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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.

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marked as duplicate by knzhou, ZeroTheHero, sammy gerbil, Yashas, Qmechanic quantum-mechanics Apr 14 '17 at 5:47

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ If you want more answers to your original question, you can just put a bounty on it instead of creating a copy. $\endgroup$ – knzhou Apr 14 '17 at 1:15
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    $\begingroup$ @knzhou It's not a copy. Where can you see mathematics in the answers of that question? $\endgroup$ – Dove Apr 14 '17 at 1:21
  • $\begingroup$ @knzhou I got only paragraphs there. Here, I'm talking about the mathematics. $\endgroup$ – Dove Apr 14 '17 at 1:23
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    $\begingroup$ @knzhou : I think this is a legitimate and clearer statement of the original question (which you've suggested as a duplicate). The original question ended up with answers to the original version and nothing much to the quite different final version. This question will allow more focused answers. $\endgroup$ – StephenG Apr 14 '17 at 1:23
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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.

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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.

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