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In theoretical physics Shape Dynamics is a theory of gravity that implements Mach's principle. Shape dynamics is dynamically equivalent to the canonical formulation of General Relativity, known as ADM formalism. Shape dynamics is not formulated as an implementation of spacetime diffeomorphism invariance, but as an implementation of spatial relationalism based spatial diffeomorphism- and spatial Weyl symmetry[1]. An important consequence of shape dynamics the absence of a problem of time in canonical quantum gravity.
Background edit
Mach's principle has been an important inspiration for the construction of general relativity, but the physical interpretation of Einstein's formulation of general relativity still requires external clocks and rods and thus fails to be manifestly relational[2]. Mach's principle would be fully implemented if the predictions of general relativity where independent of the choice of clocks and rods. Barbour and Bertotti conjectured that Jacobi's principle and a mechanism they called best matching where construction principles for a fully Machian theory[3]. Barbour implemented these principles in collaboration with Niall O Murchadha, Edward Anderson, Brendan Foster and Bryan Kelleher to derive the ADM formalism in constant mean curvature gauge[4]. This did not implement Mach's principle, because the predictions of general relativity in constant mean curvature gauge depend on the choice of clocks and rods. Mach's principle was successfully implemented by a group around Perimeter Institute researcher Tim Koslowski[5].
Shape dynamics principles edit
Construction of shape dynamics edit
The construction of shape dynamics requires trading refoliation invariance for spatial Weyl invariance and the identification of a parametrized dynamical system.
Relation with general relativity edit
Shape dynamics posses the same dynamics as general relativity, but has different gauge orbits[6]. The link between general relativity and shape dynamics can be established using the ADM formalism.
Consequences edit
Bibliography edit
- Background
- Construction of shape dynamics
- Gomes, Henrique; Koslowski, Tim (2012), "The Link between General Relativity and Shape Dynamics", Classical and Quantum Gravity, 29 (7), arXiv:1101.5974, doi:10.1088/0264-9381/29/7/075009
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- Gomes, Henrique; Koslowski, Tim (2012), "The Link between General Relativity and Shape Dynamics", Classical and Quantum Gravity, 29 (7), arXiv:1101.5974, doi:10.1088/0264-9381/29/7/075009
- Implications of shape dynamics
- Popular accounts
External Links edit
References edit
- ^ Barbour, Julian (2012). "Gravity as Machian Shape Dynamics" (PDF). fqxi talk.
- ^ Merali, Zeeya (2012). "Is Einstein's Greatest Work All Wrong—Because He Didn't Go Far Enough?". Discover magazine. Retrieved 4-10-2012.
{{cite web}}: Check date values in:|accessdate=(help) - ^ Barbour, Julian; Bertotti, Bruno (1982). "Mach's principle and the structure of dynamical theories" (PDF). Proceedings of the Royal Society (London) A. 382.
- ^ Anderson, Edward; Barbour, Julian; Foster, Brendan; Kelleher, Bryan; O Murchadha, Niall (2005). "The physical gravitational degrees of freedom". Classical and Quantum Gravity. 22.
- ^ Perimeter Institute (2011). "What if size really doesn't matter?". annual report 2011.
- ^ Gomes, Henrique; Koslowski, Tim (2012). "The Link between General Relativity and Shape Dynamics". Classical and Quantum Gravity. 29 (7). arXiv:1101.5974. doi:10.1088/0264-9381/29/7/075009.
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