Chapter 16 Chapter Eleven God's Judgment

one Pxz－Pzy≤1＋Pxy Well, this inequality looks so ordinary that it doesn't seem to have any magical power, let alone make the ultimate verdict on the nature of our universe.Does it really have such power? Let's take a look at what Bell's inequality means.As we have described in the previous chapter, Pxy represents the correlation between the two events that particle A is + in the x direction, and particle B is also + in the y direction at the same time.Relevance is a manifestation of a degree of cooperation (whether the two parties are surprisingly consistent or inconsistent means a high degree of cooperation), while cooperation requires that both parties understand each other's situation so that they can coordinate effectively.In the hidden variable theory, our description of the two particles is in line with common sense: whether observed or not, the two particles always exist in the objective reality, and their states are certain from the moment of splitting.If we prohibit the propagation of signals beyond the speed of light in the universe, then theoretically when we observe two particles at the same time, no information can be exchanged between them, and the maximum degree of cooperation they can achieve is only limited to the limit given by the classical world.This limit is the Bell Inequality derived by classical methods.

If the essence of the world is classical, specifically, if our world satisfies at the same time: 1. Localized, that is, there is no propagation of superluminal signals. 2. Real, that is, there exists an external world independent of our observation.Then we randomly take three directions to observe the spins of A and B, and the degree of cooperation they show must be limited within Bell's inequality.In other words, if God is the kind "old man" imagined by Einstein who doesn't throw dice, then Bell's inequality is the sacred bondage he has set for the universe.No matter how our observation direction is taken, the two particles in the EPR experiment can never offend the dignity of his elders, and dare to break through this forbidden area.In fact, this is not a question of dare or not, but that two classical particles do not have such an ability logically: since they cannot exchange signals between them, they must not behave intimately.

However, the predictions of quantum theory are different!Bell proved that in quantum theory, as long as we make the angle θ between a and b small enough, Bell's inequality can be broken!The specific proof requires slightly more complex physics and mathematics knowledge, which I will skip over here, but please believe me, in a quantum-dominated world, the two particles A and B are very far apart. , can still show a high degree of cooperation in different directions, so that Bell's inequality does not hold.This could never have happened in the classical scenario. Let's imagine the EPR experiment in this way: two criminals robbed a bank and fled from the crime scene, but they panicked and fled in two opposite directions. The police captured them separately.Now let's take their confessions, assuming that policeman A asks criminal A: "Are you the one who took the lead?" A's answer is nothing more than "yes" or "no".On the other side of the road, if policeman B asks criminal B the same question: "Are you the one who takes the lead?" Then B's answer must be the opposite of A's, because there can only be one big brother, either A with B or B with him. a.The questions asked by the two policemen are in the "same direction". Knowing the answer of A is equivalent to knowing the answer of B. Their answers are 100% different, and the cooperation rate is 100%.At this point, both the classical world and the quantum world are the same.

However, going back to the classic world, if two policemen ask questions from different angles, for example, ask A: "Do you need to hire a lawyer yourself?" Ask B: "Do you want to drink water now?" Questions that are unrelated to each other (in different directions), A may answer "yes" or "don't", but this should have nothing to do with how B answers the question, because B and A have theoretically lost contact, and B cannot follow the A's actions weigh his own answer. However, this is only a criminal in the classical world. If we have two "quantum criminals", it will be different.When A decides to hire a lawyer, B will be more likely to want to drink water, and vice versa!It seems that there is a kind of magical telepathy between A and B, which makes them answer strangely the same even when faced with different questions!Bonnie & Clyde in the quantum world, even though they are thousands of miles apart, still cooperate seamlessly. According to Copenhagen’s explanation, this is because before the specific answer to the question, the two people do not exist in the “reality” at all, but merge into one, diffuse according to the wave function .Using the terms invented by Schrödinger, before observation, two people (particles) are in a state of "entanglement" (entanglement), they are a whole, with a kind of "inseparability" (inseparability)!

It is of course a simplification to say this, and the specific condition is still our Bell inequality.All in all, if the world is classical, then Bell's inequality must be satisfied in EPR, otherwise it can be broken.This mysterious inequality in our hands has become the touchstone to determine the most basic nature of the universe. It seems to be the key to open the door of mystery, which can lead us to understand the ultimate mystery of nature. And the most exciting thing is that, unlike some cranky experiments (such as crazy quantum suicide), EPR is not unfeasible either technically or ethically!We can indeed do some experiments to see whether the world we live in is localized and real as Einstein prayed, or whether its magic is beyond our imagination after all, so that we mortals have to Continue to explore its deeply hidden secrets with even greater awe.

In 1964, Bell published his inequality in the first issue of a journal called "Physics", entitled "On the EPR Paradox" (On the Einstein-Podolsky-Rosen Paradox).This thesis is a famous article in the history of physics in the 20th century. Its demonstration and derivation are so simple and clear yet profound in its essence, which makes people overwhelmed. Brian D. Josephson, winner of the Nobel Prize in Physics in 1973, called Bell's inequality "the most important new development in physics". The one that collapsed) called it "the most profound discovery in science".

The journal Physics, however, had no luck publishing this brilliant paper, and the journal closed after only one year of publication.The best way to find Bell's original paper these days is in his book Speakable and Unspeakable in Quantum Mechanics (Cambridge 1987). Before that, Bell discovered von Neumann's error and wrote an article for the journal Reviews of Modern Physics.Although due to various reasons, this article was not published until 1966, but in any case it has changed such an embarrassing situation, that is, there is von Neumann's "proof" of the impossibility of implicit function theory on the one hand, but the other side does exist With Bohm's quantum potential!Von Neumann's spell is now broken.

Now, Bell seems full of ambition: all obstacles to Einstein's dream have been cleared for him, von Neumann is no longer in the way, and Bohm has taken the first step.And he has created a weapon enough to kill quantum theory, that is, the infinitely powerful inequality.Bell is convinced of the reality of the world. Nature cannot exist depending on our observations. Does it need to be said?Now, it seems that we only need to arrange an EPR-style experiment to tell the world with irrefutable evidence: no matter under any circumstances, Bell's inequality is also established.Telepathic cooperation between particles is pure nonsense, ridiculous delusion, quantum theory has messed up our thinking, it is time to return to normal conditions.Quantum uncertainty is... well, a beautiful piece of work, a nice attempt, and deserves its rightful place in the history of physics, after all, it works.However, it cannot be real, but only an approximation!What is more reliable and closer to the truth must be a traditional hidden variable theory, which makes people feel as safe as the theory of relativity, without dice flying around, there is no wonderful multiverse, and there is no superluminal signal.Yes, only in this way can the glory of physics be restored, the physics that deserves our pride and ostentation, the true, majestic lawgiver of the universe, and not the opportunist ruled by luck and randomness.

Really, maybe it's just that small step before we can go back to the glory days of old.The long-lost Elysium since Heisenberg, the great picture in which everything in the universe operates in a strict and orderly manner, is the classical era that nostalgic people yearn for.Indeed, it is almost a step away, perhaps, soon we will be singing to the accompaniment of the organ the sacred and immortal sentence of Milton: In the past, there was a paradise, and the years are full of joy. If a son is unfaithful, Tian Hess is angry. Lost in exile, the reason for defending crimes. When one converts, all are redeemed.

Now I come to think and chant his reply. This heart is persevering, and there is no wrong path. All the sins and sins were washed away and returned to the right path. Zhanbi Eden, rising barren. ("Paradise Restored" Volume 1, 1-7) It's just that Bell seems to have forgotten one thing: powerful weapons are often double-edged swords. *********** After-dinner gossip: Bohm and the McCarthy era Bohm was an American scientist, but his greatest contribution was made in England, thanks to the rise of McCarthyism in the United States in the late 1940s and early 1950s. McCarthyism is a product of the Cold War, and its essence is crazily anti-communist and xenophobic.The "red fear" craze reached its climax, fueled by Senator Joseph McCarthy.Almost everyone was suspected of being a Soviet spy, or a hostile element plotting to overthrow the government.Bohm participated in the Manhattan Project for a while during World War II, but he didn't do much real work and soon quit.After the war, he went to Princeton to teach and work with Einstein. At this time, he was subpoenaed by the notorious "Un-American Activities Committee" (Un-American Activities Committee) and asked him to investigate some of his colleagues who were also in Berkeley. Bohm angrily refused to testify on his political position, citing the Fifth Amendment in his defense.

Originally, this incident would have passed, but the McCarthy era had just begun, and panic quickly spread throughout the United States.Two years later, Bohm was tried for refusing to answer the committee's questions. Although he was acquitted, Princeton refused to renew his contract, even when Einstein asked him to stay as an assistant.Bohm finally left the United States, he went to Brazil and Israel, and finally settled at Birkbeck College, University of London.There he developed his theory of implicit functions. The McCarthy era was an era of madness and disgrace, with more than 20 million people subjected to so-called "loyalty checks."From General George Marshall, to Charlie Chaplin, and down to countless ordinary people, they were greatly affected.People are neurotically looking for so-called communists, just like medieval Europe was crazy about witch hunting.In the academic world, nearly a hundred professors left their posts because of "viewpoints". Those with a Chinese background such as Qian Xuesen were censored. The famous quantum chemistry master Pauling was suspected of being a spy of the US Communist Party.More and more people are being called to testify for the political positions of their colleagues. There are a lot of people, some of them categorically refuse like Bohm, and some of them behave unexpectedly.Perhaps the most famous case is the case of Oppenheimer. Oppenheimer was the leader of the Manhattan Project. Even he was suspected of being "disloyal" to the country. It seems inconceivable.All the physicists were on his side, yet Edward Teller had the physics community hardly believe its ears.The Hungarian-born physicist, who is also Yang's mentor, said that while he didn't think Oppenheimer would do anything bad for the country, "if public affairs were left in other people's hands, I would Personally, I feel safer." Oppenheimer's loyalty was not condemned in the end, but his security clearance was confiscated, and top-secret material was no longer sent to him.While some (such as Wheeler) felt sympathy for Taylor, the scientific community as a whole hardly forgave him. Taylor was also a big advocate and one of the actual designers of the hydrogen bomb (he is called "the father of the hydrogen bomb"), he tried to prevent the signing of the Treaty Banning Above-ground Nuclear Tests, and he peddled the "Star Wars" program to Reagan ( SDI Defense).He died last September (2003) at the age of 95.In a book by Carl Sagan, he was drawn out as a typical example that scientists should be responsible for their views. Taylor himself certainly has his own reasons. He believes that the manufacture of hydrogen bombs actually makes human society "safer".As for us, maybe we can only sincerely hope that science itself will not be interfered too much by politics. Although this may be just a utopian dream, we still wish so. two Bohr or Einstein?That's the problem. Physicists are finally taking action, ready to take practice as the only criterion for testing truth, and really explore whether the world conforms to the description of which of the two giants of science.The debate between Bohr and Einstein was just like a philosophical empty talk. Pauli once said to Born that arguing with Einstein about the nature of quantum theory is like arguing about how many angels can sit on the tip of a needle. It is generally illusory, but it is different now, we now have Bell's inequality in our hands.Will the two particles obediently submit to this sacred prohibition of the classical God, or will they defy any shackles with a kind of quantum revolution-like restlessness, and break through this seemingly solemn and inviolable rule?Now we can finally put it into practice, and everything is waiting for the final judgment of the god of fate. In 1969, Clauser et al improved Bohm's EPR model to make it easier to implement.A series of preliminary experiments followed, at Berkeley, Harvard, and Texas, and perhaps to Bell's surprise, all but one pointed vaguely to the predictions of quantum theory.However, the initial experiments were imprecise and far from the prototype of EPR, where the photon pairs radiated by the atoms were passed through polarizers, but technical limitations allowed us to obtain only a single + in all cases. The result, not + and -, so the original inference of EPR still depends on indirect reasoning.And the light sources used at the time often produced only weak signals. With the advancement of technology, especially the advancement of laser technology, more precise and rigorous experiments are possible.In the 1980s, a group of scientists at the Institute of Theoretical and Applied Optics (Institut d'Optique Theorique et Appliquee, Orsay Cedex) in France prepared to test the EPR for the first time in a precise sense. Aspect (Alain Aspect). The French used calcium atoms as the source of photon pairs. They excited the calcium atom to a very high quantum state, and when it fell back to the unexcited state, it released energy, that is, a pair of photons.What is actually used is a beam of calcium atoms, but can be focused with a laser so that they are excited precisely, thus creating a strong signal source.Aspect et al. flew two photons about 12 meters apart, so that it took 40 nanoseconds (ns) for the signal to travel between them, even at the speed of light.Photons enter a pair of polarizers through a gate, but the gate can also change direction, directing them to two polarizers with different polarization directions.If the orientation of the two polarizers is the same, then either both photons will pass through or none will pass through, and if the orientations are different, then theoretically (according to Einstein's world view), the correlation must obey Bell's inequality.In order to ensure that there is no information exchange between the two photons, the scientists quickly switched the position of the gate, changing the direction every 10 ns on average, which is much shorter than the time between the two parties at the speed of light. It is impossible for a photon to know whether the other party has passed through. got the polarizer there. As a comparison, we also examine the situation where no polarizer is placed on both sides, and only one side is placed with a polarizer, in order to eliminate the systematic error in the experiment. So, the thing to do now is to record the actual cooperation degree of the two photons.If it conforms to Bell's inequality, Einstein's belief will be redeemed, and the world will return to its independent, reliable and objective status.On the contrary, we still have to take Borna's seemingly mysterious concept of quantum seriously. The time is 1982, at the turn of late summer and early autumn.In the fashion capital of Paris, people seem to be busy trying to figure out what styles of fashion will be popular in this autumn and winter.In bars, sports fans are still bemoaning the national team's crush on the World Cup in Spain.That year, under the leadership of Platini, the national team considered to be the strongest in history defeated Brazil in a classic match, but finally lost to the West Germans on penalties.The noble gentlemen talked freely about the general trend of the world in the salon, and talked about how the old enemy, the British, manipulated Argentina in the Falklands.The Louvre and the Musée d'Orsay were, as always, crowded with art lovers from all over the world, and the Seine slowly flowed through the city center, reflecting the shadows of the Eiffel Tower and Notre Dame Cathedral, as well as the organists on the side of the road clear eyes. However, how many people know that in the Orsay Institute of Optics not far away, pairs of wonderful photons are being excited from calcium atoms and rushing towards those fateful polarizers; our world is undergoing a The ultimate test, to reveal to us her true face hidden behind the veil of mystery? If Einstein and Bohr are not ambiguous, perhaps they are also watching the results of this experiment in heaven, right?If there is a God, what is the old man doing?Perhaps, even he has to leave it all to fate, using a golden balance and two weights representing fate to determine the nature of this world, just like Achilles and Hector The legendary duel at Troy. One pair, two pairs, three pairs... The data gradually accumulated. After 12,000 seconds, that is, more than 3 hours later, the result came out.The scientists all let out a sigh of relief. Einstein lost!The experimental results were in full agreement with the predictions of quantum theory, but deviated from Einstein's predictions by 5 standard deviations - enough to determine everything.The double-edged sword of Bell's inequality is indeed powerful, but what it cuts off is not the brilliance of quantum theory, but in turn shatters the dream that Einstein insisted on! When Aspect et al.'s report was published in Physics Review Letters in December of that year, the initial reaction from the scientific community was eerily silent.Everyone knows the significance of this result, but they don't seem to know what to say. Einstein lost?what does this mean?Is it true that the world is more mysterious and wonderful than we can imagine, so that our poor common sense is finally about to shatter in front of it?This world doesn't depend on you or me, it just "exists out there", isn't that obvious?Why is there an irreparable gap between the conclusions derived from such a basic assumption and the experimental results?Is God crazy, or are you and I crazy? People all over the world are trying to repeat Aspect's experiment, and new methods have been introduced continuously, and the experimental model is getting closer and closer to Einstein's original EPR idea.Scientists in Maryland and Rochester used ultraviolet light to study the continuous rather than discrete output correlations of the observations.In Malvern, UK, two entangled photons were guided using optical fibers to separate them by more than 4 kilometers, and in Geneva, the distance was tens of kilometers.Even at such distances, Bell's inequality is still relentlessly violated. In addition, according to Bell's original idea, we should not allow photon pairs to "know in advance" which directions to observe, that is, in order to ensure that they can perform some kind of seemingly inconceivable long-distance cooperation on events that are unpredictable to them. (According to the prediction of quantum mechanics), we should make random observation direction arrangements on their way of flight.In the Aspect experiment, we saw that they switched the gate at a speed of 10 ns, but the distance they were able to separate the two photons of 12 meters was still too short to be safe. In 1998, scientists at the University of Innsbruck in Austria sent photons flying 400 meters apart, which gave them 1.3 microseconds to complete the random arrangement of the polarizers.This time there was more than enough time, and the result was so indisputable: Einstein lost even worse this time - 30 standard deviations! In 1990, Greenberger, Horne, and Zeilinger showed that even without Bell's inequality, we have a better way to show the sharpness between quantum mechanics and a "classical theory" (local hidden variable theory) The collision, known as the GHZ test (named after the trio's initials), involves the entanglement of three or more photons. In 2000, Pan Jianwei, Bouwmeester, Daniell and others reported in the journal Nature that their experimental results once again rejected the possibility of local reality, that is, Einstein's belief - 8 standard deviations! In 2001, Rowe et al. described a more sophisticated Be ion trapping experiment. In 2003, Pittman and Franson reported the violation of Bell's inequality for photons produced by two independent sources; and Hasegawa et al. found the result of breaking through the Bell-like relationship in the interferometry of single neutrons. In laboratories around the world, particles tenaciously maintain a delicate but magical connection.As if intending to show off their abilities, they repeatedly mocked the so-called unbreakable shackles set by the classic world for them, stepping down the dogma that was declared inviolable time and time again.This phenomenon has become so indisputable that in the field of quantum information it has become a routine way of testing whether two qubits are still entangled (with the added benefit of knowing if your message has been eavesdropped on the way) !). Although we may make more and more precise experiments in the future, overall, the breakthrough of Bell's inequality in EPR is an irrefutable fact.Perhaps in the future, new experiments will overthrow all our current conclusions and restore the world to its classic appearance, but from the current point of view, this possibility is extremely slim. I don't know what would Einstein say if he was alive today?Maybe he'll say something flexible.We seem to hear that in the distant heaven, he and Bohr are still repeating that classic dialogue: Einstein: Bohr, dear God does not play dice! Bohr: Einstein, don't tell God what to do! Now, let us be arrogant and announce in a Nietzschean manner: Einstein's God is dead. three Aspect's experiment in 1982 (accurately, a series of experiments) is one of the most far-reaching experiments in the history of physics in the 20th century, and its significance can even be compared with the Michelson-Morley experiment in 1886.However, compared to Michelson's experiment that stunned everyone, the results obtained by Aspect were "expected".Most people expected early on that the victory of quantum theory would be a no-brainer.Since quantum theory was founded in 1927, it has experienced more than 50 years of ups and downs. It has shown such a powerful force in every field that no experimental results can question it even a little bit.The greatest physicists (such as Einstein and Schrödinger) fired at it, trying to subvert it fundamentally, but its brilliant brilliance is even more dazzling and pleasing to the eye.From a practical point of view, quantum theory is the most successful theory in history. It not only far exceeds the theory of relativity and Maxwell's electromagnetic theory, but even surpasses Newton's classical mechanics!Quantum theory grew up in a precarious and chaotic world. A warrior who has been tested by the revolution, his temperament has been honed to be more tenacious and invincible under the severe torture of wind, knife, frost and sword.Indeed, not many people would have imagined that such a theory would be easily knocked down by an inconspicuous experiment, and never turn over again.The success of Aspect's experiment was but another test (albeit the most severe) of quantum theory, adding another badge of honor to its armor of victorious victories.We now know that it was successful even under such harsh conditions.Yes, as expected!This news did not bring a huge emotional shock to people, causing a sensational effect. But it does push physicists into an awkward position.Originally, people are usually willing to pursue an ostrich policy on the issue of whether the world is real, and try not to discuss it if they can keep silent.As long as quantum theory works, why do we have to get to the bottom of what is the philosophical meaning behind it?Although there are people like Einstein who are worried about it, most scientists still don't care.But now, Aspect has finally forced people to a showdown: it is useless to blindly shrink your head, people must face the fact that the experiment has rejected the possibility of the classical picture! Einstein's dream shattered like a bubble in the face of ruthless data. We can no longer go back to that warm and comfortable nest, but must face the harsh reality of wind and rain.We must once again look at our common sense and ask how reliable it is and how misleading it really is.For Bell, the inequality he discovered ultimately betrayed his ideals, not only did not bring the world back to the classic image, but in turn pushed it to a dead end.After the Aspect experiment, we had to convince ourselves of one thing: Local hidden variable theory does not exist! In other words, our world cannot be both localized (there is no propagation of superluminal signals) and real (there is an objective and independent world that can be determined by hidden variables) as Einstein dreamed. describe).Local realism has been experimentally excluded from our universe, and we must now make a difficult choice: give up locality or give up reality. If we give up reality, we go back to the old way of quantum theory, admitting that two particles do not exist in "objective reality" until we observe them.They do not have physical properties in the usual sense (like spin), which only become meaningful when observed.In the EPR experiment, until the very last moment, our two particles in the entangled state must be regarded as an inseparable whole. two particles".The so-called two particles become real things only after observation (the wave function collapses).Of course, after making such a heart-wrenching concession, we can still choose according to our own tastes: whether to go further and completely defeat determinism, that is, to retain the Copenhagen interpretation; or from a high-level perspective , to keep the determinism, or to adopt the multi-universe explanation!What needs to be explained is that whether MWI is considered a localized (local) theory is still different among people.Apart from opponents such as Stapp, even among its supporters (such as Deutsch, Tegmark or Zeh), the tone is not uniform.However, this may only be a matter of definition and terminology, because quantum entanglement itself may be defined as a nonlocal physical process (Zeh, Found. of Physics Letters 13, 2000, p22), but everyone agrees that MWI Certainly not a theory of localized reality, and faster-than-light signal transmission does not exist within it.The point is that, according to the MWI, every time we make an observation there is more than one outcome (in fact, all possible outcomes) in "reality"!This is very different from the traditional "reality" that Einstein acquiesced. In doing so, the psychologically solid world crumbles (or does it "collapse"?).Whether God rolls the dice or not, what he has built for us is not a strictly independent edifice in an absolute external world.Every one of its walls, every floor, every staircase...is intimately related to the activities going on within it, whether or not that activity involves intelligent (conscious) observers.Far from being a monolithic building, each floor of the building is intertwined in a certain and wonderful way, so that the residents living separately on the top floor and the ground floor still maintain a kind of sympathy. However, if you can't stand all this, we can also go another way, that is, to preserve the reality of the world at any cost.Of course, locality must be given up in this way.It is still possible for us to establish a hidden variable theory. If some kind of superluminal signal is allowed to go back and forth in its system, it can still explain everything we observe very well.For example, in EPR, two electrons at the opposite ends of the sky can still ensure successful cooperation between them through a kind of faster-than-light instantaneous communication.In fact, Bohm's system survived Aspect's experiment quite well, because his "quantum potential" did imply such an action at a distance. But if this is the case, we may not feel that life is much easier!A faster-than-light signal?Boss, what does that mean?Think about what Einstein would say about this, faster than light speed means gaining the ability to go back in time!In this way, we will get into even more tricky and confusing dilemmas than uncertainties, such as imagining those famous scenes in science fiction: you go back in time and kill you as a baby, what happens What are the logical consequences?Although Bohm may be able to show us mathematically that despite this so-called superluminal non-local correlation, his theory of implicit functions can still prohibit us from doing such signaling in practice: because roughly In other words, we cannot "control" quantum phenomena precisely, so in real experiments, we will obtain the observation limit consistent with the prediction of relativity theory in a statistical sense.That is to say, although there are superluminal signals in a deep sense, we cannot intentionally and effectively use them to create a logical strange circle.But in any case, we should be very careful about this sensitive issue.Giving up locality is no more comfortable than giving up reality! After the results of the Aspect experiment came out, BBC broadcast producer Julian Brown and Newcastle University physics professor Paul Davies (now at Macquarie University in Australia, who is also a contemporary One of the most prestigious science writers) decided to investigate how the scientific community would react to this important experiment.They invited eight of the most prestigious experts in the field of quantum theory to conduct interviews and solicit their views on quantum mechanics and Aspect's experiment.These interviews were eventually compiled into a book, published by Cambridge Press in 1986, titled The Ghost in the Atom. Reading these interview records is really a wonderful experience and feeling.You will see how the most eminent experts have different opinions, and have very different, even diametrically opposed views on the same issue.Aspect himself affirmed that his experiment fundamentally ruled out the possibility of localized reality. He did not appreciate the faster-than-light argument, but expressed sympathy for the existing quantum mechanics.Although Bell admitted that the results of the experiment were not unexpected, he still never accepted the God of dice.He still firmly believes that quantum theory is a strategy of profit, and he imagines that quantum theory will one day be proved wrong by more complicated experiments.贝尔愿意以抛弃定域性为代价来换取客观实在，他甚至设想复活“以太”的概念来达到这一点。惠勒的观点有点暧昧，他承认一度支持埃弗莱特的多宇宙解释，但接着又说因为它所带来的形而上学的累赘，他已经改变了观点。惠勒讨论了玻尔的图像，意识参予的可能性以及他自己的延迟实验和参予性宇宙，他仍然对于精神在其中的作用表现得饶有兴趣。 鲁道夫?佩尔斯（Rudolf Peierls）的态度简明爽快：“我首先反对使用'哥本哈根解释'这个词。”他说，“因为，这听上去像是说量子力学有好几种可能的解释一样。其实只存在一种解释：只有一种你能够理解量子力学的方法（也就是哥本哈根的观点！）。”这位曾经在海森堡和泡利手下学习过的物理学家仍然流连于革命时代那波澜壮阔的观念，把波函数的坍缩认为是一种唯一合理的物理解释。大卫?德义奇也毫不含糊地向人们推销多宇宙的观点，他针对奥卡姆剃刀对于“无法沟通的宇宙的存在”提出的诘问时说，MWI是最为简单的解释。相对于种种比如“意识”这样稀奇古怪的概念来说，多宇宙的假设实际上是最廉价的！他甚至描述了一种“超脑”实验，认为可以让一个人实际地感受到多宇宙的存在！接下来是玻姆，他坦然地准备接受放弃物理中的定域性，而继续维持实在性。“对于爱因斯坦来说，确实有许多事情按照他所预料的方式发生。”玻姆说，“但是，他不可能在每一件事情上都是正确的！”在玻姆看来，狭义相对论也许可以看成是一种普遍情况的一种近似，正如牛顿力学是相对论在低速情况下的一种近似那样。作为玻姆的合作者之一，巴西尔?海利（Basil Hiley）也强调了隐函数理论的作用。而约翰?惠勒（John Taylor）则描述了另一种完全不同的解释，也就是所谓的“系综”解释（the ensemble interpretation）。系综解释持有的是一种非常特别的统计式的观点，也就是说，物理量只对于平均状况才有意义，对于单个电子来说，是没有意义的，它无法定义！我们无法回答单个系统，比如一个电子通过了哪条缝这样的问题，而只能给出一个平均统计！我们在史话的后面再来详细地介绍系综解释。 在这样一种大杂烩式的争论中，阿斯派克特实验似乎给我们的未来蒙上了一层更加扑朔迷离的影子。爱因斯坦有一次说：“虽然上帝神秘莫测，但他却没有恶意。”但这样一位慈祥的上帝似乎已经离我们远去了，留给我们一个难以理解的奇怪世界，以及无穷无尽的争吵。我们在隐函数这条道路上的探索也快接近尽头了，关于玻姆的理论，也许仍然有许多人对它表示足够的同情，比如John Gribbin在他的名作《寻找薛定谔的猫》（In Search of Schrodinger's Cat）中还把自己描述成一个多宇宙的支持者，而在10年后的《薛定谔的猫以及对现实的寻求》（Schrodinger's Kittens and the Search for Reality）一书中，他对MWI的热情已经减退，而对玻姆理论表示出了谨慎的乐观。我们不清楚，也许玻姆理论是对的，但我们并没有足够可靠的证据来说服我们自己相信这一点。除了玻姆的隐函数理论之外，还有另一种隐函数理论，它由Edward Nelson所发明，大致来说，它认为粒子按照某种特定的规则在空间中实际地弥漫开去（有点像薛定谔的观点），类似波一般地确定地发展。我们不打算过多地深入探讨这些观点，我们所不满的是，这些和爱因斯坦的理想相去甚远！为了保有实在性而放弃掉定域性，也许是一件饮鸩止渴的事情。我们不敢说光速绝对地不可超越，只是要推翻相对论，现在似乎还不大是时候，毕竟相对论也是一个经得起考验的伟大理论。 我们沿着这条路走来，但是它当初许诺给我们的那个美好蓝图，那个爱因斯坦式的理想却在实验的打击下终于破产。也许我们至少还保有实在性，但这不足以吸引我们中的许多人，让他们付出更多的努力和代价而继续前进。阿斯派克特实验严酷地将我们的憧憬粉碎，它并没有证明量子论是对的（它只是支持了量子论的预言，正如我们讨论过的那样，没什么理论可以被“证明”是对的），但它无疑证明了爱因斯坦的世界观是错的！事实上，无论量子论是错是对，我们都已经不可能追回传说中的那个定域实在的理想国，而这，也使我们丧失了沿着该方向继续前进的很大一部分动力。就让那些孜孜不倦的探索者继续前进，而我们还是退回到原来的地方，再继续苦苦追寻，看看有没有柳暗花明的一天。 *********** 饭后闲话：超光速 EPR背后是不是真的隐藏着超光速我们仍然不能确定，至少它表面上看起来似乎是一种类似的效应。不过，我们并不能利用它实际地传送信息，这和爱因斯坦的狭义相对论并非矛盾。 假如有人想利用这种量子纠缠效应，试图以超光速从地球传送某个消息去到半人马座α星（南门二，它的一颗伴星是离我们地球最近的恒星，也即比邻星），他是注定要失败的。假设某个未来时代，某个野心家驾驶一艘宇宙飞船来到两地连线的中点上，然后使一个粒子分裂，两个子粒子分别飞向两个目标。他事先约定，假如半人马星上观测到粒子是“左旋”，则表示地球上政变成功，反之，如是“右旋”则表示失败。这样的通讯建立在量子论的这个预测上：也就是地球上观测到的粒子的状态会“瞬间”影响到遥远的半人马星上另一个粒子的状态。但事到临头他却犯难了：假设他成功了，他如何确保他在地球上一定观测到一个“右旋”粒子，以保证半人马那边收到“左旋”的信息呢？他没法做到这点，因为观测结果是不确定的，他没法控制！他最多说，当他做出一个随机的观测，发现地球上的粒子是“右旋”的时候，那时他可以有把握地，100％地预言遥远的半人马那里一定收到“左”的信号，虽然理论上说两地相隔非常遥远，讯息还来不及传递过来。如果他想利用贝尔不等式，他也必须知道，在那一边采用了什么观测手段，而这必须通过通常的方法来获取。这一切都并不违反相对论，你无法利用这种“超光速”制造出信息在逻辑上的自我矛盾来（例如回到过去杀死你自己之类的）。 在这种原理上的量子传输（teleportation）事实上已经实现。我国的潘建伟教授在此领域多有建树。 2000年，王力军，Kuzmich等人在Nature上报道了另一种“超光速”（Nature V406），它牵涉到在特定介质中使得光脉冲的群速度超过真空中的光速，这本身也并不违反相对论，也就是说，它并不违反严格的因果律，结果无法“回到过去”去影响原因。同样，它也无法携带实际的信息。 其实我们的史话一早已经讨论过，德布罗意那“相波”的速度c^2/v就比光速要快，但只要不携带能量和信息，它就不违背相对论。相对论并非有些人所想象的那样已被推翻，相反，它仍然是我们所能依赖的最可靠的基石之一。 Four 这已经是我们第三次在精疲力竭之下无功而返了。隐变量所给出的承诺固然美好，可是最终的兑现却是大打折扣的，这未免教人丧气。虽然还有玻姆在那里热切地召唤，但为了得到一个决定性的理论，我们付出的代价是不是太大了点？这仍然是很值得琢磨的事情，同时也使得我们不敢轻易地投下赌注，义无反顾地沿着这样的方向走下去。 如果量子论注定了不能是决定论的，那么我们除了推导出类似“坍缩”之类的概念以外，还可以做些什么假设呢？ 有一种功利而实用主义的看法，是把量子论看作一种纯统计的理论，它无法对单个系统作出任何预测，它所推导出的一切结果，都是一个统计上的概念！也就是说，在量子论看来，我们的世界中不存在什么“单个”（individual）的事件，每一个预测，都只能是平均式的，针对“整个集合”（ensemble）的，这也就是“系综解释”（the ensemble interpretation）一词的来源。 大多数系综论者都喜欢把这个概念的源头上推到爱因斯坦，比如John Taylor，或者加拿大McGill大学的BC Sanctuary。爱因斯坦曾经说过：“任何试图把量子论的描述看作是对于'单个系统'的完备描述的做法都会使它成为极不自然的理论解释。但只要接受这样的理解方式，也即（量子论的）描述只能针对系统的'全集'，而非单个个体，上述的困难就马上不存在了。”这个论述成为了系综解释的思想源泉（见于Max Jammer《量子力学的哲学》一书）。 嗯，怎么又是爱因斯坦？我们还记忆犹新的是，隐变量不是也把他拉出来作为感召和口号吗？或许爱因斯坦的声望太隆，任何解释都希望从他那里取得权威性，不过无论如何，从这一点来说，系综和隐变量实际上是有着相同的文化背景的。但是它们之间不同的是，隐变量在作出“量子论只不过是统计解释”这样的论断后，仍然怀着满腔热情去寻找隐藏在它背后那个更为终极的理论，试图把我们所看不见的隐变量找出来以最终实现物理世界所梦想的最高目标：理解和预测自然。它那锐意进取的精神固然是可敬的，但正如我们已经看到的那样，在现实中遭到了严重的困难和阻挠，不得不为此放弃许多东西。 相比隐变量那勇敢的冲锋，系综解释选择固本培元，以退为进的战略。在它看来，量子论是一个足够伟大的理论，它已经界定了这个世界可理解的范畴。的确，量子论给我们留下了一些盲点，一些我们所不能把握的东西，比如我们没法准确地同时得到一个电子的位置和动量，这叫一些持完美主义的人们觉得坐立不宁，寝食难安。但系综主义者说：“不要徒劳地去探索那未知的领域了，因为实际上不存在这样的领域！我们的世界本质上就是统计性质的，没有一个物理理论可以描述'单个'的事件，事实上，在我们的宇宙中，只有'系综'，或者说'事件的全集'才是有物理意义的。” What does it mean?我们还是用大家都熟悉的老例子，双缝前的电子来说明问题。当电子通过双缝后，假设我们没有刻意地去观察它，那么按照量子论，它应该有一个确定而唯一的，按照时间和薛定谔方程发展的态矢量： 电子>＝ 穿过左缝>＋ 穿过右缝> 按照标准哥本哈根解释，这意味着单个电子必须同时处在左>和右>两个态的叠加之中，电子没有一个确定的位置，它同时又在这里又在那里！按照MWI，这是一种两个世界的叠加。按照隐变量，所谓的叠加都是胡扯，量子论的这种数学形式是靠不住的，假如我们考虑了不可见的隐变量，我们就能确实地知道，电子究竟通过了左边还是右边。那么，系综解释对此又有何高见呢？ 它所持的是一种外交式的圆滑态度：量子论的数学形式经得起时间考验，是一定要保留的。但“叠加”什么的明显违背常识，是不对的。反过来，一味地急功冒进，甚至搞出什么不可观察的隐变量，这也太过火了，更不能当真。再怎么说，实验揭示给我们的结果是纯随机性质的，没人可以否认。 那么，我们应该怎么办呢？ 系综解释说：我们应当知足，相信理论告诉我们的已经是这个世界的本质：它本就是统计性的！所以，徒劳地去设计隐变量是没有用的，因为实验已经告诉我们定域的隐变量理论是没有的，而且实验也告诉我们对同样的系统的观测不会每次都给出确定的结果。但是，我们也不能相信所谓的“叠加”是一种实际上的存在，电子不可能又通过左边又通过右边！我们的结论应该是：对于电子的态矢量，它永远都只代表系统“全集”的统计值，也就是一种平均情况！ 什么叫只代表“全集”呢？换句话说，当我们写下： 电子>＝1/SQRT(2) [ 穿过左缝>＋ 穿过右缝> ] 这样的式子时（1/SQRT(2)代表根号2分之1，我们假设两种可能相等，所以系数的平方，也就是概率之和等于1），我们所指的并不是“一个电子”的运动情况，而永远是无限个电子在相同情况下的一个统计平均！这个式子只描述了当无穷多个电子在相同的初状态下通过双缝（或者，一个电子无穷次地在同样的情况下通过双缝）时会出现的结果。根据量子论，世界并非决定论的，也就是说，哪怕我们让两个电子在完全相同的状态下通过双缝，观测到的结果也不一定每次都一样，而是有多种可能。而量子论的数学所能告诉我们的，正是所有这些可能的“系综”，也就是统计预期！ 如此一来，当我们说“电子＝左＋右”的时候，意思就并非指一个单独的电子同时处于左和右两个态，而只是在经典概率的概念上指出它有50％的可能通过左，而50％的可能通过右罢了。当我们“准备”这样一个实验的时候，量子论便能够给出它的系综，在一个统计的意义上告诉我们实验的结果。 态矢量只代表系统的系综！嗯，听上去蛮容易理解的，似乎皆大欢喜。可是这样一来，量子论也就变成一个统计学的理论了，好吧，当许多电子穿过双缝时，我们知道有50％通过了左边，50％通过了右边，可现在我们关心的是单个电子！单个电子是如何通过双缝并与自己发生干涉，最后在荧屏上打出一个组成干涉图纹的一点的呢？我们想听听系综解释对此有何高见。 但要命的是，它对此什么都没说！在它看来，所谓“单个电子通过了哪里”之类的问题，是没有物理意义的！当John Taylor被问道，他是否根本没有想去描述单个系统中究竟发生了什么的时候，他甚至说，这是不被允许的。量子物理所给出的只是统计性，that's all，没有别的了。如果这个世界能够被我们用数学方法去理解的话，那就是在一种统计的意义上说的，我们不自量力地想去追寻更多，那只不过是自讨苦吃。单个电子的轨迹，那是一个没有物理定义的概念，正如“时间被创造前1秒”，“比光速更快1倍”，或者“绝对零度低1度”这样的名词，虽然没有语法上的障碍阻止我们提出这样的问题，但它们在物理上却是没什么意思的。和哥本哈根派不同的是，玻尔等人假设每个电子都实际地按照波函数发散开来，而系综解释则是简单地把这个问题踢出了理论框架中去，来个眼不见为净：现在我们不必为“坍缩”操心了，谈论单个电子是没有意义的事情！ 不过，这实在是太掩耳盗铃了。好吧，量子论只给出系综，可是我们对于物理理论的要求毕竟要比这样的统计报告要高那么一点啊。假如我去找占卜师算命，想知道我的寿限是多少，她却只告诉我：这个城市平均寿命是70岁，那对我来说似乎没有很大的用处啊，我还不如去找保险公司！更可恨的是，她居然对我说，你一个人的寿命是没什么意义的，有意义的只是千千万万个你的寿命的“系综”！ 系综解释是一种非常保守和现实主义的解释，它保留了现有量子论的全部数学形式，因为它们已经被实践所充分证明。但在令人目眩的哲学领域，它却试图靠耍小聪明而逃避那些形而上的探讨，用划定理论适用界限这样的方法来把自己封闭在一个刀枪不入的外壳中。是的，如果我们采纳系综主义，那么的确在纯理论方面说，我们的一切问题都解决了：没有什么坍缩，电子永远只是粒子（波性只能用来描述粒子的“全集”），不确定原理也只是被看成一个统计极限，而不理会单个电子到底能不能同时拥有动量和位置（这个问题“没有意义”）。但是，这样似乎有点自欺欺人的味道，把搞不清楚的问题划为“没有意义”也许是方便的，但的确是这样的问题使得科学变得迷人！每个人都知道，当许多电子通过双缝时产生了干涉图纹，可我们更感兴趣的还是当单个电子通过时究竟发生了什么，而不是简单地转过头不去面对！ Taylor在访谈中的确被问道，这样的做法不是一个当“逃兵”的遁词吗？他非常精明地回答说：“我认为你应当问一问，如果陷进去是否比逃之夭夭确实会惹出更多的麻烦。”系综主义者持有的是极致的实用主义，他们炮轰隐变量和多宇宙解释，因为后两者都带来了许多形而上学的“麻烦”。只要我们充分利用现有的体系，搞出一个又不违反实验结果，又能在逻辑上自洽的体系，那不就足够了吗？系综解释的精神，就是尽可能少地避免“麻烦”，绝不引入让人头痛的假设，比如多宇宙或者坍缩之类的。 但是，我们还是不能满足于这样的关起门来然后自称所有的问题都已经解决的做法。或许，是因为我们血液中的热情还没有冷却，或许，是因为我们仍然年少轻狂，对于这个宇宙还怀有深深的激动和无尽的好奇。我们并不畏惧进入更为幽深和神秘的峡谷和森林，去探究那事实的真相。哪怕注定要被一些更加恼人和挥之不去的古怪精灵所缠绕，我们还是不可以放弃了前进的希望和动力，因为那是我们最宝贵的财富。 接下来我们还要去看看两条新的道路，虽然它们都新辟不久，坎坷颠簸，行进艰难，但沿途那奇峰连天，枯松倒挂，瀑布飞湍，冰崖怪石的绝景一定不会令你失望。 Fives 我们已经厌倦了光子究竟通过了哪条狭缝这样的问题，管它通过了哪条，这和我们又有什么关系呢？一个小小的光子是如此不起眼，它的世界和我们的世界相去霄壤，根本无法联系在一起。在大多数情况下，我们甚至根本没法看见单个的光子（有人做过实验，肉眼看见单个光子是有可能的，但机率极低，而且它的波长必须严格地落在视网膜杆状细胞最敏感的那个波段），在这样的情况下，大众对于探究单个光子究竟是“幽灵”还是“实在”无疑持有无所谓的态度，甚至觉得这是一种杞人忧天的探索。 真正引起人们担忧的，还是那个当初因为薛定谔而落下的后遗症：从微观到宏观的转换。如果光子又是粒子又是波，那么猫为什么不是又死而又活着？如果电子同时又在这里又在那里，那么为什么桌子安稳地呆在它原来的地方，没有扩散到整间屋子中去？如果量子效应的基本属性是叠加，为什么日常世界中不存在这样的叠加，或者，我们为什么从未见过这种情况？ 我们已经听取了足够多耐心而不厌其烦的解释：猫的确又死又活，只不过在我们观测的时候“坍缩”了；有两只猫，它们在一个宇宙中活着，在另一个宇宙中死去；猫从未又死又活，它的死活由看不见的隐变量决定；单个猫的死活是无意义的事件，我们只能描述无穷只猫组成的“全集”……诸如此类的答案。也许你已经对其中的某一种感到满意，但仍有许多人并不知足：一定还有更好，更可靠的答案。为了得到它，我们仍然需要不断地去追寻，去开拓新的道路，哪怕那里本来是荒芜一片，荆棘丛生。毕竟世上本没有路，走的人多了才成为路。 现在让我们跟着一些开拓者小心翼翼地去考察一条新辟的道路，和当年扬帆远航的哥伦布一样，他们也是意大利人。这些开拓者的名字刻在路口的纪念碑上：Ghirardi，Rimini和Weber，下面是落成日期：1986年7月。为了纪念这些先行者，我们顺理成章地把这条道路以他们的首字母命名，称为GRW大道。 这个思路的最初设想可以回溯到70年代的Philip Pearle：哥本哈根派的人物无疑是伟大和有洞见的，但他们始终没能给出“坍缩”这一物理过程的机制，而且对于“观测者”的主观依赖也太重了些，最后搞出一个无法收拾的“意识”不说，还有堕落为唯心论的嫌疑。是否能够略微修改薛定谔方程，使它可以对“坍缩”有一个让人满意的解释呢？ 1986年7月15日，我们提到的那3位科学家在《物理评论》杂志上发表了一篇论文，题为《微观和宏观系统的统一动力学》（Unified dynamics for icroscopic and macroscopic systems），从而开创了GRW理论。GRW的主要假定是，任何系统，不管是微观还是宏观的，都不可能在严格的意义上孤立，也就是和外界毫不相干。它们总是和环境发生着种种交流，为一些随机（stochastic）的过程所影响，这些随机的物理过程——不管它们实质上到底是什么——会随机地造成某些微观系统，比如一个电子的位置，从一个弥漫的叠加状态变为在空间中比较精确的定域（实际上就是哥本哈根口中的“坍缩”），尽管对于单个粒子来说，这种过程发生的可能性是如此之低——按照他们原本的估计，平均要等上10^16秒，也就是近10亿年才会发生一次。所以从整体上看，微观系统基本上处于叠加状态是不假的，但这种定域过程的确偶尔发生，我们把这称为一个“自发的定域过程”（spontaneous localization）。GRW有时候也称为“自发定域理论”。 关键是，虽然对于单个粒子来说要等上如此漫长的时间才能迎来一次自发过程，可是对于一个宏观系统来说可就未必了。拿薛定谔那只可怜的猫来说，一只猫由大约10^27个粒子组成，虽然每个粒子平均要等上几亿年才有一次自发定域，但对像猫这样大的系统，每秒必定有成千上万的粒子经历了这种过程。 Ghirardi等人把薛定谔方程换成了所谓的密度矩阵方程，然后做了复杂的计算，看看这样的自发定域过程会对整个系统造成什么样的影响。他们发现，因为整个系统中的粒子实际上都是互相纠缠在一起的，少数几个粒子的自发定域会非常迅速地影响到整个体系，就像推倒了一块骨牌然后造成了大规模的多米诺效应。最后的结果是，整个宏观系统会在极短的时间里完成一次整体上的自发定域。如果一个粒子平均要花上10亿年时间，那么对于一个含有1摩尔粒子的系统来说（数量级在10^23个），它只要0.1微秒就会发生定域，使得自己的位置从弥漫开来变成精确地出现在某个地点。这里面既不要“观测者”，也不牵涉到“意识”，它只是基于随机过程！ 如果真的是这样，那么当决定薛定谔猫的生死的那一刻来临时，它的确经历了死/活的叠加！只不过这种叠加只维持了非常短，非常短的时间，然后马上“自发地”精确化，变成了日常意义上的，单纯的非死即活。因为时间很短，我们没法感觉到这一叠加过程！这听上去的确不错，我们有了一个统一的理论，可以一视同仁地解释微观上的量子叠加和宏观上物体的不可叠加性。 但是，GRW自身也仍然面临着严重的困难，这条大道并不是那样顺畅的。他们的论文发表当年，海德堡大学的E.Joos就向《物理评论》递交了关于这个理论的评论，而这个评论也在次年发表，对GRW提出了置疑。自那时起，对GRW的疑问声一直很大，虽然有的人非常喜欢它，但是从未在物理学家中变成主流。怀疑的理由有许多是相当技术化的，对于我们史话的读者，我只想在最肤浅的层次上稍微提一些。 GRW的计算是完全基于随机过程的，而并不引入类如“观测使得波函数坍缩”之类的假设。他们在这里所假设的“自发”过程，虽然其概念和“坍缩”类似，实际上是指一个粒子的位置从一个非常不精确的分布变成一个比较精确的分布，而不是完全确定的位置！换句话说，不管坍缩前还是坍缩后，粒子的位置始终是一种不确定的分布，必须为统计曲线（高斯钟形曲线）所描述。所谓坍缩，只不过是它从一个非常矮平的曲线变成一个非常尖锐的曲线罢了。在哥本哈根解释中，只要一观测，系统的位置就从不确定变成完全确定了，而GRW虽然不需要“观测者”，但在它的框架里面没有什么东西是实际上确定的，只有“非常精确”，“比较精确”，“非常不精确”之类的区别。比如说当我盯着你看的时候，你并没有一个完全确定的位置，虽然组成你的大部分物质（粒子）都聚集在你所站的那个地方，但真正描述你的还是一个钟形线（虽然是非常尖锐的钟形线）！我只能说，“绝大部分的你”在你所站的那个地方，而组成你的另外的那“一小撮”（虽然是极少极少的一小撮）却仍然弥漫在空间中，充斥着整个屋子，甚至一直延伸到宇宙的尽头！ 也就是说，在任何时候，“你”都填满了整个宇宙，只不过“大部分”的你聚集在某个地方而已。作为一个宏观物体的好处是，明显的量子叠加可以在很短的时间内完成自发定域，但这只是意味着大多数粒子聚集到了某个地方，总有一小部分的粒子仍然留在无穷的空间中。单纯地从逻辑上讲，这也没什么不妥，谁知道你是不是真有小到无可觉察的一部分弥漫在空间中呢？但这毕竟违反了常识！如果必定要违反常识，那我们干脆承认猫又死又活，似乎也不见得糟糕多少。 GRW还抛弃了能量守恒（当然，按照相对论，其实是质能守恒）。自发的坍缩使得这样的守恒实际上不成立，但破坏是那样微小，所需等待的时间是那样漫长，使得人们根本不注意到它。抛弃能量守恒在许多人看来是无法容忍的行为。我们还记得，当年玻尔的BKS理论遭到了爱因斯坦和泡利多么严厉的抨击。 还有，如果自发坍缩的时间是和组成系统的粒子数量成反比的，也就是说组成一个系统的粒子越少，其位置精确化所要求的平均时间越长，那么当我们描述一些非常小的探测装置时，这个理论的预测似乎就不太妙了。比如要探测一个光子的位置，我们不必动用庞大而复杂的仪器，而可以用非常简单的感光剂来做到。如果好好安排，我们完全可以只用到数十亿个粒子（主要是银离子）来完成这个任务。按照哥本哈根，这无疑也是一次“观测”，可以立刻使光子的波函数坍缩而得到一个确定的位置，但如果用GRW的方法来计算，这样小的一个系统必须等上平均差不多一年才会产生一次“自发”的定域。 Roland Omnes后来提到，Ghirardi在私人的谈话中承认了这一困难。但他争辩说，就算在光子使银离子感光这一过程中牵涉到的粒子数目不足以使系统足够快地完成自发定域，我们谁都无法意识到这一点！如果作为观测者的我们不去观测这个实验的结果，谁知道呢，说不定光子真的需要等上一年来得到精确的位置。可是一旦我们去观察实验结果，这就把我们自己的大脑也牵涉进整个系统中来了。关键是，我们的大脑足够“大”（有没有意识倒不重要），足够大的物体便使得光子迅速地得到了一个相对精确的定位！ 推而广之，因为我们长着一个大脑袋，所以不管我们看什么，都不会出现位置模糊的量子现象。要是我们拿复杂的仪器去测量，那么当然，测量的时候对象就马上变得精确了。即使仪器非常简单细小，测量以后对象仍有可能保持在模糊状态，它也会在我们观测结果时因为拥有众多粒子的“大脑”的介入而迅速定域。我们是注定无法直接感觉到任何量子效应了，不知道一个足够小的病毒能否争取到足够长的时间来感觉到“光子又在这里又在那里”的奇妙景象（如果它能够感觉的话！）？ 最后，薛定谔方程是线性的，而GRW用密度矩阵方程将它取而代之以后，实际上把整个理论体系变成了非线性的！这实际上会使它作出一些和标准量子论不