Chaotic gravitational waves
From Biocrawler, the free encyclopedia.
One proposed approach to reconciling the incompatibility between general relativity and quantum mechanics is to observe that gravitational waves in a chaotic n-body system would themselves be chaotic. It is possible to derive an uncertainty principle in general relativity as follows, which qualitatively resembles the Heisenberg uncertainty principle. The relativistic gravitational waves produced by a chaotic n-body system, with n equal to the number of massive particles in the observable universe, would cause each body to follow a deterministic but chaotic trajectory. To an observer not able to predict the chaotic gravitational waves impinging on a given particle, the particle’s location and velocity would appear stochastic. A known example of this behavior is the Brownian motion of black holes at a galactic center, due to n-body behavior (Laun and Merritt [1] (http://arxiv.org/abs/astro-ph/0408029)).
Chaotic gravitational waves would impose a constraint on any measurement, by jiggling any measurement equipment in an unpredictable way. An exact prediction in a chaotic system requires complete information about the system. However, the model for prediction is itself part of the chaotic system. The subset of the system used for prediction must incorporate a complete model of the entire system. Furthermore, to make predictions about events before they happen, the subsystem would need to prepare a forecast faster than the entire system itself evolves. This is clearly unlikely, although we do not have a formal proof. Thus, unless a relativistic n-body system can model itself locally, any observer that is part of that system will be constrained by an uncertainty principle.
In light of the above, non-locality, such as violations of the Bell inequality, appears to be a more fundamental point of tension between relativity and quantum mechanics. An n-body relativistic system is subject to the speed of light, and an observer capable of predicting the system’s behavior will not perceive any Bell violations except by coincidence or conspiracy. Nonetheless, a better understanding of how chaotic gravitational waves interact with the measurement equipment of an observer subject to the above uncertainty principle would help delineate which quantum phenomena might have gravitational explanations.
