# Unification: what does it mean for the forces to become equal?

The Coulomb force constant $k_c$ has si-units of $Nm^2C^{-2}$. The gravitational force constant $G$ has si-units of $Nm^2kg^{-2}$. What does it mean that at very high energies these forces become equal? How can we compare different forces?

The weak force at high energies becomes equal to the EM force. Physically, why? Because at high energies ($mc^2$ where $m$ the mass of the weak bosons) you can actually create $W$ and $Z$ bosons to carry the interaction.
• Let's take the example of the weak force. Quantitatively, you should include a factor proportional to $\frac{1}{q^2-m^2}$ where $q$ is the 4-momentum and $m$ the mass of the weak boson. I'm taking $c=1$. If the momentum-energy regime you are dealing with ($q$) is much lower than the mass of the boson, the factor is small and the interaction is small. As you increase $q$, the denominator decreases so the force becomes bigger. – SuperCiocia Aug 15 '15 at 18:17
• I think you are thinking of the classical equations for EM and gravity, given by Coulomb and Newton. They are not valid in the quantum(-field theory) regime. A force is not necessarily associated with a particular equation, rather with a gauge field that mediates an interaction. In QFT terms, the EM "force" is the EM field $A_{\mu}$ that can either exist on its own (free photons) or couple to the fermions's wavefunctions (Quantum Electro-Dynamics, charged particles interactions). --> cont – SuperCiocia Aug 16 '15 at 14:21