Three Roads to Quantum Gravity

by Lee Smolin

  • Causality will be a necessary component of the fundamental theory. That theory will describe the quantum universe in terms of discrete events and their causal relations. The notion of causality will survive at a level in which space will no longer be a meaningful concept.

  • The final theory will not be able to predict unique values for the masses of the elementary particles. The theory will allow a set of possible values for these and other quantities in fundamental physics. But there will be a rational, non-anthropic and falsifiable explanation for the values of the parameters we observe.

  • We shall have the basic framework of the quantum theory of gravity by 2010, 2015 at the outside. The last step will be the discovery of how to reformulate Newton’s principle of inertia in the language of a quantum spacetime. It will take many more years to work out all the consequences, but the basic framework will be so compelling and natural as to remain fixed, once it is discovered.

  • Within ten years of having the theory new kinds of experiment will be invented which will be able to test it. And the quantum theory of gravity will make predictions about the early universe which will be tested by observations of radiation from the big bang, including the cosmic microwave background radiation and gravitational radiation.

  • By the end of the twenty-first century, the quantum theory of gravity will be taught to high-school students all around the world.

  POSTSCRIPT

  I started Three Roads to Quantum Gravity in the fall of 1999 and sent off final corrections to the publisher in October 2000. Since then the field has seen very dramatic progress on the road to quantum gravity.

  The most exciting development is the possibility of observing the atomic structure of space itself. I mentioned this possibility briefly at the end of Chapter 10. Now there are even stronger indications that the atomic structure of space can be observed by current experiments. Indeed, Giovanni Amelino-Camelia and Tsvi Piran have pointed out that such observations may already have occurred.

  These new observations are potentially as important as any that have occurred in the history of physics, for if they mean what some of us believe they mean, they mark the end of one era and the beginning of another.

  Vast as it is, our universe is nowhere near empty. Where there is nothing else, there is radiation. We know of several different forms of radiation that travel in the spaces between the galaxies. One of them consists of very energetic particles, which we call cosmic rays. These appear to be mainly protons, with a mixture of heavier particles. Their distribution on the sky is uniform, which suggests they come from outside our galaxy. Scientists have observed these cosmic rays hitting the Earth’s atmosphere with energies more than 10 million times the force achievable by the largest particle accelerators.

  These cosmic rays are said to originate in highly energetic events in the centers of certain galaxies, which serve as a kind of natural particle accelerator. The rays come from regions of huge magnetic fields, perhaps produced by a super-massive black hole. Such things were once the stuff of fantasy, but we have more and more evidence for their existence. Although there are still uncertainties in our understanding of the origins of the cosmic rays, it seems most probable that the most energetic ones come from far outside our galaxy.

  Consider then the most energetic cosmic ray protons observed, traveling toward us from a distant galaxy. At the energies they are traveling, about 1010 times the energy of the proton, or more than 10 million times the energy of the largest human-made particle accelerator, they are traveling very, very close to the speed of light. As our proton travels, it encounters another form of radiation that fills the space between galaxies—the cosmic microwave background.

  The cosmic microwave background is a bath of microwaves that we understand as vestiges left over from the big bang. This radiation has been observed to come at us equally from all directions, up to small deviations of around a few parts in a hundred thousand. It now has a temperature of 2.7 degrees above absolute zero, but it was once at least as hot as the center of a star and cooled to its present temperature as the universe expanded. Given how uniformly we observe it to come from all directions of the universe, it is inconceivable that this radiation does not fill all space.

  As a consequence, we know that our cosmic ray proton will encounter many photons from the microwave background as it travels through space. Most of the time nothing happens as a result of these interactions, because the cosmic ray proton has so much more energy and momentum than the photon it encounters. But if the proton has enough energy, it sometimes produces another elementary particle. When this happens, the cosmic ray slows down and loses energy because it takes energy to create the new particle.

  The lightest particle that can be created in this way is called a pion. Using the basic laws of physics, including Einstein’s special theory of relativity, one can work out a simple prediction about the processes by which cosmic ray protons and photons from the cosmic microwave background interact to make pions. The prediction is that there is a certain energy—called a threshold—above which this is very likely to happen. A proton above this energy will continue to interact in this way, losing energy each time, until it is slowed down enough that its energy falls below the threshold.

  This works something like a 100% tax. Suppose there were some income, say $1 billion, above which all income would be taxed at 100%. Then no one would ever earn above $1 billion a year, because 100% of their income above this amount would be taxed. Our case is like a 100% tax on energy, as all the energy that a cosmic ray proton may have above the threshold will be removed, through processes that produce pions by its interacting with the cosmic microwave background.

  This formula dictates that cosmic ray protons cannot hit the earth with an energy greater than the threshold energy. There is ample time in the protons’ journey for any additional energy to be siphoned off in creating multiple pions.

  I want to emphasize that this formula derives from the well-tested laws of special relativity—the results should therefore be very reliable. Thus, when this prediction was proposed by three Russian physicists with the names of Greisen, Zatsepin, and Kuzmin in the 1960s, it was very well received in the scientific community. Researchers had no reason to believe that cosmic ray protons would ever be seen with energies greater than the threshold.

  Convincing as it was, Greisen, Zatsepin, and Kuzmin’s prediction turned out to be wrong. In the last several years, many cosmic rays have been seen with energies greater than the threshold. This startling piece of news has galvanized scientists in the field. It is called the Ultra High Energy Cosmic Ray, or UHECR, anomaly.

  Three explanations have been proposed for this effect. The first is astrophysical, and suggests that cosmic rays, or at least those above the threshold, are produced inside our galaxy, close enough that the effect may not have removed all their energy. The second solution is physical, and posits that the particles making up the very high energy cosmic rays are not protons, but actually much heavier particles, which do not lose energy by interacting with the microwave background. Instead, they decay over time, giving rise to the protons we observe. However, their lifetime is hypothesized to be extremely long, so that they are able to travel for many millions of years before they decay.

  Both of these explanations appear far-fetched. There is no evidence for either nearby sources of cosmic rays or such heavy meta-stable particles. Moreover, both theories would require careful adjustments of parameters to unusual values just to fit these observations.

  The third explanation has to do with quantum gravity. The atomic structure predicted by loop quantum gravity, which I described in Chapters 9 and 10, is expected to modify the laws that govern the interactions of elementary particles. This modification has the effect of changing the location of the threshold, and it is very natural that the result may be to raise the threshold enough to explain all the observations so far made.

  This explanation leads to new predictions. First, the threshold ma
y be seen at higher energy, in new experiments that will be able to detect cosmic rays at still higher energies. This is not the case with the other two explanations. Second, the effect must be universal, as the quantum geometry of spacetime must affect all particles that move. Hence the same effect must be seen in other particles.

  There is in fact one case in which a similar effect may have been observed. Very energetic busts of photons arrive on Earth. These busts are called gamma ray busts and blazars, and they are believed to originate far outside our galaxy and travel for billions of years before arriving on Earth. Their origin is controversial, but it is possible they are the result of collisions among neutron stars or black holes. The most energetic of these are subject to a threshold for a similar reason, because they may interact with a background of diffuse starlight coming from all the stars in the universe. As in the case of the cosmic rays, photons have been seen with energies that exceed that threshold, coming from an object called Markarian 501.

  Thus, all of a sudden, there is a real possibility that quantum gravity has become an experimental science. This is the most important thing that could have happened. It means that experimental relevance, rather than individual taste or peer pressure, must now become the determining factor for the correctness of an idea about quantum gravity.

  Moreover, in the last several months, a startling implication of the theory of quantum gravity has emerged. This is the possibility that the speed of light may depend on the energy carried by a photon. This effect appears to come about as a result of the interaction of light with the atomic structure of space. These effects are tiny and so do not contradict the fact that so far all observations have concluded that the speed of light is constant. But for photons that travel very long distances across the universe, they add up to a significant effect, which can be observed with current technology.

  The effect is very simple. If higher frequency light travels slightly faster than lower frequency light, then if we observe a very short burst of light coming from very far away, the higher energy photons should arrive slightly before those of lower energy. This could be observed in the gamma ray busts. The effect has not yet been seen, but if it is indeed there, it may be observed in experiments planned for the near future.

  At first I was completely shocked by this idea. How could it be right? Relativity, based on the postulate of the constancy of the speed of light, is the foundation of all our understanding of space and time.

  But as some wiser people explained to me, these new developments do not necessarily contradict Einstein. The basic principles enunciated by Einstein, such as the relativity of motion, may remain true. There still is a universal speed of light, which is the speed of the least energetic photons. What these developments imply is that Einstein’s insights must be deepened to take into account the quantum structure of space and time, just as Einstein deepened Descartes’s and Galileo’s insights about the relativity of motion. It may be time for us to add another layer of insight into our understanding of what motion is.

  Exactly how relativity is to be modified is a subject of hot debate at the moment. Some people argue that special relativity theory must be modified to account for the atomic structure of spacetime predicted by loop quantum gravity. According to loop quantum gravity, all observers see the discrete structure of space below the planck length. This seems to contradict relativity, which tells us that lengths are measured differently by different observers—the famous length contraction effect. One resolution is that special relativity can be modified so that there is one length scale, or one energy scale, that all observers agree on. Thus, while all other lengths will be measured differently by different observers, for the special case of the Planck length all observers will agree. There is still complete relativity of motion, as posited by Galileo and Einstein. But one consequence is that the speed of light can pick up a small dependence on energy.

  I heard about the possibility of such a new twist on relativity from several people at once: Giovanni Amelino-Camelia, Jurek Kowalski-Glikman, and Joao Magueijo. At first I told them this was the craziest thing I’d ever heard, but Joao, who was my colleague in London at the time, was patient enough to keep coming back many times, until I finally got it. Since then I’ve seen other people go through this process. It is interesting to observe one of Thomas Kuhn’s famous paradigm shifts in action.

  Another hot topic is whether the possible variation of the speed of light with energy has consequences for our understanding of the history of the universe. Suppose that the speed of light increases with energy. (This is not the only possibility, but it is so far allowed by the observations we have.) When the universe was in its early stages, then, the average speed of light would have been higher, because the universe was then very hot, and hot photons have more energy. This idea has the possibility of solving a number of puzzles that cosmologists are very concerned about. For example, we don’t know why the temperature in early times was nearly the same everywhere in the universe, in spite of the fact that there had not yet been time for all the regions to interact with one another. If the speed of light is higher than we currently think, there may have been time for all parts of the universe to have been in contact, and the mystery is solved! Indeed, cosmologists such as Andrew Albrecht and Joao Magueijo had already speculated about this possibility.

  These puzzles have inspired a theory called inflation, which posits that the universe expanded at an exponentially increasing rate during a short period very early in its history. This theory has had some successes, but there have remained open questions about its connection with the more fundamental theory—the theory of quantum gravity. It is fascinating that a new idea has emerged based on our theories of quantum gravity, which may address this puzzle. This is good, because it is a spur to new observations that may decide which solution is right. It is often easier to use experiment to choose between two competing theories than it is to demonstrate that a single theory is right or wrong. Of course, the experiments may show instead that some combination of the two theories is right.

  But most important, new observations that give evidence for or against the effects of quantum gravity on the propagation of light offer the chance to prove the validity of the theories described in this book. String theory and loop quantum gravity, for example, are likely to make different predictions for the results of these experiments. Loop quantum gravity appears to require modifications in special relativity. String theory, on the other hand, at least in its simplest versions, assumes that special relativity remains true no matter how small the distances are probed.

  This is good news indeed, for as soon as the light of experiment is turned on, sociological forces such as govern academic politics and fashion must slink back to the shadows, as the judgement of nature supercedes the judgements of professors.

  This is not the only place where cosmological observation and fundamental theory are confronting each other. An even more exciting—and for some disturbing—case has to do with the cosmological constant. This refers to the possibility—first realized by Einstein—that empty space might have a non-zero energy density. This energy density would be observable in the effect it has on the expansion of the universe.

  Once this possibility was accepted, it led to a major crisis in theoretical physics. The reason is that the most natural possibility allowed for the value of this empty space energy density is that it should be huge—more than a hundred powers of ten larger than is compatible with observation. The exact value—which is what the name cosmological constant refers to—cannot be predicted by current theory. In fact, we can adjust a parameter to get any value for the cosmological constant we want. The problem is that to avoid a huge cosmological constant, the parameter has to be adjusted to an accuracy of at least 120 decimal places. How such a precise adjustment is to be obtained is a mystery.

  This is perhaps the most serious problem facing fundamental physics, and it recently got worse. Until a few years ago, it was almost universally belie
ved that even if it required a very precise adjustment, in the end the cosmological constant would be exactly zero. We had no idea why the cosmological constant would be zero, but at least zero is a simple answer. However, recent observations have suggested that the cosmological constant is not zero; it has instead a very small, but positive, value. This value is tiny on the scales of fundamental physics; in Planck units it is around 10-120 (or .0000. . . .) with 120 zeros before one encounters a non-zero digit.

  But even though tiny when measured in fundamental units, this value is large enough to have a profound effect on the evolution of our universe. This cosmological constant would make the energy density of empty space equal to about twice the current value of the energy density of everything else that has been observed. This may seem surprising, but the point is that the energy density of all the kinds of matter that have been observed is currently very small. This is because the universe is very old. When measured in fundamental units, its present age is about 1060 Planck times. And it has been expanding all this time, thus diluting the density of matter.

  The energy density due to the cosmological constant does not, as far as we know, dilute as the universe expands. This gives rise to a very troubling question: Why is it that we live at a time when the matter density has diluted to the point that it is of the same order of magnitude as the density due to the cosmological constant?