Invariant set postulate
The Invariant set postulate concerns the possible relationship between fractal geometry and quantum mechanics and in particular the hypothesis that the former can assist in resolving some of the challenges posed by the latter. It is underpinned by nonlinear dynamical systems theory and black hole thermodynamics.[1]
Overview
Climate scientist and physicist Tim Palmer (who works at the European Centre for Medium-Range Weather Forecasts and who had the same PhD supervisor as Stephen Hawking)[2] argues that the postulate may help to resolve some of the paradoxes of quantum mechanics that have been discussed since the Bohr–Einstein debates of the 1920s and 30s and which remain unresolved. The idea backs Einstein's view that quantum theory is incomplete, but also agrees with Bohr's contention that quantum systems are not independent of the observer.
The key idea involved is that if the Universe is a complex system affected by chaos then its invariant set (a fixed state of rest) is likely to be a fractal. According to Palmer this could resolve problems posed by the Kochen–Specker theorem, which appears to indicate that physics may have to abandon the idea of any kind of objective reality, and the apparent paradox of action at a distance. In a paper submitted to the Proceedings of the Royal Society he indicates how the idea can account for quantum uncertainty and problems of "contextuality".[2] For example, exploring the quantum problem of wave-particle duality, one of the central mysteries of quantum theory, the author claims that "in terms of the Invariant Set Postulate, the paradox is easily resolved, in principle at least".[1] The paper and a related talk given at the Perimeter Institute also explores the role of gravity in quantum physics.[1][3]
New Scientist quotes Bob Coeke of Oxford University as stating "What makes this really interesting is that it gets away from the usual debates over multiple universes and hidden variables and so on. It suggests there might be an underlying physical geometry that physics has just missed, which is radical and very positive".[2]
See also
References
- ^ a b c Palmer, T. N. (Submitted 5 December 2008) "The Invariant Set Postulate: A New Geometric Framework for the Foundations of Quantum Theory and the Role Played by Gravity". Cornell University Library. Retrieved 22 July 2009.
- ^ a b c Buchanan, Mark (30 March 2009) “Can fractals make sense of the quantum world?” New Scientist. No 2701. pp. 37–39.
- ^ Palmer, T. N. (21 October 2008) “Hawking Boxes and Invariant Sets - A New Look at the Foundations of Quantum Theory and the Associated Role of Gravity”. Perimeter Institute. PIRSA:08100022.