Chapter 13 Chapter 12 New Expedition

one In 1953, the young but versatile physicist Murray.Murray Gell-Mann left Princeton to become a lecturer at the University of Chicago.Chicago at that time was still shrouded in Enrico.Under the brilliance of Fermi, nearly sixteen years have passed since this scientific giant won the Nobel Prize in 1938 for his outstanding contribution to the theory of nuclear physics.Gell-Mann might not have imagined that in another sixteen 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 spread out was because someone was watching 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, and 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 of decoherence was developed in Zurek and Zeh et al. It has also been established under the efforts ofIn the 1980s, Everett's multiverse explanation revived in the physics community, and quickly aroused everyone's interest. All external conditions gradually matured. In 1984, Robert Griffiths published his After the paper, the decoherence history (abbreviated as DH) explanation was officially established.

We also remember Everett's MWI: the universe is projected into multiple worlds in the evolution of the Schrödinger equation, producing different results 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 insight.They began to shout: No!The facts are just the opposite of Everett's assumption: there is only one world, but many histories! When we mention the word History, 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, what we are really talking about is a set that contains all the moments from t0, t1, t2, all the way to tn.So the history we talk about 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 k-th round of the league (moment k), if we observe, we 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 histories 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 gambling websites 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 possibility of a history of winning 1:0 is 10%, and losing 1:2 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 two goals? , then it must be equal to the sum of all historical probabilities of a goal difference of two goals, that 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 electrons passing through the left slit is one history, and electrons passing through the right slit is another history, then what is the probability that electrons pass through the left slit or through the right slit?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 history through the left seam.Those who stay on (right, right) are 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 two histories of the left and the right!Unfortunately, calculations often show that these interference terms do not work.

In other words, the two histories of passing through the left slit and passing through the right slit are not independent, but intertwined with each other, and there are interference terms between them.When we calculate the situation that electrons pass 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 that 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, the history of 1:0 and the history of 2:0 interfere with each other, so their probabilities are not additive!In other words, if the probability of 1:0 is ten percent and the probability of 2:0 is fifteen percent, then the probability of 1:0 or 2:0 is not twenty-five percent, but some kind of vague something, it cannot be given 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 we can't calculate probabilities, what else can we do?But don't worry, because something wonderful is about to happen: although we can't predict the probability of one: or two:, 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 its outcome, we actually ignore a lot of information.For example, when we discuss a history of wins, wins, draws, losses, wins, losses, rather than 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, and 3:1, all specific results that can be summarized as victory.In terminology, we call each specific possible score a fine-grained history, and a history like wins and losses as a coarse-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: wins, draws, and losses.If the probability of winning is 30% and the probability of drawing is 40%, what is the probability of winning or drawing, that is, being 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: undefeated probability = 30 + 40 = 70%! Why is this?It turns out that when we calculated the relationship between wins and peaces, we actually calculated the relationship between all the grain histories contained within them!If we put wins and peace in the matrix to calculate, we will indeed get interference items such as (win, tie), 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!In other words, it includes interference between 1:0 and 0:0, interference between 1:0 and 1:1, interference between 2:0 and 1:1, and so on.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 Shengping and Heping has become small enough to be ignored, if not completely disappeared.The two coarse-grained histories of Shengping and Heping are no longer relevant, they are decoherent! In quantum mechanics, we can specifically use the so-called path integral (path integral) method to construct a decoherence function to calculate all these histories.We have 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 a Nobel Prize in Physics in 1965.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 often end up cancel each other 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 one: or two:, 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 build a sufficiently coarse-grained history.It's like I sent you two digital photos of Jennifer.Lopez and Jennifer.A close-up of Aniston, and then ask you, who do you think is more beautiful between the two.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 by turning down the resolution low enough or stepping 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 conclusion, 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 the two histories of electrons passing through the left slit and electrons passing through the right slit. They are happening at the same time!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 kind of coarse-grained history.We can boil it down to two things: We observe particles to the left and we observe particles to 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. How many photons are coming in on us, through the window, interacting with us? In theory, each different situation should correspond to a specific kind of history, such as we ate ramen noodles and we observed electrons on the left and we ate hamburgers The electrons we observe on the left are actually two different histories.Observing the electron on the left and being hit by 100 million photons at the same time and observing the electron on the left and being hit by 100 million and one photons at the same time are also two different histories, but we don't care about these, we just simplify them. And until we observe that electrons are in the left category, so we actually construct a very coarse-grained history. Now, when we calculate the interference between two histories where we observed the electron to be on the left and when we observed the electron to be on the right, we're actually doing a ergodic summation over too many things.We have traversed the different fates of you who ate hamburgers, you who ate sushi, and 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 that the position of the electron we observe is a system, there are n particles that make up this system , among them, the states of m particles actually determine 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, the states of all particles at every moment, no matter in the past or in the future, have also been 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.In the end, the two coarse-grained histories that we observe that the electron is on the left and we observe that the electron is on the right are decoherent, and they are no longer connected with 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 paved the way for it, and soon in 1991 Hartle began to expand and perfect it.Soon Gell-Mann and Omnes (Roland Omn's) joined the ranks, and these outstanding 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 the decoherence history (DH), if we divide the history of the universe finely enough, then in fact, there are many fine-grain histories happening 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 title and not winning the league title.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: winning the championship with a winning rate of more than 50% and winning the championship but not exceeding 50%.Similarly, we can keep dividing until the total number of games won, the specific outcome of each game, and 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 can no longer be divided into specific scores. The bottom layer is the leaves, also known as the maximally fine-grained histories. For two leaves, they are usually related to each other.We cannot clearly distinguish between 1:win and 2:win histories, and thus cannot compute 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: victory, draw and loss, because they have lost interference and decoherence.In this way, we can calculate these histories using traditional classical probability, which forms a decoherent family of histories, and only within the same family can we use the usual rational logic to deal with them. probability relationship between them.Sometimes, we don't talk about decoherence, but call it consistent histories. Griffith, one of the founders of DH, loves to use this term, so decoherence history is often called consistent history interpretation. 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, it does, as far as the atom itself is concerned, 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!Whether the cat is dead or the cat is alive is a very vague statement. It takes 10^27 particles to describe a cat. When we say that the cat is alive, we ignore all the interactions between the cat and the outside world, such as it How to breathe, how to exchange 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 life and cat death are actually the sum of the two categories of history, just like winning is the sum of 1:0, 2:0, 2:1 and other histories.When we calculate the interference between cat dead and cat alive, we actually exhaust the interference between every pair of seminal histories under these two categories of histories, and most of them cancel out eventually.The inextricable connection between the cat's death and the cat's life is cut off, they are decoherent, and only one of them really happens in the end!If we 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: 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 the cat's 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 between.In the DH interpretation, what we do is just a little more complicated. From a mathematical point of view, DH is a well-defined theory, and from a philosophical point of view, its proponents are quite proud to claim that it is a theory with the least assumptions and the best reflection of physical reality.However, DH's life is not as easy as it is advertised. The most violent attack on it comes from GianCarlo Ghirardi, one of the founders of the GRW theory we mentioned in the previous chapter.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 mutually decoherent history when they satisfy the so-called consistency condition family.For example, in our league, for a specific game, win, draw, and loss are a legitimate historical family, and only one of them can happen, because they have almost no connection with each other.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 do another kind of coarse-graining, distinguishing the result of the game as no goal, one goal, two goals and more than two goals.Mathematically, these four 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 victory, 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 victory, we assume that all the histories of the fine grains under it are happening, such as 1:0, 2:1, 2:0, and 3:0, all the histories have happened, but we observe They are not interested in specific fine-grained results.But for the same game, we may also observe that two goals were 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 we consider a certain kind of fine particle history, say one: such a history.Although we have never actually observed such a history, this does not prevent us from asking: 1: Did the history of the past happen?When the observation was a win, it obviously happened; when the observation was 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 dumb and can't tell if he suffers from eating coptis.1: The physical description of whether the history of China 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 have obtained such a conclusion in the history of victory, draw, and loss, we must not bring it to another history (such as no goal, one goal, two goals) , scoring more than two goals) and compare them with each other.They summed this up in what they called the single family rule, which they declared to be the most important principle in quantum theory. Putting this aside, another problem with DH is that there are actually a great variety of decoherent families in theory, but we observe only 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, and lose.This family includes three coarse-grained histories, all of which decorrelate with each other.This looks not bad at all, but the problem is that not only winning, drawing, and losing are possible, there are infinite other ways of scoring, most of which are even strange and not in line with common sense, but Theory doesn't explain why we don't observe these other categories! For example, we theoretically define three histories: wins and draws, wins and losses, and draws and losses. These three histories also constitute a legal and complete decoherence family in mathematics: their probabilities can be added classically, and you No matter which one of these is observed, the other two cannot be observed.But obviously in reality, it is impossible to win and lose in a game, so DH owes us an explanation, it must explain why in reality the game is divided into wins, draws, and losses instead of wins and draws, although they Not much 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, it is mathematically true to say that one cow plus one cow equals two cows and one sphinx plus one sphinx equals two sphinxes, but mathematics has no obligation to explain why in the real world, the actual We have only cattle to add to, not monsters like the sphinx.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 explains our world in ten dimensions, six of which are curled up, but its failure to explain why six rather than five or eight dimensions has drawn some pointed heckling.But positivists often wonder about such pursuit: because only assuming six-dimensional curling can explain the real world we observe (the real world is four-dimensional), that’s enough, isn’t that all reason?How come there are so many deep-rooted questions? However, if DH supporters maintain such a positivist position, they may temporarily ignore the original intention of establishing this theory, which is to get rid of the Copenhagen interpretation of Bohr and Heisenberg, which 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.Quantum magic, after haunting us for more than a hundred years, still refuses to reveal its deepest secrets to the world.Perhaps, this secret will eventually become a permanent mystery. After-dinner gossip: The arrow of time We live in a four-dimensional world, where three dimensions are space and one dimension is time.Time is a wonderful thing, it seems to be very different from other three-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 the past to the future, not the other way around!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 summed up in one very powerful law, the famous second law of thermodynamics, which says that there is always increasing disorder in an isolated system, a measure of which is called entropy.In other words, entropy is always increasing, and the arrow of time points in the direction of increasing entropy! We now consider quantum theory.In this section we discussed the DH interpretation, all histories are well defined, no matter when you measure, these histories have been there from the past to the future.We can ask how the histories decorrelate after observing time t0, but it is equally legitimate to observe how the previous moments decorrelate by observing time tn.In fact, when we add time over time with path integrals, we still haven't considered the direction of time, it's indistinguishable in both directions!Besides, if we examine the basic mathematical form of quantum theory, then the Schrödinger equation itself is still time-symmetric, and the only asymmetry is caused by the so-called collapse in Copenhagen. Is the passage of time actually equivalent to the continuous collapse of the wave function?However, DH does not recognize this kind of collapse. Perhaps what we should consider is the pruning of the history tree?蓋爾曼和哈特等人也試圖從DH中建立起一個自發的時間箭頭來，並將它運用到量子宇宙學中去。 我們先不去管DH，如果仔細考慮坍縮，還會出現一個奇怪現象：假如我們一直觀察系統，那麼它的波函數必然總是在坍縮，薛定諤波函數從來就沒有機會去發展和演化。這樣，它必定一直停留在初始狀態，看上去的效果相當於時間停滯了。也就是說，只要我們不停地觀察，波函數就不演化，時間就會不動！這個佯謬叫做量子芝諾效應（quantum Zeno effect），我們在前面已經討論過了芝諾的一個悖論，也就是阿喀琉斯追烏龜，他另有一個悖論是說，一支在空中飛行的箭，其實是不動的。why?因為在每一個瞬間，我們拍一張snapshot，那麼這支箭在那一刻必定是不動的，所以一支飛行的箭，它等於千千萬萬個不動的組合。問題是，每一個瞬間它都不動，連起來怎麼可能變成動呢？所以飛行的箭必定是不動的！在我們的實驗裡也是一樣，每一刻波函數（因為觀察）都不發展，那麼連在一起它怎麼可能發展呢？所以它必定永不發展！ 從哲學角度來說我們可以對芝諾進行精采的分析，比如恩格斯漂亮地反駁說，每一刻的箭都處在不動與動的矛盾中，而真實的運動恰好是這種矛盾本身！不過我們不在意哲學探討，只在乎實驗證據。已經有相當多的實驗證實，當觀測頻繁到一定程度時，量子體系的確表現出芝諾效應。這是不是說，如果我們一直盯著薛定諤的貓看，則它永遠也不會死去呢？ 時間的方向是一個饒有趣味的話題，它很可能牽涉到深刻的物理定律，比如對稱性破缺的問題。在極早期宇宙的研究中，為了徹底弄明白時間之矢如何產生，我們也迫切需要一個好的量子引力理論，在後面我們會更詳細地講到這一點。我們只能向著未來，而不是過去前進，這的確是我們神奇的宇宙最不可思議的方面之一。 三 好了各位，到此為止，我們在量子世界的旅途已經接近尾聲。我們已經流覽了絕大多數重要的風景點，探索了大部分先人走過的道路。但是，正如我們已經強烈地感受到的那樣，對於每一條道路來說，雖然一路上都是峰迴路轉，奇境疊出，但越到後來卻都變得那樣地崎嶇不平，難以前進。雖說入之愈深，其進愈難，而其見愈奇，但精神和體力上的巨大疲憊到底打擊了我們的信心，阻止了我們在任何一條道上頑強地衝向終點。 當一次又一次地從不同的道路上徒勞而返之後，我們突然發現，自己已經處在一個巨大的迷宮中央。在我們的身邊，曲折的道路如同蛛網一般地輻射開來，每一條都通向一個幽深的不可捉摸的未來。我已經帶領大家去探討了哥本哈根、多宇宙、隱變數、系綜、GRW、退相干歷史等六條道路，但要告訴各位的是，仍然還有非常多的偏僻的小道，我們並沒有提及。比如有人認為當進行了一次觀測之後，宇宙沒有分裂，只有我們大腦的狀態（或者說精神）分裂了！這稱為多精神解釋（many-minds intepretation），它名副其實地算得上一種精神分裂症！還有人認為，在量子層面上我們必須放棄通常的邏輯（布林邏輯），而改用一種量子邏輯來陳述！另一些人不那麼激烈，他們覺得不必放棄通常的邏輯，但是通常的概率概念則必須修改，我們必須引入複的概率，也就是說概率並不是通常的0到1，而是必須描述為複數！華盛頓大學的物理學家克拉默（John G Cramer）建立了一種非定域的交易模型（The transactional model），而他在牛津的同行彭羅斯則認為波函數的縮減和引力有關。彭羅斯宣稱只要空間的曲率大於一個引力子的尺度，量子線性疊加規則就將失效，這裡面還牽涉到量子引力的複雜情況諸如物質在跌入黑洞時如何損失了資訊等等，諸如此類。即便是我們已經描述過的那些解釋，我們的史話所做的也只是掛一漏萬，只能給各位提供一點最基本的概念。事實上，每一種解釋都已經衍生出無數個變種，它們打著各自的旗號，都在不遺餘力地向世人推銷自己，這已經把我們搞得頭暈腦脹，不知所措了。現在，我們就像是被困在克里特島迷宮中的那位忒修斯（Theseus），還在茫然而不停地摸索，苦苦等待著阿里阿德涅（Ariadne）我們那位可愛的女郎把那個指引方向，命運攸關的線團扔到我們手中。 一九九七年，在馬里蘭大學巴爾的摩郡分校（UMBC）召開了一次關於量子力學的研討會。有人在與會者中間做了一次問卷調查，統計究竟他們相信哪一種關於量子論的解釋。結果是這樣的：哥本哈根解釋十三票，多宇宙八票，玻姆的隱變數四票，退相干歷史四票，自發定域理論（如GRW）一票，還有十八票都是說還沒有想好，或者是相信上述之外的某種解釋。到了一九九九年，在劍橋牛頓研究所舉行的一次量子計算會議上，又作了一次類似的調查，這次哥本哈根四票，修訂過的運動學理論（它們對薛定諤方程進行修正，比如GRW）四票，玻姆二票，而多世界（MWI）和多歷史（DH）加起來（它們都屬於那種認為沒有坍縮存在的理論）得到了令人驚奇的三十票。但更加令人驚奇的是，竟然有五十票之多承認自己尚無法作出抉擇。在宇宙學家和量子引力專家中，MWI受歡迎的程度要高一些，據統計有五十八％的人認為多世界是正確的理論，而只有十八％明確地認為它不正確。但其實許多人對於各種解釋究竟說了什麼是搞不太清楚的，比如人們往往弄不明白多世界和多歷史到底差別在哪裡，或許，它們本來就沒有明確的分界線。就算是相信哥本哈根的人，他們互相之間也會發生嚴重的分歧，甚至關於它到底是不是一個決定論的解釋也會造成爭吵。量子論仍然處在一個戰國紛爭的時代，玻爾，海森堡，愛因斯坦，薛定諤他們的背影雖然已經離我們遠去，但他們當年曾戰鬥過的這片戰場上仍然硝煙彌漫，他們不同的信念仍然支撐著新一代的物理學家，激勵著人們為了那個神聖的目標而繼續奮戰。 想想也真是諷刺，量子力學作為二十世紀物理史上最重要的成就之一，到今天為止它的基本數學形式已經被創立了將近整整八十年。它在每一個領域內都取得了巨大的成功，以致和相對論一起成為了支撐物理學的兩大支柱。八十年！任何一種事物如果經歷了這樣一段漫長時間的考驗後仍然屹立不倒，這已經足夠把它變成不朽的經典。歲月將把它磨礪成一個完美的成熟的體系，留給人們的只剩下深深的崇敬和無限的唏噓，慨歎自己為何不能生於亂世，提三尺劍立不世功名，參與到這個偉大工作中去。但量子論是如此地與眾不同，即使在它被創立了八十年之後，它仍然沒有被最後完成！人們仍在為了它而爭吵不休，為如何解釋它而鬧得焦頭爛額，這在物理史上可是前所未有的事情！想想牛頓力學，想想相對論，從來沒有人為了如何解釋它們而操心過，對比之下，這更加凸現出量子論那獨一無二的神秘氣質。 人們的確有理由感到奇怪，為什麼在如此漫長的歲月過去之後，我們不但沒有對量子論瞭解得更清楚，反而越來越感覺到它的奇特和不可思議。最傑出的量子論專家們各執一詞，人人都聲稱只有他的理解才是正確的，而別人都錯了。量子謎題已經成為物理學中一個最神秘和不可捉摸的部位，Zeilinger有一次說：我做實驗的唯一目的，就是給別的物理學家看看，量子論究竟有多奇怪。到目前為止，我們手裡已經攥下了超過一打的所謂解釋，而且它的數目仍然有望不斷地增加。很明顯，在這些花樣繁多的提議中間，除了一種以外，絕大多數都是錯誤的。甚至很可能，到目前為止所有的解釋都是錯誤的，但這卻並沒有妨礙物理學家們把它們創造出來！我們只能說，物理學家的想像力和創造力是非凡的，但這也引起了我們深深的憂慮：到底在多大程度上，物理理論如同人們所驕傲地宣稱的那樣，是對於大自然的深刻發現，而不屬於物理學家們傑出的智力發明？ 但從另外一方面看，我們對於量子論本身的確是沒有什麼好挑剔的。它的成功是如此巨大，以致於我們除了咋舌之外，根本就來不及對它的奇特之處有過多的評頭論足。從它被創立之初，它就挾著雷霆萬鈞的力量橫掃整個物理學，把每個角落都塑造得煥然一新。或許就像狄更斯說的那樣，這是最壞的時代，但也是最好的時代。 量子論的基本形式只是一個大的框架，它描述了單個粒子如何運動。但要描述在高能情況下，多粒子之間的相互作用時，我們就必定要涉及到場的作用，這就需要如同當年普朗克把能量成功地量子化一樣，把麥克斯韋的電磁場也進行大刀闊斧的量子化建立量子場論（quantum field theory）。這個過程是一個同樣令人激動的宏偉故事，如果鋪展開來敘述，勢必又是一篇規模龐大的史話，因此我們只是在這裡極簡單地作一些描述。這一工作由狄拉克開始，經由約爾當、海森堡、泡利和維格納的發展，很快人們就認識到：原來所有粒子都是彌漫在空間中的某種場，這些場有著不同的能量形態，而當能量最低時，這就是我們通常說的真空。因此真空其實只不過是粒子的一種不同形態（基態）而已，任何粒子都可以從中被創造出來，也可以互相湮滅。狄拉克的方程預言了所謂的反物質的存在，任何受過足夠科普薰陶的讀者對此都應該耳熟能詳：比如一個正常的氫原子由帶正電的質子和帶負電的電子組成，但在一個反氫原子中，質子卻帶著負電，而電子帶著正電！當一個原子和一個反原子相遇，它們就轟隆一聲放出大量的能量輻射，然後雙方同時消失得無影無蹤，其關係就符合二十世紀最有名的那個物理方程：E＝mc^2！ 最早的反電子由加州理工的安德森（Carl Anderson）於一九三二年在研究宇宙射線的時候發現。它的意義是如此重要，以致於僅僅過了四年，諾貝爾獎評委會就罕見地授予他這一科學界的最高榮譽。 但是，雖然關於輻射場的量子化理論在某些問題上是成功的，但麻煩很快就到來了。一九四七年，在《物理評論》上刊登了有關蘭姆移位和電子磁矩的實驗結果，這和現有的理論發生了微小的偏差，於是人們決定利用微擾辦法來重新計算準確的值。但是，算來算去，人們驚奇地發現，當他們想盡可能地追求準確，而加入所有的微擾項之後，最後的結果卻適得其反，它總是發散為無窮大！ 這可真是讓人沮喪的結果，理論算出了無窮大，總歸是一件荒謬的事情。為了消除這個無窮大，無數的物理學家們進行了艱苦卓絕，不屈不撓的鬥爭。這個陰影是如此難以驅散，如附骨之蛆一般地叫人頭痛，以至於在一段時間裡把物理學變成了一個讓人無比厭憎的學科。最後的解決方案是日本物理學家朝永振一郎、美國人施溫格（Julian S Schwiger）和戴森（Freeman Dyson），還有那位傳奇的費因曼所分別獨立完成的，被稱為重正化（renormalization）方法，具體的技術細節我們就不用理會了。雖然認為重正化牽強而不令人信服的科學家大有人在，但是採用這種手段把無窮大從理論中趕走之後，剩下的結果其準確程度令人吃驚得瞠目結舌：處理電子的量子電動力學（QED）在經過重正化的修正之後，在電子磁距的計算中竟然一直與實驗值符合到小數點之後第十一位！亙古以來都沒有哪個理論能夠做到這樣教人咋舌的事情。 實際上，量子電動力學常常被稱作人類有史以來最為精確的物理理論，如果不是實驗值經過反覆測算，這樣高精度的資料實在是讓人懷疑是不是存心偽造的。但巨大的勝利使得一切懷疑都最終迎刃而解，QED也最終作為量子場論一個最為悠久和成功的分支而為人們熟知。雖然最近彭羅斯聲稱說，由於對赫爾斯-泰勒脈衝星系統的觀測已經積累起了如此確鑿的關於引力波存在的證明，這實際上使得廣義相對論的精確度已經和實驗吻合到十的負十四次方，因此超越了QED（赫爾斯和泰勒獲得了一九九三年諾貝爾物理獎）。但無論如何，量子場論的成功是無人可以否認的。朝永振一郎，施溫格和費因曼也分享了一九六五年的諾貝爾物理獎。 拋開量子場論的勝利不談，量子論在物理界的幾乎每一個角落都激起激動人心的浪花，引發一連串美麗的漣漪。它深入固體物理之中，使我們對於固體機械和熱性質的認識產生了翻天覆地的變化，更打開了通向凝聚態物理這一嶄新世界的大門。在它的指引下，我們才真正認識了電流的傳導，使得對於半導體的研究成為可能，而最終帶領我們走向微電子學的建立。它駕臨分子物理領域，成功地解釋了化學鍵和軌道雜化，從而開創了量子化學學科。如今我們關於化學的幾乎一切知識，都建立在這個基礎之上。而材料科學在插上了量子論的雙翼之後，才真正展翅飛翔起來，開始深刻地影響社會的方方面面。在量子論的指引之下，我們認識了超導和超流，我們掌握了雷射技術，我們造出了電晶體和積體電路，為一整個新時代的來臨真正做好了準備。量子論讓我們得以一探原子內部那最為精細的奧秘，我們不但更加深刻地理解了電子和原子核之間的作用和關係，還進一步拆開原子核，領略到了大自然那更為令人驚歎的神奇。在浩瀚的星空之中，我們必須借助量子論才能把握恒星的命運會何去何從：當它們的燃料耗盡之後，它們會不可避免地向內坍縮，這時支撐起它們最後骨架的就是源自泡利不相容原理的一種簡並壓力。當電子簡並壓力足夠抵擋坍縮時，恒星就演化為白矮星。要是電子被征服，而要靠中子出來抵抗時，恒星就變為中子星。最後，如果一切防線都被突破，那麼它就不可避免地坍縮成一個黑洞。但即使黑洞也不是完全黑的，如果充分考慮量子不確定因素的影響，黑洞其實也會產生輻射而逐漸消失，這就是以其鼎鼎大名的發現者史蒂芬．霍金而命名的霍金蒸發過程。 當物質落入黑洞的時候，它所包含的資訊被完全吞噬了。因為按照定義，沒什麼能再從黑洞中逃出來，所以這些資訊其實是永久地喪失了。這樣一來，我們的決定論再一次遭到毀滅性的打擊：現在，即使是預測概率的薛定諤波函數本身，我們都無法確定地預測！因為宇宙波函數需要掌握所有物質的資訊，而這些資訊卻不斷地被黑洞所吞沒。霍金對此說了一句同樣有名的話：上帝不但擲骰子，他還把骰子擲到我們看不見的地方去！這個看不見的地方就是黑洞奇點。不過由於蒸發過程的發現，黑洞是否在蒸發後又把這些資訊重新吐出來呢？在這點上人們依舊爭論不休，它關係到我們的宇宙和骰子之間那深刻的內在關係。 最後，很有可能，我們對於宇宙終極命運的理解也離不開量子論。大爆炸的最初發生了什麼？是否存在奇點？在奇點處物理定律是否失效？因為在宇宙極早期，引力場是如此之強，以致量子效應不能忽略，我們必須採取有效的量子引力方法來處理。在採用了費因曼的路徑積分手段之後，哈特爾（就是提出DH的那個）和霍金提出了著名的無邊界假設：宇宙的起點並沒有一個明確的邊界，時間並不是一條從一點開始的射線，相反，它是複數的！時間就像我們地球的表面，並沒有一個地方可以稱之為起點。為了更好地理解這些問題，我們迫切地需要全新的量子宇宙學，需要量子論和相對論進一步強強聯手，在史話的後面我們還會講到這個事情。 量子論的出現徹底改變了世界的面貌，它比史上任何一種理論都引發了更多的技術革命。核能、電腦技術、新材料、能源技術、資訊技術這些都在根本上和量子論密切相關。牽強一點說，如果沒有足夠的關於弱相互作用力和晶體衍射的知識，DNA的雙螺旋結構也就不會被發現，分子生物學也就無法建立，也就沒有如今這般火熱的生物技術革命。再牽強一點說，沒有量子力學，也就沒有歐洲粒子物理中心（CERN），而沒有CERN，也就沒有互聯網的www服務，更沒有劃時代的網路革命，各位也就很可能看不到我們的史話，呵呵。 如果要評選二十世紀最為深刻地影響了人類社會的事件，那麼可以毫不誇張地說，這既不是兩次世界大戰，也不是共產主義運動的興衰，也不是聯合國的成立，或者女權運動，殖民主義的沒落，人類探索太空等等。它應該被授予量子力學及其相關理論的創立和發展。量子論深入我們生活的每一個角落，它的影響無處不在，觸手可得。許多人喜歡比較二十世紀齊名的兩大物理發現相對論和量子論究竟誰更偉大，從一個普遍的意義上來說這樣的比較是毫無意義的，所謂偉大往往不具有可比性，正如人們無聊地爭論李白還是杜甫，莫札特還是貝多芬，漢朝還是羅馬，貝利還是馬拉多納，Beatles還是滾石，阿甘還是肖申克但僅僅從實用性的角度而言，我們可以毫不猶豫地下結論說：是的，量子論比相對論更加有用。 也許我們仍然不能從哲學意義上去真正理解量子論，但它的進步意義依舊無可限量。雖然我們有時候還會偶爾懷念經典時代，懷念那些因果關係一絲不苟，宇宙的本質簡單易懂的日子，但這也已經更多地是一種懷舊情緒而已。正如電影《亂世佳人》的開頭不無深情地說：曾經有一片屬於騎士和棉花園的土地叫做老南方。在這個美麗的世界裡，紳士們最後一次風度翩翩地行禮，騎士們最後一次和漂亮的女伴們同行，人們最後一次見到主人和他們的奴隸。而如今這已經是一個只能從書本中去尋找的舊夢，一個隨風飄逝的文明。雖然有這樣的傷感，但人們依然還是會歌頌北方揚基們最後的勝利，因為我們從他們那裡得到更大的力量，更多的熱情，還有對於未來更執著的信心。 四 但量子論的道路仍未走到盡頭，雖然它已經負擔了太多的光榮和疑惑，但命運仍然註定了它要繼續影響物理學的將來。在經歷了無數的風雨之後，這一次，它面對的是一個前所未有強大的對手，也是最後的終極挑戰廣義相對論。 標準的薛定諤方程是非相對論化的，在它之中並沒有考慮到光速的上限。而這一工作最終由狄拉克完成，最後完成的量子場論實際上是量子力學和狹義相對論的聯合產物。當我們僅僅考慮電磁場的時候，我們得到的是量子電動力學，它可以處理電磁力的作用。大家在中學裡都知道電磁力：同性相斥，異性相吸，量子電動力學認為，這個力的本質是兩個粒子之間不停地交換光子的結果。兩個電子互相靠近並最終因為電磁力而彈開，這其中發生了什麼呢？原來兩個電子不停地在交換光子。想像兩個溜冰場上的人，他們不停地把一隻皮球拋來拋去，從一個人的手中扔到另一個人那裡，這樣一來他們必定離得越來越遠，似乎他們之間有一種斥力一樣。在電磁作用力中，這個皮球就是光子！那麼同性相吸是怎麼回事呢？你可以想像成兩個人背靠背站立，並不停地把球扔到對方面對的牆壁上再反彈到對方手裡。這樣就似乎有一種吸力使兩人緊緊靠在一起。 但是，當處理到原子核內部的事務時，我們面對的就不再是電磁作用力了！比如說一個氦原子核，它由兩個質子和兩個中子組成。中子不帶電，倒也沒有什麼，可兩個質子卻都帶著正電！如果說同性相斥，那麼它們應該互相彈開，而怎麼可能保持在一起呢？這顯然不是萬有引力互相吸引的結果，在如此小的質子之間，引力微弱得基本可以忽略不計，必定有一種更為強大的核力，比電磁力更強大，才可以把它們拉在一起不致分開。這種力叫做強相互作用力。 聰明的各位也許已經猜到了，既然有強相互作用力，必定相對地還有一種弱相互作用力，事實正是如此。弱作用力就是造成許多不穩定的粒子衰變的原因。這樣一來，我們的宇宙中就總共有著四種相互作用力：引力、電磁力、強相互作用力和弱相互作用力。它們各自為政，互不管轄，遵守著不同的理論規則。 但所有這些力的本質是什麼呢？是不是也如同電磁力那樣，是因為交換粒子而形成的？日本物理學家湯川秀樹他或許是日本最著名的科學家預言如此。在強相互作用力中，湯川認為這是因為核子交換一種新粒子介子（meson）而形成的。他所預言的介子不久就為安德森等人所發現，不過那卻是一種不同的介子，現在稱為μ子，它和湯川理論無關。湯川所預言的那種介子現在稱為π子，它最終在一九四七年為英國人鮑威爾（Cecil Frank Powell）在研究宇宙射線時所發現。湯川獲得了一九四九年的諾貝爾物理獎，而鮑威爾獲得了一九五○年的。對於強相互作用力的研究仍在繼續，人們把那些感受強相互作用力的核子稱為強子，比如質子、中子等。一九六四年，我們的蓋爾曼提出，所有的強子都可以進一步分割，這就是如今家喻戶曉的誇克模型。每個質子或中子都由三個誇克組成，每種誇克既有不同的味道，更有不同的顏色，在此基礎上人們發明了所謂的量子色動力學（QCD），來描述。誇克之間同樣通過交換粒子來維持作用力，這種被交換的粒子稱為膠子（gluon）。各位也許已經有些頭暈腦脹，我們就不進一步描述了。再說詳細描述基本粒子的模型需要太多的筆墨，引進太多的概念，但我們的史話所留下的篇幅已經不多，所以只能這樣簡單地一筆帶過。如果想更好地瞭解有關知識，蓋爾曼曾寫過一本通俗的讀物《誇克與美洲豹》，而偉大的阿西莫夫（Isaac Asimov）則有更多精采的論述，雖然時代已經不同，但許多作品卻仍然並不過時！ 強相互作用是交換介子，那麼弱相互作用呢？湯川秀樹同樣預言它必定也交換某種粒子，這種粒子被稱為中間玻色子。與強作用力所不同的是，弱相互作用力的理論形式看上去同電磁作用力非常相似，這使得人們開始懷疑，這兩種力實際上是不是就是同一種東西，只不過在不同的環境中表現得不盡相同而已？特別是當李政道與楊振寧提出了弱作用下宇稱不守恆之後，這一懷疑愈加強烈。終於到了六十年代，統一弱相互作用力和電磁力的工作由美國人格拉肖（Sheldon Glashow）、溫伯格（Steven Weinberg）和巴基斯坦人薩拉姆（Aldus Salam）所完成，他們的成果被稱為弱電統一理論，三人最終為此得到了一九七九年的諾貝爾獎。該理論所預言的三種中間玻色子（W＋，W－和Z0）到了八十年代被實驗所全部發現，更加證實了它的正確性。 物理學家們現在開始大大地興奮起來了：既然電磁力和弱作用力已經被證明是同一種東西，可以被一個相同的理論所描述，那麼我們又有什麼理由不去相信，所有的四種力其實都是同一種東西呢？所有的物理學家都相信，上帝大自然的創造者他老人家是愛好簡單的，他不會把我們的世界搞得複雜不堪，讓人搖頭嘆氣，他必定按照某一種標準的模式創造了這個宇宙！而我們要做的工作，就是把上帝所依據的這個藍圖找出來。這藍圖必定只有一份，而所有的物理現象，物理力都被涵蓋在這個設計之中！如果模仿《獨立宣言》中那著名的句子，物理學家完全願意宣稱： 我們認為這是不言而喻的事實：每一種力都是被相同地創造的。 We hold the truth to be self-evident, that all forces are created equal. 是啊，要是真有那麼一個理論，它可以描述所有的四種力，進而可以描述所有的物理現象，那該是怎樣一幅壯觀的場面啊！那樣一來，整個自然，整個物理就又重新歸於統一之中，就像史詩中所描寫的那個傳奇的黃金時代與偉大的經典帝國，任何人都無法抗拒這樣一種誘人的景象，仿佛一個新的偉大時代就在眼前。戎馬已備，戈矛已修，浩浩蕩蕩的大軍終於就要出發，去追尋那個失落已久的統一之夢。 現在，弱作用力和電磁力已經被合併了，下一個目標是強相互作用力，正如我們已經介紹的那樣，這塊地域目前為止被量子色動力學所統治著。但幸運地是，雖然兵鋒指處，形勢緊張嚴峻，大戰一觸即發，但兩國的君主卻多少有點血緣關係，這給和平統一留下了餘地：它們都是在量子場論的統一框架下完成的。一九五四年，楊振寧和米爾斯建立了規範場論，而吸取了對稱性破缺的思想之後，這使得理論中的某些沒有品質的粒子可以自發地獲得品質。正因為如此，中間玻色子和光子才得以被格拉肖等人包含在同一個框架內。而反觀量子色動力學，它本身就是模仿量子電動力學所建立的，連名字都模仿自後者！所不同的是光子不帶電荷，但膠子卻帶著顏色荷，但如果充分地考慮自發對稱破缺的規範場，將理論擴充為更大的單群，把膠子也拉進統一中來並非不可能。這樣的理論被驕傲地稱為大統一理論（Grand Unified Theory，GUT），它後來發展出了多個變種，但不管怎樣，其目標是一致的，那就是統一弱相互作用力、強相互作用力和電磁力三種力，把它們合併在一起，包含到同一個理論中去。不同的大統一理論預言了一些不同的物理現象，比如質子可能會衰變，比如存在著磁單極子，或者奇異弦，但可惜的是，到目前為止這些現象都還沒有得到確鑿的證實。退一步來說，由於理論中一些關鍵的部分比如希格斯玻色子的假設到目前為止都尚未在實驗中發現，甚至我們連粒子的標準模型也不能一百％地肯定正確。但無論如何，大統一理論是非常有前途的理論，人們也有理由相信它終將達到它的目標。 可是，雖然號稱大統一，這樣的稱號卻依舊是名不副實的。就算大統一理論得到了證實，天下卻仍未統一，四海仍未一靖。人們怎麼可以遺漏了那塊遼闊的沃土引力呢？GUT即使登基，他的權力仍舊是不完整的，對於引力，他仍舊鞭長莫及。天無二日民無二君，雄心勃勃的物理學家們早就把眼光放到了引力身上，即使他們事實上連強作用力也仍未最終征服。正可謂尚未得隴，便已望蜀。 引力在宇宙中是一片獨一無二的區域，它和其他三種力似乎有著本質的不同。電磁力有時候互相吸引，有時候互相排斥，但引力卻總是吸引的！這使它可以在大尺度上累加起來。當我們考察原子的時候，引力可以忽略不計，但一旦我們的眼光放到恒星、星雲、星系這樣的尺度上，引力便取代別的力成了主導因素。想要把引力包含進統一的體系中來是格外困難的，如果說電磁力、強作用力和弱作用力還勉強算同文同種，引力則傲然不群，獨來獨往。何況，我們並沒有資格在它面前咆哮說天兵已至，為何還不服王化云云，因為它的統治者有著同樣高貴的血統和深厚的淵源：這裡的國王是愛因斯坦偉大的廣義相對論，其前身則是煌煌的牛頓力學！ 物理學到了這個地步，只剩下了最後一個分歧，但也很可能是最難以調和和統一的分歧。量子場論雖然爭取到了狹義相對論的合作，但它還是難以征服引力：廣義相對論拒絕與它聯手統治整個世界，它更樂於在引力這片保留地上獨立地呼風喚雨。從深層