1) Differential geometry is fairly hard — or at least fiddly with all the tensors and indices.

2) Even when you grasp it, it seems like you just know how to turn the mathematical crank. Without much geometrical or physical intutition.

I did not understand what the Ricci tensor was untill I read “The Meaning of Einstein’s Equation” here http://math.ucr.edu/home/baez/einstein/

]]>Anton I am referring to this for example

http://arxiv.org/abs/gr-qc/0411023 (which refers to 1970 paper

by Stanley Deser)

Feynman’s own work is outlined in his lectures on GR book (which came out in 1995)

Certainly! The point is to extend the superiority of complex analysis over 2D vector algebra into higher dimensions. The cost is loss of commutativity – but it is well worth it. (Quaternions are the 3D version.) You get a unified language that encompasses and improves on vector and tensor analysis, spinors, etc. Try the Cambridge trio’s paper “Imaginary Numbers Are not Real – the Geometric Algebra of Spacetime” in *Foundations of Physics* vol. 23, p1175-1201 (1993). This is one of several papers in which they recast the ideas of David Hestenes (the key man in this field) and set out what physics looks like in them. The one on emag is a stunner too. Or for fullest details the trio’s 2003 book “Geometric Algebra for Physicists” (Cambridge UP).

I’m not familiar with Feynman’s approach to GR so I can’t give a Yes/No answer, but I do know that people formulated GR as a gauge theory before the Cambridge trio (Anthony Lasenby, Chris Doran, Steve Gull) did. The earlier results were messy, however, and the trio found a much more natural gauge theory by working in Clifford Algebra. Their theory could of course be translated into conventional mathematical language, but they think – and I agree – that it is worth learning Clifford Algebra for much else in theoretical physics as well as this application. I’ll suggest why in my reply to Joseph’s question posed above at 12.07am on Nov 29, 2015. The Cambridge theory is set out in “Gravity, gauge theories and geometric algebra”, *Philosophical Transactions of the Royal Society of London A* vol. 356, pp. 487-582, 1998. The Cambridge theory involves two gauge fields obeying first order differential equations (not the metric which obeys 2nd order ones). I’d bet that more progress can be made quantising the Cambridge fields than the metric…

I confess I haven’t found Clifford algebra to be all that transparent. However, I’ve never taken a course in it and just relied on self-study from textbooks picked by what looked attractive on the university library shelf. Have you got a recommendation of one that makes Clifford algebras clear to the mathematically-trained-but-still-ignorant?

]]>Aha! I have heard terms such as gravitomagnetic and gravitoelectric, which may have something to do with the correspondence you are talking about.

]]>The unknown values are the metric tensors, that it is symmetric, but Bahram Mashhoon (for me the most complete explanation until now) use a linear perturbation of the Minkowski spacetime to obtain a low energy approximation of the Einstein field equation that are equations for scalar and vector potentials, from which he obtain equations for the electromagnetic fields, that are differential forms; so that it is not a direct correspondence between metric tensors and electromagnetic fields (if I understand precisely the analysis).

]]>Yes, of course space is something. Basically, “there is no Ether” means that this ‘something’ is very different from any medium like water or air.

]]>Well at least on the surface they are different as the main unknown in the Einstein equations is a symmetric (metric) tensor, and the fields in the Maxwell equations are differential forms (or vector fields). But I think there are reformulations of these equations that make them look similar.

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