Paul Adrian Maurice
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#12956625 · 15 Mar 2009, 01:36 · · პროფილი · პირადი მიმოწერა · ჩატი
დვალის ძველი სტატია საინთიფიქ ამერიკანში. აშკარად კოფირაითს ვარღვევ.
Abstract:
Maybe cosmic acceleration isn't caused by dark energy after all but by an inexorable leakage of gravity out of our world. Cosmologists and particle physicists have seldom felt so confused. Although our standard model of cosmology has been confirmed by recent observations, it still has a gaping hole: nobody knows why the expansion of the universe is accelerating. Researchers commonly attribute the acceleration to some mysterious entity called dark energy, but there is little physics to back up these fine words. The only thing that is becoming clear is that at the largest observable distances, gravity behaves in a rather strange way, turning into a repulsive force. The laws of physics say that gravity is generated by matter and energy, so they attribute a strange sort of gravity to a strange sort of matter or energy. Over the years, physicists have come up with a few plausible approaches to quantum gravity, the most prominent being string theory. When Astronomers encountered the cosmic acceleration, their first reaction was to attribute it to the so-called cosmological constant. To get around this problem, a number of physicists have proposed that the acceleration is caused not by space itself but by an energy field that suffuses space like a thin fog. INSETS: FROM FLATLAND TO FOUR DIMENSIONS;THREE WAYS TO ADD A DIMENSION;THE SURLY BONDS OF BRANES;THE POLARIZED BRANE
Author Affiliations:
1GEORGI DVALI grew up in the former Soviet republic of Georgia and received his Ph.D. from the Andronikashvili institute of Physics in Tbilisi. After working at the University of Pisa in Italy, at CERN near Geneva and at the International Center for Theoretical Physics in Trieste, he joined the physics faculty of New York University. He enjoys overcoming gravity by mountain hiking, as well as taking advantage of this mysterious force by downhill skiing.
UT OF THE DARKNESS
Contents
1. Quintessence Even from Nothingness
2. Prison Life
3. Physics on the Brane
4. Brane (and Brain) Bending
5. Scofflaws
6. Overview/Gravitational Leaks
7. MORE TO EXPLORE
Section: SPECIAL REPORT
Maybe cosmic acceleration isn't caused by dark energy after all but by an inexorable leakage of gravity out of our world
Cosmologists and particle physicists have seldom felt so confused. Although Our standard model of cosmology has been confirmed by recent observations, it still has a gaping hole: nobody knows why the expansion of the universe is accelerating. If you throw a stone straight up, the pull of Earth's gravity will cause it to slow down; it will not accelerate away from the planet. Similarly, distant galaxies, thrown apart by the big bang expansion, should pull on one another and slow down. Yet they are accelerating apart. Researchers commonly attribute the acceleration to some mysterious entity called dark energy, but there is little physics to back up these fine words. The only thing that is becoming clear is that at the largest observable distances, gravity behaves in a rather strange way, turning into a repulsive force.
The laws of physics say that gravity is generated by matter and energy, so they attribute a strange sort of gravity to a strange sort of matter or energy. That is the rationale for dark energy. But maybe the laws themselves need to be changed. Physicists have a precedent for such a change: the law of gravity that Newton formulated in the 17th century, which had various conceptual and experimental limitations, gave way to Einstein's general theory of relativity in 1915. Relativity, too, has limitations; in particular, it runs into trouble when applied to extremely short distances, which are the domain of quantum mechanics. Much as relativity subsumed Newtonian physics, a quantum theory of gravity will ultimately subsume relativity.
Over the years, physicists have come up with a few plausible approaches to quantum gravity, the most prominent being string theory. When gravity operates over microscopic distances-for instance, at the center of a black hole, where a huge mass is packed into a subatomic volume--the bizarre quantum properties of matter come into play, and string theory describes how the law of gravity changes.
Over greater distances, string theorists have generally assumed that quantum effects are unimportant. Yet the cosmological discoveries of the past several years have encouraged researchers to reconsider. Four years ago my colleagues and I asked whether string theory would change the law of gravity not just on the smallest scales but also on the largest ones. The feature of string theory that could bring about this revision is its extra dimensions--additional directions in which particles can roam.: The theory adds six or seven dimensions to the usual three.
In the past, string theorists have argued that the extra dimensions are too small for us to see or move in. But recent progress reveals that some or all of the new dimensions could actually be infinite in size. They are hidden from view not because they are small but because the particles that make up our bodies are trapped in three dimensions. The one particle that eludes confinement is the particle that transmits the force of gravity, and as a result, the law of gravity changes.
Quintessence Even from Nothingness
WHEN ASTRONOMERS ENCOUNTERED the cosmic acceleration, their first reaction was to attribute it to the so-called cosmological constant. Notoriously introduced and then retracted by Einstein, the constant represents the energy inherent in space itself. A completely empty volume of space, devoid of all matter, would still contain this energy--equivalent to roughly 10-26 kilogram per cubic meter. Although the cosmological constant is consistent with all the existing data so far, many physicists find it unsatisfying. The problem is its inexplicable smallness, so small that it had little effect for most of cosmic history, including the formative early period of the universe. Worse, it is much smaller than the energy scales of the physical processes that would create it [see "From Slowdown to Speedup," by Adam G. Riess and Michael S. Turner, on page 62].
To get around this problem, a number of physicists have proposed that the acceleration is caused not by space itself but by an energy field that suffuses space like a thin fog. The potential energy of certain spatially uniform fields can act much like a cosmological constant. One such field, known as the inflaton, is thought to have driven a period of accelerated expansion, or inflation, in the early universe. Perhaps another such field has reared its head, driving the universe into another inflationary period. This second field goes under the name of quintessence. Like the cosmological constant, it must have a bizarrely small value, but proponents argue that it should be easier for a dynamic entity to settle into such a value than for a static constant to do so [see "The Quintessential Universe," by Jeremiah P. Ostriker and Paul J. Steinhardt; SCIENTIFIC AMERICAN, January 2001].
Both the cosmological constant and quintessence fall into the general category of dark energy. So far a compelling explanation for either one remains absent, which is why physicists are thinking seriously about higher-dimensional theories. The appeal of additional dimensions is that they would automatically alter how gravity behaves. When gravity operates according to the rules of either Newton's theory Or general relativity, its strength falls off with the square of the distance between objects. The reason is simple geometry: according to a principle formulated by 19th-century physicist Carl Friedrich Gauss, the strength of gravity is determined by the density of lines of gravitational force, and as the distance increases these lines are spread out over an ever larger boundary. In three-dimensional space, the boundary is a two-dimensional surface--that is, an area, the size of which increases as the square of the distance.
But if space were four-dimensional, the boundary would be three-dimensional--a volume, whose size increases as the cube of the distance. In this case, the density of lines of force would decrease with the cube of the distance. Gravity would thus be weaker than in a three-dimensional world. On cosmological scales, the weakening of gravity can lead to cosmic acceleration, for reasons I will discuss later.
If gravity is free to move into the extra space, why have we not noticed it before? Why does the standard three-dimensional inverse-square law explain the motions of baseballs, rockets and planets so precisely? The traditional answer in string theory is that the additional dimensions are compact--curled up into finite, minuscule circles. For a long time, the size of these circles was assumed to be the so-called Planck length, about 10-3s meter, but recent theoretical and experimental work shows they could be as big as 0.2 millimeter ["The Universe's Unseen Dimensions," by Nima Arkani-Hamed, Savas Dimopoulos and Georgi Dvali; SCIENTIFIC AMERICAN, August 2000]. If the dimensions are curled up, they interfere with the workings of gravity only over short distances--comparable to or smaller than the radius of the compact dimensions. Over larger distances, the standard law of gravity holds.
Prison Life
THE IDEA OF compact dimensions has its difficulties, however. One could ask, for example, why some dimensions (the extra ones) are tightly knotted, whereas others (the familiar ones) go on forever? To put it a different way, under the influence of the matter and energy in the universe, the curled-up dimensions should uncurl, unless something stabilizes them. One interesting possibility is that magnetic like fields predicted by string theory prevent the dimensions from either shrinking or expanding. Another potential solution emerged in 1999. Maybe all the dimensions, even the extra ones, are infinite in size. The observable universe is a three-dimensional surface, or membrane ("brane" for short), in a higher-dimensional world. Ordinary matter is confined to the brane, but some forces, such as gravity, can escape.
Gravity has this Houdini-like ability because it is fundamentally unlike other forces. According to quantum field theory, the force of gravity is carried by a special particle called the graviton. Gravitational attraction results from a flow of gravitons between two bodies, much as the force of electricity or magnetism results from a flow of photons between two charged particles. When gravity is static, these gravitons are "virtual" although their effects can be measured, they cannot be observed as independent particles. The sun holds Earth in orbit because it emits virtual gravitons that our planet absorbs. "Real," or directly observable, gravitons correspond to the gravitational waves that are given off under certain circumstances [see "Ripples in Spacetime," by W. Wayt Gibbs; SCIENTIFIC AMERICA.N, April 2002].
As conceived by string theory, gravitons, like all particles, are ultimately the vibrations of tiny strings. But whereas the electron, proton and photon are vibrations of open-ended strings, like violin strings, the graviton is the vibration of a closed loop, like a rubber band. Joseph Polchinski of the Kavli Institute for Theoretical Physics in Santa Barbara has shown that the ends of open strings cannot flap around; they must be tied down to a brane. If you tried to pull an open string out of a brane, it would get longer, like an elastic cord, but remain attached to the brane. In contrast, closed strings such as gravitons cannot get stuck. They are free to explore the full 10-dimensional space.
To be sure, gravitons cannot have absolute freedom. If they did, the standard law of gravity would fail conspicuously. The authors of the infinite-dimensions hypothesis, Lisa Randall of Harvard University and Raman Sundrum of Johns Hopkins University, suggested that gravitons are hindered because the extra dimensions, unlike our familiar three, are very strongly curved--creating a steep-walled valley that is hard to leave.
The trick is, because the extra dimensions are so strongly curved, their volume is effectively finite, even though they are infinite in extent. How can an infinite space have a finite volume? Imagine pouring gin into a bottomless martini glass whose radius shrinks in inverse proportion to its depth. To fill the glass, a finite amount of gin would suffice. Because of the curvature of the glass, its volume is concentrated near the top. This is very similar to what happens in the Randall-Sundrum scenario. The volume of the extra space is concentrated around our brane. Consequently, a graviton is forced to spend most of its time near the brahe. The probability of detecting the graviton quickly diminishes as a function of distance. In quantum jargon, the wave function of the graviton is peaked at the brane--an effect referred to as localization of gravity.
Though conceptually different from the idea of compact dimensions, the Randall-Sundrum scenario has much the same outcome. Both models modify the law of gravity on short distances but not on large distances, so neither bears on the problem of cosmic acceleration.
Physics on the Brane
A THIRD APPROACH, though, does predict the breakdown of the standard laws Of gravity on cosmological scales and explains acceleration without having to invoke dark energy. In 2000 Gregory Gabadadze and Massimo Porrati, both now at New York University, and i proposed that the extra dimensions are exactly like the three dimensions that we see around us. They are neither compact nor strongly curved.
Even so, gravitons are not completely free to go where they like. Emitted by stars and other objects located on the brane, they can escape into the extra dimensions, but only if they travel a certain critical distance. The gravitons behave like sound in a metal sheet. Hitting the sheet with a hammer creates a sound wave that travels along its surface. But the sound propagation is not exactly two-dimensional; part of the energy is .lost into the surrounding air. Near the location of the hammer blow, this energy loss is negligible. Farther away, however, it becomes noticeable.
This leakage has a profound effect on the gravitational force between objects separated by more than the critical distance. Virtual gravitons exploit every possible route between the objects, and the leakage opens up a huge number of multidimensional detours, which bring about a change in the law of gravity. Real gravitons that leak away are simply lost forever, and for those of us stuck on the brane, it looks as though they have disappeared into thin air.
The extra dimensions also reveal themselves on very small scales, just as in the compact and Randall-Sundrum scenarios. Over intermediate distances--larger than the size of the strings but smaller than the leakage distance--gravitons are three-dimensional and closely obey the conventional law of gravity.
The key to this scenario is the brahe itself. It is a material object in its own right, and gravity spreads through it differently than through the surrounding space. The reason is that ordinary particles such as electrons and protons can exist on the brane and only on the brane. Even a seemingly empty brane contains a seething mass of virtual electrons, protons and other particles, continuously created and destroyed by quantum fluctuations. Those particles both generate and respond to gravity. The surrounding space, in contrast, is truly empty. Gravitons can flutter through it but have nothing to act on except one another.
An analogy is a dielectric material, such as plastic, ceramic or pure water. The material, unlike a vacuum, contains electrically charged particles and can respond to an electric field. Although charged particles cannot flow through a dielectric (as they can through an electrical conductor), they can still redistribute themselves within it. If you apply an electric field, the material becomes electrically polarized. In water, for example, the molecules rotate so that their positive ends (the two hydrogen atoms) point in one direction and their negative ends (the oxygen atom) point in the opposite direction. In sodium chloride, the positive sodium ions and negative chloride ions move slightly apart.
The redistributed charges set up an electric field of their own, which partially cancels the external field. A dielectric can thus affect the propagation of photons, which are nothing more than oscillating electric and magnetic fields. Photons penetrating into a dielectric polarize it and, in turn, are partially canceled out. To bring about this effect, a photon must have a wavelength in a certain range: long-wavelength (low-momentum) photons are too weak to polarize a dielectric, and short wavelength (high-momentum) photons oscillate too quickly for the charged particles to respond. For this reason, water is transparent to radio waves (which have a long wavelength) and to visible light (short wavelength) but opaque to microwaves (intermediate wavelength). Microwave ovens rely on this effect.
Similarly, quantum fluctuations convert the brane into the gravitational equivalent of a dielectric. It is as if the brane is populated by positive-energy and negative-energy virtual particles. If you apply an external gravitational field, the brane becomes gravitationally polarized. Positive-energy particles move slightly away from negative-energy ones. A graviton, which embodies an oscillating gravitational field, can polarize the brane and get canceled out if its wavelength falls into the right range-which, we calculate, lies between 0.1 millimeter (or smaller, depending on the number of extra dimensions) and approximately 10 billion light-years.
This cancellation affects only gravitons traveling into or out of the brane. Gravitons, like photons, are transverse waves: they oscillate perpendicular to their direction of propagation. A graviton entering or exiting the brane tends to push particles along the brane, a direction in which the particles are able to move. Thus, these gravitons can polarize the brane and, in turn, get cancelled out. But gravitons moving along the brane try to push particles out of the brane, a direction in which they cannot go. Therefore these gravitons do not polarize the brane. They move without encountering resistance. In practice, most gravitons fall between these two extremes. They zip through space at an oblique angle to the brane and may cover billions of light-years before getting canceled out.
Brane (and Brain) Bending
IN THIS WAY, THE BRANE shields itself from the extra dimensions. If an intermediate-wavelength graviton attempts to escape from or penetrate into the brane, particles within the brane redistribute themselves and block it. The gravitons must instead move along the brane, so gravity follows an inverse square law. Long-wavelength gravitons, however, are free to pass through the extra dimensions. These gravitons are insignificant over short distances but dominate on distances comparable to their Wavelength, and they undermine the brane's ability to isolate itself from the extra dimensions. The law of gravity approaches an inverse-cube law (if only one of the extra dimensions is infinite), an inverse-fourth-power law (if two are infinite) or an even steeper law. In all these cases, gravity is weakened.
Cédric Deffayet, now at the Paris Institute of Astrophysics, Gabadadze and I have found that the extra dimensions not only sap the strength of gravity but also force cosmic expansion to accelerate without any need to stipulate the existence of dark energy. It is tempting to say that by weakening the gravitational glue that retards expansion, graviton leakage reduces the deceleration, so much so that the deceleration becomes negative-that is, an acceleration. But the effect is more subtle. It has to do with how leakage alters general relativity.
The central idea of Einstein's theory is that gravitation is a consequence of the curvature of space-time, which is related to the density of matter and energy within it. The sun attracts Earth by warping the spacetime around it. No matter and no energy mean no warping and no gravity, in the higher-dimensional theory, however, the relation between curvature and density changes. The extra dimensions introduce a correction term into the equations, which ensures that the curvature of an empty brane is not zero. In effect, graviton leakage puts tension on the brane, giving it an irreducible warp that does not depend on the density of matter and energy within it.
Over time, as matter and energy get diluted, the curvature that they cause decreases, and so the irreducible warp becomes increasingly important. The curvature of the universe approaches a constant value. The same effect would be brought about if the universe were filled with a substance that did not get diluted over time. Such a substance is none other than a cosmological constant. Therefore, the irreducible warp of the brane acts like a cosmological constant, which speeds up cosmic expansion.
Scofflaws
OUR THEORY IS NOT the only one that postulates the breakdown of the standard gravitational law at large distances. In 2002 Thibault Damour and Antonios Papazoglou of the Institute for Higher Scientific Studies in France and Ian Kogan of the University of Oxford suggested that gravitons come in an additional variety--one that, unlike normal gravitons, possesses a small mass. As physicists have long known, if gravitons have mass, gravity does not obey an inverse-square law. They are unstable and gradually decay, with much the same effect as graviton leakage: gravitons traveling for long distances vanish, gravity gets weaker, and cosmic expansion accelerates. Sean Carroll, Vikram Duvvuri and Michael Turner of the University of Chicago and Mark Trodden of Syracuse University have modified Einstein's theory in three dimensions by introducing tiny terms that are inversely proportional to spacetime curvature. Such terms would be negligible in the early universe but would speed expansion later on. Other research teams have also suggested modifying the law of gravity, but their proposals do not eliminate the need for dark energy to cause acceleration.
Observations will be the final arbiter of all these models. Supernova surveys provide one direct test. The transition from deceleration to acceleration is Very different in a leakage scenario than in other dark-energy scenarios. Further improvements in the precision of these surveys could differentiate among the theories.
Planetary motion offers another empirical test. A gravitational wave, just like an ordinary electromagnetic wave, can have a preferred direction of oscillation. General relativity permits two such directions, but alternative theories of gravity allow for more. These additional possibilities modify the gravitational force in a small but nonnegligible way, yielding potentially observable corrections to planetary motion. Andrei Gruzinov and Matias Zaldarriaga of New York University and I have calculated that graviton leakage would cause the moon's orbit to process slowly. Every time the moon completed one orbit, its closest approach to Earth would shift by about a trillionth of a degree, or about half a millimeter. This motion is almost large enough to be seen by lunar-ranging experiments, which monitor the moon's orbit by bouncing laser beams off mirrors left on the lunar surface by the Apollo astronauts. Current ranging measurements have a precision of one centimeter, and Eric Adelberger and his colleagues at the University of Washington propose using more powerful lasers to improve the sensitivity 10-fold. Spacecraft tracking could look for a similar precession of Mars's orbit.
The mere fact that observers are talking about probing string theory is exciting. For years, the theory was assumed to be a theory of the very small--so small that no experiment could ever prove or disprove it. Cosmic acceleration may be a rear window of opportunity, a gift from nature, that lets us peer into the extra dimensions that are otherwise invisible to us. It may be a bridge between the very small and the ultra large. The fate of the universe may be hanging from a string.
Overview/Gravitational Leaks
• Astronomers typically ascribe the accelerated expansion of the universe to a shadowy dark energy. It might, however, be a sign that the standard laws of physics break down on the largest scales.
• A new law of gravity emerges from string theory, one of the leading efforts to prepare an ultimate unified theory of nature. String theory is usually considered a theory of the very small, but it can also have macroscopic consequences.
• In particular, the theory predicts that the universe has extra dimension into which gravity, unlike ordinary matter, may be able to escape. This leakage would warp the spacetime continuum and cause cosmic expansion to accelerate. It might even have a minute but observable effect on planetary motion.
MORE TO EXPLORE
The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. Brian Greene. W. W. Norton, 2003.
An Alternative to Compactification. Lisa Randall and Raman Sundrum in Physical Review Letters, Vol. 83, No. 23, page 4690-4693; December 6, 1999. Available online at arXiv.org/abs/hep-th/9906064
Accelerated Universe from Gravity Leaking to Extra Dimensions. Cédric Deffayet, Gia Dvali and Gregory Gabadadze in Physical Review B, Vol. 65, paper number 044023; 2002. arXiv.org/abs/astro-ph/0105068
The Accelerated Universe and the Moon. Gia Dvali, Andrei Gruzinov and Matias Zaldarriaga in Physical Review D, Vol. 68, paper number 024012; 2003. arXiv;org/abs/hep-ph/0212069
Tests of the Gravitational Inverse-Square Law. E. G. Adelberger, B. R. Heckel and A. E. Nelson in Annual Review of Nuclear and Particle Science, Vol. 53, pages ??-121; December 2003. arXiv.org/abs/hep.ph/0307284 An introduction to string theory can be found at superstringtheory.com
PHOTO (COLOR): LEAKING OUT of our universe, particles of gravity could explore a higher-dimensional space. The leakage becomes apparent only on cosmic scales.
~~~~~~~~
By Georgi Dvali, GEORGI DVALI grew up in the former Soviet republic of Georgia and received his Ph.D. from the Andronikashvili institute of Physics in Tbilisi. After working at the University of Pisa in Italy, at CERN near Geneva and at the International Center for Theoretical Physics in Trieste, he joined the physics faculty of New York University. He enjoys overcoming gravity by mountain hiking, as well as taking advantage of this mysterious force by downhill skiing.
FROM FLATLAND TO FOUR DIMENSIONS
A FAMOUS POSTER by artist Gerry Mooney proclaims: "Gravity: It isn't just a good idea. It's the law." Yet the law is actually rather flexible. For instance, it depends on the number of spatial dimensions. The key is that gravity weakens with distance because, as it propagates, it gets spread out over an ever larger boundary {red in diagrams below}.
TWO DEMENSIONS: The boundary is one-dimensional[ a line) and grows in direct proportion to the propagation distance. Thus, the strength of gravity drops in inverse proportion to distance.
THREE DIMENSIONS. The boundary is two-dimensional, so gravity attenuate in inverse proportion to the square of the distance. Objects at a given distance are lighter than they would be in two dimensions.
FOUR DIMENSIONS: This situation is hard to visualize, but the same basic rules apply. The boundary is three-dimensional, so gravity follows an inverse-cube law. Objects are even lighter than they were in three dimensions.
GRAPH
PHOTO (COLOR): Weight of 100-kg man on Earth's surface: 10[45] newtons
PHOTO (COLOR): Weight: 10[3] newtons
PHOTO (COLOR): Weight: 10[-39] newton
PHOTO (COLOR)
PHOTO (COLOR)
PHOTO (COLOR)
THREE WAYS TO ADD A DIMENSION
ALBERT EINSTEIN and other scientists of his generation, notably Theodor Kaluza and Oskar Klein, were enamored of the idea that space has hidden dimensions. This hypothesis lives on in string theory. For the sake of clarity, think of our three-dimensional universe as a flat grid. At each grid point is a line that represents one of the extra dimensions.
TRADITIONAL STRING THEORY: String theorists long assumed that the extra dimensions were finite in size small circles of sub-subatomic size. Moving in this dimension, a tiny creature would eventually return to its starting point.
INFINITE-VOLUME MODEL. The author and his colleagues have proposed that the extra dimensions are infinite in size and uncurved, just like our ordinary three dimensions.
RANDALL-SUNDRUM MODEL: More recently, string theorists have suggested that the extra dimensions are infinite in size--but strongly Curved, so that their volume is concentrated around our universe.
PHOTO (COLOR)
PHOTO (COLOR)
PHOTO (COLOR)
THE SURLY BONDS OF BRANES
SADLY, even if extra dimensions exist, humans will never be able to venture into them. Particles in our bodies-electrons, protons, neutrons-are thought to be the vibrational patterns of open-ended strings. By their very nature, they are tied down to the membrane, or brane, that constitutes our universe. Gravitons, the particles of 8ravitational force, elude these bonds because they have no ends to tie down.
PHOTO (COLOR)
THE POLARIZED BRANE
GRAVITONS do not have untrammeled freedom to traipse through extra dimensions. Our three-dimensional universe, or brane [shown here as a flat sheet], is filled with "virtual" particles that bubble in and out of existence. One way to model their effect on gravitons is to think of them as coming in pairs. One particle in each pair is endowed with positive energy [blue], the other with negative energy [red]. Such pairs can block gravatons from entering or exiting the brane.
NO GRAVITON: In the absence of a graviton, the virtual particles are aligned randomly and generate no net gravitational force.
PERPENDICULAR GRAVITON: When a graviton moves into or out of the brane, it aligns, or "polarizes," the virtual particles. The polarized particles generate a gravitational force that opposes the motion of the graviton.
PARALLEL GRAVITON: When a graviton moves along the brane, it has no effect on the virtual particles, because the forces it exerts act at right angles to the brane. The virtual particles, in turn, do not impede the graviton.
PHOTO (COLOR)
PHOTO (COLOR)
PHOTO (COLOR)
GRAVITY NEAR AND FAR
PARTICLES IN OUR UNIVERSE tend to block out gravitons, but only if the gravitons have enough momentum to provoke a response. Low-momentum gravitons [which have a long wavelength] enter or exit the brane at will.
The sun exerts a force on Earth by emitting virtual gravitons. These gravitons have a relatively short wavelength [high momentum], so they are blocked from leaving the brane. They behave as if the extra dimensions did not exist.
Two distant galaxies emit gravitons with a long wavelength [low momentum]. These gravitons are not blocked from escaping into the extra dimensions. The law of gravity changes, weakening the force between the galaxies.
PHOTO (COLOR)
PHOTO (COLOR)
* * *
მე მგონი ეს არის იმ სტატიის პოლულარული ვერსია რომლითაც სახელი გაითქვა
The Universe's UNSEEN DIMENSIONS.
Authors:
Arkani-Hamed, Nima
Dimopoulos, Savas
Dvali, Georgi
Source:
Scientific American; Aug2000, Vol. 283 Issue 2, p62, 8p, 8 diagrams, 1 color
Document Type:
Article
Subject Terms:
*DIMENSIONS
*GRAVITY
*FOKKER-Planck equation
*PHYSICS
Abstract:
Describes a physics theory in which everything we see is confined to a three-dimensional membrane that lies within a higher-dimensional realm and is based on developments in string theory. Problem of the weakness of gravity, which the theory would solve, and with the Planck scale; Why we cannot see the dimensions; Types of experiments which would substantiate the theory; Implications, including the possibility that dark matter resides in parallel universes.
Full Text Word Count:
5628
ISSN:
00368733
Accession Number:
3313457
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THE UNIVERSE'S UNSEEN DIMENSIONS
Contents
1. The Inexplicable Weakness of Gravity
2. Gravity and Large Spatial Dimensions
3. Our Universe on a Wall
4. Is It Alive?
5. Answers by 2010
6. Parallel Universes
7. IN A NUTSHELL
8. Further Information
The visible universe could lie on a membrane floating within a higher-dimensional space. The extra dimensions would help unify the forces of nature and could contain parallel universes
The classic 1884 story Flatland: A Romance of Many Dimensions, by Edwin A. Abbott, describes the adventures of "A. Square," a character who lives in a two-dimensional world populated by animated geometric figures--triangles, squares, pentagons, and so on. Toward the end of the story, on the first day of 2000, a spherical creature from three-dimensional "Spaceland" passes through Flatland and carries A. Square up off his planar domain to show him the true three-dimensional nature of the larger world. As he comes to grasp what the sphere is showing him, A. Square speculates that Spaceland may itself exist as a small subspace of a still larger four-dimensional universe.
Amazingly, in the past two years physicists have begun seriously examining a very similar idea: that everything we can see in our universe is confined to a three-dimensional "membrane" that lies within a higher-dimensional realm. But unlike A. Square, who had to rely on divine intervention from Spaceland for his insights, physicists may soon be able to detect and verify the existence of reality's extra dimensions, which could extend over distances as large as a millinaeter ( 1/25 of an inch). Experiments are already looking for the extra dimensions' effect on the force of gravity. If the theory is correct, upcoming high-energy particle experiments in Europe could see unusual processes involving quantum gravity, such as the creation of transitory micro black holes. More than just an idle romance of many dimensions, the theory is based on some of the most recent developments in string theory and would solve some long-standing puzzles of particle physics and cosmology.
The exotic concepts of string theory and multidimensions actually arise from attempts to understand the most familiar of forces: gravity. More than three centuries after Isaac Newton proposed his law of gravitation, physics still does not explain why gravity is so much weaker than all the other forces. The feebleness of gravity is dramatic. A small magnet readily overcomes the gravitational pull of the entire mass of the earth when it lifts a nail off the ground. The gravitational attraction between two electrons is 1043 times weaker than the repulsive electric force between them. Gravity seems important to us--keeping our feet on the ground and the earth orbiting the sun--only because these large aggregates of matter are electrically neutral, making the electrical forces vanishingly small and leaving gravity, weak as it is, as the only noticeable force left over.
The Inexplicable Weakness of Gravity
Electrons would have to be 10[sup22] times more massive for the electric and gravitational forces between two of them to be equal. To produce such a heavy particle would take 10[sup19] gigaelectron volts (GeV) of energy, a quantity known as the Planck energy. A related quantity is the Planck length, a tiny 10[sup-35] meter. By comparison, the nucleus, of a hydrogen atom, a proton, is about 10[sup19] times as large and has a mass of about 1 GeV. The Planck scale of energy and length is far out of reach of the most powerful accelerators. Even the Large Hadron Collider at CERN will probe distances only down to about 10[sup-19] meter when it commences operations five years from now [see "The Large Hadron Collider," by Chris Llewellyn Smith; SCIENTIFIC AMERICAN, July]. Because gravity becomes comparable in strength to electromagnetism and the other forces at the Planck scale, physicists have traditionally assumed that the theory unifying gravity with the other interactions would reveal itself only at these energies. The nature of the ultimate unified theory would then be hopelessly out of reach of direct experimental investigation in the foreseeable future [see "A Unified Physics by 2050?" by Steven Weinberg; SCIENTIFIC AMERICAN, December 1999].
Today's most powerful accelerators probe the energy realm between 100 and 1,000 GeV (one teraelectron volt, or TeV). In this range, experimenters have seen the electromagnetic force and the weak interaction (a force between subatomic particles responsible for certain types of radioactive decay) become unified. We would understand gravity's extraordinary weakness if we understood the factor of 10[sup16] that separates the electroweak scale from the Planck scale.
Alas, physicists' extremely successful theory of particle physics, called the Standard Model, cannot explain, the size of this huge gap, because the theory is carefully adjusted to fit the observed electroweak scale. The good news is that this adjustment (along with about 16 others) serves once and for all to fit myriad observations. The bad news is that we must free-rune the underlying theory to an accuracy of about one part in 10[sup32]; otherwise, quantum effects--instabilities--would drag the electroweak scale all the way back up to the Planck scale. The presence of such delicate balancing in the theory is like walking into a room and finding a pencil standing perfectly on its tip in the middle of a table. Though not impossible, the situation is highly unstable, and we are left wondering how it came about.
For 20 years, theorists have attacked this conundrum, called the hierarchy problem, by altering the nature of particle physics near 10[sup-19] meter (or 1 TeV) to stabilize the electroweak scale. The most popular modification of the Standard Model that achieves this goal involves a new symmetry called supersymmetry. Going back to our pencil analogy, supersymmetry acts like an invisible thread holding up the pencil and preventing it from falling over. Although accelerators have not yet turned up any direct evidence for supersymmetry, some suggestive indirect evidence supports the supersymmetric extension of the Standard Model. For example, when the measured strengths of the strong, weak and electromagnetic forces are theoretically extrapolated to shorter distances, they meet very accurately at a common value only if supersymmetric roles govern the extrapolation. This result hints at a supersymmetric unification of these three forces at about 10[sup-32] meter, about 1,000 times larger than the Planck length but still far bey6nd the range of particle colliders.
Gravity and Large Spatial Dimensions
For two decades, the only viable framework for tackling the hierarchy problem has been to change particle physics near 1049 meter by introducing new processes such as supersymmetry. But in the past two years theorists have proposed a radically different approach, modifying space-time, gravity and the Planck scale itself. The key insight is that the extraordinary size of the Planck scale, accepted for a century since Planck first introduced it, is based on an untested assumption about how gravity behaves over short distances.
Newton's inverse square law of gravity--which says the force between two masses falls as the square of the distance between them--works extremely well over macroscopic distances, explaining the earth's orbit around the sun, the moon's around the earth, and so on. But because gravity is so weak, the law has been experimentally tested down to distances of only about a millimeter, and we must extrapolate across 32 orders of magnitude to conclude that gravity only becomes strong at a Planck scale of 10[sup-35] meter.
The inverse square law is natural in three-dimensional space [see upper illustration on opposite page]. Consider lines of gravitational force emanating uniformly from the earth. Farther from the earth, the lines are spread over a spherical shell of greater area. The surface area increases as the square of the distance, and so the force is diluted at that rate. Suppose there were one more dimension, making space four-dimensional. Then the field lines emanating from a point would get spread over a four-dimensional shell whose surface would increase as the cube of the distance, and gravity would follow an inverse cube law.
The inverse cube law certainly doesn't describe our universe, but now imagine that the extra dimension is curled up into a small circle of radius R and that we're looking at field lines coming from a tiny point mass [see lower illustration on opposite page]. When the field lines are much closer to the mass than the distance R, they can spread uniformly in all four dimensions, and so the force of gravity falls as the inverse cube of distance. Once the lines have spread fully around the circle, however, only three dimensions remain for them to continue spreading through, and so for distances much greater than R the force varies as the inverse square of the distance.
The same effect occurs if there are many extra dimensions, all curled up into circles of radius R. For n extra spatial dimensions at distances smaller than R, the force of gravity will follow an inverse 2 + n power law. Because we have measured gravity only down to a millimeter, we would be oblivious to changes in gravity caused by extra dimensions whose size R is smaller than a millimeter. Furthermore, the 2 + n power law would cause gravity to reach "Planck-scale strength" well above 10[-35] meter. That is, the Planck length (defined by where gravity becomes strong) would not be that small, and the hierarchy problem would be reduced.
One can solve the hierarchy problem completely by postulating enough extra dimensions to move the Planck scale very close to the electroweak scale. The ultimate unification of gravity with the other forces would then take place near 10[sup-19] meter rather than 10[sup-35] meter as traditionally assumed How many dimensions are needed depends on how large they are. Conversely, for a given number of extra dimensions we can compute how large they must be to make gravity strong near 10[sup-19] meter. If there is only one extra dimension, its radius R must be roughly the distance between the earth and the sun. Therefore, this case is already excluded by observation. Two extra dimensions, however, can solve the hierarchy problem if they are about a millimeter in size--precisely where our direct knowledge of gravity ends: The dimensions are smaller still if we add more of them, and for seven extra dimensions we need them to be around 10[sup-14] meter big, about the size of a uranium nucleus. This is tiny by everyday standards but huge by the yardstick of particle physics.
Postulating extra dimensions may seem bizarre and ad hoc, but to physicists it is an old, familiar idea that dates back to the 1920s, when Polish mathematician Theodor Kaluza and Swedish physicist Oskar Klein developed a remarkable unified theory of gravity and electromagnetism that required one extra dimension. The idea has been revived in modern string theories, which require a total of 10 spatial dimensions for internal mathematical consistency. In the past, physicists have assumed that the extra dimensions are curled up into tiny circles with a size near the traditional Planck length of 10[sup-35] meter; making them undetectable but also leaving the conundrum of the hierarchy problem. In contrast, in the new theory that we are discussing, the extra dimensions are wrapped into big circles of at least 10[sup-14] meter radius and perhaps as enormous as a millimeter.
Our Universe on a Wall
If these dimensions are that large, why haven't we seen them yet? Extra dimensions a millimeter big would be discernible to the naked eye and obvious through a microscope. And although we have not measured gravity below about a millimeter, we have a wealth of experimental knowledge concerning all the other forces at far shorter distances approaching 10[sup-19] meter, all of it consistent only with three-dimensional space. How could there possibly be large extra dimensions?
The answer is at once simple and peculiar: all the matter and forces we know of--with the sole exception of gravity-are stuck to a "wall" in the space of the extra dimensions [see illustration on next page]. Electrons and protons and photons and all the other particles in the Standard Model cannot move in the extra dimensions; electric and magnetic field lines cannot spread into the higher-dimensional space. The wall has only three dimensions, and as far as these particles are concerned, the universe might as well be three-dimensional. Only gravitational field lines can extend into the higher-dimensional space, and only the particle that transmits gravity, the graviton, can travel freely into the extra dimensions. The presence of the extra dimensions can be felt only through gravity.
To make an analogy, imagine that all the particles in the Standard Model, like electrons and protons, are billiard balls moving on the surface of a vast pool table. As far as they are concerned, the universe is two-dimensional. Nevertheless, pool-table inhabitants made out of "billiard balls" could still detect the higher-dimensional world: when two balls hit each other sufficiently hard, they produce sound waves, which travel in all three dimensions, carrying some energy away from the table surface [see illustration on opposite page]. The sound waves are analogous to gravitons, which can travel in the full higher-dimensional space. In high-energy particle collisions, we expect to observe missing energy, the result of gravitons escaping into the extra dimensions.
Although it may seem strange that some particles should be confined to a wall, similar phenomena are quite familiar. For instance, electrons in a copper wire can move only along the one-dimensional space of the wire and do not travel into the surrounding three-dimensional space. Likewise, water waves travel primarily on the surface of the ocean, not throughout its depth. The specific scenario we are describing, in which all particles except gravity are stuck to a wall, can arise naturally in string theory. In fact, one of the major insights triggering recent breakthroughs in string theory has been the recognition that the theory contains such "walls," known as D-branes, where "brane" comes from the word "membrane" and "D" stands for "Dirichlet," which indicates a mathematical property of the branes. D-branes have precisely the required features: particles such as electrons and photons are represented by tiny lengths of string that each have two endpoints that must be stuck to a D-brane. Gravitons, on the other hand, are tiny closed loops of string that can wander into all the dimensions because they have no endpoints anchoring them to a D-brane.
Is It Alive?
One of the first things good theorists do when they have a new theory is to try to kill it by finding an inconsistency with known experimental results. The theory of large extra dimensions changes gravity at macroscopic distances and alters other physics at high energies, so surely it is easy to kill. Remarkably, however; despite its radical departure from our usual picture of the universe, this theory does not contradict any known experimental results. A few examples of the sorts of tests that are passed shows how surprising this conclusion is.
One might initially worry that changing gravity would affect objects held together by gravity, such as stars and galaxies. But they are not affected. Gravity changes only at distances shorter than a millimeter, whereas in a star, for example, gravity acts across thousands of kilometers to hold distant parts of the star together. More generally, even though the extra dimensions strengthen gravity much more quickly than usual at short distances, it still only catches up with the other forces near 1049 meter and remains very feeble compared with them at larger distances.
A much more serious concern relates to gravitons, the hypothetical particles that transmit gravity in a quantum theory. In the theory with extra dimensions, gravitons interact much more strongly with matter (which is equivalent to gravity being stronger at short distances), so many more of them should be produced in high-energy particle collisions. In addition, they propagate in all the dimensions, thus taking energy away from the wall, or membrane, that is the universe where we live.
When a star collapses and then explodes as a supernova, the high temperatures can readily boil off gravitons into extra dimensions [see upper illustration on page 68]. From observations of the famous Supernova 1987A, however, we know that a supernova explosion emits most of its energy as neutrinos, leaving little room for any energy leakage by gravitons. Our understanding of supernovae therefore limits how strongly gravitons can couple to matter. This constraint could easily have killed the idea of large extra dimensions, but detailed calculations show that the theory survives. The most severe limit is for only two extra dimensions, in which ease gravitons cool supernovae too much if the fundamental Planck scale is reduced below about 50 TeV. For three or more extra dimensions, this scale can be as low as a few TeV without causing supernovae to fizzle.
Theorists have examined many other possible constraints based on unacceptable changes in systems ranging from the successful big bang picture of the early universe to collisions of ultrahigh-energy cosmic rays. The theory passes all these experimental checks, which turn out to be less stringent than the supernova constraint. Perhaps surprisingly, the constraints become less severe as more dimensions are added to the theory. We saw this right from the start: the case of one extra dimension was excluded immediately because gravity would be altered at solar system distances. This indicates why more dimensions are safer; the dramatic strengthening of gravity begins at shorter distances and therefore has a smaller impact on the larger-distance processes.
Answers by 2010
The theory solves the hierarchy problem by making gravity a strong force near TeV energies, precisely the energy scale to be probed using upcoming particle accelerators. Experiments at the Large Hadron Collider (LHC), due to begin around 2005, should therefore uncover the nature of quantum gravity! For instance, if string theory is the correct description of quantum gravity, particles are like tiny loops of string, which can vibrate like a violin string. The known fundamental particles correspond to a string that is not vibrating, much like an unbowed violin string. Each different "musical note' that a string can carry by vibrating would appear as a different exotic new particle. In conventional string theories, the strings have been thought of as only 10-35 meter big, and the new particles would have masses on the order of the traditional Planck energy--the "music" of such strings would be too high-pitched for us to "hear" at particle colliders. But with large extra dimensions, the strings are much longer, near 10[sup-19] meter, and the new particles would appear at TeV energies--low enough to hear at the LHC.
Similarly, the energies needed to create micro black holes in particle collisions would fall within experimental range [see lower illustration on next page]. Such holes, about 10[sup-19] meter in size, would be too small to cause problems--they would emit energy called Hawking radiation and evaporate in less than 10[sup-27] second. By observing such phenomena, physicists could directly probe the mysteries of quantum black hole physics.
Even at energies too low to produce vibrating strings or black holes, particle collisions will produce large numbers of gravitons, a process that is negligible in conventional theories. The experiments could not directly detect the emitted gravitons, but the energy they carry off would show up as energy missing from the collision debris. The theory predicts specific properties of the missing energy--how it should vary with collision energy and so on--so evidence of graviton production can be distinguished from other processes that can carry off energy in unseen particles. Current data from the highest-energy accelerators already mildly constrain the large-dimensions scenario. Experiments at the LHC should either see evidence of gravitons or begin to exclude the theory by their absence.
A completely different type of experiment could also substantiate the theory, perhaps much sooner than the particle colliders. Recall that for two extra dimensions to solve the hierarchy problem, they must be as large as a millimeter. Measurements of gravity would then detect a change from Newton's inverse square law to an inverse fourth power law at distances near a millimeter. Extensions of the basic theoretical framework lead to a whole host of other possible deviations from Newtonian gravity, the most interesting of which is repulsive forces more than a million times stronger than gravity occurring between masses separated by less than a millimeter. Tabletop experiments using exquisitely built detectors are now under way, testing Newton's law from the centimeter range down to tens of microns [see illustration on page 69].
To probe the gravitational force at submillimeter distances, one must use objects not much larger than a millimeter, which therefore have very small masses. One must carefully screen out numerous effects such as residual electrostatic forces that could mask or fake the tiny gravitational attraction. Such experiments are difficult and subtle, but it is exciting. that they might uncover dramatic new physics. Even apart from the search for extra dimensions, it is important to extend our direct knowledge of gravity to these short distances. Three researchers are currently conducting such experiments: John C. Price of the University of Colorado, Aharon Kapitulnik of Stanford University and Eric G. Adelberger of the University of Washington. They expect preliminary results this year.
The idea of extra dimensions in effect continues the Copernican tradition in understanding our place in the world: The earth is not the center of the solar system, the sun is not the center of our galaxy, our galaxy is just one of billions in a universe that has no center, and now our entire three-dimensional universe would be just a thin membrane in the full space of dimensions. If we consider slices across the extra dimensions, our universe would occupy a single infinitesimal point in each slice, surrounded by a void.
Perhaps this is not the full story. Just as the Milky Way is not the only galaxy in the universe, might our universe not be alone in the extra dimensions? The membranes of other three-dimensional universes could lie parallel to our own, only a millimeter removed from us in the extra dimensions [see illustration on preceding page]. Similarly, although all the particles of the Standard Model must stick to our own membrane universe, other particles beyond the Standard Model in addition to the graviton might propagate through the extra dimensions. Far from being empty, the extra dimensions could have a multitude of interesting structures.
The effects of new particles and universes in the extra dimensions may provide answers to many outstanding mysteries of particle physics and cosmology. For example, they may account for the masses of the ghostly elementary particles called neutrinos. Impressive new evidence from the Super Kamiokande experiment in Japan indicates that neutrinos, long assumed to be massless, have a minuscule but nonzero mass [see "Detecting Neutrino Mass," by Edward Kearns, Takaaki Kajita and Yoji Totsuka; Scientific American August 1999]. The neutrino can gain its mass by interacting with a partner field living in the extra dimensions. As with gravity, the interaction is greatly diluted by the partner being spread throughout the extra dimensions, and so the neutrino acquires only a tiny mass.
Parallel Universes
Another example is the mystery in cosmology of what constitutes "dark matter," the invisible gravitating substance that seems to make up more than 90 percent of the mass of the universe. Dark matter may reside in parallel universes. Such matter would affect our universe through gravity and is necessarily "dark" because our species of photon is stuck to our membrane, so photons cannot travel across the void from the parallel matter to our eyes.
Such parallel universes might be utterly unlike our own, having different particles and forces and perhaps even being confined to membranes with fewer or more dimensions. In one intriguing scenario, however, they have identical properties to our own world. Imagine that the wall where we live is folded a number of times in the extra dimensions [see illustration on preceding page]. Objects on the other side of a fold will appear to be very distant even if they are less than a millimeter from us in the extra dimensions: the light they emit must travel to the crease and back to reach us. If the crease is tens of billions of light-years away, no light from. the other side could have reached us since the universe began.
Dark matter could be composed of ordinary matter, perhaps even ordinary stars and galaxies, shining brightly on their own folds. Such stars would produce interesting observable effects, such as gravitational waves from supernovae and other violent astrophysical processes. Gravity-wave detectors scheduled for completion in a few years could find evidence for folds by observing large sources of gravitational radiation that cannot be accounted for by matter visible in our own universe.
The theory we have presented here was not the first proposal involving extra dimensions larger than 10[sup-35] meter. In 1990 Ignatios Antoniadis of Ecole Polytechnique in France suggested that some of string theory's dimensions might be as large as 1049 meter, but he kept the scale of quantum gravity near 10[sup-35] meter. In 1996 Petr Horava of the California Institute of Technology and Edward Witten of the Institute for Advanced Study in Princeton, N.J., pointed out that a single extra dimension of 10[sup-30] meter would neatly unify gravity along with the supersymmetric unification of the other forces, all at 10[sup-32] meter. Following this idea, Joseph Lykken of Fermi National Accelerator Laboratory in Batavia, Ill., attempted to lower the unification scale to near 10[sup-19] meter (without invoking large extra dimensions). Keith Dienes of the University of Arizona and Emilian Dudas and Tony Gherghetta of CERN observed in 1998 that extra dimensions smaller than 10[sup-19] meter could allow the forces to unify at much larger distances than 10[sup-32] meter.
Since our proposal in 1998 a number of interesting variations have appeared, using the same basic ingredients of extra dimensions and our Universe-on-a-wall. In an intriguing model, Lisa Randall of Princeton University and Raman Sundrum of Stanford proposed that gravity itself may be concentrated on a membrane in a five-dimensional space-time that is infinite in all directions. Gravity appears very weak in our universe in a natural way if we are on a different membrane.
For 20 years, the conventional approach to tackling the hierarchy problem, and therefore understanding why gravity is so weak, has been to assume that the Planck scale near 10[sup-35] meter is fundamental and that particle physics must change near 10[sup-19] meter. Quantum gravity would remain in the realm of theoretical speculation, hopelessly out of the reach of experiment. In the past two years we have realized that this does not have to be the case. If there are large new dimensions, in the next several years we could discover deviations from Newton's law near 6 x 10[sup-5] meter say, and we would detect stringy vibrations or black holes at the LHC. Quantum gravity and string theory would become testable science. Whatever happens, experiment will point the way to answering a 300-year-old question, and by 2010 we will have made decisive progress toward understanding why gravity is so weak. And we may find that we live in a strange Flatland, a membrane universe where quantum gravity is just around the corner.
IN A NUTSHELL
Dimensions. Our universe seems to have four dimensions: three of space (up-down, left-right, forward-backward) and one of time. Although we can barely imagine additional dimensions, mathematicians and physicists have long analyzed the properties of theoretical spaces that have any number of dimensions.
Size of dimensions. The four known space-time dimensions of our universe are vast. The dimension of time extends back at least 13 billion years into the past and may extend infinitely into the future. The three spatial dimensions may be infinite; our telescopes have detected objects more than 12 billion light-years away. Dimensions can also be finite. For example, the two dimensions of the surface of the earth extend only about 40,000 kilometers--the length of a great circle.
Small extra dimensions. Some modern physics theories postulate additional real dimensions that are wrapped up in circles so small (perhaps 10[sup-35]-meter radius) that we have not detected them. Think of a thread of cotton: to a good approximation, it is one-dimensional. A single number can specify where an ant stands on the thread. But using a microscope, we see dust mites crawling on the thread's two-dimensional surface: along the large length dimension and around the short circumference dimension.
Large extra dimensions. Recently physicists realized that extra dimensions as "big" as a millimeter could exist and remain invisible to us. Surprisingly, no known experimental data rule out the theory, and it could explain several mysteries of particle physics and cosmology. We and all the contents of our known three-dimensional universe (except for gravity) would be stuck on a "membrane," like pool balls moving on the two-dimensional green baize of a pool table.
Dimensions and gravity. The behavior of gravity--particularly its strength--is intimately related to how many dimensions it pervades. Studies of gravity acting over distances smaller than a millimeter could thus reveal large extra dimensions to us. Such experiments are under way. These dimensions would also enhance the production of bizarre quantum gravity objects such as micro black holes, graviton particles and superstrings, all of which could be detected sometime this decade at high-energy particle accelerators.
--Graham P. Collins, staff writer
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If (if ducks waddle then 5 is a prime) then (if (either Churchill drinks brandy or ducks waddle) then (either Churchill drinks brandy or 5 is a prime))
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