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army1987 comments on Einstein's Arrogance - Less Wrong
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The Einstein field equation itself is actually extremely simple:
G = 8*pi*T
Sure, if we don't mind that G and T take a full page to write out in terms of the derivatives of the metric tensor. By this logic every equation is extremely simple -- it simply asserts that A=B for some A,B. :-)
Yeah, but there are only three objects you can write in terms of the metric tensor which transform the “right” way (G, T, and g itself). So the most general equation which satisfies those transformation laws is aG + bT + cg = 0.
Now, a is non-zero (otherwise you get an universe where there's no matter/energy other than “dark energy”), so by redefining b and c we have G + bT + cg = 0; b is negative (because things attract each other rather than repelling each other) and we call it -8piG/c^4 (it's just a matter of choice of units of measurement; we might as well set it to 1); and c is the cosmological constant.
I doubt that Scott will reply to this, 5 years later and on a different site, so let me try instead.
Hindsight bias? There are plenty of such objects. Google f(R) gravity, for example. There are also many different contractions of powers of products of R, T and G that fit. There is also torsion, and probably other things (supergravity and string theory tend to add a few).
You might want to argue that G=T is "the simplest", but it is anything but, for the reasons Scott explained. Once you find something that works, you call it G and T, write G=T and call it "simple". That's what Einstein did, since his first attempt, R=T, did not work out.
Interesting...