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!

 

[sir-pinski]

This is a great question! The unification of the strong, weak, and electromagnetic forces at the scale of 10^16 GeV is known as the Grand Unified Theory (GUT). This theory suggests that at high energies, these three forces are actually different manifestations of a single, unified force. However, as the energy decreases, the differences between these forces become more apparent, and they eventually become distinct forces at lower energies.

The reason for the unification of the weak and electromagnetic forces at the scale of 10^2 GeV is due to the Higgs mechanism. This mechanism explains why the weak force is short-range while the electromagnetic force is long-range. At high energies, the Higgs field is present and gives particles mass, resulting in the weak force and electromagnetic force appearing to have similar strengths. However, as the energy decreases, the Higgs field weakens, causing the weak force to become weaker and the electromagnetic force to become stronger. This is why their coupling strengths do not intersect at the scale of 10^2 GeV.

As for the unification scale of GUT and gravity, it is believed that gravity becomes a strong force at this scale and cannot be unified with the other forces. This is because gravity is described by a different theory, general relativity, which does not fit into the GUT framework. Therefore, the unification scale of GUT and gravity is higher at 10^19 GeV.

In summary, the unification of the strong, weak, and electromagnetic forces at the scale of 10^16 GeV is due to the Higgs mechanism, while the unification of GUT and gravity at a higher scale is not possible due to the different nature of gravity. I hope this helps clarify your question.