Chapter 17 Afterword The Future of the Unthinkable
Is there any truth we can never capture?Are there any areas of cognition that are inaccessible even to present-day civilization?Among all the technologies analyzed above, only perpetual motion machines and precognition are classified as "third-class incredible".Are there other technologies that are equally unachievable?
Mathematics can already provide enough theoretical basis to prove that some things are indeed impossible to realize.To give a simple example, we cannot divide an angle into thirds using only a compass and a ruler—this was proved as early as 1837.
Impossibility exists even in a system as simple as arithmetic.As I mentioned before, not all true propositions can be proved under the basic assumptions of arithmetic.There are always some true propositions in arithmetic that can only be proved when you use a broader system that includes arithmetic as a subset.
While some things are unrealizable in mathematics, in physics it is dangerous to claim that something is completely unrealizable.Let me remind you of Nobel laureate Albert A. Michelson's 1894 speech at the Ryerson Physical Lab at the University of Chicago: "In physics the very important Fundamental laws and facts have been discovered, and we are now all firmly convinced that the chances of them being superseded by new discoveries are remote... our future discoveries must be sought to the sixth decimal place."
His speech came on the eve of certain upheavals in the history of science—the quantum revolution of 1900 and the relativity revolution of 1905.The point is that what seems impossible today violates the known laws of physics: but we know that the laws of physics can change.
In 1825, the great French philosopher Auguste Comte declared in his Cours de Philosophic that science cannot determine the composition of stars.At the time, the statement seemed safe, since no one knew anything about the nature of stars.They are too far away.People at that time could not go to visit.However, just a few years after he made this statement, physicists announced (using spectroscopy) that the sun is made of hydrogen.In fact, we now know that by analyzing the spectral lines emitted by stars billions of years ago, humans can determine the chemical composition of most stars in the universe.
Comte listed a long list of other "impossibles" that challenged the scientific community:
In the 19th century, it was reasonable to propose these "impossibles", because people at that time knew so little about basic science.Hardly any secrets about matter and life are known.Today, however, we have atomic theory, which opens up a whole new world of scientific inquiry into the structure of matter.We understand DNA and quantum theory, which unlock the secrets of the chemistry of life.We also learn about meteorite impacts in space, an event that not only affects the course of life on Earth, but also helps shape life on Earth.
Astronomer John Barrow notes: "Historians are still debating the claim that Comte's ideas were in part responsible for the subsequent decline of French science."
The mathematician David Hilbert, who opposed Comte's remarks, wrote: "I think the real reason why Comte could not find an unsolvable problem is that they are all solvable."
But scientists today present a whole new set of impossibilities: We'll never know what happened before the Big Bang (or why it happened in the first place);
Physicist John Wheeler commented on the first "impossible" question: "Two hundred years ago, you could ask anyone: 'Will we someday understand how life came to be?' and he would have said to you , 'Ridiculous! How is that possible!' I feel the same way about the question 'Will we ever learn how the universe came to be?'."
Astronomer John Barrow also said: "The speed of light is finite and, therefore, our knowledge of the structure of the universe is also finite. We cannot know whether it is finite or infinite, whether it has a beginning or whether it will have an end, physics Whether the structure of the universe is the same everywhere, or whether the universe is an ordered or chaotic place ... all these big questions about the nature of the universe - from its origin to its end - seem unanswerable."
Barrow was adamant that we will never understand the nature of the universe, and rightly so.But it is possible that we can gradually solve these unresolved problems and get infinitely closer to the final answer.We should think of these "impossibles" not as absolute limits of human knowledge, but as challenges for the next generation of scientists.These boundaries are like pie crust, born to be broken.
In the study of the Big Bang, scientists are developing a new generation of detectors to address some of these challenges.The radiation detectors we use in outer space today can only measure microwave radiation emitted 300,000 years after the Big Bang—when the first atoms were formed—and cannot detect 30 years after the Big Bang with this microwave radiation. In the situation within ten thousand years, because the radiation emitted by the first fireball formed by the big bang is extremely high temperature and extremely chaotic, it is difficult to produce useful information.
But if we analyze other types of radiation, maybe we can get closer to the Big Bang.For example, tracking neutrinos (neutrinos are so eerie that they could travel through an entire solar system made of solid lead) could bring us closer to the moment of the Big Bang.Neutrino radiation can transport us to the mere seconds after the Big Bang.
But finally unraveling the mystery of the Big Bang may require the study of “gravity waves”—waves that move along the fabric of space-time, as University of Chicago physicist Rocky Kolb ) said, "By measuring the properties of the neutrino background, we can trace the situation back to 1 second after the Big Bang, and the gravitational waves emitted from the expansion region are the remains of the universe 10 to 35 seconds after the Big Bang. ".
In 1916, Einstein first predicted the existence of gravitational waves.They may end up being the most important tools for exploring astronomy.Every new type of radiation exploited throughout history ushered in a new era in astronomy.The first type of radiation is visible light, which Galileo used to probe the solar system.The second type of radiation is sound waves, which eventually allowed us to go deep into the center of the galaxy and find black holes.Gravitational waves may be able to unravel the mystery of the origin of species.
To some extent, the existence of gravitational waves is inevitable.To understand this statement, consider a well-worn question: What would happen if the sun suddenly disappeared?According to Newton, we feel its effects instantly.The earth will be thrown out of its original orbit in an instant and enter darkness.This is because Newton's law of gravity does not take velocity into account, so the force acts on the entire universe instantaneously.But according to Einstein's theory, nothing moves faster than the speed of light, so the earth will not perceive it until 8 minutes after the sun disappears.In other words, the sun's gravity creates a spherical "shock wave" that eventually hits Earth.In the area outside the range of this gravitational wave, everything is as if the sun is still shining, because the "information" of the disappearance of the sun has not yet reached the earth.And in the area within the range of this gravitational wave, as the shock wave generated by the gravitational wave continues to expand and move forward at the speed of light, the sun has disappeared.
Another way to understand why gravitational waves must exist is to imagine a large bed sheet.According to Einstein, space-time is like a fabric that can be bent or stretched, like a crumpled bed sheet.If we grab a sheet and shake it quickly, we will see ripples on the surface of the sheet, moving at a certain speed.Likewise, gravitational waves can also be viewed as ripples moving along the fabric of space-time.
Gravitational waves are one of the hottest and fastest-growing topics in physics today. In 2003, the first large-scale gravitational wave detector was put into operation - known as LIGO (Laser Interferometer Gravitational Wave Observatory, Laser Interferometer Gravitational Wave Observatory).The 2.5-mile facility, with one facility in Hanford, Washington, and the other in Livingston Parish, Louisiana, is expected to be detected by the $365 million LIGO Radiation from colliding neutron stars and black holes.
Another major advance will take place in 2015, when a whole new generation of satellites will be launched to analyze gravitational radiation in outer space since the moment of the Big Bang.The three satellites that make up LISA (Laser Interferometer Space Antenna), a joint project between NASA and the European Space Agency, will be sent into orbit around the sun.The satellites will be able to detect gravitational waves emitted 1/1 trillionth of a second after the Big Bang.If a still-circling gravitational wave from the big bang hit one of the satellites, the laser beam would be disrupted, and scientists can precisely measure this disturbance, giving us a "basic picture" of how the universe was formed. ".
Consisting of three satellites arranged in a triangle around the sun and linked to each other by 3 million miles of laser beams, LISA is the world's largest scientific instrument.The system of three satellites will orbit the Sun at a distance of 30 million miles from Earth.
Each satellite emits a laser beam with a power of only half a watt.By comparing the rays emanating from the other two satellites, each satellite will be able to build a map of light interference.If a gravitational wave interferes with the laser beam, the interference map is changed so that the satellites can detect the interference (gravitational waves do not vibrate the satellite. In fact it warps the space between the three satellites .
Although the laser beams are very weak, their precision cannot be underestimated.They can detect vibrations that are 1/1,000,000,000,000,000,000,000 in magnitude, or 1/100th the size of an atom.Each laser ray is capable of detecting gravitational waves 9 billion light-years away, which covers most of the visible universe.
The sensitivity of LISA makes it possible to distinguish between several different "pre-Big Bang" scenarios.One of the hottest topics in theoretical physics today is estimating the properties of the universe before the big bang.At present, the inflation theory can well describe the evolution of the universe after the big bang, but the inflation theory cannot explain the motivation of the big bang.Scientists aim to use these inferred models of the pre-Big Bang period to measure the gravitational waves emitted by the Big Bang. Each pre-Big Bang theory makes different predictions.For example, the radiation from the Big Bang predicted by the Big Splat theory is different from that predicted by some theories of inflation.So LISA might be able to rule out some of these theories.Clearly, these pre-Big Bang models cannot be tested directly, since that would require us to know the state of the universe before time came into existence.But we can verify them indirectly, because each theory predicts a different spectrum of post-Big Bang radiation.
Physicist Kip Thorne writes: "Sometime between 2008 and 2030, gravitational waves from the Big Bang singularity will be discovered. This will be followed by an epoch lasting at least until 2050...the results will be reveal some important details about the Big Bang singularity, and thus be able to confirm that a version of superstring theory is the correct quantum theory of gravity."
If L1SA can't distinguish between different pre-Big Bang theories, then perhaps its next generation, the Big Bang Observer (BBO), can.It is tentatively scheduled to launch in 2025. BBO will be able to scan the entire universe for binary systems including neutron stars and black holes less than 1,000 times the mass of the sun.But its main task is to analyze the gravitational waves emitted during the expansion period of the Big Bang.In this sense, the BBO is specifically designed to explore the predictions of the expanding Big Bang theory.
BBO has certain similarities with LISA in design.It will also consist of three satellites orbiting the Sun together, each separated by 50,000 kilometers (which is much closer than the satellites in LISA).Each satellite will be able to emit a 300-watt laser beam. BBO will be able to detect gravitational waves with frequencies between LIGO and LISA, which fills an important gap (LISA can detect gravitational waves between 10-3000 Hz, while LIGO can detect gravitational waves between 10 microhertz and 10 millihertz. gravitational waves in between. BBO will be able to detect gravitational waves covering the above two frequency ranges).
"By 2040, we will use those laws of (quantum gravity) to find relatively certain answers to profoundly difficult questions," Thorne wrote, "including . . . what happened before the Big Bang singularity, or whether Is there a state of 'before'? Are there other universes? If so, how are they connected and related to our universe?...Do the laws of physics allow highly developed civilizations to create or maintain wormholes to achieve Interstellar travel, or inventing a time machine to turn back time?"
The point is that over the next few decades, there will be enough data from gravitational-wave detectors in space to distinguish between the various pre-Big Bang theories.
Will the universe die with a bang or a low hum, asked the poet TS Eliot?Robert Frost asks, shall we all disappear in flame or ice?The latest evidence points to the fact that the universe will die in a big freeze, when the temperature will be close to absolute zero, and all intelligent life will be extinct.But are we sure about that?
Someone asked another "impossible" problem.How can we know the ultimate fate of the universe, they ask, since this is an event eons away?Scientists believe "dark energy" or vacuum energy appears to be tearing galaxies apart at unprecedented rates, suggesting the universe appears to be spinning out of control.This expansion would lower the temperature of the universe, eventually leading to the Big Freeze.But is this expansion temporary?Will it reverse itself in the future?
For example, in a "majestic collision" scenario in which two membranes collide and create the universe, it appears that the membranes collide periodically.If this is the case, then the expansion that appears to be causing the Great Freeze is merely a temporary condition that will eventually correct itself.
It is dark energy that is currently accelerating the universe, and it may be causing it in turn.So the key is to understand this mysterious constant, or vacuum energy.Does this constant change over time?Or is it really a constant?Now no one knows for sure.We know from the WMAP satellite that is currently orbiting the earth that this cosmological constant seems to be accelerating the current universe, but we don't know if this is temporary or forever.
In fact, it's an old conundrum, dating back to 1916, when Einstein first introduced the concept of the cosmological constant.Shortly after proposing the general theory of relativity in 1915, he deduced the cosmic implications from his theory.To his surprise, he discovered that the universe is dynamic, expanding or contracting.But that idea seems to contradict those data.
Einstein encountered the Bentley paradox, a paradox that troubled even Newton.As early as 1692, the Reverend Richard Bentley wrote a frank letter to Newton, but it was devastating to Newton's theories.Why hasn't the universe collapsed, Bentley asks, if Newton's gravitational force is always attractive?If the universe is composed of a finite series of mutually attracting stars, then these stars should keep coming together, and the universe will become a big fireball and destroy!Newton was deeply troubled by the letter because it pointed out a major hole in his laws of gravity: any theory of gravitation that is attractive is itself unstable.Under the action of universal gravitation, any finite collection of stars must be destroyed.
Newton replied that the only way to create a stable universe was if the universe was infinite and perfectly uniform, with every star being pulled equally by forces in all directions, so all forces would cancel out.It was a clever solution, but Newton was also clever enough to realize that this stability was self-deceiving.Like a stack of dominoes, even the slightest shock can cause the entire deck to topple over.This is the "metastability state" in which it remains temporarily stable until the slightest jolt causes it to collapse.Newton concluded that it was necessary for God to move these stars slightly periodically to keep the universe from collapsing.
When Einstein was troubled by Bentley's Paradox in 1916, his equations correctly told him that the universe was dynamic—expanding or contracting; The next crash.But astronomers at the time insisted that the universe was static and unchanging.So Einstein, succumbing to the observations of astronomers, introduced the cosmological constant—an antigravitational force that pushes stars away from each other to balance the gravitational convergence that would cause the universe to collapse (this antigravitational force corresponds to due to vacuum energy. In this case, even the vastness of empty space contains a large amount of invisible energy).In order to counteract the attractive effect of gravity, this constant needs to be chosen precisely.
Not long after, in 1929, when Edwin Hubble proved that the universe was actually expanding, Einstein might have called the cosmological constant his "biggest blunder."However, as of today, 70 years later, Einstein's "mistake"—the cosmological constant, which actually appears to be the largest source of energy in the universe—constitutes 73% of the matter-energy in the universe (conversely, our human body high-order elements accounted for only 0.03%).Einstein's blunders may well determine the ultimate fate of the universe.
But where did the cosmological constant come from?No one knows at this time.At the beginning of time, the antigravity force may have been large enough to cause the universe to expand, causing the Big Bang, and then for some unknown reason, this force suddenly disappeared (the universe was still expanding during this period, but at a slower rate).Then, about 8 billion years after the Big Bang, this antigravity force reappeared, pushing galaxies apart and causing the universe to speed up again.
So is it "impossible" to know the ultimate fate of the universe?Maybe not.Most physicists believe that quantum interactions ultimately determine the size of the cosmological constant.A calculation using an initial version of quantum theory naively yields a value for the cosmological constant that is off by a factor of 10120.This is the biggest error in the history of science.
But there is also a consensus among physicists that this anomalous error is a sign that we need a theory of quantum gravity.Since the cosmological constant arises through quantum corrections, it is necessary to find a theory of everything that allows us to calculate not only the Standard Model, but also the value of the cosmological constant that will determine the ultimate fate of the universe.
Therefore, in order to determine the ultimate destiny of the universe, it is necessary to find an ultimate principle of all things.But ironically, some physicists believe that finding a theory of everything is impossible.
As I mentioned before, superstring theory is the most powerful contender for "the truth of everything", but there are also opponents who question whether superstring theory is qualified.On the one hand, there are those who are very supportive, such as Max Tegmark, a professor at the Massachusetts Institute of Technology, who wrote: "In 2056, I think you can buy T-shirts with equations describing the unified physical laws of our universe ’ ” On the other hand, an emerging group of critics firmly asserts that superstring theory has not yet become mainstream.Some say that no matter how many amazing articles or TV documentaries are produced about superstring theory, the theory still doesn't provide a solid fact.It is not a theory of everything, critics say, but a theory of nothing. The debate in physics reached a fever pitch in 2002 when Stephen Hawking reversed course, citing the "incompleteness theorem" and claiming that the Theory of Everything might not even be mathematically feasible.
The debate pits physicists against each other.This is not surprising, since the goal is so high and elusive.The desire to unify all the laws of nature has fascinated philosophers and physicists for millennia.Socrates himself said: "It is a supreme thing for me to know the definition of all things, their origin, their death, and their existence."
Humans first formally proposed the theory of everything as far back as 500 BC, when the Greek Pythagoreans were authorized to decipher the mathematical laws of music.By analyzing the knots and vibrations of the lyre strings, they concluded that music obeys very simple mathematical laws.Then they speculated that everything in nature could be explained by the concerto of lyre strings (in a sense, superstring theory evokes the Pythagorean school).
In modern times, almost all the great physicists of the 20th century are trying to find a unified theory.But as Freeman Dyson warned everyone: "The field of physics is already full of corpses of grand unified theories."
In 1928, a sensational headline appeared in the "New York Times": "Einstein is about to make a major discovery, please do not disturb." This news made the media almost fanatical about the truth of all things. "Einstein Shocked by Theory's Frenzy," read the headline. "Attracted 100 Journalists for a Week," as many journalists gathered around his Berlin home, waiting around the clock to see what happened. A genius writes news.Einstein had to go into seclusion.
Astronomer Arthur Eddington wrote to Einstein: "It may sound funny to you that Selfridges, one of our largest department stores in London, has posted your paper in the window (6 pages of papers are pasted page by page), so that passers-by can read the full text. A large group of people gathered together and rushed to read." (In 1923, Eddington proposed his own unified field theory, which has been worked on the theory until his death in 1944.)
In 1946 Erwin Schrödinger, one of the Mokis of quantum mechanics, held a press conference to announce his unified field theory, and even Irish Prime Minister Eamon De Valera was in attendance this press conference.When a reporter asked Schrödinger what he would do if his theory was wrong, Schrödinger replied: "I believe I am right. If I am wrong, I will look like a fool."( When Einstein politely pointed out the fallacies in his theory, Schrödinger was embarrassed.)
Of all the critics, the most severe attack on unification was the physicist Wolfgang Pauli, who rebuked Einstein: "What God tore apart, no one should put back together. together." He ruthlessly satirizes and suppresses unfinished theories: "It's not even wrong." So it's quite ironic that the deeply cynical Pauli himself inevitably "falls into a cliché" . In the 1950s, he and Weiner Heisenberg jointly proposed their own unified field theory.
In 1958, Pauli proposed the Heisenberg-Pauli unification theory at Columbia University.Niels Bohr was also present, but Yi was not impressed.Bohr stood up and said, "We, the audience, believe your theory is crazy. But what makes us disagree is whether your theory is crazy enough." Comments abounded.Since all proposed theories have been considered to be negative, a true unified field theory must be quite different from the theories of the past.The Heisenberg-Pauli theory is just too old-fashioned and commonplace, lacking the madness needed for truth. (That year, Heisenberg explained on a radio broadcast that their theory was only missing a few technical details. Pauli was not pleased. He wrote a letter to Heisenberg and drew a blank , captioned "This proves to the world that I can draw as well as -, only missing some technical details.")
The main (and only) thing that has the potential to be the truth of everything today is string theory.But the voice of rebuttal followed like a shadow.Opponents say you have to study string theory to secure tenure at a top university.If you don't, you will be fired.It was a frenzy at the time, not conducive to the development of physics.
I laughed when I heard that comment, because physics, like all other human endeavors, is subject to fads.The fortunes of great theories—especially those at the cutting edge of human knowledge—have their ups and downs.In fact, the situation has changed a few years ago. String theory is a theory abandoned by history, long out of date, and a victim of the herd effect.
String theory was born in 1968 when two young postdocs, Gabriel Veneziano and Mahiko Suzuki, stumbled upon a formula that seemed to describe the collisions of subatomic particles.Soon it was discovered that this great formula could be derived from the collision of vibrating strings.But the theory faded away by 1974. A new theory—quantum cbromodynamics (QCD), or the theory of the strong interaction between quarks—emerged out of nowhere, eclipsing all other theories, and an army of people abandoned string theory for QCD.All the money, jobs, and fame go to the physicists who work on the quark model.
I still remember those dark times vividly.Only the brave and stubborn persist in working on string theory.And when it was discovered that the strings vibrated only in ten dimensions, the theory became a big joke.The pioneer of string theory, Caltech's John Schwarz, would sometimes run into Richard Feynman in an elevator.The witty Feynman would ask him: "John, so how many dimensions have you entered today?" We used to joke that string theorists can only be found among the unemployed. (Murray GeUMann, the Nobel laureate and moki man of the quark model, once confided to me that he was so sympathetic to string theorists that Caltech created an "Endangered String Theorist Nature Reserve” so that people like John would not be out of work.)
Given the rush of many young physicists today to work on string theory, Steven Weinberg writes: "String theory provides a final theory with the few resources we currently have—how can we think that so many of the most Shouldn't bright young theorists be working on it?"
One of the main criticisms of string theory today is that it cannot be tested.Critics say a nuclear particle accelerator the size of the Milky Way would be needed to test the theory.
But that criticism ignores the fact that most science works indirectly rather than directly.No one has ever done direct research on the sun, but we know that it is composed of hydrogen by analyzing its spectral lines.
Take black holes, for example.Black hole theory began in 1783, when John Michell published an article in the Philosophjca Transaxtions of the Royal Society in which he claimed that some stars were so massive that they "would All light emitted from the star returns under the gravitational pull of the star itself".Michel's "dark star" theory was dimmed for centuries because it was impossible to directly verify it. In 1939, Einstein even wrote a paper showing that such dark stars cannot form naturally.Critics have argued that these dark stars are inherently unverifiable because they are by definition invisible.However, today's Hubble Space Telescope has provided us with perfect evidence about black holes.We now believe that there are billions of black holes lurking in galaxies, and there are dozens of black holes wandering in our Milky Way.But the point is that the evidence for the existence of black holes is obtained indirectly, that is, we gather information about them by analyzing the absorbing disks that surround them.
In addition, many "unverifiable" theories have finally become verifiable. After (Democritus) first proposed the atom theory, it took humans two thousand years to prove the existence of atoms. Nineteenth-century physicists such as Ludwig Boltzmann were killed for believing in this theory.Today, however, we have magnificent pictures of atoms.Pauli himself conceived the concept of neutrinos in 1930, which behave in such a strange way that they can pass through matter the size of entire galaxies of solid lead without being absorbed.Pauli said: "I was essentially wrong; I proposed a particle that could not be observed at all." Detecting neutrinos was "impossible," so for decades it was dismissed as science fiction.Today, however, we can create beams of neutrinos.
In fact, physicists hope that a number of experiments will provide the first indirect tests of string theory:
Scientists also hope that a series of other experiments (such as studying the polarization of neutrinos at the S pole) will detect tiny black holes and other exotic matter by analyzing anomalies in cosmic rays - whose energies far exceed those of the LHC The presence.The cosmic ray experiment and the LHC will open up a new and exciting frontier of research beyond the Standard Model.
In 1980, Stephen Hawking published "Is the End of Theoretical Physics Coming?" "(Is the End in Sight for Theoretical Physics?) speech, stimulated people's interest in the truth of all things.In the speech, he said: "In the lifetime of some people here, we may see a complete theory." He claimed that 50% of the folios will find a final theory in the next 20 years.But when the year 2000 came, the academic community did not reach a consensus on the truth of everything, so Hawking changed his mind, saying that there will be a probability of finding the theory of everything in the next 20 years.
In 2002, Hawking changed his mind again, declaring that Gödel's incompleteness theorem might point to a fatal flaw in his original way of thinking.He wrote: "Some people will be very disappointed if there is not a final theory expressed in terms of finite principles. I belonged to this group too, but I have changed my mind now... Gödelder's theorem shows that , mathematicians are never finished. I think M-theory has the same meaning for physicists."
His statement is not new: since mathematics is incomplete, and the language of physics is mathematics, there will always be physical theories that we cannot understand, so the ultimate principle of everything cannot exist.Just as the incompleteness theorem killed the Greeks' dream of proving all true propositions of mathematics, it will also make the truth of everything always elusive.
Freeman Dyson wrote very eloquently: "Godel proved that the world of pure mathematics is infinite; no fixed set of axioms or laws of inference can cover the whole of mathematics...I hope something similar holds true for physics. If my vision of the future is correct, it means that the worlds of physics and astronomy are also endless; no matter how far into the future we can explore, new things will appear, new information will come, new worlds wait Let's explore the endless expanse of life, consciousness, and memory." Astrophysicist John Barrow summed up the logic this way: "Science is based on mathematics. Mathematics cannot discover the whole truth, so neither can science. .”
Such an assertion may or may not be true, but it is potentially flawed. Most professional mathematicians ignore the incompleteness theorem as they work, because the theorem begins with an analysis of a proposition pointing to itself, that is, , which are self-assigning.For example, the following proposition is self-contradictory:
In the first proposition, if the statement is true, then it also means "this statement is false".And if the statement is false, then the proposition is true.Likewise, if I am telling the truth, it means "I am lying"; and if I am lying, then the statement is true.In the last sentence, if the proposition is true, then it cannot be proved to be true.
(The second proposition is the famous liar paradox. The Cretan philosopher Epimenides once explained this paradox with this sentence: "All Cretans are liars." But Saint Paul misses the point entirely, writing to Titus: "A prophet in Crete said, 'All Cretans Men are liars, vicious cruels, lazy gluttons'. He certainly spoke the truth.")
Incompleteness theorems build on propositions such as "This statement cannot be proved by arithmetic principles" and weave a complex web of self-assigning contradictory propositions.
然而，霍金运用不完备定理证明不存在一个万有理论。他声称哥德尔不完备定理的关键在于，数学是自我指设的，物理学也有着同样的毛病。由于观测者无法同观测进程分离开来，这就意味着物理学永远会指向自身，因为我们不可能脱离宇宙。在最终的分析中，观测者亦是由原子和分子组成的，因此必然是其正在进行的实验的一部分。
但也有一个方法可以避免霍金的该论断。为了避免哥德尔定理中的内在矛盾，今天的很多职业数学家都简单地声称，他们的研究排除了所有自我指设的命题。这样他们就可以绕开不完备定理。从很大程度上来说，哥德尔之后数学的迅速发展，仅仅是由于这些数学家们不去理会不完备定理，即假定他们的研究不作出任何自我指涉的命题。
同样地，构建一个能够解释所有已知的、脱离了观测者/观测对象二分论的实验的万有理论，或许也是可能的。如果这样一个万有理论能够解释从大爆炸起源到环绕我们的可见宇宙中的所有事物，那么我们如何描述观测者和观测对象之间的关系就变得很有学术性。事实上，万物至理的一个标准应为：它的结论完全不取决于我们如何划分观测者和观测对象之间的界限。
此外，自然或许是无穷无尽的，即使它的法则屈指可数。想想国际象棋。让一个从别的星球来的人仅仅通过看比赛就指出象棋的规则，不一会儿，他就可以告诉你，兵卒、主教和国王分别是怎么走的。比赛的规则是有限而简单的，但可能下出的棋局种类却是天文数字。同样，自然的法则也可能是有限而简单的，但对这些法则的应用却是无尽的。我们的目标是找到物理学的法则。
从某种程度上说，我们已经有一个关于大多数现象的完备理论。还没有人从麦克斯韦的光学方程中看出缺陷。标准模型常被称为“准万物至理”。现在假设我们可以脱离引力，那么标准模型就成为解释除引力之外其他一切现象的完美理论。理论本身看上去或许不太漂亮，但的确可行。即使有不完备定理，我们还是可以有一个非常合理的万物至理（除了引力）。
对我而言，只要一张白纸就能写下统治所有已知物理现象——包括43个数量级，从100多亿光年开外的遥远宇宙到夸克和中微子的微观世界——的定律，这是一件令人惊叹的事情。在这张白纸上只会有两个方程式，爱因斯坦的引力定律和标准模型。我认为他们揭示了自然界本质上的简单与和谐。宇宙或许曾经是反常、混乱而变化无常的，但现在呈现在我们面前的宇宙是完整、和谐与美丽的。
诺贝尔奖得主斯蒂夫·温伯格将我们对万物至理的追寻比作科学家寻找N极。几个世纪以来，古代航海家们一直使用着没有N极的地图。所有的指南针和航海图都奔着这块地图上缺失的部分而去，但没有人真的造访过那里。同样，我们所有的数据和理论都是为了寻获万物至理。这是我们缺失的—个方程式。
总有事物是我们所不可及的，亦无法探究（如电子的精确位置，或是光速之外的世界）。但我相信，基本的定律是可知的、有限的。而未来几年的物理学界也将是最为振奋人心的，因为我们使用了新一代粒子加速器、空间引力波探测仪以及其他新技术来探索宇宙。我们并没有走到终点，而是站在—个新物理学的起点。但无论我们发现了什么，前方也总还有新的地平线等着我们跨越。
Notes:
Notes: