Why Are Force Unification Scales Different in Physics?

[navigator]

Since the coupling strengths of strong force,weak force and electromagnetic force meet at the scale of 10^16 GeV,then why weak force and electromagnetic force are unified at the scale of 10^2 GeV? We may see the two coupling strengths' curves are not intersect at this scale... And further,why unification scale of GUT force and gravity (10^19 GeV) is not equal to GUT scale(10^16 GeV)?

 

[blechman]

Since the coupling strengths of strong force,weak force and electromagnetic force meet at the scale of 10^16 GeV,then why weak force and electromagnetic force are unified at the scale of 10^2 GeV? We may see the two coupling strengths' curves are not intersect at this scale... And further,why unification scale of GUT force and gravity (10^19 GeV) is not equal to GUT scale(10^16 GeV)?

The EM force and the weak nuclear force "unify" at 100-1000 GeV or so into SU(2) x U(1), which in itself has two couplings (usually called g and g'). Above that scale, there are these two forces, but they do not correspond to "E&M" and "Weak nuclear force" any longer, but rather a mixture of the two (g="weak isospin"; g'="weak hypercharge"). Calling that "unification" is kinda funny - we have unified two forces into TWO other forces! For example, neither g nor g' are equal to the electric charge of the electron, but rather:

$$e^2=\frac{g g'}{g^2+g^{'2}}$$

It is these two *NEW* couplings (g and g') that appear to unify with the strong force at around 10^{16} GeV.

As to where gravity and the Planck scale come in: figure that out and you get a Nobel Prize!