Universe chaotic from very beginning

Northwestern University ^ | September 7, 2010 | Unknown

[decimon]

Researchers show that the big bang was followed by chaos

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).

The paper is titled "(Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows."

[decimon]

Absolute chaos ping.

[AZLiberty]

When do we emerge from it?

[TigersEye]

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.

I don't theenk that word means what they theenk it means.

[fishtank]

“In the beginning God created the heavens and the earth.

Now the earth was formless and empty, darkness was over the surface of the deep.........”

Genesis 1:1-2

Hmmmmm.

Of course, God organized it all later ..... including the neurons of the average, just average, mind you, university physics professor.............

[SunkenCiv]

Thanks decimon.

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[Hoosier-Daddy]

The immutable is chaotic, as anything can come from it. It is neither logical or illogical. It encompasses ‘is’.

[csense]

Researchers show that the big bang was followed by chaos

Really? As opposed to what...the other big bang that was followed by order?

If what we have is the result of chaos, what exactly would be the result of order. An interesting question since the consequences would necessarily render the terms "chaos" and "order" incoherent.

[onedoug]

Nice try.

[samtheman]

I know I don’t know what the word (chaos) means, not in the context of this article. I don’t think it means entropy... can anybody clear this up?

What is the “chaos” being discussed here?

[TigersEye]

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.

In all seriousness I found those two statements to be contradictory. When I think of the word 'chaos' I don't even see entropy as a synonym as even the breaking down of an ordered system has a certain order to it. Chaos means to me no order whatsoever.

So how could something as perfectly ordered as a rigorous mathematical argument describe total disorder? Wouldn't all mathematical equations, even the simplest, fail to apply to true chaos by the very nature of those opposing concepts? I missed the boat here.

[E8crossE8]

Some folks have asked about the meaning of the word chaos in the quoted article. In the context used by the author of the paper referred to in the article, the word "chaos" has a very specific, technical meaning. This technical meaning of the word "chaos" is different from the regular usage in everyday speech - for instance the crappy chaos we see all around us caused by Obozo and the blithering idiots in the Congress who support/enable him is one usage of the word, but the way we use the word 'chaos' in physics is different.

In physics, the evolution of a physical system is determined by the solution(s) of an equation (or a system of equations) called the equation(s) of motion. For most interesting physical problems, the equations of motion are differential equations. In the case of those physical systems the evolution of which is determined by linear differential equations, the solutions to the equations, irrespective of whatever other characteristics they may or may not exhibit, do not exhibit the property of chaos. In those cases for which the equations of motion are nonlinear differential equations, it is sometimes the case that the solutions will exhibit the property of "chaos." This technical term means something specific: Associated to the equations of motion of a physical system is a mathematical "space" - the "place" in which the solutions to the equations evolve. This space is generically referred to as "phase space." Solutions of the equations of motion yield what are "trajectories" in this phase space. There is a particular type of technically-defined quantity, called the "Lyapunov exponent," associated to different such trajectories in phase space. For a given system of equations of motion, there is actually a set of Lyapunov exponents, called the Lyapunov spectrum. For this spectrum there is a largest (sometimes unique) Lyapunov exponent. Depending on the value of this largest Lyapunov exponent, the system is called "chaotic" or not. Specifically, if the largest Lyapunov exponent is a positive number, then the system is "chaotic" (most of the time - this is a very technical subject with a large number of qualifications that are not possible to go into in a blog.)

So much for a (partial) mathematical characterization. What does it mean qualitatively if a system has a largest Lyapunov exponent that is positive, and the system is thus (usually) chaotic? Roughly speaking, if a system is "chaotic" in the technical sense of physical dynamics, it means the following: if you let the system evolve under a given set of initial conditions, you will see a certain behavior: call this the "default behavior.". If you "nudge" the system a "little bit" (this roughly means that you only slightly alter the initial conditions on the solutions to the differential equations of motion), and if the system is chaotic, the result will be a BIG change in that default behavior. On the other hand, if the system is NOT chaotic, a "little nudge" will produce only a little change in the behavior of the solution. (Solutions describing non-chaotic systems, such as all solutions to systems described by linear differential equations of motion, do NOT behave this way: if you nudge things "a little," the solutions also only change "a little.") Another way of describing a system that exhibits chaos is to say that, in a chaotic system, two trajectories in phase space that are initially "very close" (this can be defined mathematically rigorously) together, will separate from each other exponentially quickly as a function of time in phase space.

[TigersEye]

Wow! that’s a great response. Thank you. If I have understood the essence of your explanation it is that ‘chaos’ (in the context you describe) is roughly synonymous with ‘instability.’ A ‘non-chaotic’ system is a relatively stable system.

[sadponies]

My guess is white noise. like when you put the tv on channel 3.

[E8crossE8]

Wow! that’s a great response. Thank you.

My pleasure.

If I have understood the essence of your explanation it is that ‘chaos’ (in the context you describe) is roughly synonymous with ‘instability.’ A ‘non-chaotic’ system is a relatively stable system.

Just as is the case for the word 'chaos,' the word ‘stability’ has a very technically specific meaning in physical dynamics. Rather than using the word stability, I would prefer to say that a chaotic system exhibits exquisitely sensitive dependence on the so-called boundary conditions to the solutions of the underlying equations of motion of the system. Phyiscal systems that are not chaotic are decribed by equations of motion the solutions of which do not exhibit such extreme sensitivity to boundary conditions. (“Boundary conditions” are constraints that need to be specified in order to obtain particular solutions to differential equations – unlike algebraic equations which don’t require additional information in the form of “boundary conditions” in order to be solved.)

[ The reason I want to avoid using the word 'stability’ here is that it is entirely possible for a non-chaotic system to exhibit an "unstable" solution. As an example, one way in which a perfectly non-chaotic physical system, such as one described by linear differential equations of motion, can possess an unstable solution is if a quantity called the "potential function" (this quantity is part of the equation of motion) is what is called "unbounded from below". ]

[TigersEye]

OK, I see your point. How about if I said ‘a chaotic system is a system in precarious balance a non-chaotic system has an “entrenched” (for lack of a better word) balance?’

[E8crossE8]

OK, I see your point. How about if I said ‘a chaotic system is a system in precarious balance a non-chaotic system has an “entrenched” (for lack of a better word) balance?’

That sounds like a perfectly good qualitative description - it captures the essence!

[TigersEye]

Thank you. I was just looking for a way to put it in layman’s terms. I loaned out my Physics for Dummies book and never got it back. ;^)

[AFPhys]

Excellent description of chaos.

The only thing that I’ll add is that in a chaotic system, after your “nudge”, the tiniest change in the initial conditions:
is extremely likely to result in the system at a relatively short, later time appearing very different from what the system would have appeared without the “nudge”.

[SunkenCiv]

Welcome to FR. :’)