Chapter 13 Chapter 9 Measurement Problems-2

This is actually an enhanced version of the "anthropic principle" (anthropic principle).The anthropic principle is that the very fact of our existence determines why certain properties of the universe are one way and not the other.That is to say, the premise of our discussion of all issues is that there are actually some intelligent creatures like us to discuss these issues.Let's recall Descartes' "first principle": No matter what I doubt, there is one thing I cannot doubt, and that is "I am doubting" itself. "Cogito ergo sum"!A similar principle applies to the anthropic principle: no matter what the nature of the universe is, it must make it possible for intelligent life to exist in it, otherwise no one will ask the question "Why is the universe like this?"No matter what kind of question you ask, you must first ensure that there is a "person" to ask the question, otherwise it will be meaningless.

For example, currently the universe seems to be expanding at a "just right" rate.As long as it expands just a little faster, the original matter will fly away, and it will not be able to condense into galaxies and planets.Conversely, if it is just a little slower, gravity will pull all matter together into a hodgepodge of incredible density and temperature.And we happen to be at a "critical speed", which makes the birth of various complex structures and life in the universe possible.How accurate is this speed?It is about one part of 10^55. What kind of concept is this?You can aim from one end of the universe and hit a fly on the other (30 billion light-years away) with an accuracy of 1 in 10^30.There are dozens of similar astonishingly accurate cosmological constants.

We ask: why is the universe expanding at such a rate?The answer of the anthropic principle is: the universe must expand at such a rate, otherwise there would be no "you" to ask this question.Because only at such a speed of expansion can life and wisdom be born, thus making it possible to raise questions!Obviously no one will ask: "Why is the universe expanding at a rate of 1 m/s?" Because the universe expanding at this rate is a ball of fire, and no one will exist there. The participatory universe is an enhanced anthropic principle, which not only shows that our existence affects the nature of the universe, but even more, our existence creates the universe and its history itself!It is conceivable that various cosmological constants are an uncertain superposition at first, and become definite only after being observed by the observer.But then they have to stay within some precise range in order to create a good environment for observers to be able to exist in the universe and observe them!It seems like a logical loop: we chose the universe, and the universe created us.This strange thing is called "self-referencing" or "self-exciting", where the existence of consciousness in turn creates its own past!

Readers, please be sure that I am as big as a bucket and buzzing like you when I write this.The weirdness of this theory has almost exceeded the psychological limit we can bear. We are exhausted in "consciousness" and unable to move on.It is not only us laymen who find this unacceptable. John Bell, who was already famous at the time, Bell (we'll get to him shortly) muttered, "Has the cosmic wave function been waiting for a single-celled organism for eons before collapsing? Or is it waiting a little longer until a Qualified observer with a doctorate?" If Einstein was alive, how would he feel if someone published such a weird, causal-defying model on his birthday?

Even in terms of the Copenhagen interpretation itself, "consciousness" seems to have gone too far.Most "mainstream" physicists still approach this issue with caution, taking a more "orthodox" Copenhagen view.However, the so-called "orthodoxy" is actually a kind of ostrich policy. It actually puts this problem aside, simply assumes that the wave function collapses as soon as it is observed, and does not know how, when, and why it collapses. Do not ask.As long as quantum theory works in practice, we are more concerned about some practical issues than this kind of mysterious exposition!

However, in any case, when the new physics touches the core of such an ontology problem that has troubled mankind for thousands of years, it undoubtedly aroused the enthusiasm and curiosity of many physicists.Indeed, some scientists have continued to explore along Wigner's direction and demonstrated the role of consciousness in the interpretation of quantum theory.The representative figure here is the American physicist Henry Stapp of the Lawrence National Physical Laboratory in Berkeley. Stapp), he has been arguing with other physicists since he published the book "Mind, Matter, and Quantum Mechanics" (Mind, Matter, and Quantum Mechanics) in 1993 (if you are interested, you can go to him 's webpage

j. Bierman claims to have demonstrated experimentally that human consciousness "does" collapse the wave function.However, the supporters of this faction have still been unable to establish a convincing model for "consciousness". Regarding their claims, we'd better adopt a slightly cautious and conservative attitude when we are afraid, and look at the future development How to say again. We followed the path blazed by the Copenhagenists, but perhaps went too far, went astray, and found that at the end there was a monster called "consciousness" that horrified us.This is not the original intention of Bohr and the Copenhagen faction. Let's go back to where most people stand and see if there is any other way forward.Well, we found that there are indeed a few small roads leading to unknown ends. Let us try to change a few roads and see if it will lead us to a bright and broad road.But let us first mark the original road, write the words "monster of consciousness" prominently and put an exclamation point to alert future generations.Well, now we set off to explore another road, which appears to be shrouded in a thick fog, and which seems to split into infinite forks in the distance.I seem to have a bad premonition, but let's wipe off our sweat and have the courage to go and have a look.

*********** Gossip after dinner: Heisenberg and the German atomic bomb program (7) Heisenberg soon learned from the newspapers the actual weight of the bomb: 200 kilograms, with only a few kilograms of explosive core.He looked irritated and wondered where his calculations had gone wrong.He told Hartke: "How did they do it? I would be ashamed if we professors who have done the same work can't even understand how they did it (theoretically)." German Various possibilities were discussed, but it wasn't until the 14th that things took a decisive turn. On August 14th, Heisenberg finally realized the correct calculation method (not all), he gave a lecture in front of other scientists, and generally got relatively correct results.He concluded with a 6.2cm radius - 16kg!When he was teaching, other scientists showed ignorance about it, and their questions were often childish and ridiculous.The Germans paid the ultimate price for their arrogance.

Further analysis of this matter can be found in the two books "Heisenberg and the Nazi Atomic Bomb Program" (Paul Rose) published in 1998 and "Hitler's Uranium Club" (Jeremy Bernstein) published in 2000. Very detailed information.On the whole, there have been relatively few serious historians who have disputed the matter in recent years, at least in the English-speaking world. We have also made a breakthrough with regard to the meeting of Heisenberg and Bohr in Copenhagen in 1941, the scene explored in the play Copenhagen.There was so much discussion about the meeting that Bohr's family released some of his unsent letters 10 years in advance (they were supposed to be kept secret for 50 years) that talked about the 1941 meeting (we know, Bohr almost never talked about these during his lifetime), in order to prevent people from "misunderstanding their content".These letters were published on Bohr's official website on February 6, 2002 (

In these letters, which were revealed for the first time, we can see Bohr's attitude towards Heisenberg's visit.The main one of these letters was to be sent to Heisenberg after Bohr received Robert Jungk's new book Brighter than a Thousand Suns, which, as we have said, praised the German The scientific ethics shown on the issue of the atomic bomb (based on interviews with Heisenberg himself!).Bohr made it clear that he clearly remembered every conversation of that year, and he and his wife Margaret left a strong impression: Heisenberg and Weizack tried hard to convince Bohr that Germany's final victory was inevitable. Avoid, therefore it is unwise to take an uncooperative attitude.Bohr said that when Heisenberg talked about the atomic bomb program, the only feeling he left was that under Heisenberg's leadership, Germany was getting everything done step by step.He emphasized that he remained silent not because, as Heisenberg later claimed, he was shocked by the feasibility of the atomic bomb, but because Germany was committed to building an atomic bomb!Bohr was clearly dissatisfied with the misleadingness of Heisenberg's and Jungk's books.In other letters, he also mentioned that Heisenberg and others explained to other Danish scientists that their attitude towards Germany was unwise, because Germany's victory was so obvious.Bohr seemed to have wanted to have a private conversation with Heisenberg many times in order to clarify the misunderstandings about this period of history, but in the end none of his letters were sent out, presumably because he thought it over and over again, and let it go.

These files can be found at It is easy to understand why, when Mrs. Bohr saw Heisenberg and Weizack again many years later, she angrily said to others: "No matter what others say, it was not a friendly visit!" These documents also partially support Heisenberg's biographer Cassidy's Physics Today article in 2000 (this article was written for the play "Copenhagen"). Cassidy believes that Heisenberg went to Copenhagen to convince Bohr that German occupation of Europe was not the worst thing (at least better than Soviet occupation of Europe), and hoped that Bohr would use his influence to persuade allied scientists not to build atomic bombs. Of course, there are still those who defend Heisenberg, the main representative being one of his students Klaus Gottstein, and Weizak, who was traveling with him back then, still believes that Bohr made a "terrible memory error". Regardless of the facts, Heisenberg's true image may have been that of an ordinary man—an ordinary German caught unprepared in the war years.He is not a hero, nor is he a villain. His disapproval attitude towards the Nazis is obvious to all. He may just be involuntarily doing all the helpless things during the war years.While historians are increasingly agreeing, the scientific community tends to be more sympathetic to him. Duck of Rice University and Sudarshan of the University of Texas said: "Great people are only great 10% of the time... what matters is that they have made original, important, important contributions...so Hessen It doesn't matter to us whether Bauer was a perfect man in the second half of his life, what matters is that he founded quantum mechanics." In the history of science, the image of Heisenberg may always be the big boy who brought the dawn of physics at sunrise on Helgeland Island? Four Take a fall, gain a wisdom, let's sum up the lesson.The reason why we will encounter such terrible things as "consciousness" is that we cannot accurately define an "observer"!What is the difference between a person and a camera? Everyone can't tell the truth, so "consciousness" takes the opportunity to enter.And it is the damned "collapse" that pushes us to the point where we have to define what an "observer" is.An observer makes the wave function collapse?This seems to confer a sort of cosmic supremacy on the so-called observers, who enjoy some sort of privilege beyond the fundamental laws of physics and can create some truly wondrous things. Really, tracing back to the source, the culprit lies in the ambiguous "wave function collapse".This seems to be a curse of the Copenhagen School, which still traps us today, and the future of physics looks bleak under its curse.Cornell physicist Kurt Gottfried Gottfried's words, this "collapse" is like "an ugly scar on a beautiful theory," clouded, plausible, blurred, and everyone clamoring about it in their own way.How to draw the line between observers and non-observers?Does the wave function of Schrödinger's cat collapse the moment we open the box?Or does it have to wait until photons enter our eyes and spark electrical impulses in the retina?Or does it have to wait a little longer until the signal travels somewhere in the cortex and finally becomes a "mental activity" before it actually collapses?The future doesn't seem so good if we go too far on it. So, is there a way to bypass this so-called "collapse" and "observer", kick the intervention of intelligent beings out of physics, and bring it back to the track we are familiar with and love?Let's revisit the classic double-slit dilemma: Do electrons go through the left slit, or the right?According to the Copenhagen explanation, when we are not observing, its wave function presents two possible linear superpositions.Once observed, a peak appears on one side, the wave function "collapses", and randomly chooses to pass through a slit on the left or right.The randomness of the quantum world is best expressed in collapses. To get rid of this dilemma and not admit the collapse, the only way is to admit that the wave function never "chooses" left or right, and it always maintains a state of linear superposition, no matter whether it is observed or not.But this is obviously inconsistent with our actual experience, because no one has ever observed electrons passing through the left and right slits at the same time in reality, and no one has seen a cat that is dead and alive at the same time (half dead, half dead, dying) There are quite a few).We are now in a dilemma, and the curse of Copenhagen has haunted us. If we don't muster up the courage to make the most shocking assumptions, we will be doomed. If the wave function does not collapse, it must remain a linear superposition.Electrons must be a left/right superposition, but this phenomenon has never been observed in the real world. There is a madness that can lift this heinous curse, although it sounds really crazy, but if we don't choose our way, we are nothing to lose.What is lost is only the shackles, but maybe what is gained is the whole world? yes!The electron is still in a left/right superposition even after observation, but our world is only part of the superposition!When the electrons pass through the double slit, it is not only the electrons that are in a superposition state, but also our whole world!That is to say, when an electron passes through the double slit, two superimposed worlds appear, in one of which the electron passes through the left slit, and in the other world, the electron passes through the right! The wave function does not need to "collapse" to randomly choose left or right. In fact, both possibilities have occurred!It's just that it appears as a superposition of the whole world: people living in one world see electrons passing through the slit on their left, while in the other world people observe electrons on the right!Quantum process creates "two worlds"!This is the "Many Worlds Interpretation" (MWI for short) of quantum theory. To better understand MWI, one has to learn from its founder, the legendary Hugh Everett III (Hugh Everett III, his grandfather and father are both named Hugh Everett, so he is actually "Everett III"). On November 9, 1930, Einstein published his famous article "On Science and Religion" in the "New York Times Magazine", and his famous words still echo in our ears today: "Science without religion is lame." Religion without science is blind.” Two days later, Everett Jr. was born in Washington. Everett had a deep respect for Einstein. When he was only 12 years old, he wrote to Einstein in Princeton to ask some questions about the universe, and Einstein actually replied to him. .When he got his undergraduate degree in chemical engineering, he also enrolled in Princeton.At first he entered the mathematics department, but he quickly managed to switch to physics. The 1950s was the time when quantum theory was in the ascendant, and the Copenhagen interpretation was in full swing and dominated the world.Everett knew many physics students in this area, including Bohr's assistant Aage Peterson, who discussed with him the observational problems in quantum theory, which aroused Everett's great interest.He soon came into contact with John Wheeler, who encouraged his thinking in this area, and by 1954 Everett had submitted two papers to Wheeler, The Many-Worlds Theory (sometimes called "Everett -Everettism") made its first appearance. According to Everett, the wave function never collapses, but only the world and the observer itself go into superposition.When electrons pass through the double slit, the whole world, including ourselves, becomes two independent superpositions, and in each world, electrons appear as one possibility.But unfortunately, Everett used a misleading and ambiguous word "splitting" (splitting). He made an analogy, saying that the universe is like an amoeba. When electrons pass through the double slit, the bug Self-fission, reproduction into two almost identical amoebas.The only difference is that one bug remembers that the electrons passed from the left, and the other remembers that the electrons passed from the right. Perhaps aware of the misuse of the term, Wheeler wrote in the margin of his paper: "Splitting? Better to change the word." But most physicists don't know his opinion.Perhaps Wheeler should have dramatized it a bit, writing "I thought of a brilliant word, but the space is too small to fit." For a long time, Everett's theory was understood as : When electrons pass through the double slit, the universe magically "splits" into two separate universes, with electrons passing through the left slit in one and the opposite in the other.In this way, the history of the universe is like a fork in the road. Every time an observation is made, it forks into a number of small roads, each road corresponding to a possible outcome.And every forked road splits further as we continue to observe, until infinity.But each path is real, but they cannot communicate with each other. Suppose we observe a double-slit experiment and find that electrons pass through the left slit.In fact, the moment we observe, the universe has been "split" unknowingly, and it has become two almost identical.The one we're in is called the "left universe," and there's another "right universe," where we'll find electrons going through the right slit, but otherwise everything is exactly like our universe.You might ask, "Why am I in the left universe and not the right universe?" This kind of question obviously doesn't make sense, because in another universe, another you might also ask, "Why am I in the right universe, Rather than in the left universe?" The position of the observer is no longer important, because the universe will split anyway, and in fact "all results" will appear, and everything that may be produced by the quantum process corresponds to a corresponding universe, but in In most "wild universes", there are no intelligent beings to ask questions. In this way, Schrödinger's cat no longer has to worry about life and death.It's just that the universe split into two, one with live cats and one with dead cats.For the universe of living cats, cats are always alive, and there is no problem of superposition of life and death.For the universe of dead cats, the cat is literally dead at the moment of splitting, and don't wait for people to open the box to "collapse" to make a final conclusion. Since the birth of the universe, there have been countless such splits, and its number has grown exponentially, and will soon tend to infinity.The universe we are in now is just one of them, and there are many other universes outside of it.Some are very close to us, having recently split off on the family tree, while universes that have parted ways from us in distant antiquity may be very different.Perhaps in some universe, the asteroid did not hit the earth, and the dinosaurs still ruled the world.In a certain universe, Cleopatra's nose was a little shorter to teach Caesar and Antony to thump.Those "nosed historians" who oppose historical determinism will definitely be very interested in the later development to see if there is really a historical butterfly effect.In some universe, Grouchy wasn't late at Waterloo and Hitler didn't give the order to stop the attack before Dunkirk.And in more universes, because the physical constants are not suitable, there is no life and planets at all. Strictly speaking, everything that may happen in history and in the future has actually happened or will happen.It's just that they're in some other universe that doesn't have any physical contact with the one we're in.These universes are parallel to our world and have no connection. According to the principle of Occam's razor, these wonderful universes are meaningless to us.The theory of many worlds is sometimes called the theory of "parallel universes" because of this reason. The "split" of the universe should actually be regarded as a misunderstanding, but until now, most people, including many physicists, still understand Everett in this way!In this way, this theory seems to be too fussy, for a small electron to pass through from the left or the right, we have to mobilize a large number of people to involve the split of the entire universe!Many people's comments on this are "killing a chicken with a bull's knife".Einstein once said: "I can't believe that a mouse has changed the universe drastically just by looking at it." People's thinking: It is too uneconomical and cheap to cater to the random selection of electrons at the cost of sacrificing the universe, and it also produces so many unobservable "parallel universe" waste materials. One of MWI's most active advocates later, Bryce S. DeWitt of the University of Texas, described the first time he heard about MWI: "I still vividly remember when I was shocked when I first encountered the concept of many worlds. 100 slightly flawed copies of myself, all constantly splitting into further copies, and finally unrecognizable. This idea is hardly consistent with common sense. This It's a complete schizophrenia..." For us, it may be easier to accept "consciousness" than to believe in "universe division"! It is not difficult to imagine that after Everett's MWI was published as a doctoral dissertation in 1957, despite Wheeler's recommendation and revision, it still received a lukewarm response in the physics community.Everett once flew to Copenhagen to meet Bohr in 1959, but Bohr didn't want to discuss any new interpretation of quantum theory at all, and he didn't want to make any comments on it, which made him disheartened.As for Bohr, of course he firmly maintained the Copenhagen theory all his life. For some other explanations that emerged in the 1950s, such as Bohr's implicit function theory (we will talk about it later), his comment is "This is like We hope to prove that 2×2=5 is the same in the future.” In the last interview before Bohr’s death, he was still criticizing some philosophers, claiming: “They don’t know that it (the principle of complementarity) is an objective description, And it's the only possible objective description." Everett, who was neglected, gradually withdrew from the physics field. He first worked for the Ministry of Defense, and later became one of the founders and chairman of the famous Lambda company, which made him a millionaire soon.But his insights—which came to be called "one of the best-kept secrets of the 20th century"—had long been ignored.It wasn't until the 1970s that DeWitt rediscovered his many-worlds explanation and promoted it among physicists, so that MWI began to be known and quickly became one of the hot topics.Today, this interpretation already has a large number of supporters, and it is firmly in the second place after the Copenhagen interpretation, and it is likely to catch up from behind.For this reason, Everett himself had planned to come back and return to the physics world to do some research work on quantum mechanics, but unfortunately he died of a heart attack in 1982. Everett was one of the most revered men at UT, where Wheeler and DeWitt were.When he was invited to give a lecture on quantum theory, he was given special permission to smoke because he was a heavy smoker.It was the only exception in the history of that auditorium. Fives In response to the common misunderstanding of MWI, some scientists have recently tried to rectify its name, clarifying that this weird "cosmic split" is not the original intention of MWI and Everett (such as Tegmark1998), we might as well talk about it here .Of course, to accurately describe it requires the use of very complex mathematical tools and mathematical expressions. Our historical stories are still based on history, and try to be as simple as possible in theory.Here is just the most superficial discussion with you. The mathematics used is guaranteed not to exceed the middle school level. I hope that the judges will not be discouraged. First, let's talk about the concept of the so-called "phase space".Everyone who has read middle school mathematics should have established a two-dimensional Cartesian plane: draw an x-axis and a y-axis perpendicular to it, and add arrows and scales.In such a planar system, each point can be assigned a coordinate with two variables (x, y), such as (1, 2), or (4.3, 5.4), these two numbers represent the projection of the point on the x-axis and y-axis respectively.Of course, it is not necessary to use a Cartesian coordinate system, and a point can also be described in polar coordinates or other coordinate systems, but in any case, for a 2-dimensional plane, a point can be uniquely specified with two numbers.If we want to describe a point in three-dimensional space, then our coordinates must have 3 numbers, such as (1, 2, 3), and these 3 numbers represent the projection of the point in 3 mutually perpendicular dimensions. Let's expand our thinking: If there is a point in a four-dimensional space, how should we describe it?Obviously we need to use coordinates with 4 variables, such as (1, 2, 3, 4), if we use a Cartesian coordinate system, then these 4 numbers represent the projection of the point in 4 mutually perpendicular dimensions , extended to n dimensions, the situation is the same.You don’t need to bother trying to imagine in your mind how the 4-dimensional or 11-dimensional space is perpendicular to each other in 4 or even 11 directions. In fact, this is just a hypothetical system we constructed mathematically.What we care about is: a point in n-dimensional space can be uniquely described by n variables, and conversely, n variables can also be covered by a point in n-dimensional space. Now let's go back to the physical world, how do we describe an ordinary particle?At each time t, it should have a definite position coordinates (q1, q2, q3) and a definite momentum p.Momentum is speed multiplied by mass. It is a vector with components in each dimension. Therefore, to describe momentum p, three numbers must be used: p1, p2 and p3, respectively representing its speed in three directions.All in all, to fully describe the state of a physical particle at time t, we need to use a total of 6 variables.As we have seen before, these 6 variables can be summarized by a point in 6-dimensional space, so with a point in 6-dimensional space, we can describe the classical behavior of an ordinary physical particle.Our deliberately constructed high-dimensional space is the phase space of the system. If a system consists of two particles, then at each time t the system must be described by 12 variables.But again, we can replace it with a point in 12-dimensional space.For some macroscopic objects, such as a cat, it contains too many particles, assuming there are n, but this is not an essential problem, we can still use a particle in a 6n-dimensional phase space to describe it.In this way, the activity of a cat in any period of time can actually be equivalent to the movement of a point in 6n space (assuming that the number of particles composing the cat remains unchanged).We do this not because we are full and too idle, but because in mathematics, it is more convenient to describe the motion of a point, even a point in 6n-dimensional space, than to describe a cat in ordinary space .In classical physics, for such a point in the phase space representing the whole system, we can use the so-called Hamiltonian equation to describe and draw many useful conclusions. As mentioned earlier in our history, both Heisenberg's matrix mechanics and Schrödinger's wave mechanics were transformed from Hamilton's equations, so it is not surprising that they were later proved to be equivalent to each other.Now, in quantum theory, we can also use a method similar to phase space to describe the state of a system, but transform the classical phase space into a complex Hilbert vector space.Readers can ignore the specific details, as long as they grasp the essence: the state of a complex system can be regarded as a point or a vector in some kind of high-dimensional space.For example, a live cat corresponds to a state vector in a certain Hilbert space. If we use the symbol introduced by Dirac, we can use a bracket with a sharp angle to represent it, and write it as: live cat> .A dead cat can be written similarly: dead cat >. Having said all that, what does this have to do with quantum theory or MWI? Let's look back at a quantum process, such as the classic double-slit dilemma.As we have repeatedly mentioned, if we do not observe which slit the electron passes through, it should pass through two slits at the same time and cause interference.At this time, its wave function is a linear superposition, and it evolves strictly according to the Schrödinger equation.That is, ψ> can be expressed as: a through the left seam > b through the right seam > We also remember that the square of the wave function's strength is the probability, and for the sake of simplicity we assume that the probability of a particle passing through the left and right slits is equal, and nothing else is possible.In this way, a^2 b^2=1, and both a and b are 1/2 of the root sign.However, these are just coefficients indicating the probability, and we don't care about it. The key is that the system must be a superposition of "left > right >" when it is not observed! If we do not disturb the system, it develops strictly according to the Schrödinger wave equation.For the convenience of expression, we call this "U process" according to Penrose's words, which is a definite, strict, classical, reversible (time symmetric) process.But it is worth mentioning that the Schrödinger equation is "linear", that is, as long as left > and right > are possible solutions, then a left > b right> must also satisfy the equation!No matter how the U process develops, the system will always remain in the state of linear superposition. Only when we observe the actual behavior of the electron, the electron is forced to behave as a particle and choose a certain slit to pass through.In the words of the Copenhagen school, the wave function of the electron "collapses", and in the end we are left with only one state in the left> or right>.This process is like a miracle, it occurs completely randomly according to the probability, and it is no longer reversible, just as you cannot let what has actually happened return to the uncertain superposition of many probabilities.Still according to Penrose's name, we call this "R process", which is actually the so-called collapse.How to explain the occurrence of the R process is a difficult problem that bothers us.The Copenhagen school believes that the "observer" triggers this process, and some extremes involve "consciousness". So, what is the opinion of MWI? Its statement may surprise you: there is no such thing as a "collapse" at all, and the R process never actually happened!Since the beginning of the world, at any moment, the wave function of any isolated system evolves strictly according to the Schrödinger equation in the U process!If the system is in a superposition state, it must always evolve according to the superposition state! But, wait a minute, it's exhilarating and exhilarating to say so, but it doesn't answer our basic confusion!If superposition states are unavoidable, why have we never observed electrons passing through the double slit at the same time in reality, or cats that are both dead and alive?They appear to be in superposition only when we don't observe them. How does MWI explain our observational conundrum? Let's take a closer look at Everett's assumption: "Any isolated system must evolve strictly according to the Schrödinger equation".The so-called isolated system refers to a system that is completely isolated from the outside world, without energy or material communication. This is an ideal state, but it is difficult to achieve in reality, so it is almost impossible.只有一样东西例外——我们的宇宙本身！因为宇宙本身包含了一切，所以也就无所谓“外界”，把宇宙定义为一个孤立系统似乎是没有什么大问题的。宇宙包含了n个粒子，n即便不是无穷，也是非常非常大的，但这不是本质问题，我们仍然可以把整个宇宙的状态用一个态矢量来表示，描述宇宙波函数的演化。 MWI的关键在于：虽然宇宙只有一个波函数，但这个极为复杂的波函数却包含了许许多多互不干涉的“子世界”。宇宙的整体态矢量实际上是许许多多子矢量的叠加和，每一个子矢量都是在某个“子世界”中的投影，代表了薛定谔方程一个可能的解，但这些“子世界”却都是互相垂直正交，彼此不能干涉的！ 为了各位容易理解，我们假想一种没有维度的“质点人”，它本身是一个小点，而且只能在一个维度上做直线运动。这样一来，它所生活的整个“世界”，便是一条特定的直线，对于这个质点人来说，它只能“感觉”到这条直线上的东西，而对别的一无所知。现在我们回到最简单的二维平面。假设有一个矢量（1, 2），我们容易看出它在x轴上投影为1，y轴上投影为2。如果有两个“质点人”A和B，A生活在x轴上，B生活在y轴上，那么对于A君来说，他对我们的矢量的所有“感觉”就是其在x轴上的那段长度为1的投影，而B君则感觉到其在y轴上的长度为2的投影。因为A和B生活在不同的两个“世界”里，所以他们的感觉是不一样的！但事实上，“真实的”矢量只有一个，它是A和B所感觉到的“叠加”！ 我们的宇宙也是如此。“真实的，完全的”宇宙态矢量存在于一个非常高维的希尔伯特空间中，但这个高维的空间却由许许多多低维的“世界”所构成（正如我们的三维空间可以看成由许多二维平面构成一样），每个“世界”都只能感受到那个“真实”的矢量在其中的投影。因此在每个“世界”看来，宇宙都是不同的。但实际上，宇宙波函数是按照薛定谔方程演化的叠加态。 但还剩下一个问题：如果说每一种量子态代表一个“世界”，为什么我们感觉不到别的“世界”呢？而相当稀奇的是，未经观测的电子却似乎有特异功能，可以感觉来自“别的世界”的信息。比如不受观察的电子必定同时感受到了“左缝世界”和“右缝世界”的信息，不然如何产生干涉呢？这其实还是老问题：为什么我们一“观察”，量子层次上的叠加态就土崩瓦解，绝不会带到宏观世界中来？ 非常妙的解释是：这牵涉到我们所描述“世界”的维数，或者说自由度的数量。在上面的例子中，我们举了A和B分别生活在x轴和y轴上的例子。因为x轴和y轴互相垂直，所以A世界在B世界上根本没有投影，也就是说，B完全无法感觉到A所生活的那个世界究竟是怎样的。但是，这是一个非常极端的例子，事实上如果我们在二维平面上随便取两条直线作为“两个世界”，则它们很有可能并不互相垂直。态矢量在这两个世界上的投影在很大程度上仍然是彼此“相干”（coherent）的，B仍然能够在很大程度上感受到A世界的观测结果，反之亦然（参见附图）。 但是，假如不是2维，而是在很多维的空间中，我们随便画两条直线，其互相垂直的程度就很可能要比2维中的来得大。因为它比2维有着多得多的维数，亦即自由度，直线可以寻求在多个方向上的发展而互不干扰。如果有一个非常高维的空间，比如说1000亿维空间，那么我们随便画两条直线或者平面，它们就几乎必定是基本垂直了。如果各位不相信，不妨自己动手证明一下。 在双缝实验中，假如我们不考虑测量仪器或者我们自己的态矢量，不考虑任何环境的影响，单单考虑电子本身的态矢量的话，那么所涉及的变量是相对较少的，也就是说，单纯描述电子行为的“世界”是一个较低维的空间。我们在前面已经讨论过了，在双缝实验中，必定存在着两个“世界”：左世界和右世界。宇宙态矢量分别在这两个世界上投影为通过左缝> 和通过右缝>两个量子态。但因为这两个世界维数较低，所以它们互相并不是完全垂直的，每个世界都还能清晰地“感觉”到另外一个世界的投影。这两个世界仍然彼此“相干”着！因此电子能够同时感觉到双缝而自我干涉。 请各位密切注意，“左世界”和“右世界”只是单纯地描述了电子的行为，并不包括任何别的东西在内！当我们通过仪器而观测到电子究竟是通过了左还是右之后，对于这一事件的描述就不再是“左世界”等可以胜任的了。事实上，为了描述“我们发现了电子在左”这个态，我们必须动用一个更大的“世界”，叫做“我们感知到电子在左”世界，或者简称“知左”世界。这个世界包括了电子、仪器和我们本身在内，对它的描述就要用到比单个电子多得多的变量（光我们本身就有n个粒子组成）。“知左”世界的维度，要比“左”世界高出不知凡几，现在“知左”和“知右”世界，就很难不互相垂直了，这个戏剧性的变化在于拥有巨大变量数目的环境的引入：当电子层次上的量子态叠加被仪器或者任何宏观事物放大，我们所用于描述该态的“世界”的维数也就迅速增加，这直接导致了原本相干的两个投影变成基本垂直而互不干涉。这个过程叫做“离析”或者“退相干”（decoherence），量子叠加态在宏观层面上的瓦解，正是退相干的直接后果。 用前面所引的符号来表示可能会直观一些，在我们尚未进行观测时，唯一的不确定是电子本身，只有它是两个态的叠加。此时宇宙的态可以表示为： （a 通过左缝> b 通过右缝>）× 未进行观测的我们>× 宇宙的其他部分> ×号表示“并且”（AND），这里无非是说，宇宙的态由电子态，我们的态和其他部分的态共同构成。在我们尚未进行观测时，只有电子态处在叠加中，而正如我们讨论过的，仅涉及电子时，这两个态仍然可能在另一个世界里造成投影而互相感觉。可是，一旦我们进行了观测，宇宙态就变成： （a 通过左缝> 观测到左的我们> b 通过右缝> 观测到右的我们>）× 宇宙的其他部分> 现在叠加的是两个更大的系统态：“ 通过左缝> 观测到左的我们>”和“ 通过右缝> 观测到右的我们>”，它们可以简并成我们发现电子在左>和我们发现电子在右>，分别存在于“知左”和“知右”世界。观测者的“分裂”，也就在这一刻因为退相干而发生了。因为维数庞大，“知左”和“知右”世界几乎不互相干涉，因此在这个层次上，我们感觉不到量子态的叠加。 但是，作为宇宙态矢量本身来说，它始终按照薛定谔方程演化。只有一个“宇宙”，但它包含了多个“世界”。所谓的“坍缩”，只不过是投影在的某个世界里的“我们”因为身在此山中而产生的幼稚想法罢了。最后要提醒大家的是，我们这里所说的空间、维度，都是指构造的希尔伯特空间，而非真实时空。事实上，所有的“世界”都发生在同一个时空中（而不是在另一些维度中），只不过因为互相正交而无法彼此交流。你一定会觉得很不可思议，但量子论早就已经不止一次地带给我们无比的惊讶了，不是吗？