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.