Chapter 12 Chapter Eleven God's Judgment

one |Pxz-Pzy|<one+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: no matter whether it is observed or not, the two particles always exist in the objective reality, and their state is 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, they cannot exchange any information, 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 take any three directions to observe the spins of A and B, and the degree of cooperation they show must be limited within Bell's inequality.That is to say, 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 ran away from the crime scene, but they panicked, and the two fled in opposite directions, and they were guarded at both ends of the road at the same time The police officers were arrested separately.Now let's take their confessions. Suppose policeman A asks criminal A: Are you the one who takes the lead? The answer to A is either yes or no.On the other side of the road, if policeman B asks criminal B the same question: are you the one who took the lead?Then B's answer must be the opposite of A, because there can only be one elder brother, either A with B or B with A.The questions asked by the two police officers 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 police officers ask questions from different angles, for example, ask A: Do you need to hire a lawyer yourself?Question B: Would you like to drink water now?These are two unrelated questions (in different directions), A may answer yes or no, 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 A's actions weigh his own answer. However, this is just 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 answering the question specifically, the two people do not exist in reality at all, but become one and diffuse according to the wave function.To use the term 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 paper is a famous article in the history of physics in the 20th century. Its demonstration and derivation are so simple and clear but deeply rooted in the essence, which makes people overwhelmed.Brian D. Josephson, the Nobel Prize winner in physics in 1973, called Bell's inequality the most important new development in physics. Henry Stapp, as we mentioned earlier, advocated that the spirit makes waves function collapse) called it the most profound discovery in science (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, one side has von Neumann's proof of the impossibility of implicit function theory, and the other side does. There is a quantum potential of Bohm!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 experiment, and deserves its rightful place in the history of physics, because 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.Fanned by Senator Joseph McCarthy, the winds of red fear reached a crescendo.Almost everyone was suspected of being a Soviet spy, or a hostile element plotting to overthrow the government.Bohm was briefly involved in the Manhattan Project during World War II, but he quit shortly thereafter without doing much real work.After the war, he went to Princeton to teach and work with Einstein, when he was subpoenaed by the notorious Un-American Activities Committee (Un-American Activities Committee), asking him to investigate the political positions of some colleagues who were also in Berkeley. To testify, Bohm angrily declined, 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 a crazy and humiliating time when more than 20 million people were subjected to so-called loyalty checks.Up to George.General Marshall, middle to Charlie.Chaplin, down to countless ordinary people have been greatly impacted.People are neurotically looking for so-called communists, just like medieval Europe was crazy about witch hunting.In the academic world, nearly 100 professors left their posts because of their opinions. Those with Chinese backgrounds 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 is the Oppenheimer case. Oppenheimer was the leader of the Manhattan Project. Even he was suspected of disloyalty to the country. It seems inconceivable.All physicists are on his side, but Edward.Taylor (Edward Teller) made the entire physics community hardly believe its ears.The Hungarian-born physicist (who is also Yang Zhenning's mentor) said that although he doesn't think Oppenheimer will do things that are not good for the country, if public affairs are in the hands of others, I personally will 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 also sold the Star Wars project to Reagan (SDI Defense ).He passed away last September (2003) at the age of ninety-five.Carl.In his book "A World Infested With Devils", Sagan once pulled him out as a typical example that scientists should be responsible for their own opinions. 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's nothing but nothingness, but it's 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 atoms were passed through polarizers, but technical limitations made it possible to obtain only a single + result in all cases , instead of + 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 in the Institut d'Optique Th'orique et Appliqu'e, Orsay C'dex, France, prepared to test the EPR in a precise sense for the first time. This group is Allen.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 twelve meters apart, so that it took forty 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, and it is impossible for the photons 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 an ultimate crisis. Will the test 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 of materials gradually accumulated.After 12,000 seconds, that is, more than three hours later, the result came out.The scientists all let out a sigh of relief. Einstein lost!The experimental results are in full agreement with the predictions of quantum theory, but they deviate from Einstein's predictions by five standard deviations, which is 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 that mean?Is it true that the world is more mysterious and wonderful than we can imagine, so that our poor common sense will finally be broken in front of it?This world doesn't depend on you or me, it just exists there, isn't it 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, optical fibers were used to guide two entangled photons so that they were more than four kilometers apart, 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 let the photon pairs know in advance which direction the observation is, that is, in order to ensure that they can carry out some kind of seemingly inconceivable long-distance cooperation on events that are unpredictable to them (according to predictions of quantum mechanics), we should make random observation direction arrangements on the way of their 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 randomly arrange the polarizers.This time there was more than enough time, and the result was so indisputable: Einstein lost thirty standard deviations worse this time! In 1990, Greenberger, Horne, and Zeilinger showed that even without using Bell's inequality, we have a better way to show the relationship between quantum mechanics and a classical theory (local hidden variable theory) Sharp collisions, known as the GHZ test (named after the trio's initials), involve the entanglement of three or more photons.In 2000, Pan Jianwei, Bouwmeester, Daniell and others reported in the journal Nature that their experimental results rejected the local reality again, that is, the eight standard deviations of the possibility of Einstein's belief! 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 generated from two independent sources; and Hasegawa et al. even found the result of breaking 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.The 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 bonus of knowing if your information 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 (or rather, a series of experiments) was one of the most far-reaching experiments in the history of physics in the twentieth century, and its significance can even be compared with that of Michelson in 1886- Morley's experiment.However, compared to Michelson's experiment that stunned everyone, Aspect's results 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 ups and downs for more than 50 years. It has shown such a powerful force in every field, and no experimental results can even propose it. A little doubt.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 overthrown 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 front of the ruthless data. We can no longer go back to that warm and comfortable nest, but must face the harsh reality of the 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 transmission 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 abandon 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 an EPR experiment, until the very last minute, both of our entangled particles must be seen as an inseparable whole, when in reality there is only one particle (superimposed of course), not 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 non-localized physical process (Zeh, Found.of Physics Letters 13, 2000, p22), but everyone agrees, 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 MWI, every time we make an observation, in reality more than one outcome (in fact, all possible outcomes) is produced!This is very different from the conventional reality that Einstein acquiesced to. 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 wall, every floor, every staircase of it is intimately related to the activities that take place 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 theory of hidden variables. 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 opposite ends of the sky can still ensure successful cooperation between them through a kind of faster-than-light transient 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. For example, imagine those famous scenes in science fiction: you go back in time and kill you as a baby, what will happen? What 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 observational limits consistent with the predictions of relativity 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, the BBC's broadcast producer Julian.Brown (Julian Brown) and Newcastle University physics professor Paul.Paul Davies (now at Macquarie University in Australia and one of the most prestigious science writers of our time) 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 to 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 measure of interests, and he imagines that quantum theory will eventually be proved wrong by more complicated experiments one day.Bell is willing to sacrifice locality in exchange for objective reality, and he even envisions resurrecting the concept of aether to achieve this.惠勒的觀點有點曖昧，他承認一度支持埃弗萊特的多宇宙解釋，但接著又說因為它所帶來的形而上學的累贅，他已經改變了觀點。惠勒討論了玻爾的圖像，意識參與的可能性以及他自己的延遲實驗和參與性宇宙，他仍然對於精神在其中的作用表現得饒有興趣。 Rudolph.佩爾斯（Rudolf Peierls）的態度簡明爽快：我首先反對使用哥本哈根解釋這個詞。他說，因為，這聽上去像是說量子力學有好幾種可能的解釋一樣。其實只存在一種解釋：只有一種你能夠理解量子力學的方法（也就是哥本哈根的觀點！）。這位曾經在海森堡和泡利手下學習過的物理學家仍然流連於革命時代那波瀾壯闊的觀念，把波函數的坍縮認為是一種唯一合理的物理解釋。david德義奇也毫不含糊地向人們推銷多宇宙的觀點，他針對奧卡姆剃刀對於無法溝通的宇宙的存在提出的詰問時說，MWI是最為簡單的解釋。相對於種種比如意識這樣稀奇古怪的概念來說，多宇宙的假設實際上是最廉價的！他甚至描述了一種超腦實驗，認為可以讓一個人實際地感受到多宇宙的存在！接下來是玻姆，他坦然地準備接受放棄物理中的定域性，而繼續維持實在性。對於愛因斯坦來說，確實有許多事情按照他所預料的方式發生。玻姆說，但是，他不可能在每一件事情上都是正確的！在玻姆看來，狹義相對論也許可以看成是一種普遍情況的一種近似，正如牛頓力學是相對論在低速情況下的一種近似那樣。作為玻姆的合作者之一，巴西爾．海利（Basil Hiley）也強調了隱函數理論的作用。And John.惠勒（John Taylor）則描述了另一種完全不同的解釋，也就是所謂的系綜解釋（the ensemble interpretation）。系綜解釋持有的是一種非常特別的統計式的觀點，也就是說，物理量只對於平均狀況才有意義，對於單個電子來說，是沒有意義的，它無法定義！我們無法回答單個系統，比如一個電子通過了哪條縫這樣的問題，而只能給出一個平均統計！我們在史話的後面再來詳細地介紹系綜解釋。 在這樣一種大雜燴式的爭論中，阿斯派克特實驗似乎給我們的未來蒙上了一層更加撲朔迷離的影子。愛因斯坦有一次說：雖然上帝神秘莫測，但他卻沒有惡意。但這樣一位慈祥的上帝似乎已經離我們遠去了，留給我們一個難以理解的奇怪世界，以及無窮無盡的爭吵。我們在隱函數這條道路上的探索也快接近盡頭了，關於玻姆的理論，也許仍然有許多人對它表示足夠的同情，比如John Gribbin在他的名作《尋找薛定諤的貓》（In Search of Schrodinger's Cat）中還把自己描述成一個多宇宙的支持者，而在十年後的《薛定諤的貓以及對現實的尋求》（Schrodinger's Kittens and the Search for Reality）一書中，他對MWI的熱情已經減退，而對玻姆理論表示出了謹慎的樂觀。我們不清楚，也許玻姆理論是對的，但我們並沒有足夠可靠的證據來說服我們自己相信這一點。除了玻姆的隱函數理論之外，還有另一種隱函數理論，它由Edward Nelson所發明，大致來說，它認為粒子按照某種特定的規則在空間中實際地彌漫開去（有點像薛定諤的觀點），類似波一般地確定地發展。我們不打算過多地深入探討這些觀點，我們所不滿的是，這些和愛因斯坦的理想相去甚遠！為了保有實在性而放棄掉定域性，也許是一件飲鴆止渴的事情。我們不敢說光速絕對地不可超越，只是要推翻相對論，現在似乎還不大是時候，畢竟相對論也是一個經得起考驗的偉大理論。 我們沿著這條路走來，但是它當初許諾給我們的那個美好藍圖，那個愛因斯坦式的理想卻在實驗的打擊下終於破產。也許我們至少還保有實在性，但這不足以吸引我們中的許多人，讓他們付出更多的努力和代價而繼續前進。阿斯派克特實驗嚴酷地將我們的憧憬粉碎，它並沒有證明量子論是對的（它只是支持了量子論的預言，正如我們討論過的那樣，沒什麼理論可以被證明是對的），但它無疑證明了愛因斯坦的世界觀是錯的！事實上，無論量子論是錯是對，我們都已經不可能追回傳說中的那個定域實在的理想國，而這，也使我們喪失了沿著該方向繼續前進的很大一部分動力。就讓那些孜孜不倦的探索者繼續前進，而我們還是退回到原來的地方，再繼續苦苦追尋，看看有沒有柳暗花明的一天。 飯後閒話：超光速 EPR背後是不是真的隱藏著超光速我們仍然不能確定，至少它表面上看起來似乎是一種類似的效應。不過，我們並不能利用它實際地傳送資訊，這和愛因斯坦的狹義相對論並非矛盾。 假如有人想利用這種量子糾纏效應，試圖以超光速從地球傳送某個消息去到半人馬座α星（南門二，它的一顆伴星是離我們地球最近的恒星，也即比鄰星），他是註定要失敗的。假設某個未來時代，某個野心家駕駛一艘太空船來到兩地連線的中點上，然後使一個粒子分裂，兩個子粒子分別飛向兩個目標。他事先約定，假如半人馬星上觀測到粒子是左旋，則表示地球上政變成功，反之，如是右旋則表示失敗。這樣的通訊建立在量子論的這個預測上：也就是地球上觀測到的粒子的狀態會瞬間影響到遙遠的半人馬星上另一個粒子的狀態。但事到臨頭他卻犯難了：假設他成功了，他如何確保他在地球上一定觀測到一個右旋粒子，以保證半人馬那邊收到左旋的資訊呢？他沒法做到這點，因為觀測結果是不確定的，他沒法控制！他最多說，當他做出一個隨機的觀測，發現地球上的粒子是右旋的時候，那時他可以有把握地，一百％地預言遙遠的半人馬那裡一定收到左的信號，雖然理論上說兩地相隔非常遙遠，訊息還來不及傳遞過來。如果他想利用貝爾不等式，他也必須知道，在那一邊採用了什麼觀測手段，而這必須通過通常的方法來獲取。這一切都並不違反相對論，你無法利用這種超光速製造出資訊在邏輯上的自我矛盾來（例如回到過去殺死你自己之類的）。 在這種原理上的量子傳輸（teleportation）事實上已經實現。我國的潘建偉教授在此領域多有建樹。 二○○○年，王力軍，Kuzmich等人在Nature上報導了另一種超光速（Nature V406），它牽涉到在特定介質中使得光脈衝的群速度超過真空中的光速，這本身也並不違反相對論，也就是說，它並不違反嚴格的因果律，結果無法回到過去去影響原因。同樣，它也無法攜帶實際的資訊。 其實我們的史話一早已經討論過，德布羅意那相波的速度c^2／v就比光速要快，但只要不攜帶能量和資訊，它就不違背相對論。相對論並非有些人所想像的那樣已被推翻，相反，它仍然是我們所能依賴的最可靠的基石之一。 Four 這已經是我們第三次在精疲力竭之下無功而返了。隱變數所給出的承諾固然美好，可是最終的兌現卻是大打折扣的，這未免教人喪氣。雖然還有玻姆在那裡熱切地召喚，但為了得到一個決定性的理論，我們付出的代價是不是太大了點？這仍然是很值得琢磨的事情，同時也使得我們不敢輕易地投下賭注，義無反顧地沿著這樣的方向走下去。 如果量子論註定了不能是決定論的，那麼我們除了推導出類似坍縮之類的概念以外，還可以做些什麼假設呢？ 有一種功利而實用主義的看法，是把量子論看作一種純統計的理論，它無法對單個系統作出任何預測，它所推導出的一切結果，都是一個統計上的概念！也就是說，在量子論看來，我們的世界中不存在什麼單個（individual）的事件，每一個預測，都只能是平均式的，針對整個集合（ensemble）的，這也就是系綜解釋（the ensemble interpretation）一詞的來源。 大多數系綜論者都喜歡把這個概念的源頭上推到愛因斯坦，比如John Taylor，或者加拿大McGill大學的BC Sanctuary。愛因斯坦曾經說過：任何試圖把量子論的描述看作是對於單個系統的完備描述的做法都會使它成為極不自然的理論解釋。但只要接受這樣的理解方式，也即（量子論的）描述只能針對系統的全集，而非單個個體，上述的困難就馬上不存在了。這個論述成為了系綜解釋的思想源泉（見於Max Jammer《量子力學的哲學》一書）。 嗯，怎麼又是愛因斯坦？我們還記憶猶新的是，隱變數不是也把他拉出來作為感召和口號嗎？或許愛因斯坦的聲望太隆，任何解釋都希望從他那裡取得權威性，不過無論如何，從這一點來說，系綜和隱變數實際上是有著相同的文化背景的。但是它們之間不同的是，隱變數在作出量子論只不過是統計解釋這樣的論斷後，仍然懷著滿腔熱情去尋找隱藏在它背後那個更為終極的理論，試圖把我們所看不見的隱變數找出來以最終實現物理世界所夢想的最高目標：理解和預測自然。它那銳意進取的精神固然是可敬的，但正如我們已經看到的那樣，在現實中遭到了嚴重的困難和阻撓，不得不為此放棄許多東西。 相比隱變數那勇敢的衝鋒，系綜解釋選擇固本培元，以退為進的戰略。在它看來，量子論是一個足夠偉大的理論，它已經界定了這個世界可理解的範疇。的確，量子論給我們留下了一些盲點，一些我們所不能把握的東西，比如我們沒法準確地同時得到一個電子的位置和動量，這叫一些持完美主義的人們覺得坐立不寧，寢食難安。但系綜主義者說：不要徒勞地去探索那未知的領域了，因為實際上不存在這樣的領域！我們的世界本質上就是統計性質的，沒有一個物理理論可以描述單個的事件，事實上，在我們的宇宙中，只有系綜，或者說事件的全集才是有物理意義的。 What does it mean?我們還是用大家都熟悉的老例子，雙縫前的電子來說明問題。當電子通過雙縫後，假設我們沒有刻意地去觀察它，那麼按照量子論，它應該有一個確定而唯一的，按照時間和薛定諤方程發展的態向量： |電子>＝|穿過左縫>＋|穿過右縫> 按照標準哥本哈根解釋，這意味著單個電子必須同時處在|左>和|右>兩個態的疊加之中，電子沒有一個確定的位置，它同時又在這裡又在那裡！按照MWI，這是一種兩個世界的疊加。按照隱變數，所謂的疊加都是胡扯，量子論的這種數學形式是靠不住的，假如我們考慮了不可見的隱變數，我們就能確實地知道，電子究竟通過了左邊還是右邊。那麼，系綜解釋對此又有何高見呢？ 它所持的是一種外交式的圓滑態度：量子論的數學形式經得起時間考驗，是一定要保留的。但疊加什麼的明顯違背常識，是不對的。反過來，一味地急功冒進，甚至搞出什麼不可觀察的隱變數，這也太過火了，更不能當真。再怎麼說，實驗揭示給我們的結果是純隨機性質的，沒人可以否認。 那麼，我們應該怎麼辦呢？ 系綜解釋說：我們應當知足，相信理論告訴我們的已經是這個世界的本質：它本就是統計性的！所以，徒勞地去設計隱變數是沒有用的，因為實驗已經告訴我們定域的隱變數理論是沒有的，而且實驗也告訴我們對同樣的系統的觀測不會每次都給出確定的結果。但是，我們也不能相信所謂的疊加是一種實際上的存在，電子不可能又通過左邊又通過右邊！我們的結論應該是：對於電子的態向量，它永遠都只代表系統全集的統計值，也就是一種平均情況！ 什麼叫只代表全集呢？換句話說，當我們寫下： |電子>＝1／SQRT（2）[|穿過左縫>＋|穿過右縫>] 這樣的式子時（1／SQRT（2）代表根號二分之一，我們假設兩種可能相等，所以係數的平方，也就是概率之和等於一），我們所指的並不是一個電子的運動情況，而永遠是無限個電子在相同情況下的一個統計平均！這個式子只描述了當無窮多個電子在相同的初狀態下通過雙縫（或者，一個電子無窮次地在同樣的情況下通過雙縫）時會出現的結果。根據量子論，世界並非決定論的，也就是說，哪怕我們讓兩個電子在完全相同的狀態下通過雙縫，觀測到的結果也不一定每次都一樣，而是有多種可能。而量子論的數學所能告訴我們的，正是所有這些可能的系綜，也就是統計預期！ 如此一來，當我們說電子＝左＋右的時候，意思就並非指一個單獨的電子同時處於左和右兩個態，而只是在經典概率的概念上指出它有五十％的可能通過左，而五十％的可能通過右罷了。當我們準備這樣一個實驗的時候，量子論便能夠給出它的系綜，在一個統計的意義上告訴我們實驗的結果。 態向量只代表系統的系綜！嗯，聽上去蠻容易理解的，似乎皆大歡喜。可是這樣一來，量子論也就變成一個統計學的理論了，好吧，當許多電子穿過雙縫時，我們知道有五十％通過了左邊，五十％通過了右邊，可現在我們關心的是單個電子！單個電子是如何通過雙縫並與自己發生干涉，最後在螢幕上打出一個組成干涉圖紋的一點的呢？我們想聽聽系綜解釋對此有何高見。 但要命的是，它對此什麼都沒說！在它看來，所謂單個電子通過了哪裡之類的問題，是沒有物理意義的！當John Taylor被問道，他是否根本沒有想去描述單個系統中究竟發生了什麼的時候，他甚至說，這是不被允許的。量子物理所給出的只是統計性，that's all，沒有別的了。如果這個世界能夠被我們用數學方法去理解的話，那就是在一種統計的意義上說的，我們不自量力地想去追尋更多，那只不過是自討苦吃。單個電子的軌跡，那是一個沒有物理定義的概念，正如時間被創造前一秒，比光速更快一倍，或者絕對零度低一度這樣的名詞，雖然沒有語法上的障礙阻止我們提出這樣的問題，但它們在物理上卻是沒什麼意思的。和哥本哈根派不同的是，玻爾等人假設每個電子都實際地按照波函數發散開來，而系綜解釋則是簡單地把這個問題踢出了理論框架中去，來個眼不見為淨：現在我們不必為坍縮操心了，談論單個電子是沒有意義的事情！ 不過，這實在是太掩耳盜鈴了。好吧，量子論只給出系綜，可是我們對於物理理論的要求畢竟要比這樣的統計報告要高那麼一點啊。假如我去找占卜師算命，想知道我的壽限是多少，她卻只告訴我：這個城市平均壽命是七十歲，那對我來說似乎沒有很大的用處啊，我還不如去找保險公司！更可恨的是，她居然對我說，你一個人的壽命是沒什麼意義的，有意義的只是千千萬萬個你的壽命的系綜！ 系綜解釋是一種非常保守和現實主義的解釋，它保留了現有量子論的全部數學形式，因為它們已經被實踐所充分證明。但在令人目眩的哲學領域，它卻試圖靠耍小聰明而逃避那些形而上的探討，用劃定理論適用界限這樣的方法來把自己封閉在一個刀槍不入的外殼中。是的，如果我們採納系綜主義，那麼的確在純理論方面說，我們的一切問題都解決了：沒有什麼坍縮，電子永遠只是粒子（波性只能用來描述粒子的全集），不確定原理也只是被看成一個統計極限，而不理會單個電子到底能不能同時擁有動量和位置（這個問題沒有意義）。但是，這樣似乎有點自欺欺人的味道，把搞不清楚的問題劃為沒有意義也許是方便的，但的確是這樣的問題使得科學變得迷人！每個人都知道，當許多電子通過雙縫時產生了干涉圖紋，可我們更感興趣的還是當單個電子通過時究竟發生了什麼，而不是簡單地轉過頭不去面對！ Taylor在訪談中的確被問道，這樣的做法不是一個當逃兵的遁詞嗎？他非常精明地回答說：我認為你應當問一問，如果陷進去是否比逃之夭夭確實會惹出更多的麻煩。系綜主義者持有的是極致的實用主義，他們炮轟隱變數和多宇宙解釋，因為後兩者都帶來了許多形而上學的麻煩。只要我們充分利用現有的體系，搞出一個又不違反實驗結果，又能在邏輯上自洽的體系，那不就足夠了嗎？系綜解釋的精神，就是盡可能少地避免麻煩，絕不引入讓人頭痛的假設，比如多宇宙或者坍縮之類的。 但是，我們還是不能滿足於這樣的關起門來然後自稱所有的問題都已經解決的做法。或許，是因為我們血液中的熱情還沒有冷卻，或許，是因為我們仍然年少輕狂，對於這個宇宙還懷有深深的激動和無盡的好奇。我們並不畏懼進入更為幽深和神秘的峽谷和森林，去探究那事實的真相。哪怕註定要被一些更加惱人和揮之不去的古怪精靈所纏繞，我們還是不可以放棄了前進的希望和動力，因為那是我們最寶貴的財富。 接下來我們還要去看看兩條新的道路，雖然它們都新辟不久，坎坷顛簸，行進艱難，但沿途那奇峰連天，枯松倒掛，瀑布飛湍，冰崖怪石的絕景一定不會令你失望。five 我們已經厭倦了光子究竟通過了哪條狹縫這樣的問題，管它通過了哪條，這和我們又有什麼關係呢？一個小小的光子是如此不起眼，它的世界和我們的世界相去天壤，根本無法聯繫在一起。在大多數情況下，我們甚至根本沒法看見單個的光子（有人做過實驗，肉眼看見單個光子是有可能的，但機率極低，而且它的波長必須嚴格地落在視網膜杆狀細胞最敏感的那個波段），在這樣的情況下，大眾對於探究單個光子究竟是幽靈還是實在無疑持有無所謂的態度，甚至覺得這是一種杞人憂天的探索。 真正引起人們擔憂的，還是那個當初因為薛定諤而落下的後遺症：從微觀到宏觀的轉換。如果光子又是粒子又是波，那麼貓為什麼不是又死而又活著？如果電子同時又在這裡又在那裡，那麼為什麼桌子安穩地呆在它原來的地方，沒有擴散到整間屋子中去？如果量子效應的基本屬性是疊加，為什麼日常世界中不存在這樣的疊加，或者，我們為什麼從未見過這種情況？ 我們已經聽取了足夠多耐心而不厭其煩的解釋：貓的確又死又活，只不過在我們觀測的時候坍縮了；有兩隻貓，它們在一個宇宙中活著，在另一個宇宙中死去；貓從未又死又活，它的死活由看不見的隱變數決定；單個貓的死活是無意義的事件，我們只能描述無窮只貓組成的全集諸如此類的答案。也許你已經對其中的某一種感到滿意，但仍有許多人並不知足：一定還有更好，更可靠的答案。為了得到它，我們仍然需要不斷地去追尋，去開拓新的道路，哪怕那裡本來是荒蕪一片，荊棘叢生。畢竟世上本沒有路，走的人多了才成為路。 現在讓我們跟著一些開拓者小心翼翼地去考察一條新闢的道路，和當年揚帆遠航的哥倫布一樣，他們也是義大利人。這些開拓者的名字刻在路口的紀念碑上：Ghirardi，Rimini和Weber，下面是落成日期：一九八六年七月。為了紀念這些先行者，我們順理成章地把這條道路以他們的首字母命名，稱為GRW大道。 這個思路的最初設想可以回溯到七十年代的Philip Pearle：哥本哈根派的人物無疑是偉大和有洞見的，但他們始終沒能給出坍縮這一物理過程的機制，而且對於觀測者的主觀依賴也太重了些，最後搞出一個無法收拾的意識不說，還有墮落為唯心論的嫌疑。是否能夠略微修改薛定諤方程，使它可以對坍縮有一個讓人滿意的解釋呢？ 一九八六年七月十五日，我們提到的那三位科學家在《物理評論》雜誌上發表了一篇論文，題為《微觀和宏觀系統的統一動力學》（Unified dynamics for microscopic and macroscopic systems），從而開創了GRW理論。GRW的主要假定是，任何系統，不管是微觀還是宏觀的，都不可能在嚴格的意義上孤立，也就是和外界毫不相干。它們總是和環境發生著種種交流，為一些隨機（stochastic）的過程所影響，這些隨機的物理過程不管它們實質上到底是什麼會隨機地造成某些微觀系統，比如一個電子的位置，從一個彌漫的疊加狀態變為在空間中比較精確的定域（實際上就是哥本哈根口中的坍縮），儘管對於單個粒子來說，這種過程發生的可能性是如此之低按照他們原本的估計，平均要等上10^15秒，也就是近十億年才會發生一次。所以從整體上看，微觀系統基本上處於疊加狀態是不假的，但這種定域過程的確偶爾發生，我們把這稱為一個自發的定域過程（spontaneous localization）。GRW有時候也稱為自發定域理論。 關鍵是，雖然對於單個粒子來說要等上如此漫長的時間才能迎來一次自發過程，可是對於一個宏觀系統來說可就未必了。拿薛定諤那只可憐的貓來說，一隻貓由大約10^27個粒子組成，雖然每個粒子平均要等上幾億年才有一次自發定域，但對象貓這樣大的系統，每秒必定有成千上萬的粒子經歷了這種過程。 Ghirardi等人把薛定諤方程換成了所謂的密度矩陣方程，然後做了複雜的計算，看看這樣的自發定域過程會對整個系統造成什麼樣的影響。他們發現，因為整個系統中的粒子實際上都是互相糾纏在一起的，少數幾個粒子的自發定域會非常迅速地影響到整個體系，就像推倒了一塊骨牌然後造成了大規模的多米諾效應。最後的結果是，整個宏觀系統會在極短的時間裡完成一次整體上的自發定域。如果一個粒子平均要花上十億年時間，那麼對於一個含有一摩爾粒子的系統來說（數量級在10^23個），它只要.一微秒就會發生定域，使得自己的位置從彌漫開來變成精確地出現在某個地點。這裡面既不要觀測者，也不牽涉到意識，它只是基於隨機過程！ 如果真的是這樣，那麼當決定薛定諤貓的生死的那一刻來臨時，它的確經歷了死／活的疊加！只不過這種疊加只維持了非常短，非常短的時間，然後馬上自發地精確化，變成了日常意義上的，單純的非死即活。因為時間很短，我們沒法感覺到這一疊加過程！這聽上去的確不錯，我們有了一個統一的理論，可以一視同仁地解釋微觀上的量子疊加和宏觀上物體的不可疊加性。 但是，GRW自身也仍然面臨著嚴重的困難，這條大道並不是那樣順暢的。他們的論文發表當年，海德堡大學的E. Joos就向《物理評論》遞交了關於這個理論的評論，而這個評論也在次年發表，對GRW提出了置疑。自那時起，對GRW的疑問聲一直很大，雖然有的人非常喜歡它，但是從未在物理學家中變成主流。懷疑的理由有許多是相當技術化的，對於我們史話的讀者，我只想在最膚淺的層次上稍微提一些。 GRW的計算是完全基於隨機過程的，而並不引入類如觀測使得波函數坍縮之類的假設。他們在這裡所假設的自發過程，雖然其概念和坍縮類似，實際上是指一個粒子的位置從一個非常不精確的分佈變成一個比較精確的分佈，而不是完全確定的位置！換句話說，不管坍縮前還是坍縮後，粒子的位置始終是一種不確定的分佈，必須為統計曲線（高斯鐘形曲線）所描述。所謂坍縮，只不過是它從一個非常矮平的曲線變成一個非常尖銳的曲線罷了。在哥本哈根解釋中，只要一觀測，系統的位置就從不確定變成完全確定了，而GRW雖然不需要觀測者，但在它的框架裡面沒有什麼東西是實際上確定的，只有非常精確，比較精確，非常不精確之類的區別。比如說當我盯著你看的時候，你並沒有一個完全確定的位置，雖然組成你的大部分物質（粒子）都聚集在你所站的那個地方，但真正描述你的還是一個鐘形線（雖然是非常尖銳的鐘形線）！我只能說，絕大部分的你在你所站的那個地方，而組成你的另外的那一小撮（雖然是極少極少的一小撮）卻仍然彌漫在空間中，充斥著整個屋子，甚至一直延伸到宇宙的盡頭！ 也就是說，在任何時候，你都填滿了整個宇宙，只不過大部分的你聚集在某個地方而已。作為一個宏觀物體的好處是，明顯的量子疊加可以在很短的時間內完成自發定域，但這只是意味著大多數粒子聚集到了某個地方，總有一小部分的粒子仍然留在無窮的空間中。單純地從邏輯上講，這也沒什麼不妥，誰知道你是不是真有小到無可覺察的一部分彌漫在空間中呢？但這畢竟違反了常識！如果必定要違反常識，那我們乾脆承認貓又死又活，似乎也不見得糟糕多少。 GRW還拋棄了能量守恆（當然，按照相對論，其實是質能守恆）。自發的坍縮使得這樣的守恆實際上不成立，但破壞是那樣微小，所需等待的時間是那樣漫長，使得人們根本不注意到它。拋棄能量守恆在許多人看來是無法容忍的行為。我們還記得，當年玻爾的BKS理論遭到了愛因斯坦和泡利多麼嚴厲的抨擊。 還有，如果自發坍縮的時間是和組成系統的粒子數量成反比的，也就是說組成一個系統的粒子越少，其位置精確化所要求的平均時間越長，那麼當我們描述一些非常小的探測裝置時，這個理論的預測似乎就不太妙了。比如要探測一個光子的位置，我們不必動用龐大而複雜的儀器，而可以用非常簡單的感光劑來做到。如果好好安排，我們完全可以只用到數十億個粒子（主要是銀離子）來完成這個任務。按照哥本哈根，這無疑也是一次觀測，可以立刻使光子的波函數坍縮而得到一個確定的位置，但如果用GRW的方法來計算，這樣小的一個系統必須等上平均差不多一年才會產生一次自發的定域。 Roland Omnes後來提到，Ghirardi在私人的談話中承認了這一困難。但他爭辯說，就算在光子使銀離子感光這一過程中牽涉到的粒子數目不足以使系統足夠快地完成自發定域，我們誰都無法意識到這一點！如果作為觀測者的我們不去觀測這個實驗的結果，誰知道呢，說不定光子真的需要等上一年來得到精確的位置。可是一旦我們去觀察實驗結果，這就把我們自己的大腦也牽涉進整個系統中來了。關鍵是，我們的大腦足夠大（有沒有意識倒不重要），足夠大的物體便使得光子迅速地得到了一個相對精確的定位！ 推而廣之，因為我們長著一個大腦袋，所以不管我們看什麼，都不會出現位置模糊的量子現象。要是我們拿複雜的儀器去測量，那麼當然，測量的時候物件就馬上變得精確了。即使儀器非常簡單細小，測量以後物件仍有可能保持在模糊狀態，它也會在我們觀測結果時因為擁有眾多粒子的大腦的介入而迅速定域。我們是註定無法直接感覺到任何量子效應了，不知道一個足夠小的病毒能否爭取到足夠長的時間來感覺到光子又在這裡又在那裡的奇妙景象（如果它能夠感覺的話！）？ 最後，薛定諤方程是線性的，而GRW用密度矩陣方程將它取而代之以後，實際上把整個理論體系變成了非線性的！這實際上會使它作出一些和標準量子論不同的預言，而它們可以用實驗來檢驗（只要我們的技術手段更加精確一些）！可是，標準量子論在實踐中是如此成功，它的輝煌是如此燦爛，以致任何想和它在實踐上比高低的企圖都顯得前途不太美妙。我們已經目睹了定域隱變數理論的慘死，不知GRW能否有更好的運氣？另一位量子論專家，因斯布魯克大學的Zeilinger（提出GHZ檢驗的那個）在二○○○年為Nature雜誌撰寫的慶祝量子論誕生一百周年的文章中大膽地預測，將來的實驗會進一步證實標準量子論的預言，把非線性的理論排除出去，就