I read the article What is a background-free theory? by John Baez and was wondering that if I add a fifth dimension to a background independent theory like general relativity I get a background dependent theory like the Maxwell's equations. The only difference: In Maxwell's equations you have electromagnetic fields. In five dimensions you have spacetime fields,- or spacetime-fluidflows or whatever you want to call it. I couldn't find good arguments against or in favor of this viewpoint.
Asked
Active
Viewed 216 times
2 Answers
1
By a five-dimensional extension of general relativity that unifies it with electromagnetism, you presumably mean Kaluza-Klein theory or something very similar. As explained here, K-K is indeed background-dependent; as with string theory decades later, this is considered a problem.
J.G.
- 25,615
1
A background consists of non-dynamical data for a theory. E.g. for field theories in curved spacetimes, the metric $g_{\mu\nu}$ is a non-dynamical fixed background. In contract, for general relativity in any spacetime dimension, the metric $g_{\mu\nu}$ is a dynamically active field, and hence not a background.
For the notion of background-independence, see e.g. Wikipedia.
Qmechanic
- 220,844