this post was submitted on 17 Apr 2024
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Quantum mechanics and relativity are, at least currently, incompatible theories. Relativity depends on continuous things, which is why it has singularities and what not. But quantum mechanics has minimum discrete units that don't play nice with gravity and relativity.
Also, it's still an open debate as to whether quantum mechanics is applicable to all sizes of things. There's some consequences around that being the case and it's one of the suggestions for an assumption resolving recent paradoxes around incompatibilities between the theory and our expectations for behaviors. If it does apply to larger objects, the consequences are basically that either there's no free will and superderminism is true or else that quanta don't actually exist until observed.
In fact, currently we haven't been able to observe quantum behavior in anything large enough to measure gravitational effects from. Which may be where a fundamental limit exists, given the incompatibility between relativity and QM.
Quantum mechanics is incompatible with general relativity, it is perfectly compatible with special relativity, however. I mean, that is literally what quantum field theory is, the unification of special relativity and quantum mechanics into a single framework. You can indeed integrate all aspects of relativity into quantum mechanics just fine except for gravity. It's more that quantum mechanics is incompatible with gravity and less that it is incompatible with relativity, as all the other aspects we associate with relativity are still part of quantum field theory, like the passage of time being relative, relativity of simultaneity, length contraction, etc.
Gravity is where the whole continuous singularities are, so yeah.