# Maxwell's equations and spacetime

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1. Feb 7, 2014

### DarthMatter

Hi,

I'm just beginning to learn relativity, but I have a question about why gravity is so different from other forces of nature in GR. As a start, I read that Einstein tried to find a differential geometric representation of the physical universe which represents the Maxwell equations in a similiar way that the curvature of spacetime in GR represents gravitation - but failed. Could someone elaborate on that, or point me to sources where I can read more about it?

Thanks in advance.

2. Feb 7, 2014

### Bill_K

IMHO you'd be better off spending your time learning about correct theories rather than incorrect ones!

3. Feb 7, 2014

### Mentz114

Try Googling 'Kaluza-Klein theory'. It goes some way towards this.

4. Feb 7, 2014

### strangerep

+1 for what Bill_K said.

Those alternate theories have long been discredited. Don't waste your time, at least not until you've mastered modern GR in all its g[l]ory detail.

5. Feb 7, 2014

### WannabeNewton

We can cast EM in a differential geometric light, in fact we can cast all gauge theories in a differential geometric light. The upshot is that the "gauge covariant derivative" $D_{\mu} = \partial_{\mu} + ie A_{\mu}$ used in EM isn't associated with a physical space-time but rather with the more abstract concept of a $U(1)$-principal bundle, whereas the covariant derivative $\nabla_{\mu}$ in GR is of course associated with a physical space-time.

See here: http://www.nikhef.nl/~t45/ftip/Ch11.pdf and here: http://www.theorie.physik.uni-goettingen.de/~tedesco/files/connections.pdf [Broken]

Last edited by a moderator: May 6, 2017
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