Comment on Einstein's Arrogance

Fri, 03 Aug 2012 23:00:37 GMT

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.

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.

Discuss