(PhysOrg.com) -- 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."

**Explore further:**
What is time?

**More information:**
The paper is titled "(Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows." www.springer.com/physics/journal/220

## maxcypher

"They were generated by singularities induced by the choice of the time coordinate, which are not present for physically admissible observables."

I can understand many of the more constrained concepts within the sentence, but when the sentence is contemplated as a whole, I get confused. =/

## Skeptic_Heretic

Still looks like word salad so the 5 cent version is:

We've mathematically shown that initially after the big bang the universe wobbled like a jello mold. The top got short while the sides blew out, then the sides contracted and the top balloned, etc.

Chaotic fluxuation is the situation initially after the "Big Bang".

Very interesting research.

## Noumenon

In GR certain measurable quantities are invariant, meaning the values are independent of the observer's coordinate system (like the square of the space time interval in Minkowski sp); are left the same under coordinate transformations. Other measurable quantities are dependent on the observer reference frame.

It appears to me, that they where able to "established the conditions under which the indicators of chaos are relativistic invariants", and in so doing explained why "Francisco and Matsas, found that different descriptions of the same events were leading to different conclusions about the chaotic nature of the early universe" (not relativistically invariant, a problem),.. because they [Francisco and Matsas events] where "generated by singularities induced by the choice of the time coordinate, which are not present for physically admissible observables."

## chandram

## MrPressure

Sep 08, 2010## hodzaa

Sep 08, 2010## hodzaa

Well, every stable object in it will be formed with transverse waves of 2cm in wavelength preferably. At both large, both small scales the transverse waves will disperse into longitudinal waves, which will be the more pronounced, the larger is the distance from observer.

## hodzaa

Actually our visual experience with observable Universe shouldn't differ conceptually from experience of hypothetical observer, sitting like bubble of 2cm in diameter at the water surface and detecting neighboring objects (i.e. bubbles or density fluctuations) via transverse waves there.

What such observer will see?

## hodzaa

At the larger distance from observer scale all objects will become gradually regular and symmetric (i.e. spherical). This is why both atoms and atom nuclei, both planets and stars are of roughly spherical shape. This intermediate distance scale is just the scope of validity of quantum mechanics and relativity theories, where our Universe can be described with simple set of rules.

But at even larger distance the regularity and symmetry of Universe will decrease again and very small or large objects will change into fuzzy unparticle objects again. These objects are observed in mostly longitudinal waves there, so they're lack sharp boundaries. They appear rather like density fluctuations inside of gas.

## hodzaa

This is because at the water surface the very small ripples are spreading in the same longitudinal way, like the very large ones. We can say, at the dimensional scales which are very distant from 2cm scale we will see our Universe from both inside, both outside perspective. At small scale all objects from outside will appear like very large objects from inside - and vice-versa. Recently physicists got the same insight with finding, elementary particles appear like tiny black holes, whereas whole Universe appears like interior of black hole. With using of water surface model you can IMAGINE, why is it so...

http://www.techno...v/23530/

http://www.tgdail...hysicist

## hodzaa

At this wavelength the laws of quantum mechanics are switching into laws of relativity and vice-versa. The gravity becomes repulsive force of radiation pressure bellow this size and the seeming expansion of Universe is replaced with seeming contraction here. The Lorentz symmetry is violated with refraction and dispersion and the inverse square law is violated in most pronounced way there due the presence of many composite forces, which are spreading in extradimensions, which are all around us.

This number of these extradimensions makes our Universe so complex just at the 2cm distance scale.

## marjon

What does this mean?

## danman5000

No, gravity does that.

## MrPressure

Sep 10, 2010## _nigmatic10

## frajo

## _nigmatic10

Sep 12, 2010## Graeme

## chandram

## exequus

## _nigmatic10