Combining gravity with other forces

Question

We all know we have 4 fundamental forces, and among them we can combine 3 forces but not gravity as in Standard model and some other. But force is something we can measure, as Einstein told us in general relativity so gravity in reality doesn't count as force, so why we tried to combine it with other forces because in reality it's just property of space?

Answer 1

Technically, Quantum Field Theory (the "other 3 forces") uses Special Relativity (flat spacetime) as a background for the spacetime that the forces act within. When we say we are trying to "unify" all the "forces", what we are really saying is that we want to use General Relativity (curved spacetime) as a background for the other 3 forces. But General Relativity and Quantum Field Theory just do not mix together.

Answer 2

"Unification" is a loaded word when it comes to "combining" gravity with the other three (EM, weak, and strong) forces of the nature.

Actually, they are already "unified" in a lot of ways:

1. Using General Relativity (curved spacetime) as a background for the other 3 forces: Done! One only has to change the flat spacetime YM Lagrangian $$ \frac{1}{4}F^{\mu\nu}F_{\mu\nu} = \frac{1}{4}F_{\mu'\nu'}F_{\mu\nu}\eta^{\mu'\mu}\eta^{\nu'\nu} $$ to the curved spacetime YM Lagrangian $$ \frac{\sqrt{-g}}{4}F^{\mu\nu}F_{\mu\nu} = \frac{\sqrt{-g}}{4}F_{\mu'\nu'}F_{\mu\nu}g^{\mu'\mu}g^{\nu'\nu}. $$
2. Quantizing gravity: Done! Gravity is usually regarded as non-renormalizable and hence deficient, since the gravity coupling constant is of mass dimension -2. However, in the modern effective theory interpretation of QFT, non-renormalizable theories are perfectly acceptable too. In the effective theory framework, quantum corrections to gravity can be accurately calculated without any issue! For example, the leading order quantum gravity potential is $$ V (r) = −\frac{Gm_1m_2}{r}(1 -\frac{G(m_1 + m_2)}{rc^2}), $$ where the first term is the classical Newtonian potential $−\frac{Gm_1m_2}{r}$. See here for quantum gravity calculation details.
3. Treating gravity as a gauge theory, akin to the other 3 (EM, weak, and strong) gauge forces: Done! In the Einstein-Cartan gravity framework, gravity is actually transformed into the local gauge theory of Lorentz group $SO(1,3)$ (see here). Therefore, all four forces of nature are describes as the gauge theory with the underlying gauge group $$ SO_{gravity}(1,3)*SU_{color}(3)*SU_{weak}(2)*U_Y(1). $$

Given the above 3 points, gravity and the other 3 force are already "unified". Well, some of you might disagree and subscribe the notion that unification means

1. Renormalizable quantum gravity (even though the non-renormalizable effective theory quantum gravity works just fine)
2. A single gauge group (thus a single coupling constant) encompassing both gravity and other 3 forces, speculating that the running of the coupling constants of the 4 forces will converge at the GUT/TOE scale (even though the directly multiplied gauge group $SO_{gravity}(1,3)*SU_{color}(3)*SU_{weak}(2)*U_Y(1)$ with separate coupling constants works just fine)

At the end of the day, the interpretation of "unification" is a matter of personal taste. Some regard it as a done deal, while others still strive for more "satisfying" synthesis.