Big Bang Was Followed by Chaos, Mathematical Analysis Shows

ScienceDaily (Sep. 8, 2010) — Seven years ago Northwestern University physicist Adilson E. Motter conjectured that the expansion of the universe at the time of the big bang was highly chaotic. Now he and a colleague have proven it using rigorous mathematical arguments.

The study, published by the journal Communications in Mathematical Physics, reports not only that chaos is absolute but also the mathematical tools that can be used to detect it. When applied to the most accepted model for the evolution of the universe, these tools demonstrate that the early universe was chaotic.

Certain things are absolute. The speed of light, for example, is the same with respect to any observer in the empty space. Others are relative. Think of the pitch of a siren on an ambulance, which goes from high to low as it passes the observer. A longstanding problem in physics has been to determine whether chaos -- the phenomenon by which tiny events lead to very large changes in the time evolution of a system, such as the universe -- is absolute or relative in systems governed by general relativity, where the time itself is relative.

A concrete aspect of this conundrum concerns one's ability to determine unambiguously whether the universe as a whole has ever behaved chaotically. If chaos is relative, as suggested by some previous studies, this question simply cannot be answered because different observers, moving with respect to each other, could reach opposite conclusions based on the ticks of their own clocks.
"A competing interpretation has been that chaos could be a property of the observer rather than a property of the system being observed," said Motter, an author of the paper and an assistant professor of physics and astronomy at Northwestern's Weinberg College of Arts and Sciences. "Our study shows that different physical observers will necessarily agree on the chaotic nature of the system."

The work has direct implications for cosmology and shows in particular that the erratic changes between red- and blue-shift directions in the early universe were in fact chaotic.

Motter worked with colleague Katrin Gelfert, a mathematician from the Federal University of Rio de Janeiro, Brazil, and a former visiting faculty member at Northwestern, who says that the mathematical aspects of the problem are inspiring and likely to lead to other mathematical developments.

An important open question in cosmology is to explain why distant parts of the visible universe -- including those that are too distant to have ever interacted with each other -- are so similar.

"One might suggest 'Because the large-scale universe was created uniform,'" Motter said, "but this is not the type of answer physicists would take for granted."

Fifty years ago, physicists believed that the true answer could be in what happened a fraction of a second after the big bang. Though the initial studies failed to show that an arbitrary initial state of the universe would eventually converge to its current form, researchers found something potentially even more interesting: the possibility that the universe as a whole was born inherently chaotic.

The present-day universe is expanding and does so in all directions, Motter explained, leading to red shift of distant light sources in all three dimensions -- the optical analog of the low pitch in a moving siren. The early universe, on the other hand, expanded in only two dimensions and contracted in the third dimension.

This led to red shift in two directions and blue shift in one. The contracting direction, however, was not always the same in this system. Instead, it alternated erratically between x, y and z.

"According to the classical theory of general relativity, the early universe experienced infinitely many oscillations between contracting and expanding directions," Motter said.

"This could mean that the early evolution of the universe, though not necessarily its current state, depended very sensitively on the initial conditions set by the big bang."

This problem gained a new dimension 22 years ago when two other researchers, Gerson Francisco and George Matsas, found that different descriptions of the same events were leading to different conclusions about the chaotic nature of the early universe. Because different descriptions can represent the perspectives of different observers, this challenged the hypothesis that there would be an agreement among different observers. Within the theory of general relativity, such an agreement goes by the name of a "relativistic invariant."

"Technically, we have established the conditions under which the indicators of chaos are relativistic invariants," Motter said. "Our mathematical characterization also explains existing controversial results. They were generated by singularities induced by the choice of the time coordinate, which are not present for physically admissible observables."

Motter also is an assistant professor of engineering sciences and applied mathematics at the McCormick School of Engineering and Applied Science, a member of the executive committee of the Northwestern Institute on Complex Systems (NICO) and a member of the Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA).

Story Source:
The above story is reprinted (with editorial adaptations by ScienceDaily staff) from materials provided by Northwestern University, via EurekAlert!, a service of AAAS.
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Journal Reference:
1.Katrin Gelfert, Adilson E. Motter. (Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows. Communications in Mathematical Physics, 2010; DOI: 10.1007/s00220-010-1120-x

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Record Set for Speedy Protons

By DENNIS OVERBYE
Published: March 19, 2010

The world’s largest particle accelerator is feeling its oats. Scientists at CERN, the European nuclear research agency, announced Friday morning that they had accelerated beams of protons at the accelerator, the Large Hadron Collider near Geneva, to energies of 3.5 trillion electron volts. That is a new record, three times the energy of any other machine on earth, and means that the collider, after 15 years and $10 billion, is on the verge of beginning to do physics experiments. Physicists hope to begin colliding the beams by the end of the month. The machine was designed to accelerate protons to 7 trillion electron volts and crash them together in search of particles and forces last seen in the Big Bang, but it is riddled with thousands of flawed electrical splices and underperforming magnets, which will require a year’s shutdown in 2012 to fix.

A Primer on the Great Proton Smashup

By DENNIS OVERBYE
Published: April 2, 2010

For those whose physics knowledge was a bit rusty, the news about the Large Hadron Collider, the world's biggest physics machine, might have been puzzling.



Yes, the collider finally crashed subatomic particles into one another last week, but why, exactly, is that important? Here is a primer on the collider - with just enough information, hopefully, to impress guests at your next cocktail party.

Let’s be basic. What does a particle physicist do?

Particle physicists have one trick that they do over and over again, which is to smash things together and watch what comes tumbling out.

What does it mean to say that the collider will allow physicists to go back to the Big Bang? Is the collider a time machine?

Physicists suspect that the laws of physics evolved as the universe cooled from billions or trillions of degrees in the first moments of the Big Bang to superfrigid temperatures today (3 degrees Kelvin) — the way water changes from steam to liquid to ice as temperatures decline. As the universe cooled, physicists suspect, everything became more complicated. Particles and forces once indistinguishable developed their own identities, the way Spanish, French and Italian diverged from the original Latin.

By crashing together subatomic particles — protons — physicists create little fireballs that revisit the conditions of these earlier times and see what might have gone on back then, sort of like the scientists in Jurassic Park reincarnating dinosaurs.

The collider, which is outside Geneva, is 17 miles around. Why is it so big?

Einstein taught us that energy and mass are equivalent. So, the more energy packed into a fireball, the more massive it becomes. The collider has to be big and powerful enough to pack tremendous amounts of energy into a proton.

Moreover, the faster the particles travel, the harder it is to bend their paths in a circle, so that they come back around and bang into each other. The collider is designed so that protons travel down the centers of powerful electromagnets that are the size of redwood trunks, which bend the particles’ paths into circles, creating a collision. Although the electromagnets are among the strongest ever built, they still can’t achieve a turning radius for the protons of less than 2.7 miles.

All in all, the bigger the accelerator, the bigger the crash, and the better chance of seeing what is on nature’s menu.

What are physicists hoping to see?

According to some theories, a whole list of items that haven’t been seen yet — with names like gluinos, photinos, squarks and winos — because we haven’t had enough energy to create a big enough collision.

Any one of these particles, if they exist, could constitute the clouds of dark matter, which, astronomers tell us, produce the gravity that holds galaxies and other cosmic structures together.

Another missing link of physics is a particle known as the Higgs boson, after Peter Higgs of the University of Edinburgh, which imbues other particles with mass by creating a cosmic molasses that sticks to them and bulks them up as they travel along, not unlike the way an entourage forms around a rock star when they walk into a club.

Have scientists ever seen dark matter?

It’s invisible, but astronomers have deduced from their measurements of galactic motions that the visible elements of the cosmos, like galaxies, are embedded in huge clouds of it.

Will physicists see these gluinos, photinos, squarks and winos?

There is no guarantee that any will be discovered, which is what makes science fun, as well as nerve-racking.

So how much energy do you need to create these fireballs?

At the Large Hadron Collider, that energy is now 3.5 trillion electron volts per proton — about as much energy as a flea requires to do a pushup. That may not sound like much, but for a tiny proton, it is a lot of energy. It is the equivalent of a 200-pound man bulking up by 700,000 pounds.

What’s an electron volt?

An electron volt is the amount of energy an electron would gain passing from the negative to the positive side of a one-volt battery. It is the basic unit of energy and of mass preferred by physicists.

When protons collide, is there a big bang?

There is no sound. It’s not like a bomb exploding.

In previous trials, there was an actual explosion.

All that current is dangerous. During the testing of the collider in September 2008, the electrical connection between a pair of the giant magnets vaporized. There are thousands of such connections in the collider, many of which are now believed to be defective. As a result the collider can only run at half-power for the next two years.

Could the collider make a black hole and destroy the Earth?

The collider is not going to do anything that high-energy cosmic rays have not done repeatedly on Earth and elsewhere in the universe. There is no evidence that such collisions have created black holes or that, if they have, the black holes have caused any damage. According to even the most speculative string theory variations on black holes, the Large Hadron Collider is not strong enough to produce a black hole.

Too bad, because many physicists would dearly like to see one.

This article has been revised to reflect the following correction:


Correction: April 11, 2010

Because of an editing error, an article last Sunday about the Large Hadron Collider referred incorrectly to the cooling effect of the Big Bang. It was the universe — not the Earth — that the Big Bang caused to coolfrom billions or trillions of degrees to superfrigid temperatures today.
A version of this article appeared in print on April 4, 2010, on page WK3 of the New York edition.

European Collider Begins Its Subatomic Exploration

In a control room, a scientist toasted the start of the Large Hadron Collider outside Geneva on Tuesday.
By DENNIS OVERBYE
Published: March 30, 2010

PASADENA, Calif. — After 16 years and $10 billion — and a long morning of electrical groaning and sweating — there was joy in the meadows and tunnels of the Swiss-French countryside Tuesday: the world’s biggest physics machine, the Large Hadron Collider, finally began to make subatomic particles collide.

After two false starts due to electrical failures, protons that were whipped to more than 99 percent of the speed of light and to record-high energy levels of 3.5 trillion electron volts apiece raced around a 17-mile underground magnetic track outside Geneva a little after 1 p.m. local time. They crashed together inside apartment-building-size detectors designed to capture every evanescent flash and fragment from microscopic fireballs thought to hold insights into the beginning of the universe.

The soundless blooming of proton explosions was accompanied by the hoots and applause of scientists crowded into control rooms at CERN, the European Organization for Nuclear Research, which built the collider. The relief spread to bleary-eyed gatherings of particle physicists around the world, who have collectively staked the future of their profession on the idea that the collider will eventually reveal new secrets of the universe.

Among their top goals are finding the identity of the dark matter that shapes the visible cosmos and the strange particle known as the Higgs boson, which is thought to imbue other particles with mass. Until now, these have been tantalizingly out of reach.

“We’re expecting some answers,” said David Politzer, a Nobel laureate and professor at the California Institute of Technology, where a conference room overflowed with Los Angeles-area physicists attending a midnight remote viewing, with refreshments including matzos, chips and pizza.

Rolf-Dieter Heuer, director general of CERN, speaking from Japan, said the new collider “opens a new window of discovery and it brings, with patience, new knowledge of the universe and the microcosm.”

“It shows what one can do in bringing forward knowledge,” he said, adding, “It will also bring out an army of children and young people who will get into the private sector and academia.”

“We are all proud and so happy,” Fabiola Gianotti, a spokeswoman for CERN, said of one of the giant particle detectors at the collider, known as Atlas.

Guido Tonelli, spokesman for a rival detector called C.M.S., said, “We are really starting physics.”

The success in producing proton collisions represents a remarkable comeback for CERN, but the lab is still only halfway back to where it wanted to be. Only a year and a half ago, the first attempt to start the collider ended with an explosion that left part of its tunnel enveloped in frigid helium gas and soot when an electrical connection between two of the powerful magnets that steer the protons vaporized.

A subsequent investigation revealed that the collider was riddled with thousands of such joints, a result of what Lucio Rossi, head of magnets at CERN, said was a “lack of adequate risk analysis,” in a recent report in the online journal Superconductor Science and Technology. As a result, the collider, which was designed to accelerate protons to seven trillion electron volts, then smash them together to reveal particles and forces that reigned during the first trillionth of a second of time as we know it, can only be safely run for now at half power.

CERN physicists say that operating the collider for a year and a half at this energy level should allow them to gather enough data to start catching up with its American rival, the trillion-electron-volt Tevatron at the Fermi National Accelerator Laboratory in Illinois. The Tevatron is smaller but has been running for years and thus has a head start in data. After that, the CERN machine will be shut down for a year so that the connections can be rebuilt.

Particle colliders get their oomph from Einstein’s equation of mass and energy. The more energy — denoted in the physicists’ currency of choice, electron volts — that these machines can pack into their little fireballs, the farther back in time they can go, closer and closer to the Big Bang, and the smaller and smaller are the things they can see.

The first modern accelerator was the cyclotron, built by Ernest Lawrence at the University of California, Berkeley, in the 1930s. An early version was a foot in diameter and accelerated protons to energies of 1.25 million electron volts.

Over the last century, universities and then nations leapfrogged each other, building bigger machines to peer deeper into the origins of the universe. But the race ended in 1993, when Congress canceled the Superconducting Supercollider, a 54-mile, 20 trillion-electron-volt machine being built underneath Waxahachie, Tex., after its projected cost ballooned to $11 billion.

The following year, CERN approved its own big collider. CERN, a 20-nation consortium that grew from the ashes of World War II, has provided a template for other pan-European organizations like the European Space Agency and the European Southern Observatory. With a budget and dues established by treaty, the organization enjoys a long-term stability that is the envy of American labs. Last winter, Europe took the lead for good when test collisions at the Hadron collider achieved energies of 1.18 trillion electron volts.

The collider first ramped up its beams to 3.5 trillion electron volts two weeks ago, but the engineers took pains to prevent them from colliding so as not to steal the thunder from what was billed as First Physics Day on Tuesday.

Because of the defective joints and some mysteriously underperforming magnets, it will still be three years at least before CERN’s collider runs at or near full strength. According to theoretical models, that would stretch out the time it should take to achieve the collider’s main goals, like producing the Higgs boson and testing more exotic ideas like extra dimensions.

Until then, the Tevatron will chase CERN for big goals like the Higgs boson, physicists say. The CERN experimenters will spend the next four to six months learning how their detectors work and rediscovering known physics. Then, anything is possible.

“It’s very exciting because we are entering a new energy range,” said Harvey Newman, a Caltech professor who works on the C.M.S. experiment. “We’re looking at all kinds of exotic things,” he said, including signs of extra dimensions. The possibilities begin between the middle and end of this year.”

Michael Barnett, a physicist from the Lawrence Berkeley National Laboratory, said that he had worked on an experiment for the Superconducting Supercollider for 10 years until the project was canceled by Congress, and later spent 16 years on the Atlas experiment at the CERN collider.

“We are on this planet and in this universe a short time,” he wrote in an e-mail message. “The dreams of a lifetime are waiting, and hopefully not much longer.”

Correction: An earlier version of this article incorrectly identified Fabiola Gianotti as a spokesman for CERN. She is a spokeswoman.