MAPPA della PAGINA: The MYTH of the BEGINNING of TIME... Agg. 17.09.2004
Ci sono domande che sembrano non avere età. Esistono, infatti, sin da quando Homo sapiens ha lasciato documenti scritti sulla natura circostante. Hanno cambiato forma di generazione in generazione: ma la loro sostanza è un'invariante dei nostri codici di comprensione, e tale rimane anche nei periodi in cui questi codici subiscono mutamenti forti. Nell'età di Galilei si stampavano immagini in cui un essere umano cercava di far passare un'asticciola o una mano al di là dei confini dell'universo. E l'immagine conteneva un quesito che ancora oggi permane nel senso comune: ovvero, se il cosmo ha un confine, quali cose popolano lo spazio situato al di là del confine stesso ? Nel 383 a.C. nasceva a Stagira il grande Aristotele, secondo il quale il mondo non aveva avuto un principio. Il cosmo era eterno, e non aveva allora senso parlare di un istante iniziale prima del quale non fosse esistito il tempo. Anche oggi, quando qualcuno parla dell'Universo in espansione, molte persone si chiedono che cosa c'era prima del big bang, e dove stava. E quando si dice "prima","che cosa" e "dove", si evocano il tempo, la materia e lo spazio. Come aveva scritto Einstein, nel nostro linguaggio siamo abituati a usare queste tre parole come nomi di entità che si possono pensare come se fossero tra loro indipendenti. Ed è noto che, a suo avviso, avremmo dovuto invece imparare a dire, più semplicemente, che "il mondo è, e non diviene". Una lezione difficile da apprendere, anche nella chiave ottimistica per cui, come Einstein annotava, la scienza èun affinamento del senso comune, anche quando ci appare da esso estranea. Se ora torniamo al big bang, incappiamo in buone ragioni per credere che si stiano aprendo nuovi scenari post-einsteniani.
String theory suggests that the big bang was not the origin of the universe but simply the outcome of a preexisting state.
Was
the big
bang really the beginning of time
? Or did the universe exist before
then ? Such a question
seemed almost blasphemous only a decade ago.
Most cosmologists insisted that it simply made
no sense--that to contemplate a time before the
big
bang was like asking for directions to a place north of the
North Pole. But developments
in theoretical physics, especially the rise of
string theory, have changed their
perspective. The pre-bang universe has become
the latest frontier of cosmology. The new willingness to consider
what might have happened before the bang
is the latest swing of an intellectual pendulum that has rocked back and forth
for millennia. In one form or another, the issue of the ultimate beginning has
engaged philosophers and theologians in nearly every culture. It is entwined
with a grand set of concerns, one famously encapsulated in an
1897 painting by Paul
Gauguin: "D'ou
venons-nous ? Que sommes-nous
? Ou allons-nous ?"
["Where
do we come from ? What are we
? Where are we going ?"]
The piece depicts the cycle of birth, life
and death--origin, identity and destiny for each
individual--and these personal concerns connect directly to cosmic
ones. We can trace our lineage back through the generations, back through our
animal ancestors, to early forms of life and protolife,
to the elements synthesized in the primordial universe, to
the amorphous energy deposited in space before that. Does
our family tree extend forever backward ? Or
do its roots terminate ? Is the
cosmos as impermanent as we are ? The ancient
Greeks debated the origin of time fiercely. Aristotle,
taking the no-beginning side, invoked the principle
that out of nothing, nothing comes. If the universe could never have
gone from nothingness to somethingness, it must always have existed. For this
and other reasons, time must stretch eternally into the past
and future. Christian theologians tended to
take the opposite point of view. Augustine
contended that God exists
outside of space and time, able
to bring these constructs into existence as surely as he could forge other aspects
of our world. When asked, "What
was God doing before he created the world ?"
Augustine
answered, "Time
itself being part of God's creation, there was simply no before!".
NOTE: String Theory: Symmetry in Multiple Dimensions: Two theories currently shape the world of physics: quantum mechanical theory, which involves small particles, and gravitational theory, which involves large particles. Physicists and mathematicians are currently trying to unify the two theories into an all-encompassing quantum theory, called string theory, that can account for the four main forces: gravity, electromagnetism, the strong force and the weak force (1) A theory of particle physics, the Standard Theory, seeks to unify the latter three, while string theory goes one step farther: trying to also incorporate a quantum theory of gravity. Theoretical calculations on the currently-favored string theory postulate that the strong and weak forces come together at temperatures that are eighteen orders of magnitude above what physicists can currently experiment with using particle accelerators (2). This property of string theory makes it hard to confirm through the use of experimental physics. String theory attempts to explain the universe in terms of tiny, vibrating, "strings" that represent the fundamental particles postulated by the Standard Theory of particle physics: bosons, which are force-carrying particles like photons, and muons, particles that make up matter such as the electron (3). These vibrating strings are quantum mechanical entities that can exist in different states. They can be closed or open-ended and can have different modes of vibration, similar to how a guitar string can vibrate differently depending on how and where you pluck it. The different vibrational states of the strings correspond to the particles. To account for these strings, a theory called superstring theory postulates that space and time exist in ten dimensions. Six of the ten dimensions are compactified: they are curled up on themselves on very small scales (on the order of 10-33 cm) (1,4). The other four consist of what we traditionally think of as space (the three spatial dimensions) and time. However, while superstring theory is a good start, it fails to explain cosmological observations, leaving mathematicians and theoretical physicists searching for a new postulate. The current prevailing string theory, called M-Theory (5), came after what scientists refer to as the "second superstring revolution." It proposes an eleven-dimensional space that consists of objects with multiple dimensions called p-branes. One type of p-brane is the d-brane, which can be related to the end points of the strings. Another string theory postulates a twenty-six dimensional space (3). Yet another seeks to use a five-dimensional space to describe the universe. The mathematical principles and equations associated with these theories are all extremely complex and difficult for the average undergraduate to understand. However, the essence of string theory is easier to understand. Theoretical physicists are still searching for the proper theory to unify gravity and quantum mechanics, and leading experts in the field believe it will take many more years and many different incarnations to get there. If and when it is discovered, string theory will most likely include symmetry, indicating that all times and spatial locations are described by the same fundamental physical principles (6). It could also involve extra dimensions of space that form a compact space (7), a property that the theories proposed so far (superstring theory, M-theory, etc.) have used. Experimental evidence will be important in confirming string theory. The super-symmetry involved in the theory postulates that the vibrations that correspond to the fundamental particles come in pairs that differ in their spin properties. The Standard Theory also predicts these partner particles, which have not been experimentally found yet. There is hope that they will be found when a new high-energy particle accelerator, the Large Hadron Collider (LHC), opens in Geneva, Switzerland in 2007 (6). Other researchers are looking to black holes for experimental evidence for string theory. Scientists have postulated the existence of theoretical black holes, called gedanken black holes, which are composed of d-branes. One property of d-branes is that their electromagnetic repulsion and gravitational attraction cancel each other out, allowing researchers to combine them into larger objects, some of which are reminiscent of black holes (2). Both string theory and the theory of general relativity agree when appropriate boundary constraints are applied to these systems, giving physicists hope that they are closer to being able to verify string theory by experiment. Black holes mostly involve gravitational force, and according to Maldacena's conjecture, "a quantum theory with gravity and strings in a given space is completely equivalent to an ordinary quantum system without gravity that lives on the boundary of that space" (2). Black holes constitute these ordinary quantum systems, and while they have not provided any breakthroughs on the nature of string theory, they do represent a real-life system that can be studied to give clues about string theory (2). Over the past thirty years, string theory has seen many forms. When it reaches its final form, physicists expect it to include symmetry and multiple dimensions, while it might not look like anything yet proposed. Since string theory can only be empirically confirmed at high energies that are many orders of magnitude above what we can currently probe experimentally, it has been tested only theoretically. If it holds up experimentally as well, physics finally will have a theory to describe all particles, including (and replacing) the currently unrelated quantum mechanical and general relativity theories.
Suggested Reading
1. D. Kestenbaum. "Practical Tests for an 'Untestable' Theory of Everything ?" (1998) Science 281, 758-9.
2. G. Taubes. "String Theorists Find a Rosetta Stone." (1999) Science 285, 512-7.
3. Schwarz, Patricia. Home page. supers-tringt heory 14 Nov. 2001.
4. G. Gibbons. "Brane-Worlds." Science 287 (2000), 49-50.
5. E. Witten. "Overview of K-theory applied to strings." (2001) International Journal of Modern Physics A 16, 693-706.
6. B. Greene. "The Elegant Universe." Vintage Books: New York, 1999.
7. J. H. Schwarz. "The Future of String Theory." (2001) Journal of Mathematical Physics 42, 2889-2895.
8. I.Ya. Aref'eva, K.S. Viswanathan,
I.V. Volovich "p-Brane
Solutions in Diverse Dimensions"
(1996)
hep-th/9609225
Two Views of the Beginning: In our expanding universe, galaxies rush away from one another like a dispersing mob. Any two galaxies recede at a speed proportional to the distance between them: a pair 500 million light-years apart separates twice as fast as one 250 million light-years apart. Therefore, all the galaxies we see must have started from the same place at the same time -the big bang. The conclusion holds even though cosmic expansion has gone through periods of acceleration and deceleration; in spacetime diagrams (right), galaxies follow sinuous paths that take them in and out of the observable region of space (yellow wedge). The situation became uncertain, however, at the precise moment when the galaxies (or their ancestors) began their outward motion.
Einstein's general theory of relativity led modern cosmologists to much the same conclusion. The theory holds that space and time are soft, malleable entities. On the largest scales, space is naturally dynamic, expanding or contracting over time, carrying matter like driftwood on the tide. Astronomers confirmed in the 1920s that our universe is currently expanding: distant galaxies move apart from one another. One consequence, as physicists Stephen Hawking and Roger Penrose proved in the 1960s, is that time cannot extend back indefinitely. As you play cosmic history backward in time, the galaxies all come together to a single infinitesimal point, known as a singularity -almost as if they were descending into a black hole. Each galaxy or its precursor is squeezed down to zero size. Quantities such as density, temperature and spacetime curvature become infinite. The singularity is the ultimate cataclysm, beyond which our cosmic ancestry cannot extend.
DIGRESSIONE...
11.02.2003 A Recycled Universe
Crashing branes and cosmic acceleration may power an infinite cycle in which our universe is but a phase.
A UNIVERSAL CYCLE of birth and rebirth occurs every trillion years or so, according to one new cosmology. Big bangs result when two 10-dimensional "branes" collide and expand and then collide again. In this scenario, our universe marks just one phase in this infinite cycle. Some questions are disquieting because they can be answered in only one of two equally mind-boggling ways. For instance, are we the sole intelligent beings in the universe, or will we find others ? Another discomforting doozy is this: did the universe begin at some remote time in the past, or was it always here ? The big bang clearly marks some kind of first. That fearsome flash of energy and expansion of space set in motion everything our eyes and telescopes can see today. But on its own, the big bang theory would leave us in a curved universe where matter and energy aren't well mixed. In fact, we now know that spacetime is flat and that galaxies and radiation are evenly distributed throughout. To shore up the big bang theory, cosmologists proposed that the universe began with a burst of exponential expansion from a single uniform patch of space, whose stamp remains on the cosmos to this day. Such inflationary cosmologies have worked so well they've crowded out all the competition. During this past year, however, one group of researchers has started to challenge that idea's preeminence, though the field of cosmology has yet to be completely taken with the new approach. Drawing on some cutting-edge but unproved notions in particle physics, the challengers interpret the big bang as a violent clash between higher-dimensional objects. In the latest installment to the saga, the authors of this interpretation have found a way to turn that single clash into a never-ending struggle that rears its fiery head every trillion years or so, making our universe just one phase in an infinite cycle of birth and rebirth. Such cyclic ideas are not new. In the 1930s, the late Richard Tolman of the California Institute of Technology wondered what would happen if a closed universe -in which all matter and energy are ultimately compacted in a big crunch- were to survive its closure and burst forth again. Unfortunately, as Tolman realized, the universe would gather entropy during each new cycle; to compensate, it would have to grow every time like a runaway snowball. And just as a snowball has to begin at some point in time, so, too, would such a universe. Then in the 1960s, physicists proved that a big crunch, too, must culminate in a singularity -a point stuffed with infinite matter and heat- where general relativity breaks down. The laws of physics are thus up for grabs. The idea of a cyclic universe has been around for a long time and it has always been plagued by a fundamental problem: what physics causes the collapsing universe to bounce back into the expanding phase ?
String-ularity
One potential way of getting around that problem is by supposing that elementary particles such as electrons, photons and quarks are really just manifestations of tiny strings of energy jiggling in higher dimensions. The thing is, such a string theory requires the universe to have at least 10 dimensions, as opposed to the usual three in space and one in time that we perceive. In string theory you learn one thing -you are in higher dimensions. Then the question is, where does our real world come from ? That's a damn good question. Paving the way for an answer in 1995 were Petr Horava, then at Princeton University, and Ed Witten of Princeton's Institute for Advanced Studies, who showed that strings could also exist in a more fundamental, 11-dimensional theory. They collapsed one of these dimensions mathematically into a minuscule line, yielding an 11-dimensional spacetime, flanked on either side by two 10-dimensional membranes, or branes, colorfully dubbed "end of the world" branes. One brane would have physical laws like our own universe. From there, Ovrut and colleagues reasoned that six of those 10 dimensions could be made extremely small, effectively hiding them from everyday view and leaving the traditional four dimensions of space and time. Early in 2001, cosmologists Justin Khoury and Paul Steinhardt of Princeton, another inflationary pioneer, Neil Turok of the University of Cambridge, and Ovrut put their branes to work on the big bang. By turning back the clock in string theory, they found that as our universal brane passed through its starting singularity in reverse, it went suddenly from a state of intense but finite heat and density to one that was cold, flat and mostly empty. In the process, it shed another kind of brane into the 11-dimensional gap. Run forward in time, the big bang appeared as nothing more than two branes smacking into each other like cymbals. They christened this process the ekpyrotic model, after the ancient Greek "conflagration" cosmology wherein the universe is born in and evolves from a fiery explosion.Without a better understanding of the singularity in string theory, however, the group could not study what would happen as our brane expands after the collision; the model only provided for a contracting universe. Then later last year, the group discovered in collaboration with Nathan Seiberg of the Institute for Advanced Study that the singularity could be interpreted as a collision between the two "end of the world" branes, in which only the gap dimension separating them shrinks down to zero for an instant. So what looks sort of disastrously singular, when you describe it as a brane collision, is not very singular at all. This scenario remains a conjecture but is mathematically identical to the description of the big bang singularity in general relativity. The ekpyrotic model had seemed a little contrived up to this point, notes Alan Guth of the Massachusetts Institute of Technology (MIT), another author of inflation. The pre-bang universe had to be dark, flat and infinite, seemingly by fiat. But why should it have begun in such a state ? The answer, according to the latest work from Steinhardt and Turok, has to do with dark energy, the force that is driving the galaxies apart at ever-increasing speeds.
Drained Branes
As the universe accelerates, it will become harder for light to travel between distant corners of space. Over time, galaxies will become isolated from their neighbors; stars will wink out; black holes will evaporate quantum mechanically into radiation; even that radiation will be diluted in a sea of space. The universe could end up much as the ekpyrotic model suggests it should appear before the big bang. Steinhardt and Turok accordingly have proposed that the dark energy, combined with the milder singularity of the ekpyrotic model, provides a tidy way of setting up a cyclic universe. Our brane and its counterpart would bounce off each other as usual, but instead of going their separate ways, they would smack each other again and again as if connected by a spring. This attractive force between branes would in fact be a special case of the kind of force that inflationary cosmologies posit to explain the early universe's blowup. The branes' oscillating motion would work to pump space into our universe like a bellows, explaining the acceleration that we see today. So when you ask why is the universe the way it is well, it's because it has to be that way in order to repeat the next time around. And because each brane is already infinitely large and flat, there would be no first cycle to worry about. The model is intriguing in drawing the ultimate link between early inflation and the current acceleration of the universe, but the case would be a lot more compelling if they were able to really show that a cyclic universe is possible. Guth [Alan Guth, professore al Massachussetts Institute of Technology (MIT) di Cambridge, autore della teoria "inflazionaria" pubblicata nel 1980 che ipotizza un'espansione dell'Universo estremamente rapida.] is also unmoved. He explains that although he awaits the day when cosmology merges with string theory, he expects inflation to be that cosmology. In general, not all physicists are convinced that colliding branes can generate the small fluctuations in matter and energy density that inflation neatly resolves. Such minute variations in these quantities are required to explain the way in which stars and galaxies clump together and the detailed properties of the cosmic microwave background radiation. In the ekpyrotic model, the necessary fluctuations are supposed to arise as the branes ripple quantum mechanically, so that different areas would strike one another and take off expanding first. The ekpyrotic camp is convinced these ripples can generate the exact variations we see today. I think it's surprising how well this model works in terms of reproducing everything we see and yet being so different. That's quite shocking and, I think, important, because we thought we were converging toward something that was a unique cosmic story. But the singularity remains as another hurdle. Despite the recent advance, no one is certain whether features such as brane ripples could actually pass unmolested from big crunch to bang. What happens at the singularity ? This is a big open question. So although the singularity in string theory may be, as Turok says, the "mildest possible" one, it is still a wild card. The dealing isn't done, however, making it too soon to say if colliding branes will hold or fold. Perhaps it will attract new players with even more imaginative ideas. I happen to think the cyclic model is a real intriguing one. It has a lot of new ingredients that people haven't had a chance to play with. When they play they might find other interesting things that we missed. Or not.
FINE DIGRESSIONE
The unavoidable singularity poses serious problems for cosmologists. In particular, it sits uneasily with the high degree of homogeneity and isotropy that the universe exhibits on large scales. For the cosmos to look broadly the same everywhere, some kind of communication had to pass among distant regions of space, coordinating their properties. But the idea of such communication contradicts the old cosmological paradigm.To be specific, consider what has happened over the 13.7 billion years since the release of the cosmic microwave background radiation. The distance between galaxies has grown by a factor of about 1,000 (because of the expansion), while the radius of the observable universe has grown by the much larger factor of about 100,000 (because light outpaces the expansion). We see parts of the universe today that we could not have seen 13.7 billion years ago. Indeed, this is the first time in cosmic history that light from the most distant galaxies has reached the Milky Way. Nevertheless, the properties of the Milky Way are basically the same as those of distant galaxies. It is as though you showed up at a party only to find you were wearing exactly the same clothes as a dozen of your closest friends. If just two of you were dressed the same, it might be explained away as coincidence, but a dozen suggests that the partygoers had coordinated their attire in advance. In cosmology, the number is not a dozen but tens of thousands -the number of independent yet statistically identical patches of sky in the microwave background. One possibility is that all those regions of space were endowed at birth with identical properties -in other words, that the homogeneity is mere coincidence. Physicists, however, have thought about two more natural ways out of the impasse: the early universe was much smaller or much older than in standard cosmology. Either (or both, acting together) would have made intercommunication possible. The most popular choice follows the first alternative. It postulates that the universe went through a period of accelerating expansion, known as inflation, early in its history. Before this phase, galaxies or their precursors were so closely packed that they could easily coordinate their properties. During inflation, they fell out of contact because light was unable to keep pace with the frenetic expansion. After inflation ended, the expansion began to decelerate, so galaxies gradually came back into one another's view. Physicists ascribe the inflationary spurt to the potential energy stored in a new quantum field, the inflaton, about 10-35 second after the big bang. Potential energy, as opposed to rest mass or kinetic energy, leads to gravitational repulsion. Rather than slowing down the expansion, as the gravitation of ordinary matter would, the inflaton accelerated it. Proposed in 1981, inflation has explained a wide variety of observations with precision [see "The Inflationary Universe," by Alan H. Guth and Paul J. Steinhardt; Scientific American, May 1984; and "Four Keys to Cosmology," Special report; Scientific American, February]. A number of possible theoretical problems remain, though, beginning with the questions of what exactly the inflaton was and what gave it such a huge initial potential energy. A second, less widely known way to solve the puzzle follows the second alternative by getting rid of the singularity. If time did not begin at the bang, if a long era preceded the onset of the present cosmic expansion, matter could have had plenty of time to arrange itself smoothly. Therefore, researchers have reexamined the reasoning that led them to infer a singularity. One of the assumptions--that relativity theory is always valid--is questionable. Close to the putative singularity, quantum effects must have been important, even dominant. Standard relativity takes no account of such effects, so accepting the inevitability of the singularity amounts to trusting the theory beyond reason. To know what really happened, physicists need to subsume relativity in a quantum theory of gravity. The task has occupied theorists from Einstein onward, but progress was almost zero until the mid-1980s.
Today two approaches stand out. One, going by the name of loop quantum gravity, retains Einstein's theory essentially intact but changes the procedure for implementing it in quantum mechanics [see "Atoms of Space and Time," by Lee Smolin; Scientific American, January]. Practitioners of loop quantum gravity have taken great strides and achieved deep insights over the past several years. Still, their approach may not be revolutionary enough to resolve the fundamental problems of quantizing gravity. A similar problem faced particle theorists after Enrico Fermi introduced his effective theory of the weak nuclear force in 1934. All efforts to construct a quantum version of Fermi's theory failed miserably. What was needed was not a new technique but the deep modifications brought by the electroweak theory of Sheldon L. Glashow, Steven Wein-berg and Abdus Salam in the late 1960s. The second approach, which I consider more promising, is string theory--a truly revolutionary modification of Einstein's theory. This WEB-page will focus on it, although proponents of loop quantum gravity claim to reach many of the same conclusions.
String theory grew out of a model to describe the world of nuclear particles (such as protons and neutrons) and their interactions. Despite much initial excitement, the model failed. It was abandoned several years later in favor of quantum chromodynamics, which describes nuclear particles in terms of more elementary constituents, quarks. Quarks are confined inside a proton or a neutron, as if they were tied together by elastic strings. In retrospect, the original string theory had captured those stringy aspects of the nuclear world. Only later was it revived as a candidate for combining general relativity and quantum theory. The basic idea is that elementary particles are not pointlike but rather infinitely thin one-dimensional objects, the strings. The large zoo of elementary particles, each with its own characteristic properties, reflects the many possible vibration patterns of a string. How can such a simple-minded theory describe the complicated world of particles and their interactions ? The answer can be found in what we may call quantum string magic. Once the rules of quantum mechanics are applied to a vibrating string--just like a miniature violin string, except that the vibrations propagate along it at the speed of light--new properties appear. All have profound implications for particle physics and cosmology. First, quantum strings have a finite size. Were it not for quantum effects, a violin string could be cut in half, cut in half again and so on all the way down, finally becoming a massless pointlike particle. But the Heisenberg uncertainty principle eventually intrudes and prevents the lightest strings from being sliced smaller than about 10-34 meter. This irreducible quantum of length, denoted ls, is a new constant of nature introduced by string theory side by side with the speed of light, c, and Planck's constant, h. It plays a crucial role in almost every aspect of string theory, putting a finite limit on quantities that otherwise could become either zero or infinite. Second, quantum strings may have angular momentum even if they lack mass. In classical physics, angular momentum is a property of an object that rotates with respect to an axis. The formula for angular momentum multiplies together velocity, mass and distance from the axis; hence, a massless object can have no angular momentum. But quantum fluctuations change the situation. A tiny string can acquire up to two units of h of angular momentum without gaining any mass. This feature is very welcome because it precisely matches the properties of the carriers of all known fundamental forces, such as the photon (for electromagnetism) and the graviton (for gravity). Historically, angular momentum is what clued in physicists to the quantum-gravitational implications of string theory. Third, quantum strings demand the existence of extra dimensions of space, in addition to the usual three. Whereas a classical violin string will vibrate no matter what the properties of space and time are, a quantum string is more finicky. The equations describing the vibration become inconsistent unless spacetime either is highly curved (in contradiction with observations) or contains six extra spatial dimensions. Fourth, physical constants--such as Newton's and Coulomb's constants, which appear in the equations of physics and determine the properties of nature--no longer have arbitrary, fixed values. They occur in string theory as fields, rather like the electromagnetic field, that can adjust their values dynamically. These fields may have taken different values in different cosmological epochs or in remote regions of space, and even today the physical "constants" may vary by a small amount. Observing any variation would provide an enormous boost to string theory. One such field, called the dilaton, is the master key to string theory; it determines the overall strength of all interactions. The dilaton fascinates string theorists because its value can be reinterpreted as the size of an extra dimension of space, giving a grand total of 11 spacetime dimensions.
Finally, quantum strings have introduced physicists to some striking new symmetries of nature known as dualities, which alter our intuition for what happens when objects get extremely small. I have already alluded to a form of duality: normally, a short string is lighter than a long one, but if we attempt to squeeze down its size below the fundamental length ls, the string gets heavier again. Another form of the symmetry, T-duality, holds that small and large extra dimensions are equivalent. This symmetry arises because strings can move in more complicated ways than pointlike particles can. Consider a closed string (a loop) located on a cylindrically shaped space, whose circular cross section represents one finite extra dimension. Besides vibrating, the string can either turn as a whole around the cylinder or wind around it, one or several times, like a rubber band wrapped around a rolled-up poster. The energetic cost of these two states of the string depends on the size of the cylinder. The energy of winding is directly proportional to the cylinder radius: larger cylinders require the string to stretch more as it wraps around, so the windings contain more energy than they would on a smaller cylinder. The energy associated with moving around the circle, on the other hand, is inversely proportional to the radius: larger cylinders allow for longer wavelengths (smaller frequencies), which represent less energy than shorter wavelengths do. If a large cylinder is substituted for a small one, the two states of motion can swap roles. Energies that had been produced by circular motion are instead produced by winding, and vice versa. An outside observer notices only the energy levels, not the origin of those levels. To that observer, the large and small radii are physically equivalent. Although T-duality is usually described in terms of cylindrical spaces, in which one dimension (the circumference) is finite, a variant of it applies to our ordinary three dimensions, which appear to stretch on indefinitely. One must be careful when talking about the expansion of an infinite space. Its overall size cannot change; it remains infinite. But it can still expand in the sense that bodies embedded within it, such as galaxies, move apart from one another. The crucial variable is not the size of the space as a whole but its scale factor--the factor by which the distance between galaxies changes, manifesting itself as the galactic redshift that astronomers observe. According to T-duality, universes with small scale factors are equivalent to ones with large scale factors. No such symmetry is present in Einstein's equations; it emerges from the unification that string theory embodies, with the dilaton playing a central role. For years, string theorists thought that T-duality applied only to closed strings, as opposed to open strings, which have loose ends and thus cannot wind. In 1995 Joseph Polchinski of the University of California at Santa Barbara realized that T-duality did apply to open strings, provided that the switch between large and small radii was accompanied by a change in the conditions at the end points of the string. Until then, physicists had postulated boundary conditions in which no force acted on the ends of the strings, leaving them free to flap around. Under T-duality, these conditions become so-called Dirichlet boundary conditions, whereby the ends stay put. Any given string can mix both types of boundary conditions. For instance, electrons may be strings whose ends can move around freely in three of the 10 spatial dimensions but are stuck within the other seven. Those three dimensions form a subspace known as a Dirichlet membrane, or D-brane. In 1996 Petr Horava of the University of California at Berkeley and Edward Witten of the Institute for Advanced Study in Princeton, N.J., proposed that our universe resides on such a brane. The partial mobility of electrons and other particles explains why we are unable to perceive the full 10-dimensional glory of space.
All the magic properties of quantum strings point in one direction: strings abhor infinity. They cannot collapse to an infinitesimal point, so they avoid the paradoxes that collapse entails. Their nonzero size and novel symmetries set upper bounds to physical quantities that increase without limit in conventional theories, and they set lower bounds to quantities that decrease. String theorists expect that when one plays the history of the universe backward in time, the curvature of spacetime starts to increase. But instead of going all the way to infinity (at the traditional big bang singularity), it eventually hits a maximum and shrinks once more. Before string theory, physicists were hard-pressed to imagine any mechanism that could so cleanly eliminate the singularity. Conditions near the zero time of the big bang were so extreme that no one yet knows how to solve the equations. Nevertheless, string theorists have hazarded guesses about the pre-bang universe. Two popular models are floating around.
The first, known as the pre-big bang scenario, combines T-duality with the better-known symmetry of time reversal, whereby the equations of physics work equally well when applied backward and forward in time. The combination gives rise to new possible cosmologies in which the universe, say, five seconds before the big bang expanded at the same pace as it did five seconds after the bang. But the rate of change of the expansion was opposite at the two instants: if it was decelerating after the bang, it was accelerating before. In short, the big bang may not have been the origin of the universe but simply a violent transition from acceleration to deceleration. The beauty of this picture is that it automatically incorporates the great insight of standard inflationary theory--namely, that the universe had to undergo a period of acceleration to become so homogeneous and isotropic. In the standard theory, acceleration occurs after the big bang because of an ad hoc inflaton field. In the pre-big bang scenario, it occurs before the bang as a natural outcome of the novel symmetries of string theory. According to the scenario, the pre-bang universe was almost a perfect mirror image of the post-bang one. If the universe is eternal into the future, its contents thinning to a meager gruel, it is also eternal into the past. Infinitely long ago it was nearly empty, filled only with a tenuous, widely dispersed, chaotic gas of radiation and matter. The forces of nature, controlled by the dilaton field, were so feeble that particles in this gas barely interacted. As time went on, the forces gained in strength and pulled matter together. Randomly, some regions accumulated matter at the expense of their surroundings. Eventually the density in these regions became so high that black holes started to form. Matter inside those regions was then cut off from the outside, breaking up the universe into disconnected pieces. Inside a black hole, space and time swap roles. The center of the black hole is not a point in space but an instant in time. As the infalling matter approached the center, it reached higher and higher densities. But when the density, temperature and curvature reached the maximum values allowed by string theory, these quantities bounced and started decreasing. The moment of that reversal is what we call a big bang. The interior of one of those black holes became our universe. Not surprisingly, such an unconventional scenario has provoked controversy. Andrei Linde of Stanford University has argued that for this scenario to match observations, the black hole that gave rise to our universe would have to have formed with an unusually large size--much larger than the length scale of string theory. An answer to this objection is that the equations predict black holes of all possible sizes. Our universe just happened to form inside a sufficiently large one. A more serious objection, raised by Thibault Damour of the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France, and Marc Henneaux of the Free University of Brussels, is that matter and spacetime would have behaved chaotically near the moment of the bang, in possible contradiction with the observed regularity of the early universe. I have recently proposed that a chaotic state would produce a dense gas of miniature "string holes"--strings that were so small and massive that they were on the verge of becoming black holes. The behavior of these holes could solve the problem identified by Damour and Henneaux. A similar proposal has been put forward by Thomas Banks of Rutgers University and Willy Fischler of the University of Texas at Austin. Other critiques also exist, and whether they have uncovered a fatal flaw in the scenario remains to be determined.
Observing
the pre-bang universe may sound like a hopeless task, but
one form of radiation could survive from that epoch: gravitational radiation.
These periodic variations in the gravitational field might be detected indirectly,
by their effect on the polarization of the cosmic
microwave background (simulated
view, left), or directly,
at ground-based observatories. The pre-big bang and ekpyrotic
scenarios predict more high-frequency gravitational
waves and fewer low-frequency ones than do conventional
models of inflation (chart).
Existing measurements of various astronomical phenomena cannot distinguish
among these models, but upcoming observations by the Planck
satellite as well as the LIGO
and VIRGO observatories
should be able to.
The other leading model for the universe before the bang is the ekpyrotic ("conflagration") scenario. Developed three years ago by a team of cosmologists and string theorists--Justin Khoury of Columbia University, Paul J. Steinhardt of Princeton University, Burt A. Ovrut of the University of Pennsylvania, Nathan Seiberg of the Institute for Advanced Study and Neil Turok of the University of Cambridge--the ekpyrotic scenario relies on the idea that our universe is one of many D-branes floating within a higher-dimensional space. The branes exert attractive forces on one another and occasionally collide. The big bang could be the impact of another brane into ours.In a variant of this scenario, the collisions occur cyclically. Two branes might hit, bounce off each other, move apart, pull each other together, hit again, and so on. In between collisions, the branes behave like Silly Putty, expanding as they recede and contracting somewhat as they come back together. During the turnaround, the expansion rate accelerates; indeed, the present accelerating expansion of the universe may augur another collision. The pre-big bang and ekpyrotic scenarios share some common features. Both begin with a large, cold, nearly empty universe, and both share the difficult (and unresolved) problem of making the transition between the pre- and the post-bang phase. Mathematically, the main difference between the scenarios is the behavior of the dilaton field. In the pre-big bang, the dilaton begins with a low value--so that the forces of nature are weak--and steadily gains strength. The opposite is true for the ekpyrotic scenario, in which the collision occurs when forces are at their weakest. The developers of the ekpyrotic theory initially hoped that the weakness of the forces would allow the bounce to be analyzed more easily, but they were still confronted with a difficult high-curvature situation, so the jury is out on whether the scenario truly avoids a singularity. Also, the ekpyrotic scenario must entail very special conditions to solve the usual cosmological puzzles. For instance, the about-to-collide branes must have been almost exactly parallel to one another, or else the collision could not have given rise to a sufficiently homogeneous bang. The cyclic version may be able to take care of this problem, because successive collisions would allow the branes to straighten themselves. Leaving aside the difficult task of fully justifying these two scenarios mathematically, physicists must ask whether they have any observable physical consequences. At first sight, both scenarios might seem like an exercise not in physics but in metaphysics--interesting ideas that observers could never prove right or wrong. That attitude is too pessimistic. Like the details of the inflationary phase, those of a possible pre-bangian epoch could have observable consequences, especially for the small variations observed in the cosmic microwave background temperature. First, observations show that the temperature fluctuations were shaped by acoustic waves for several hundred thousand years. The regularity of the fluctuations indicates that the waves were synchronized. Cosmologists have discarded many cosmological models over the years because they failed to account for this synchrony. The inflationary, pre-big bang and ekpyrotic scenarios all pass this first test. In these three models, the waves were triggered by quantum processes amplified during the period of accelerating cosmic expansion. The phases of the waves were aligned. Second, each model predicts a different distribution of the temperature fluctuations with respect to angular size. Observers have found that fluctuations of all sizes have approximately the same amplitude. (Discernible deviations occur only on very small scales, for which the primordial fluctuations have been altered by subsequent processes.) Inflationary models neatly reproduce this distribution. During inflation, the curvature of space changed relatively slowly, so fluctuations of different sizes were generated under much the same conditions. In both the stringy models, the curvature evolved quickly, increasing the amplitude of small-scale fluctuations, but other processes boosted the large-scale ones, leaving all fluctuations with the same strength. For the ekpyrotic scenario, those other processes involved the extra dimension of space, the one that separated the colliding branes. For the pre-big bang scenario, they involved a quantum field, the axion, related to the dilaton. In short, all three models match the data. Third, temperature variations can arise from two distinct processes in the early universe: fluctuations in the density of matter and rippling caused by gravitational waves. Inflation involves both processes, whereas the pre-big bang and ekpyrotic scenarios predominantly involve density variations. Gravitational waves of certain sizes would leave a distinctive signature in the polarization of the microwave background [see "Echoes from the Big Bang," by Robert R. Caldwell and Marc Kamionkowski; Scientific American, January 2001]. Future observatories, such as European Space Agency's Planck satellite, should be able to see that signature, if it exists--providing a nearly definitive test.
MORE TO EXPLORE:
The Elegant Universe.
Brian Greene. W W. Norton,
1999.
Superstring Cosmology. James E.Lidsey, David
Wands and Edmund J.Copeland in Physics
Reports, Vol. 337, Nos. 4-5,
pages 343-492; October 2000.
hep-th/9909061.
From Big Crunch to Big Bang. Justin Khoury, Burt
A.Ovrut, Nathan Seiberg, Paul J.Steinhardt
and Neil Turok in Physical Review
D, Vol. 65, No. 8,
Paper no. 086007; April 15,
2002. hep-th/0108187.
A Cyclic Model of the Universe. Paul J.Steinhardt
and Neil Turok in Science, Vol.
296, No. 5572, pages
1436-1439; May 24, 2002.
hep-th/0111030.
The Pre–Big Bang Scenario in String Cosmology. Maurizio
Gasperini and Gabriele Veneziano in Physics
Reports, Vol. 373, Nos.
1-2, pages 1-212; January
2003. hep-th/0207130.
Utenti connessi...:
CHANDRAst
