I've read paragraphs all over the internet about why they don't fit in. But, if possible, can someone please give me the mathematics of the inconsistency?
Mathematically show what happens when the formulas of quantum mechanics are applied in high gravity situations. And, give me the mathematics of what happens when General Relativity is applied to Atomic scales.
Mathematically show that both the models are inconsistent with each other.
Inconsistent theories are theories which cannot both be true. The standard model and general relativity are not inconsistent in the sense that they are contradictory. Neither theory has anything to say about what the other describes.
If you try to apply the standard model to a situation in which your interactions are occurring in a very large gravitational potential, you will not know what to do with you information about the potential because the standard model Lagrangian has no place for gravitational potentials.
If you try to use general relativity to describe atomic phenomena, you will have no mathematical machinery at hand to make any calculations about atomic phenomena, because it is not a theory of atomic physics.
A mathematical proof of inconsistency is a tall order. It would kill one of the theories, assuming the remaining theory is true, and would kill all theories that attempt to unify both theories.
I am not knowledgeable in either, but based upon whatever exposure I have - they are not inconsistent. They are (so far) more like incompatible with one another. Meaning, you start with one and can not arrive/derive the other.
Even for incompatibility, there is no mathematical proof, just that no effort to merge them have succeeded.
They are both individually consistent theories. With exception of some nonsense like quantum eraser and entanglement. I think both of these phenomena in their current form, would make the two theories inconsistent. Because one phenomena goes back in time, and the other signals faster than light.
