Does the Higgs Mechanism contradict Entropic Gravity?
It seems like it probably does. But then again, one is a microscopic theory and the other is macroscopic. Can they live together in harmony? or is the recent CERN stuff empirical evidence against EG?
It's a common misconception to think that because the Higgs mechanism is the origin of mass it is also the origin of gravity. This is a misconception because the origin of gravity is not simply mass. Instead it's a quantity called the stress-energy tensor. The stress-energy tensor is usually represented as a 4 $\times$ 4 matrix containing 10 independant entries (10 not 16 because the matrix is symmetric) and in most cases the only significant entry is the top left one, $T_{00}$, which gives the energy density.
The key point is that as far as the stress-energy tensor is concerned mass and energy are the same thing related by Einstein's famous equation $E = mc^2$.
Immediately before the electroweak transition all particles were massless, and immediately after they had a finite mass, but this change didn't make any difference to the stress-energy tensor and therefore to gravity. Before and after the transition the energy density was the same (well similar anyway) so the contribution of the particles to the stress-energy tensor and therefore to gravity was the same.
So there is no contradiction between the Higgs mechanism and the idea of entropic gravity.
