Background independence

Background independence is a condition in theoretical physics, especially in quantum gravity (QG), that requires the defining equations of a theory to be independent of the actual shape of the spacetime and the value of various fields within the spacetime, and in particular to not refer to a specific coordinate system or metric. The different configurations (or backgrounds) should be obtained as different solutions of the underlying equations.

Manifest background-independence

This is primarily an aesthetic rather than a physical requirement. It is analogous to requiring in differential geometry that equations be written in a form that is independent of the choice of charts and coordinate embeddings. If a background-independent formalism is present, it can lead to simpler and more elegant equations. However there is no physical content in requiring that a theory be manifestly background-independent - for example, the equations of general relativity can be rewritten in local coordinates without affecting the physical implications.

Theories of quantum gravity

String theory

String theory is usually formulated with perturbation theory around a fixed background. While it is possible that the theory defined this way is background-invariant, if so it is not manifest. One attempt to formulate string theory in a manifestly background-independent fashion is string field theory, but little progress has been made in understanding it.

Another approach is the AdS/CFT duality, which is believed to provide a full, non-perturbative definition of string theory in spacetimes with anti-de Sitter asymptotics. If so, this could describe a kind of superselection sector of the putative full, background-independent theory. A full non-perturbative definition of the theory in arbitrary spacetime backgrounds is still lacking.

Loop quantum gravity

A very different approach to quantum gravity called loop quantum gravity has been claimed to be background-independent. However, this theory has difficulty reproducing Einstein's theory of general relativity. Furthermore, the physics of loop quantum gravity is only background-independent in a weak sense. For example, it requires a fixed choice of the topology and dimensionality of the spacetime, while any consistent quantum theory of gravity should include topology change as a dynamical process. Topology change is an established process in string theory.

See also

• General relativity
• String theory
• Causal dynamical triangulation
• Loop quantum gravity
• Quantum field theory

External links

• Comments on Background Independence and gauge Redundancies
• The case for background independence

References

• L. Smolin, The case for background independence, hep-th/0507235
• C. Rovelli et al., Background independence in a nutshell, Class.Quant.Grav. 22 (2005) 2971-2990, gr-qc/0408079
• Edward Witten, Quantum Background Independence In String Theory, hep-th/9306122.
• J. Stachel, The Meaning of General Covariance: The Hole Story, in J. Earman, A. Janis, G. Massey and N. Rescher (eds.), Philosophical Problems of the Internal and External Worlds: Essays on the Philosophy of Adolf Grünbaum, University of Pittsburgh Press 1993, ISBN 0-8229-3738-7, pp. 129–160.
• J. Stachel, Changes in the Concepts of Space and Time Brought About by Relativity, in C. C. Gould and R. S. Cohen (eds.), Artifacts, Representations and Social Practice; Kluwer Academic 1994, ISBN 0-7923-2481-1, pp. 141–162.
• E. Zahar, Einstein's Revolution: A Study in Heuristic, ISBN 0-8126-9066-4