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Questioning Standard Theory

This and other puzzles forced physicists to look more attentively at the basic assumptions underlying the standard cosmological theory. And we found many to be highly suspicious. I will review six of the most difficult. The first, and main, problem is the very existence of the big bang. One may wonder, What came before? If space-time did not exist then, how could everything appear from nothing? What arose first: the universe or the laws determining its evolution? Explaining this initial singularity-where and when it all began-still remains the most intractable problem of modern cosmology.

A second trouble spot is the flatness of space. General relativity suggests that space may be very curved, with a typical radius on the order of the Planck length, or 10-33 centimeter. We see, however, that our universe is just about flat on a scale of 1028 centimeters, the radius of the observable part of the universe. This result of our observation differs from theoretical expectations by more than 60 orders of magnitude.

A similar discrepancy between theory and observations concerns the size of the universe, a third problem. Cosmological examinations show that our part of the universe contains at least 1088 elementary particles. But why is the universe so big? If one takes a universe of a typical initial size given by the Planck length and a typical initial density equal to the Planck density, then, using the standard big bang theory, one can calculate how many elementary particles such a universe might encompass. The answer is rather unexpected: the entire universe should only be large enough to accommodate just one elementary particle-or at most 10 of them. It would be unable to house even a single reader of Scientific American, who consists of about 1029 elementary particles. Obviously, something is wrong with this theory.

The fourth problem deals with the timing of the expansion. In its standard form, the big bang theory assumes that all parts of the universe began expanding simultaneously. But how could all the different parts of the universe synchronize the beginning of their expansion? Who gave the command?

Fifth, there is the question about the distribution of matter in the universe. On the very large scale, matter has spread out with remarkable uniformity. Across more than 10 billion light-years, its distribution departs from perfect homogeneity by less than one part in 10,000. For a long time, nobody had any idea why the universe was so homogeneous. But those who do not have ideas sometimes have principles. One of the cornerstones of the standard cosmology was the "cosmological principle," which asserts that the universe must be homogeneous. This assumption, however, does not help much, because the universe incorporates important deviations from homogeneity, namely, stars, galaxies and other agglomerations of matter. Hence, we must explain why the universe is so uniform on large scales and at the same time suggest some mechanism that produces galaxies.

Finally, there is what I call the uniqueness problem. Albert Einstein captured its essence when he said, "What really interests me is whether God had any choice in the creation of the world." Indeed, slight changes in the physical constants of nature could have made the universe unfold in a completely different manner. For example, many popular theories of elementary particles assume that space-time originally had considerably more than four dimensions (three spatial and one temporal). In order to square theoretical calculations with the physical world in which we live, these models state that the extra dimensions have been "compactified," or shrunk to a small size and tucked away. But one may wonder why compactification stopped with four dimensions, not two or five.

Moreover, the manner in which the other dimensions become rolled up is significant, for it determines the values of the constants of nature and the masses of particles. In some theories, compactification can occur in billions of different ways. A few years ago it would have seemed rather meaningless to ask why space-time has four dimensions, why the gravitational constant is so small or why the proton is almost 2,000 times heavier than the electron. Now developments in elementary particle physics make answering these questions crucial to understanding the construction of our world.

All these problems (and others I have not mentioned) are extremely perplexing. That is why it is encouraging that many of these puzzles can be resolved in the context of the theory of the self-reproducing, inflationary universe.

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This stage of self-sustained, exponentially rapid inflation did not last long. Its duration could have been as short as 10-35 second. Once the energy of the field declined, the viscosity nearly disappeared, and inflation ended. Like the ball as it reaches the bottom of the bowl, the scalar field began to oscillate near the minimum of its potential energy. As the scalar field oscillated, it lost energy, giving it up in the form of elementary particles. These particles interacted with one another and eventually settled down to some equilibrium temperature. From this time on, the standard big bang theory can describe the evolution of the universe.

The main difference between inflationary theory and the old cosmology becomes clear when one calculates the size of the universe at the end of inflation. Even if the universe at the beginning of inflation was as small as 10-33 centimeter, after 10-35 second of inflation this domain acquires an unbelievable size. According to some inflationary models, this size in centimeters can equal 101012-that is, a 1 followed by a trillion zeros. These numbers depend on the models used, but in most versions, this size is many orders of magnitude greater than the size of the observable universe, or 1028 centimeters.

This tremendous spurt immediately solves most of the problems of the old cosmological theory. Our universe appears smooth and uniform because all inhomogeneities were stretched 101012 times. The density of primordial monopoles and other undesirable "defects" becomes exponentially diluted. (Recently we have found that monopoles may inflate themselves and thus effectively push themselves out of the observable universe.) The universe has become so large that we can now see just a tiny fraction of it. That is why, just like a small area on a surface of a huge inflated balloon, our part looks flat. That is why we do not need to insist that all parts of the universe began expanding simultaneously. One domain of a smallest possible size of 10-33 centimeter is more than enough to produce everything we see now.

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Although the COBE results agree with the predictions of inflation, it would be premature to claim that COBE has confirmed inflationary theory. But it is certainly true that the results obtained by the satellite at their current level of precision could have definitively disproved most inflationary models, and it did not happen. At present, no other theory can simultaneously explain why the universe is so homogeneous and still predict the "ripples in space" discovered by COBE.

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End Special Issue

January 1998...
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ANCESTRAL QUANDARY

Neanderthals not our ancestors? Not so fast

After researchers published the first analysis of ancient human DNA in the journal Cell last July, the case was closed, or so it seemed. "Neanderthals Were Not Our Ancestors" read the cover, featuring a photograph of the archetypal specimen's skullcap with its heavy, arched browridge so unlike our own relatively smooth brows. The pattern of differences between Neanderthal and modern DNA indicated to the team that Neanderthals were an evolutionary dead end, replaced by modern humans without any interbreeding. Popular accounts hailed the research as proof of a recent African origin for all modern humans, but has the long-standing debate over human origins really been put to rest? Judging from subsequent reactions among geneticists and paleoanthropologists, apparently not.

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March 1998...

COSMOLOGY

GLOW IN THE DARK

A second cosmic background radiation permeates the sky

How do these background measurements affect theories of how and when stars and galaxies formed? The current thinking is that once star formation began, it slowly accelerated, peaked when the universe was about 40 percent of its current age and has since declined 30-fold. But the unexpectedly bright background may indicate that star formation got going faster and remained frenetic for longer. If so, theorists might need to revisit the prevailing theory of galaxy formation, which posits clumps of so-called cold dark matter and agglomeration of small protogalaxies into progressively larger units. "It would cause real trouble for the cold dark-matter model," Partridge said. "I think it's safe to say that we're seeing more energy than in all current models."

Besides identifying the source of the background, observers want to measure the glow at shorter wavelengths, determine how it has varied with the age of the universe and look for fluctuations across the sky. Upcoming missions such as the Far Infrared Space Telescope (FIRST) may prove crucial. Meanwhile the techniques developed to subtract the light from dust in our galaxy may improve measurements of other cosmological phenomena, such as large-scale galaxy motions and the expansion of the universe. In short, scientists are encountering a new kind of Olbers's paradox. The night sky isn't dark; it's too bright.

--George Musser

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July 1998... COSMOLOGY

INFLATION IS DEAD; LONG LIVE INFLATION

How an underdense universe doesn't sink cosmic inflation

Over the past year, observational astronomers have at last convinced theorists that the universe contains less matter than the theory of inflation predicts. The expansion of the universe, as traced by distant supernovae and radio-bright galaxies, is decelerating too slowly. The mass of galaxy clusters, as deduced from their internal motions and their ability to focus the light of more distant objects, is too low. The number of these clusters, which should be growing if there is sufficient raw material, has changed too little. And the abundance of deuterium, which is inversely related to the total amount of matter, is too high. It seems there is only a third of the matter needed for geometric flatness, the expected outcome of inflation.

But far from killing the theory, cosmologists say, the observations make it more necessary than ever albeit in a new form. No other theory answers a nagging question in big bang cosmology: Why is the universe even vaguely flat? Over time, the cosmos should seem ever more curved as more of it comes into view and its overall shape becomes more apparent. By now, billions of years after the big bang, the universe should be highly curved, which would make it either depressingly desolate or impenetrably dense.

Inflationary theory developed in the early 1980s by Alan H. Guth, now at the Massachusetts Institute of Technology, and Andrei D. Linde, now at Stanford University solved the problem by postulating that the universe went through a period of accelerating expansion. Once-adjacent regions separated faster than light (which space can do Einstein's special theory of relativity applies to speeds within space). As a result, we now see only a fragment of the cosmos. Its overall shape is not visible yet; each fragment looks flat. Inflation also explains the near uniformity of the universe: any lumpiness is too large scale for us to perceive.

But if observers can't find enough matter to flatten space, theorists must draw one of two awkward conclusions. The first is that some new kind of dark matter makes up the difference. The inferred matter goes by the name of "quintessence," first used in this general context by Lawrence M. Krauss of Case Western Reserve University. The usage alludes to Aristotelian ether; besides, anything that accounts for two thirds of physical reality is surely quintessential.

Quintessence joins the two previously postulated kinds of dark matter: dim but otherwise ordinary matter (possibly rogue brown dwarfs) and inherently invisible elementary particles (possibly neutrinos, if these ghostly particles have a slight mass). Both reveal themselves only by tugging at visible stars and galaxies. About quintessence, scientists know even less. Cosmic flatness dictates that it contain energy but does not specify what kind; the universe's expansion and galaxy clustering imply that quintessence exerts a gravitational repulsion and shuns ordinary matter.

A form of quintessence was already thought to have powered inflation and then died out, begetting ordinary matter. Now it may be back, challenging its progeny for control of the universe. If quintessence wins, the universe will expand forever in a new round of inflation. Our fate hinges on what makes up quintessence. The simplest possibility, Einstein's cosmological constant, inexorably gains in relative strength as cosmic expansion dilutes matter. But other forms of quintessence, such as featherweight particles or space-time kinks, might eventually fade away. In May, Christopher T. Hill of Fermi National Accelerator Laboratory speculated that the quintessence mystery is related to another: the neutrino mass.

So far the only proof for quintessence is circumstantial. The latest supernova observations suggest that cosmic expansion is accelerating, and recent cosmic microwave background measurements show that triangles may indeed subtend 180 degrees, as they should in flat space.

But the lack of direct proof as well as an observed shortage of gravitational lenses, which suggests the universe is smaller than certain forms of quintessence would make it has led many cosmologists to a different awkward conclusion: maybe inflation stopped before making space exactly flat. In traditional inflation, this would make the universe 100,000 times too lumpy. The new trick is to kill the two birds with two stones: to suppose that the uniformity of the universe does not result from the same process as its shape does. Maybe the cosmos was made uniform by a previous round of inflation, was uniform from birth or has a special shape that let it even itself out quickly.

Two-round inflationary theory was developed in 1995 by two teams: Martin Bucher of Princeton University, Neil G. Turok, now at the University of Cambridge, and Alfred S. Goldhaber of the State University of New York at Stony Brook; and Kazuhiro Yamamoto of Kyoto University and Misao Sasaki and Takahiro Tanaka of Osaka University. In this theory, the first round creates a uniform mega-universe. Within it, bubbles self-contained universes spontaneously form. Each undergoes a second round of inflation that ends prematurely, leaving it curved. The amount of curvature varies from bubble to bubble.

The second idea, announced in February by Turok and Stephen W. Hawking of Cambridge, is that the smooth universe gurgled not out of a soda universe but out of utter nothingness. Updating Hawking's decade-old work on creation ex nihilo, they devised an "instanton" loosely speaking, a mathematical formula for the difference between existence and nonexistence that implied we should indeed be living in a slightly curved universe.

Finally, maybe the universe has an unusual topology, so that different parts of the cosmos interconnect like pretzel strands. Then the universe merely gives the illusion of immensity, and the multiple pathways allow matter to mix together and become smooth. Such speculation dates to the 1920s but was dusted off two years ago by Neil J. Cornish of Cambridge, David N. Spergel of Princeton and Glenn D. Starkman of Case Western Reserve.

Like all good cosmological theories, these ideas lead to some wacky conclusions. The bubble and ex nihilo universes are infinite, which quantum laws forbid. The solution: let the universe be both infinite and finite. From the outside it is finite, keeping the quantum cops happy; inside, "space" takes on the infinite properties of time. In the pretzel universe, light from a given object has several different ways to reach us, so we should see several copies of it. In principle, we could look out into the heavens and see the earth.

More worrisome is that these models abandon a basic goal of inflationary theory: explaining the universe as the generic outcome of a simple process independent of hard-to-fathom initial conditions. The trade-off is that cosmologists can now subject metaphysical speculation including interpretations of quantum mechanics and guesses about the "before" to observational test.

Out of all this brainstorming may emerge an even deeper theory than standard inflation; by throwing a wrench into the works, observers may have fixed them. Upcoming high-resolution observations of the microwave background and galaxy clustering should be decisive. But if not, cosmologists may begin to question the underpinnings of modern physics. "If the experimental data is inconsistent with literally everything, this may be a signal for us to change gravity theory Einstein theory," Linde says.

--George Musser

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August 1998...

COSMOLOGY

A MASSIVE DISCOVERY

The weight of neutrinos offers clues to stars, galaxies and everything

Future historians may look back on 1998 as the year that particle physics got interesting again. For decades, the search for the fundamental nature of matter has been reduced to a jigsaw puzzle. The Standard Model of particle physics provided the frame, with outlines of each of the two dozen elementary particles sketched in their proper places. When an army of almost 1,000 physicists discovered the top quark in 1995, the puzzle seemed to be complete. Only a bit of bookkeeping remained: to confirm that the three lightest particles--the electron-, muon- and tau-neutrinos--indeed weigh exactly nothing, as the Standard Model predicts.

But in June the 120 Japanese and American physicists of the Super-Kamiokande Collaboration presented strong evidence that at least one of the neutrinos (and probably all of them) weighs something. That neutrinos have a small mass is no small matter. It could help explain how our sun shines, how other stars explode into brilliant supernovae and why galaxies cluster in the patterns that they do. Perhaps most important, explains Lincoln Wolfenstein, a physicist at Carnegie Mellon University, "once you accept that one neutrino has mass, you realize that the truth is something beyond the Standard Model."

Nearly all neutrino physicists have accepted the conclusion, because the new data are supported by several years of similar observations at other detectors. John Bahcall of the Institute for Advanced Study in Princeton, N.J., says the evidence "seems completely convincing to me. It is simply beautiful!"

The neutrino is certainly sublime in its subtlety. Quarks and electrons are impossible to miss; we and our world are made from them. The muon and tau, cousins of the electron, are unfamiliar because they die almost at birth. But neutrinos surround us perpetually, yet invisibly. Trillions zip through your body as you read this. Created by the big bang, by stars and by the collision of cosmic rays with earth's atmosphere, neutrinos outnumber electrons and protons by 600 million to one. "If they have a mass of just one tenth of an electron volt [an electron, in comparison, weighs about 500,000 eV], then neutrinos would account for about as much mass as the entire visible universe," says Joel Primack, a cosmologist at the University of California at Santa Cruz.

About 0.1 eV now seems to many physicists a likely mass for the muon-neutrino. They can't be certain yet, because the only way to weigh particles that can zoom almost unhindered through the earth at nearly the speed of light is to do so indirectly. By patiently watching a high-tech cistern buried 2,000 feet underneath a Japanese mountain, physicists working on the Super-Kamiokande project were able to record faint flashes emitted on the exceedingly rare occasions when a muon- or electron-neutrino collided with one out of the 50,000 tons of water molecules in the tank. Over time, traces from those neutrinos that had been created in the atmosphere started to reveal a pattern. Those arriving from above came in the expected proportion and number. "We even saw a hot spot toward the east caused by a well-known asymmetry in the earth's magnetic field" that creates more cosmic-ray collisions in that direction, says Todd Haines of Los Alamos National Laboratory. But too few muon-neutrinos arrived from below.

Two large groups of physicists worked independently to explain why. Both ruled out all explanations save one: the three kinds of neutrinos are not different particles in the way that electrons and muons are. Each neutrino is in fact a mixture of three mass states. The mixture can change as the neutrino travels, transforming muon-neutrinos created above South America into heavier tau-neutrinos by the time they reach the detector in Japan. That is why too few muon-neutrinos appeared in the Super-Kamiokande tank; some had metamorphosed into the undetectable tau type.

Theorists figure that there is no way to have mass states without having mass. But so far all that Hank Sobel, a Boston University physicist and spokesman for the collaboration, can say is that the difference between the mass of muon-neutrinos and whatever they are changing into is between 0.1 and 0.01 eV--definitely not zero.

Wolfenstein points out that "this does not solve the solar neutrino problems," the most baffling of which is the fact that only half the electron-neutrinos that theoretically should fall from the sun to the earth are actually detected here. But Bahcall adds that it does "strengthen the conviction of nearly everyone involved in the subject that the explanation of the solar neutrino problems is oscillations" of neutrinos from one variety to another on their journey to the earth.

"A little hot dark matter in the form of massive neutrinos may be just what is needed" to help reconcile another astrophysical accounting discrepancy, Primack says. Many lines of evidence suggest that there is about 10 times more matter in the universe than human instruments can see. Neutrinos will now fill in some of that missing matter.

Whether neutrinos weigh enough to make a significant difference in the fate of the universe and the composition of matter remains a mystery. "We can't build theories on this without firmer data about the masses and transition amplitudes," says Steven Weinberg, one of the architects of the Standard Model and a professor at the University of Texas. "We're still far from that. But there are some very important experiments in the wings that may answer those questions."

In January physicists will create a beam of muon-neutrinos in an accelerator near Tokyo and aim it at the Super-Kamiokande detector. Within a few years, scientists at Fermi National Accelerator Laboratory in Batavia, Ill., hope to send swarms of the particles flitting toward a detector deep in a Minnesota mine shaft by 2001. These controlled experiments may finally fill in the last blanks of the Standard Model, close that chapter of physics and perhaps, if we are lucky, open a new one.

--W. Wayt Gibbs in San Francisco

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SCIENCE AND RELIGION

BEYOND PHYSICS

Renowned scientists contemplate the evidence for God

Modern science, like every successful philosophy, has axioms that it takes on faith to be true. Allan R. Sandage, one of the fathers of modern astronomy, has just slid one of these precepts onto an overhead projector. In letters too large to ignore, it hangs before the eyes of several hundred scientists, theologians and others gathered here at the University of California at Berkeley to discuss the points of conflict and convergence between science and religion. The axiom is called Clifford's dictum: "It is wrong always, everywhere and for everyone to believe anything on insufficient evidence."

Is there sufficient evidence to support a belief in God? Although many scientists working in the U.S. would doubtless agree with Sandage that "you have to answer the question of what is �sufficient' for yourself," recent polls suggest that most of them would nonetheless answer no. But the program for this conference includes some two dozen scientists, nearly all of them at the top of their fields, who have arrived at a different conclusion.

"There is a huge amount of data supporting the existence of God," asserts George Ellis, a cosmologist at the University of Cape Town and an active Quaker. "The question is how to evaluate it," he says, because the data only rarely yield to scientific analysis.

Item one on Ellis's list of evidence is the so-called Anthropic Principle. In recent decades, explains John Barrow, an astronomer at the University of Sussex, physicists have noticed that many of the fundamental constants of nature--from the energy levels in the carbon atom to the rate at which the universe is expanding to the four perceptible dimensions of space-time--are just right for life. Tweak any of them more than a tad, and life as we know it could not exist.

John Polkinghorne, a particle physicist turned Anglican priest, points out other curiosities. "How is it that humans' cognitive abilities greatly exceed the demands imposed by evolutionary pressures, so that we can perceive the quantum nature of the universe and map its cosmic features?" he asks. And why is mathematics so surprisingly effective at describing the physical world? One possible explanation, Polkinghorne, Ellis and other well-respected physicists argue, is that the universe was designed.

"Certainly more and more top-level scientists are considering the Anthropic Principle seriously in their work," concedes Andre Linde, a Stanford University cosmologist. But he disputes that the coincidences point to God. Astronomical observations have so far supported a so-called inflationary theory of creation that Linde helped to develop. If the theory is correct, then our universe is just one bubble in a much larger, eternal foam of universes. The constants and laws of physics may well differ in each bubble. Our universe may be tuned for carbon-based life not because it was set up that way, Barrows adds, but because even such a delicate arrangement was bound to happen in one of the myriad bubbles.

Science will probably never be able to determine which case is true. "We are hitting the boundaries of what is ever going to be testable," Ellis says. And not just in cosmology. "The science of the 20th century is showing us, if anything, what is unknowable using the scientific method, what is reserved for religious beliefs," argues Mitchell P. Marcus, chairman of computer science at the University of Pennsylvania. "In mathematics and information theory, we can now guarantee that there are truths out there that we cannot find."

"The inability of science to provide a basis for meaning, purpose, value and ethics is evidence of the necessity of religion," Sandage says--evidence strong enough to persuade him to give up his atheism late in life. Ellis, who similarly turned to religion only after he was well established in science, raises other mysteries that cannot be solved by logic alone: "the reasons for the existence of the universe, the existence of any physical laws at all and the nature of the physical laws that do hold--science takes all of these for granted, and so it cannot investigate them."

"Religion is very important for answering these questions," Sandage concludes. But how exactly? Pressing the scientists on the details of their beliefs reveals that most have carved a few core principles out of one of the major religious traditions and discarded the rest. "When you start pushing on the dogma, most scientists tend to part company," observes Henry S. Thompson of the University of Edinburgh. Indeed, for Ellis, "religion is an experimental endeavor just like science: all doctrine is a model to be tested, and no proof is possible." Sandage confesses that, like many other theoretical physicists, "I am a Platonist," who believes the equations of fundamental physics are all that is real and that "we see only shadows on the wall." And Pauline M. Rudd, a biologist at the University of Oxford, observes: "I have experiences that cannot be expressed in any language other than that of religion. Whether the myths are historically true or false is not so important."

There seem only two points on which all the religious scientists agree. That God exists. And that, as Albert Einstein once put it, "science without religion is lame; religion without science is blind."

--W. Wayt Gibbs in Berkeley, Calif.

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September 1998...

COSMOLOGY

THE FLIP SIDE OF THE UNIVERSE

New cosmological observations confirm inflation

Late into the night astronomers Angelica de Oliveira-Costa and Max Tegmark worked to analyze their observations of the cosmic microwave background radiation. The next morning the young wife-and-husband team were due to present what their data revealed about the single most important unknown fact in cosmology: the shape of the universe. Their previous results, from a telescope in Saskatoon, Canada, between 1993 and 1995, had suggested that the universe is flat--the first observations to substantiate a long-held belief among cosmologists. But intrinsic uncertainties in the measurements made it impossible to be sure.

So in 1996 the QMAP team (de Oliveira-Costa, Tegmark and five colleagues from the Institute for Advanced Study in Princeton, N.J., and the University of Pennsylvania) flew instruments on a balloon 100,000 feet (30 kilometers) above Texas and New Mexico. When they finally processed the data--the night before their announcement at the Fermi National Accelerator Laboratory this past May--the situation looked grim. The Saskatoon and the balloon results were completely different.

Suddenly, however, de Oliveira-Costa realized that Tegmark had accidentally plotted the map upside down. When righted, it matched the Saskatoon data exactly. "That was my most exciting moment as a scientist, when I realized we'd flipped that map," Tegmark says. "It was then I realized, yes, Saskatoon was right. The universe is flat."

The QMAP balloon discerned much finer details in the radiation than the Cosmic Microwave Background Explorer (COBE) satellite did eight years ago. In some areas this radiation is slightly dimmer; in others, brighter. The red stripe down the middle represents the Milky Way galaxy, whose own microwave emission overpowers the cosmic signal; to avoid it, QMAP focused on a clear patch of sky around the North Star.

When the brightness fluctuations are exaggerated 100,000 times, blobs become clear. They correspond to clumps of matter that existed 300,000 years or so after the big bang. Their apparent size depends on the geometry of the universe and, in turn, on the cosmic density of matter and energy.

Combined with other observations, including those of distant supernova, the QMAP results corroborate the prevailing theory of inflation--with the twist that the universe is only one third matter (both ordinary and dark) and two thirds "quintessence," a bizarre form of energy, possibly inherent in empty space. Despite Tegmark's enthusiasm, however, this conclusion is not definitive. Astronomers are still waiting for results from two upcoming satellites, the Microwave Anisotropy Probe and Planck; meanwhile other groups are flying balloons or taking ground-based measurements. They all hope to hold up or shoot down inflationary theory. "It's like an Indiana Jones movie," says Paul Steinhardt of Penn. "Everyone sees that holy grail."

--George Musser

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October...

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November...

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PHYSICS

INCONSTANT CONSTANTS

Do distant galaxies play by different laws of physics?

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The work is the latest in an effort that began with the musings of English physicist Paul A. M. Dirac in the 1930s. He and others asked whether the constants that appear in their equations--the speed of light in a vacuum, the charge on the electron and so on--are actually constant. Even if the equations themselves are fixed, if the constants varied, nature would have worked in different ways at different times.

But looking for inconstancy is tricky. If the speed of light, for example, were slowly shrinking, we might never know it, because our measuring apparatus might be shrinking, too. For this reason, physicists focus on constants whose values are independent of the measurement system--particularly the fine-structure constant, the ratio of electromagnetic energy to the energy inherent in mass. If it once varied from its present value (roughly 1/137), subatomic particles would have interacted differently with one another and with light.

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