# Would extra dimensions really solve the hierarchy problem?

The hierarchy problem revolves around the fact that we don't have a way to explain why gravity is so much weaker than the other forces. It may just be a coincidence, but since physicists tend to understandably not like coincidences very much, we treat it as a "problem" and therefore look for a solution.
One of the proposed solutions is that gravity spreads out in some extra dimensions, and how this would explain the hierarchy problem is clear to me. My question is, would this solve the problem? From what I reckon, this would still lead to gravity to be treated differently from the other forces, and the question would just translate from "why is gravity weaker than the others" to "why does gravity span more dimensions than the others". Is there something I'm missing? Do other proposed solutions also fall into this eventual fallacy?

• The notion of "weak gravity" is "not even wrong"! It's comparing oranges to apples: it's meaningless to compare gravity with standard model interactions such as the electromagnetic force, if no circumstance (e.g the specific charges and masses in comparison) is provided. See answer to a related question here: physics.stackexchange.com/questions/145518/… Nov 17, 2020 at 18:44
• @MadMax This is a more subtle question than "compare the gravitational and electric force." There is a dimensionful scale associated with the weak interactions, which we is the mass of the Higgs. There is also a dimensionful scale associated with gravity, which is the Planck mass. You can form a dimensionless ratio from these two numbers, and the question is why this dimensionless ratio is so far from 1. The reason it is an issue is because we would generically expect quantum corrections to the Higgs mass from degrees of freedom that are active at or above the Planck scale. Nov 17, 2020 at 19:06
• @Andrew, totally agree with your point. And the weak/Planck gap was actually touched upon in my answer to the related question: physics.stackexchange.com/questions/145518/… Nov 17, 2020 at 19:18
• ah i see. thanks! and, just to be clear, I actually don't think it is clear the hierarchy problem needs to be solved, but I just wanted to clarify that it is a well-defined problem. Nov 17, 2020 at 19:46