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.
Time line of the Universe. (Credit: NASA)
The study, published by the journalCommunications 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.
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Communications in Mathematical Physics
(Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows
Katrin Gelfert and Adilson E. Motter
Abstract
We study how dynamical quantities such as Lyapunov exponents, metric entropy, topological pressure, recurrence rates, and dimension-like characteristics change under a time reparameterization of a dynamical system. These quantities are shown to either remain invariant, transform according to a multiplicative factor or transform through a convoluted dependence that may take the form of an integral over the initial local values. We discuss the significance of these results for the apparent non-invariance of chaos in general relativity and explore applications to the synchronization of equilibrium states and the elimination of expansions.
Communicated by G. Gallavotti
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Katrin Gelfert é professora da UFRJ.
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