Greene takes it for granted, and here the great majority of physicists agree with him, that the division of physics into separate theories for large and small objects is unacceptable. General relativity is based on the idea that space-time is a flexible structure pulled and pushed by material objects. Quantum mechanics is based on the idea that space-time is a rigid framework within which observations are made. The two theories are mathematically incompatible. Greene believes that there is an urgent need to find a theory of quantum gravity that applies to large and small objects alike. Quantum gravity means a unified theory that works like general relativity for large objects and like quantum mechanics for small objects. In spite of heroic efforts by many people, no consistent theory of quantum gravity was found until string theory came along. The first and greatest triumph of string theory was its success in unifying general relativity with quantum mechanics. That success gave its discoverers some justification for claiming that it could be a “theory of everything.” String theory is still incomplete and far from ready for practical application, but it does in principle provide us with a theory of quantum gravity.
As a conservative, I do not agree that a division of physics into separate theories for large and small is unacceptable. I am happy with the situation in which we have lived for the last eighty years, with separate theories for the classical world of stars and planets and the quantum world of atoms and electrons. Instead of insisting dogmatically on unification, I prefer to ask the question whether a unified theory would have any real physical meaning. The essence of any theory of quantum gravity is that there exists a particle called the graviton which is a quantum of gravity, just like the photon which is a quantum of light. Such a particle is necessary in quantum gravity, because energy is carried in discrete little packets called quanta, and a quantum of gravitational energy would behave like a particle.
The question that I am asking is whether there is any conceivable way in which we could detect the existence of individual gravitons. It is easy to detect individual photons, as Einstein showed, by observing the behavior of electrons kicked out of metal surfaces by light incident on the metal. The difference between photons and gravitons is that gravitational interactions are enormously weaker than electromagnetic interactions. If you try to detect individual gravitons by observing electrons kicked out of a metal surface by incident gravitational waves, you find that you have to wait longer than the age of the universe before you are likely to see a graviton. I looked at various possible ways of detecting gravitons and did not find a single one that worked. Because of the extreme weakness of the gravitational interaction, any putative detector of gravitons has to be extravagantly massive. If the detector has normal density, most of it is too far from the source of gravitons to be effective, and if it is compressed to a high density around the source it collapses into a black hole. There seems to be a conspiracy of nature to prevent the detector from working.
I propose as a hypothesis to be tested that it is impossible in principle to observe the existence of individual gravitons. I do not claim that this hypothesis is true, only that I can find no evidence against it. If it is true, quantum gravity is physically meaningless. If individual gravitons cannot be observed in any conceivable experiment, then they have no physical reality and we might as well consider them nonexistent. They are like the ether, the elastic solid medium which nineteenth-century physicists imagined filling space. Electric and magnetic fields were supposed to be tensions in the ether, and light was supposed to be a vibration of the ether. Einstein built his theory of relativity without the ether, and showed that the ether would be unobservable if it existed. He was happy to get rid of the ether, and I feel the same way about gravitons.
According to my hypothesis, the gravitational field described by Einstein’s theory of general relativity is a purely classical field without any quantum behavior. Gravitational waves exist and can be detected, but they are classical waves and not collections of gravitons. If this hypothesis is true, we have two separate worlds, the classical world of gravitation and the quantum world of atoms, described by separate theories. The two theories are mathematically different and cannot be applied simultaneously. But no inconsistency can arise from using both theories, because any differences between their predictions are physically undetectable.
Another major theme of Greene’s book is the interpretation of quantum mechanics and the weird phenomena of quantum entanglement. He devotes two long chapters, “Entangling Space” and “Time and the Quantum,” to this theme. He makes a valiant attempt to clarify a notoriously foggy subject. But he makes his task more difficult by insisting that quantum mechanics must include everything. He rejects without any serious discussion the dualistic interpretation of quantum mechanics, the idea that there are two separate worlds, the classical world and the quantum world, each following its own rules. The dualistic view, limiting the scope of quantum mechanics to well-defined experimental situations, makes the problems of interpretation much simpler.
The dualistic interpretation of quantum mechanics says that the classical world is a world of facts while the quantum world is a world of probabilities. Quantum mechanics predicts what is likely to happen while classical mechanics records what did happen. This division of the world was invented by Niels Bohr, the great contemporary of Einstein who presided over the birth of quantum mechanics. Lawrence Bragg, another great contemporary, expressed Bohr’s idea more simply: “Everything in the future is a wave, everything in the past is a particle.” Since the greater part of our knowledge is knowledge of the past, Bohr’s division limits the scope of quantum mechanics to a small part of science. I like Bohr’s division, because it allows the possibility that gravitons may not exist. If the scope of quantum theory is limited, gravity may legitimately be excluded from it. But Greene will not accept any such limitation. After briefly describing Bohr’s point of view, he says:
For decades, this perspective held sway. However, its calmative effect on the mind struggling with quantum theory notwithstanding, one can’t help feeling that the fantastic predictive power of quantum mechanics means that it is tapping into a hidden reality that underlies the workings of the universe.
I prefer the calmative effect of Bohr’s perspective on the mind, while Greene prefers the hidden reality. In his first chapter, Greene shows us what he means by hidden reality:
Superstring theory combines general relativity and quantum mechanics into a single, consistent theory.… And as if that weren’t enough, superstring theory has revealed the breadth necessary to stitch all of nature’s forces and all of matter into the same theoretical tapestry. In short, superstring theory is a prime candidate for Einstein’s unified theory.
These are grand claims, and, if correct, represent a monumental step forward. But the most stunning feature of superstring theory, one that I have little doubt would have set Einstein’s heart aflutter, is its profound impact on our understanding of the fabric of the cosmos.… Instead of the three spatial dimensions and one time dimension of common experience, superstring theory requires nine spatial dimensions and one time dimension.… As we don’t see these extra dimensions, superstring theory is telling us that we’ve so far glimpsed but a meager slice of reality.
The next-to-last chapter, “Teleporters and Time Machines,” is a pleasant interlude, describing some possible engineering applications of quantum entanglement and general relativity. The teleporter is a device that can scan an object at one place and reproduce a precise copy of it at another place far away, using quantum entanglement to ensure that the reproduction is exact. The good news is that such a device is in principle possible. The bad news is that it inevitably destroys the object that it copies. The time machine is a tunnel through hyperspace connecting two portals that exist at different places and times in our universe. If you can find the portal that is later in time, you can walk through the tunnel to emerge in your own past. The good news is that such a tunnel is a possible solution of the equations of general
relativity. The bad news is that a tunnel large enough to walk through would require more than the total energy output of the sun to hold it open. Neither the teleporter nor the time machine is likely to contribute much to the welfare of our descendants. Greene describes these fantasies with a proper mixture of scientific accuracy and irony.
In January 2001, I was invited to the World Economic Forum in Davos, Switzerland. Brian Greene was also invited, and we were asked to hold a public debate on the question “When will we know it all?” In other words, when will the last big problems of science be solved? The audience consisted mainly of industrial and political tycoons. Our debate was intended to entertain the tycoons, not to give them a serious scientific education. To make it more amusing, Greene was asked to take an extreme position saying “Soon,” and I was asked to take an extreme position saying “Never.”
Here is my version of Greene’s opening statement, reconstructed from my unreliable memory after we came back from Switzerland. He said that this generation of scientists is amazingly lucky. Within a few years or decades, we will discover the fundamental laws of nature. The fundamental laws will be a finite set of equations, like Maxwell’s equations of electrodynamics or Einstein’s equations of gravitation. Everything else will then follow from these equations. Once we have the fundamental equations, we are done. If we are not smart enough to find the equations, then we will leave it to our grandchildren to finish the job. Either way, the end of fundamental science is near.
Greene said his confidence in our ability to find the fundamental laws is based on the marvelous fact that the laws of nature are simple and beautiful. The history of physics shows that this is true of all the laws that we have discovered in the past. We did not need to do unending experiments to discover the laws. We guessed the laws by looking for equations which had the greatest mathematical simplicity and beauty. Then only a few experiments were needed to test the equations and find out whether we guessed right. This happened over and over again, first with Newton’s laws of motion and gravitation, then with Maxwell’s equations of electromagnetism, then with Einstein’s equations of special and general relativity, then with Schrödinger’s and Dirac’s equations of quantum mechanics. Now with string theory the game is almost over. The mathematical beauty of this theory is so compelling that it has to be right, and if it is right it explains everything from particle physics to cosmology.
Since I am reconstructing Greene’s argument from memory, it is possible that I am exaggerating the claims that he was making for theoretical physics. One thing that I remember clearly is the phrase “We are done.” I still hear him saying, “We are done,” in a tone of triumphant finality.
I began my reply by saying that nobody denies the amazing success of theoretical physics in the last four hundred years. Nobody denies the truth of Einstein’s triumphant words: “The creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.” It is true that the fundamental equations of physics are simple and beautiful, and that we have good reason to expect that the equations still to be discovered will be even more simple and beautiful. But the reduction of other sciences to physics does not work. Chemistry has its own concepts, not reducible to physics. Biology and neurology have their own concepts not reducible to physics or to chemistry. The way to understand a living cell or a living brain is not to consider it as a collection of atoms. Chemistry and biology and neurology will continue to advance and to make new fundamental discoveries, no matter what happens to physics. The territory of new sciences, outside the narrow domain of theoretical physics, will continue to expand.
Theoretical science may be divided roughly into two parts, analytic and synthetic. Analytic science reduces complicated phenomena to their simpler component parts. Synthetic science builds up complicated structures from their simpler parts. Analytic science works downward to find the fundamental equations. Synthetic science works upward to find new and unexpected solutions. To understand the spectrum of an atom, you needed analytic science to give you Schrödinger’s equation. To understand a protein molecule or a brain, you need synthetic science to build a structure out of atoms or neurons. Greene was saying, only analytic science is fundamental. I said, on the contrary, good science requires a balance between analytic and synthetic tools, and synthetic science becomes more and more creative as our knowledge increases.
Another reason why I believe science to be inexhaustible is Gödel’s theorem. The mathematician Kurt Gödel discovered and proved the theorem in 1931. The theorem says that given any finite set of rules for doing mathematics, there are undecidable statements, mathematical statements that cannot either be proved or disproved by using these rules. Gödel gave examples of undecidable statements that cannot be proved true or false using the normal rules of logic and arithmetic. His theorem implies that pure mathematics is inexhaustible. No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. Now I claim that because of Gödel’s theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel’s theorem applies to them. The theorem implies that even within the domain of the basic equations of physics, our knowledge will always be incomplete.
I ended by saying that I rejoiced in the fact that science is inexhaustible, and I hoped the nonscientists in the audience would rejoice too. Science has three advancing frontiers that will always remain open. There is the mathematical frontier, which will always remain open thanks to Gödel. There is the complexity frontier, which will always remain open because we are investigating objects of ever-increasing complexity, molecules, cells, animals, brains, human beings, societies. And there is the geographical frontier, which will always remain open because our unexplored universe is expanding in space and time. My hope and my belief is that there will never come a time when we shall say, “We are done.”
After Greene’s opening statement and my reply, the debate in Davos continued with additional remarks from us and questions from the audience. His new book and my review are a further continuation of the same debate. In the review, as in the debate, I have emphasized the points on which Greene and I disagree. There is no space here to enumerate the many points on which we agree. For both of us the most important and exciting fact is that during the last twenty years cosmology became an observational science. During the last five years, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite, an orbiting radio telescope designed by my friend David Wilkinson in Princeton, has given us more detailed and precise information about the history and structure of the cosmos than all earlier telescopes combined.
Observational cosmology has now entered its golden age, with the WMAP satellite continuing to scan the sky and with a variety of even more sensitive telescopes under construction. During the next decade we shall learn far more about the cosmos than we know today, and we shall probably find new mysteries to replace those that we shall solve. Greene and I agree that so long as observers continue to explore, cosmology will continue to deepen our understanding of where we stand and how we came to be.
Postscript, 2006
After this review was published, Brian Greene wrote me a friendly letter, thanking me for the review but saying that my recollection of his remarks in the Davos debate was wrong. Since I have no wish to perpetuate errors, I deleted from this version of the review the sentences to which he objected. As a result, what is left of his remarks does not put his case forcefully. To set the record straight, here is an extract from his letter: “What I did say in Davos is that the search for the elementary ingredients making up the universe and the deepest laws governing their interactions may be a search that one day draws to a close. The deeper we look, the simpler and more unified the laws become, and there may well be a limit to this process. However, achieving this goal would only mean that we were done with one fantastically interesting but limit
ed chapter in human exploration, the search for the basic constituents and underlying laws.”
1. Knopf, 2004.
20
OPPENHEIMER AS SCIENTIST, ADMINISTRATOR, AND POET
1. Oppenheimer as Scientist
I DIVIDE THIS chapter into three parts, the first about J. Robert Oppenheimer as a scientist, the second about Robert as an administrator, the third about Robert as a poet. To make the story complete there should be a part about Robert as a statesman, but that would require another chapter as long as this one. I won’t stick rigidly to these boundaries. I want to let Robert speak for himself as much as possible. The best part of the chapter will be direct quotes from Robert and others, telling us the story of his life as they saw it.
I begin in September 1938 with a story told by Robert Serber, the same Serber who appears in the movie The Day After Trinity. I owe this story to David Trulock, a friend of mine in Texas. The two Roberts, Serber and Oppenheimer, were at a meeting of theoretical physicists in Vancouver. The entertainment during the meeting included a boat ride among the islands offshore. The day was foggy, and navigation among the islands was done by the pilot blowing a whistle and listening for the echo. Someone asked what the consequences for physics would be if this boatload of theorists sank. Oppenheimer instantly replied, “It wouldn’t do any permanent good.”
One year later, on September 1, 1939, Hitler invaded Poland and started the Second World War. On that day, issue number 5 of Volume 55 of the Physical Review was published, containing two papers of historic importance. The first was entitled “The Mechanism of Nuclear Fission,” by Niels Bohr and John Wheeler, twenty-five pages long, containing a complete and thorough theoretical explanation of the process of nuclear fission that had been discovered in Germany only nine months earlier. The second was entitled “On Continued Gravitational Contraction,” by J. Robert Oppenheimer and Hartland Snyder, only four pages long, containing an equally thorough theoretical explanation of the objects that we now call black holes.
The Scientist as Rebel Page 22
