One could say they contradict each other. They are the best we’ve got though. Considering the strengths of each it might be better to assume that they agree on gravity being fundamentally misunderstood on a very basic level. The assumptions are wrong. If that means it’s ‘logical’ to invent multiple dimensions instead of rethinking the basic mechanism, then you would have to redefine the word logic.
It's not a matter of saying they could. They DO contradict each other. That's why Einstein spent the last 30 years of his life working on Unified Field Theory. He could not accept the contradiction between his relativity theory and quantum mechanics. But Einstein failed to resolve the contradiction. The search goes on for a better theory.
They are the best we’ve got though.
Yes, they are the best we've got at the moment.
Considering the strengths of each it might be better to assume that they agree on gravity being fundamentally misunderstood on a very basic level.
Well, if you are saying that relativity theory and quantum mechanics are incomplete, I would agree.
The assumptions are wrong.
OK, but assumptions are not arrived at through logical deduction. You start with assumptions and then deduce conclusions from these by the laws of logic. So today physicist are rethinking the assumptions, or perhaps re-imagining would be a better word. It will take some creative thinking to devise a better theory.
If that means it’s ‘logical’ to invent multiple dimensions instead of rethinking the basic mechanism, then you would have to redefine the word logic.
No, there is no reason to redefine the word logic. You are confusing logic with assumption. Let me give you a basic example. In plane geometry you start with a point, a line, and a plane. These are not even formally defined in geometry. It is assumed that they exist and you know what they are. These are the assumptions. From those three assumptions and a few definitions you use logic to build a great many theorems.
The assumption in Newtonian physics is that space and time are constant and that the speed of light is relative. But measurements in the late 19th century showed that the speed of light is constant. Physicists proposed many theories which preserved the assumptions that space and time are constant. But Einstein won the day with a change in assumptions. He said let space and time be relative. If you do that, then the math works out and the speed of light is constant.
With theories like string theory you do have to assume their are more dimensions than 4. It may be totally wrong. But you have to do this because string theory lets go of an assumption from plain geometry--the point that has no dimensions. In string theory there are no point particles. Instead there are strings that have dimension. Point particles do not occupy space. Strings do occupy space. And in string theory point particles are not the building blocks of matter. Instead strings are the basic units of matter.
String theory may be totally wrong. So which theory is your candidate to reconcile relativity and quantum mechanics?