Is EM theory in curved spacetime the same as "unification"?by pellman Tags: curved, spacetime, theory, unification 

#1
Mar1010, 04:31 PM

P: 565

I am wanting to learn about classical EM theory in curved spacetime (just curious) and I found this old thread containing some references http://www.physicsforums.com/showthread.php?t=3950
Anyway, I'd be interested if further recommended on this topic as well. 



#2
Mar1010, 05:18 PM

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#3
Mar1010, 06:17 PM

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PF Gold
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I found the following online:
http://en.wikipedia.org/wiki/Classic...field_theories Hubert F. M. Goenner, "On the History of Unified Field Theories," http://www.livingreviews.org/lrr20042 Eddington, "Space, time and gravitation: an outline of the general relativity theory," http://books.google.com/books?id=uU1...age&q=&f=false I thought the chapter from the Eddington book (which was written for a general audience) was very readable. As the WP article makes clear, there have been many decades worth of attempts in the direction of classical unified theories, and many different approaches have been tried. Therefore it's probably not possible to make categorical statements about all of them. But in the case of Weyl's theory, described in the Eddington book, the flavor of what they're trying to accomplish is not that they want to be able to create a selfconsistent theory that includes both gravity and electromagnetism; that was already accomplished as soon as GR was published. They wanted to explain things like why the classical electron radius has the value it does, and why spacetime is fourdimensional. They also wanted to make E&M fully geometrical, rather than throwing it into the source terms of the Einstein field equations. According to Goenner, there were hopes of making a theory in which electrons and protons (the only fundamental particles known at the time) would pop out of the theory naturally, rather than having to be put in by hand. 



#4
Mar1010, 06:36 PM

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Is EM theory in curved spacetime the same as "unification"?
If anyone wants to read Eddington's description of the Weyl theory and discuss it, I'd be interested in talking about it. One thing that seems odd to me about it is the following. He posits that parallel transport around a closed path can change a vector's length. This seems to me to be different in an important way from the usual GR idea that transport around a closed path can change a vector's direction. Let's call the length effect L and the direction effect D. D works the same for all vectors, regardless of what type of vector it is. But it seems to me that the same can't be true for L. L involves changing a scalar. Suppose every scalar were to change by the same amount on transport around a given loop  regardless of the type of scalar. This rapidly leads to a mathematical contradiction, since for any scalar x, 1/x is also a scalar, but you can't have x and 1/x both scale the same way. As far as I can tell, L can therefore apply only to norms of spacetime displacement vectors, i.e., to metersticks and clocks. To me, this seems ugly and contrary to the purely geometrical spirit of parallel transport in normal GR.




#5
Mar1010, 06:39 PM

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#6
Mar1010, 06:46 PM

P: 647

You can look these up on Wikipedia, and maybe this isnt what you are looking for, but here are Maxwell's equations in curved spacetime.
[tex]\frac{\partial F_{\rho\sigma}}{\partial x_{\tau}}+\frac{\partial F_{\sigma\tau}}{\partial x_{\rho}}+\frac{\partial F_{\tau\rho}}{\partial x_{\sigma}}=0[/tex] and [tex]\frac{\partial}{\partial x_{\nu}}\left(\sqrt{g}g^{\mu\alpha}g^{\nu\beta}F_{\alpha\beta}\right)=\mathcal{J}^{\mu}[/tex] these are two of my favorites of all time! 



#7
Mar1010, 08:52 PM

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#8
Mar1110, 04:37 AM

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Where's the best place to read about this theory ? There are at least two ways that do work, curvature and torsion, in GR and translational gauge gravity ( aka Teleparallel). In both of these theories the deficit is a wedge product i.e. a commutator product. There are probably mathematical reasons why a scalar deficit can't work as a repository of gravity. 



#9
Mar1110, 10:25 AM

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#10
Mar1110, 06:28 PM

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#11
Mar1110, 08:24 PM

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Now I know that someone is going to say that which one we choose is arbitrary. But that's not so obvious to me. One of them may more obviously coincide with what we think of as the EM field. I'm just beginning to look at this so none of it is obvious to me. 



#12
Mar1210, 09:51 AM

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#13
Mar1210, 09:55 AM

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#14
Mar1310, 05:53 AM

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Thanks for the replies. Very helpful.



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