" is "1:0", "2:0", "2:1"...etc. It's all the same.When we calculate the interference between "cat dead" and "cat alive", we have actually exhausted the interference between every pair of sperm histories under these two categories of histories, and most of them are eventually canceled out . The inextricable connection between "the cat dies" and "the cat lives" is cut off, they fade away, and finally only one of them really happens!If you look at the problem from the perspective of the density matrix, it shows that except for those classical probabilities on the diagonal of the matrix, other interference items are quickly reduced to 0: the matrix is ​​"diagonalized"!And there is neither spontaneous random localization, nor external "observers", nor invisible hidden variables! If the DH explanation is correct, then we are actually experiencing multiple histories every moment, and every particle in the world is actually in the superposition of all possible histories!But when it comes to macroscopic objects, what we can observe and describe is nothing more than some coarse-grained histories. When the details are erased, these histories are decoherent and permanently lost.For example, if the cat is still alive in the end, then the branch of "cat death" is excluded from the history tree. According to Occam's razor, we might as well say that these histories no longer exist in the universe. Well, as weird as it sounds, it at least makes sense, doesn't it?Coarse-grained methods may seem confusing, but they're not all that fussy, and we actually use them all the time, consciously or not.For example, in middle school we calculated the gravitational force between the earth and the sun, and we "coarse-grained" the two planets into two particles.In fact, the earth and the sun are two huge spheres, but after replacing all the points with the center of mass and ignoring their specific positions, we have actually unknowingly added the distance between each pair of mass points inside the two spheres. attraction.In the DH interpretation, what we do is just a little more complicated. Mathematically, DH is a well-defined theory, and from a philosophical point of view, its supporters are quite proud to claim that it is a theory with the least assumptions and the most "physical reality" .However, DH's life is not as easy as it is advertised. The most violent attack on it comes from GianCarlo, one of the founders of the GRW theory we mentioned in the previous chapter. Ghirardi.Since the creation of the DH theory, the Italian and his colleagues have published at least five papers in various physics journals attacking the historical interpretation of decoherence. Ghirardi astutely pointed out that the DH interpretation is no better than the traditional Copenhagen interpretation! As we have already described for you, within the framework of the DH interpretation we define a series of "coarse-grained" histories which form a mutual Decoherent history family (family).For example, in our league, for a specific game, "win", "draw", and "lose" are a legitimate historical family, and only one of them can happen, because they are almost equal to each other. Unrelated.However, using the same technique in mathematics, we can also define some other historical families, which are also legal!For example, we don't necessarily pay attention to the relationship between victory and defeat, but can consider other aspects such as the number of goals scored.Now we perform another coarse-graining, distinguishing the game results into "no goal", "one goal", "two goals" and "more than two goals".Mathematically, these four kinds of histories also meet the "consistent condition", and they constitute another complete family of decoherent histories! Now, when we observe a game, the results we get depend on the chosen history family.For the same game, we may observe "win", but from another angle, we may also observe "two goals scored".Of course, there is no contradiction between them, but it still confuses us if we think carefully about what really happened in "reality". When we observe "win", we assume that all the histories of the fine grains under it are happening, such as 1:0, 2:1, 2:0, 3:0... all the histories are happening, It's just that we don't observe specific fine-grained results, and we're not interested in them.But for the same game, we may also observe "two goals scored". At this time, our assumption is that all the history of scoring two goals happened.Such as 2:0, 2:1, 2:2, 2:3... Now let's consider a specific fine particle history, such as a history of 1:0.Although we have never actually observed such a history, this does not prevent us from asking: Did the 1:0 history happen?When the observation is "win", it obviously happened; when the observation is "two goals scored", it obviously didn't happen!However, we are describing the same game! The original intention of DH is to overthrow the Copenhagen explanation in textbooks, drive observers out of the theory, and return the physical world to an objective and real explanation.That is to say, all physical properties exist independently beyond your and my observation, and it does not change because of any subjective things.But now DH seems to be a dumb eater of Coptis chinensis—it’s hard to tell. The physical description of "whether the 1:0 history is true" really depends on the choice of the historical family, rather than "objective existence"!This seems to be the same goal as Bohr and others: there is no purely objective physical property in the universe, and all properties can only be linked with specific observation methods! But the supporters of DH defended that any rational logical reasoning (reasoning) can only be used in the same decoherent family, and cannot be used across families.For example, when we get the conclusion that "1:0 fine-grain history happened" in the history of "win, draw, and loss", we must not bring it to another family of history (such as "no goals, 1 goal, 2 goals, 2 goals or more") and compare with each other.They summarized this in what they called the "single family rule" and declared it to be the most important principle in quantum theory. Putting this point aside, another problem of DH is that there are actually a large variety of "decoherent families" in theory, but we only observe one in reality!Still take our quantum league as an example. As far as a single game is concerned, we defined a decoherent family earlier, that is, "win, draw, lose".This family contains three kinds of coarse-grained histories, all of which decorrelate with each other.This looks good at all, but the problem is that not only "win, draw, lose" is possible, there are infinite other ways to divide, most of which are even strange and not in line with common sense , but the theory doesn't explain why we don't observe these other classes! For example, we theoretically define three kinds of histories: "win and draw", "win and lose", "draw and lose", these three histories also constitute a legal and complete decoherence family in mathematics : Their probabilities can be added classically, no matter which one you observe, you cannot observe the other two.But obviously in reality, it is impossible to "win and lose" in a game, then DH owes us an explanation, it must explain why in reality the game is divided into "win, draw, lose" instead of "again and again". win and tie" and such, although they are not that different mathematically! On this issue, the defenders of DH might say that theory is only obliged to explain the operation of reality, but not the existence of reality!We start from reality to build theory, not from theory to build reality!For example, "1 cow plus 1 cow equals 2 cows" and "1 sphinx plus 1 sphinx equals 2 sphinxes" are both true in mathematics, but there is no obligation in mathematics Explain why, in the real world, the only things we can actually add up are cows, not monsters like sphinxes.On this point, positivists and Platonists often have sharp conflicts. A prominent example is superstring theory, which we will discuss a little later.String theory uses 10 dimensions to explain our world, 6 of which are curled up, but it doesn't say why 6 dimensions are curled up and not 5 or 8, which makes it subject to some pointed heckling.But positivists often wonder about such pursuit: because only assuming 6-dimensional curling can explain the real world we observe (the real world is 4-dimensional), this is enough, isn’t that all reason?How come there are so many deep-rooted questions? However, if the supporters of DH insist on such a positivist position, they may temporarily ignore the original intention of establishing this theory, which is to get rid of Bohr and Heisenberg's Copenhagen interpretation-that is the most thorough positivism!In any case, DH's attitude on this is a bit embarrassing, and the big debate about quantum mechanics is still going on, and we still can't be sure whose view is really correct.After haunting us for more than 100 years, quantum magic still refuses to reveal its deepest secrets to the world.Perhaps, this secret will eventually become a permanent puzzle. *********** After-dinner gossip: The arrow of time We live in a 4-dimensional world, where 3 dimensions are space and 1 is time.Time is a wonderful thing, it seems to be very different from other 3-dimensional space, the most critical point is that it seems to have direction!Take space as an example, there is no difference in all directions, you can go left or right, but in terms of time, you can only move from "past" to "future", not vice versa!While there are so many sci-fi stories about how people go back in time, in reality, this has never happened and likely never will!The reason for such speculation is still based on something similar to the anthropic principle: if it is theoretically possible to go back to the past, then although we cannot, people in the future can, but we have never seen them "come back" to our era.So it is very possible that people in any era in the future will not be able to make the clock turn in the opposite direction, it is theoretically impossible! This seems to be normal, and it seems to be a matter of course that there is no way to move against the arrow of time.But in physics, this is puzzling, because in theory, there seems to be no feature that shows that time has a particular direction.Both Newton's and Einstein's theories are time symmetric!The middle school teacher tells you the state at time t0, and you can move forward to the "future" and launch time tn, but you can also move forward in reverse to the "past" and launch time -tn.The theory doesn't tell us why time can only move towards tn but not vice versa!In fact, on a fundamental level, time obeys the laws of physics whether it runs forward or backward!However, once we break away from the basic level and rise to a relatively high level, the arrow of time mysteriously appears: if we consider the combination of many particles instead of a single particle, we will find a strong direction.For example, we can only get older gradually, but not younger. The cup will be broken, but it will never be pasted together automatically.These can be summarized in a very powerful law, the famous second law of thermodynamics, which says that the degree of disorder in an isolated system is always increasing, and its measure is called "entropy".In other words, entropy is always increasing, and the arrow of time points in the direction of increasing entropy! 现在我们考察量子论。在本节我们讨论了DH解释，所有的“历史”都是定义得很好的，不管你什么时候去测量，这些历史——从过去到未来——都已经在那里存在。我们可以问，当观测了t0时刻后，历史们将会如何退相干，但同样合法的是，我们也可以观测tn时刻，看“之前”的那些时刻如何退相干。实际上，当我们用路径积分把时间加遍的时候，我们仍然没有考虑过时间的方向问题，它在两个方向上都是没有区别的！再说，如果考察量子论的基本数学形式，那么薛定谔方程本身也仍然是时间对称的，唯一引起不对称的是哥本哈根所谓的“坍缩”，难道时间的“流逝”，其实等价于波函数不停的“坍缩”？然而DH是不承认这种坍缩的，或许，我们应当考虑的是历史树的裁剪？盖尔曼和哈特等人也试图从DH中建立起一个自发的时间箭头来，并将它运用到量子宇宙学中去。 我们先不去管DH，如果仔细考虑“坍缩”，还会出现一个奇怪现象：假如我们一直观察系统，那么它的波函数必然“总是”在坍缩，薛定谔波函数从来就没有机会去发展和演化。这样，它必定一直停留在初始状态，看上去的效果相当于时间停滞了。也就是说，只要我们不停地观察，波函数就不演化，时间就会不动！这个佯谬叫做“量子芝诺效应”（quantum Zeno effect），我们在前面已经讨论过了芝诺的一个悖论，也就是阿喀琉斯追乌龟，他另有一个悖论是说，一支在空中飞行的箭，其实是不动的。why?因为在每一个瞬间，我们拍一张snapshot，那么这支箭在那一刻必定是不动的，所以一支飞行的箭，它等于千千万万个“不动”的组合。问题是，每一个瞬间它都不动，连起来怎么可能变成“动”呢？所以飞行的箭必定是不动的！在我们的实验里也是一样，每一刻波函数（因为观察）都不发展，那么连在一起它怎么可能发展呢？所以它必定永不发展！ 从哲学角度来说我们可以对芝诺进行精彩的分析，比如恩格斯漂亮地反驳说，每一刻的箭都处在不动与动的矛盾中，而真实的运动恰好是这种矛盾本身！不过我们不在意哲学探讨，只在乎实验证据。已经有相当多的实验证实，当观测频繁到一定程度时，量子体系的确表现出芝诺效应。这是不是说，如果我们一直盯着薛定谔的猫看，则它永远也不会死去呢？ 时间的方向是一个饶有趣味的话题，它很可能牵涉到深刻的物理定律，比如对称性破缺的问题。在极早期宇宙的研究中，为了彻底弄明白时间之矢如何产生，我们也迫切需要一个好的量子引力理论，在后面我们会更详细地讲到这一点。我们只能向着未来，而不是过去前进，这的确是我们神奇的宇宙最不可思议的方面之一。 three 好了各位，到此为止，我们在量子世界的旅途已经接近尾声。我们已经浏览了绝大多数重要的风景点，探索了大部分先人走过的道路。但是，正如我们已经强烈地感受到的那样，对于每一条道路来说，虽然一路上都是峰回路转，奇境叠出，但越到后来却都变得那样地崎岖不平，难以前进。虽说“入之愈深，其进愈难，而其见愈奇”，但精神和体力上的巨大疲惫到底打击了我们的信心，阻止了我们在任何一条道上顽强地冲向终点。 当一次又一次地从不同的道路上徒劳而返之后，我们突然发现，自己已经处在一个巨大的迷宫中央。在我们的身边，曲折的道路如同蛛网一般地辐射开来，每一条都通向一个幽深的不可捉摸的未来。我已经带领大家去探讨了哥本哈根、多宇宙、隐变量、系综、GRW、退相干历史等6条道路，但要告诉各位的是，仍然还有非常多的偏僻的小道，我们并没有提及。比如有人认为当进行了一次“观测”之后，宇宙没有分裂，只有我们大脑的状态（或者说“精神”）分裂了！这称为“多精神解释”（many-minds intepretation），它名副其实地算得上一种精神分裂症！还有人认为，在量子层面上我们必须放弃通常的逻辑（布尔逻辑），而改用一种“量子逻辑”来陈述！另一些人不那么激烈，他们觉得不必放弃通常的逻辑，但是通常的“概率”概念则必须修改，我们必须引入“复”的概率，也就是说概率并不是通常的0到1，而是必须描述为复数！华盛顿大学的物理学家克拉默（John G Cramer）建立了一种非定域的“交易模型”（The transactional model），而他在牛津的同行彭罗斯则认为波函数的缩减和引力有关。彭罗斯宣称只要空间的曲率大于一个引力子的尺度，量子线性叠加规则就将失效，这里面还牵涉到量子引力的复杂情况诸如物质在跌入黑洞时如何损失了信息……等等，诸如此类。即便是我们已经描述过的那些解释，我们的史话所做的也只是挂一漏万，只能给各位提供一点最基本的概念。事实上，每一种解释都已经衍生出无数个变种，它们打着各自的旗号，都在不遗余力地向世人推销自己，这已经把我们搞得头晕脑胀，不知所措了。现在，我们就像是被困在克里特岛迷宫中的那位忒修斯（Theseus），还在茫然而不停地摸索，苦苦等待着阿里阿德涅（Ariadne）——我们那位可爱的女郎——把那个指引方向，命运攸关的线团扔到我们手中。 1997年，在马里兰大学巴尔的摩郡分校（UMBC）召开了一次关于量子力学的研讨会。有人在与会者中间做了一次问卷调查，统计究竟他们相信哪一种关于量子论的解释。结果是这样的：哥本哈根解释13票，多宇宙8票，玻姆的隐变量4票，退相干历史4票，自发定域理论（如GRW）1票，还有18票都是说还没有想好，或者是相信上述之外的某种解释。到了1999年，在剑桥牛顿研究所举行的一次量子计算会议上，又作了一次类似的调查，这次哥本哈根4票，修订过的运动学理论（它们对薛定谔方程进行修正，比如GRW）4票，玻姆2票，而多世界（MWI）和多历史（DH）加起来（它们都属于那种认为“没有坍缩存在”的理论）得到了令人惊奇的30票。但更加令人惊奇的是，竟然有50票之多承认自己尚无法作出抉择。在宇宙学家和量子引力专家中，MWI受欢迎的程度要高一些，据统计有58％的人认为多世界是正确的理论，而只有18％明确地认为它不正确。但其实许多人对于各种“解释”究竟说了什么是搞不太清楚的，比如人们往往弄不明白多世界和多历史到底差别在哪里，或许，它们本来就没有明确的分界线。就算是相信哥本哈根的人，他们互相之间也会发生严重的分歧，甚至关于它到底是不是一个决定论的解释也会造成争吵。量子论仍然处在一个战国纷争的时代，玻尔，海森堡，爱因斯坦，薛定谔……他们的背影虽然已经离我们远去，但他们当年曾战斗过的这片战场上仍然硝烟弥漫，他们不同的信念仍然支撑着新一代的物理学家，激励着人们为了那个神圣的目标而继续奋战。 想想也真是讽刺，量子力学作为20世纪物理史上最重要的成就之一，到今天为止它的基本数学形式已经被创立了将近整整80年。它在每一个领域内都取得了巨大的成功，以致和相对论一起成为了支撑物理学的两大支柱。80年！任何一种事物如果经历了这样一段漫长时间的考验后仍然屹立不倒，这已经足够把它变成不朽的经典。岁月将把它磨砺成一个完美的成熟的体系，留给人们的只剩下深深的崇敬和无限的唏嘘，慨叹自己为何不能生于乱世，提三尺剑立不世功名，参予到这个伟大工作中去。但量子论是如此地与众不同，即使在它被创立了80年之后，它仍然没有被最后完成！人们仍在为了它而争吵不休，为如何“解释”它而闹得焦头烂额，这在物理史上可是前所未有的事情！想想牛顿力学，想想相对论，从来没有人为了如何“解释”它们而操心过，对比之下，这更加凸现出量子论那独一无二的神秘气质。 人们的确有理由感到奇怪，为什么在如此漫长的岁月过去之后，我们不但没有对量子论了解得更清楚，反而越来越感觉到它的奇特和不可思议。最杰出的量子论专家们各执一词，人人都声称只有他的理解才是正确的，而别人都错了。量子谜题已经成为物理学中一个最神秘和不可捉摸的部位，Zeilinger有一次说：“我做实验的唯一目的，就是给别的物理学家看看，量子论究竟有多奇怪。”到目前为止，我们手里已经攥下了超过一打的所谓“解释”，而且它的数目仍然有望不断地增加。很明显，在这些花样繁多的提议中间，除了一种以外，绝大多数都是错误的。甚至很可能，到目前为止所有的解释都是错误的，但这却并没有妨碍物理学家们把它们创造出来！我们只能说，物理学家的想象力和创造力是非凡的，但这也引起了我们深深的忧虑：到底在多大程度上，物理理论如同人们所骄傲地宣称的那样，是对于大自然的深刻“发现”，而不属于物理学家们杰出的智力“发明”？ 但从另外一方面看，我们对于量子论本身的确是没有什么好挑剔的。它的成功是如此巨大，以致于我们除了咋舌之外，根本就来不及对它的奇特之处有过多的评头论足。从它被创立之初，它就挟着雷霆万钧的力量横扫整个物理学，把每个角落都塑造得焕然一新。或许就像狄更斯说的那样，这是最坏的时代，但也是最好的时代。 量子论的基本形式只是一个大的框架，它描述了单个粒子如何运动。但要描述在高能情况下，多粒子之间的相互作用时，我们就必定要涉及到场的作用，这就需要如同当年普朗克把能量成功地量子化一样，把麦克斯韦的电磁场也进行大刀阔斧的量子化——建立量子场论（quantum field theory）。这个过程是一个同样令人激动的宏伟故事，如果铺展开来叙述，势必又是一篇规模庞大的史话，因此我们只是在这里极简单地作一些描述。这一工作由狄拉克开始，经由约尔当、海森堡、泡利和维格纳的发展，很快人们就认识到：原来所有粒子都是弥漫在空间中的某种场，这些场有着不同的能量形态，而当能量最低时，这就是我们通常说的“真空”。因此真空其实只不过是粒子的一种不同形态（基态）而已，任何粒子都可以从中被创造出来，也可以互相湮灭。狄拉克的方程预言了所谓的“反物质”的存在，任何受过足够科普熏陶的读者对此都应该耳熟能详：比如一个正常的氢原子由带正电的质子和带负电的电子组成，但在一个“反氢原子”中，质子却带着负电，而电子带着正电！当一个原子和一个“反原子”相遇，它们就轰隆一声放出大量的能量辐射，然后双方同时消失得无影无踪，其关系就符合20世纪最有名的那个物理方程：E＝mc^2！ 最早的“反电子”由加州理工的安德森（Carl Anderson）于1932年在研究宇宙射线的时候发现。它的意义是如此重要，以致于仅仅过了4年，诺贝尔奖评委会就罕见地授予他这一科学界的最高荣誉。 但是，虽然关于辐射场的量子化理论在某些问题上是成功的，但麻烦很快就到来了。1947年，在《物理评论》上刊登了有关兰姆移位和电子磁矩的实验结果，这和现有的理论发生了微小的偏差，于是人们决定利用微扰办法来重新计算准确的值。但是，算来算去，人们惊奇地发现，当他们想尽可能地追求准确，而加入所有的微扰项之后，最后的结果却适得其反，它总是发散为无穷大！ 这可真是让人沮丧的结果，理论算出了无穷大，总归是一件荒谬的事情。为了消除这个无穷大，无数的物理学家们进行了艰苦卓绝，不屈不挠的斗争。这个阴影是如此难以驱散，如附骨之蛆一般地叫人头痛，以至于在一段时间里把物理学变成了一个让人无比厌憎的学科。最后的解决方案是日本物理学家朝永振一郎、美国人施温格（Julian S Schwiger）和戴森（Freeman Dyson），还有那位传奇的费因曼所分别独立完成的，被称为“重正化”（renormalization）方法，具体的技术细节我们就不用理会了。虽然认为重正化牵强而不令人信服的科学家大有人在，但是采用这种手段把无穷大从理论中赶走之后，剩下的结果其准确程度令人吃惊得瞠目结舌：处理电子的量子电动力学（QED）在经过重正化的修正之后，在电子磁距的计算中竟然一直与实验值符合到小数点之后第11位！亘古以来都没有哪个理论能够做到这样教人咋舌的事情。 实际上，量子电动力学常常被称作人类有史以来“最为精确的物理理论”，如果不是实验值经过反复测算，这样高精度的数据实在是让人怀疑是不是存心伪造的。但巨大的胜利使得一切怀疑都最终迎刃而解，QED也最终作为量子场论一个最为悠久和成功的分支而为人们熟知。虽然最近彭罗斯声称说，由于对赫尔斯-泰勒脉冲星系统的观测已经积累起了如此确凿的关于引力波存在的证明，这实际上使得广义相对论的精确度已经和实验吻合到10的负14次方，因此超越了QED（赫尔斯和泰勒获得了1993年诺贝尔物理奖）。但无论如何，量子场论的成功是无人可以否认的。朝永振一郎，施温格和费因曼也分享了1965年的诺贝尔物理奖。