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Jens 'n' Frens
Idle thoughts of a relatively libertarian Republican in Cambridge, MA, and whomever he invites. Mostly political.
"A strong conviction that something must be done is the parent of many bad measures."
-- Daniel Webster
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Tuesday, December 02, 2003 :::
I'm going to prepend a comment, because this is likely to leave some readers on the curb. Relativity suggests that any particular choice of time frame is arbitrary; chaos theory, however, defines in particular one very important parameter in terms of the time-evolution of a system. (So does quantum mechanics, hence much of the trouble of modern physics. But I digress.) The concern was that ambiguity in the concept of time would lead to systems that could be considered chaotic in some reference frames but not in others. It turns out they can't. Now, believe it or not, this is where I was going to start this post:Relativistic chaos is coordinate invariant The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. This has been further supported by the well known results that mixing is coordinate dependent and Lyapunov exponents in a cosmological model can be made positive or zero for different time parametrizations. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion regarding the noninvariance of chaos in cosmology, a major claim about chaos in general relativity, necessarily involves the violation of hypotheses required for a proper definition of the Lyapunov exponents.
::: posted by dWj at 5:42 PM
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