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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.

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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.

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  • $\begingroup$ Thanks I will read through the mentioned article. "..., this is considered a problem." I read exactly the same thing multiple times. Also related to the string theory view of quantum gravity. For example in: Making Starships and Stargates, James F. Woodward expressed the same concerns, that the string theory gravity view, is not background-independent? But then if you can draw/embed a 2d wormhole in flat 3 dimensions, why can't you draw a 4d wormhole in 5 dimensions? Also teleparallel gravity seems to indicate that the answer is not as easy as it may appear at first glance. $\endgroup$ – v217 Dec 3 '16 at 22:20
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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.

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