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In quantum systems the behaviour of a simple Hydrogen's electron is tightly bound to its proton and the atom can only absorb random amounts of energy. In a strong magnetic field the orbit of the electron increases in size as the electron moves away from the Proton called a Rydberg atom. In Classical systems behaviour is explained by classical mechanics combined with perturbation theory which accounts for the small irregularities in regular systems which do not have too many interacting variables. In Chaotic Systems behaviour is unpredictable because uncertainty about initial starting conditions results in a total loss of information on the systems state, almost identical beginnings can diverge very quickly to completely different futures. In a deterministic sense this is suggesting that events wouldn't be random if the initial starting conditions were known. Such systems with complicated patterns and unknown beginnings can only be studied with holistic theories which ignore the fine detail and monitor regularities and patterns. Complexity theory attempts to study the apparent anti-thesis of chaos, organised complexity in the form of biological systems.
Quantum Weirdness refers to the dual particle/wave nature of matter that sub atomic particles are measurable only in probability terms by mass or momentum not both and that the observer affects the sub atomic particles by trying to measure them. Larger macroscopic objects such as people and planets can have their own quantum waves the length of the wave decreasing with increased movement and mass. Einstein was upset by Heisenberg's Uncertainty principle to remark "God does not play dice with the universe". Quantum weirdness suggests that even if all the starting conditions of a system could be known its behaviour could only be measured by probability statistics (it is this % or that%) and putting it under the microscope could be changing the whole system under study. Studying large systems with many interacting variables requires a tool such as complexity theory.
Large interactive systems naturally evolve towards a critical point when a minor event precipitates major change. Vast systems such as globular clusters galaxies or even solar systems have many interacting elements (Gravity Inverse square law, chemistry electromagnetic radiation, energy and momentum of moving bodies) Complex systems on earth are subject to major change and fluctuations when a small event causes a chain reaction which affects many or every element in the system. Systems are relatively categorised as:
Critical with many sizes of chain reaction.
Sub critical low density systems with small chain reactions.
Super critical high density systems where small reactions can change the whole system.
In measuring the dynamics of a system, random result over a period of time indicates the system is not influenced by past events,
alternatively large variations between the size of the impetus and the resulting consequence indicates the system is strongly
influenced by prior events.This is especially true for natural biological systems where a small change in environmental
conditions or a small genetic mutation may mean life or death for a species. Evolution operates on the boarder of chaos with
life and death consequences for the winners and losers.
A List of some chaotic events.