What makes quantum mechanics and general relativity incompatible? (Advanced)

What makes quantum mechanics and General relativity/Gravity incompatible? If matter exists in two scales, it seems Gravity and Q.M. are completely compatible. Different scales of matter require different rules. So why aren't they compatible? Quantum mechanics dictates particle movement and particle movement determines gravitational movement. They are both equally necessary and important for matter to exist on various scales instead of as a singular universe.

This is a great question that gets at something very deep in terms of how we think about physics and models. It is correct that the two theories are applicable at different scales, and that is why we have been able to use both theories for so long now. One important fact to keep in mind is that all theories in physics are only models of physical phenomena in particular scenarios and environments, and that no model can be said to be "reality." Quantum mechanics is a description that is sufficiently accurate at small distances and small energy scales, and general relativity is a description that is sufficiently accurate at large distance and large energy scales. At very small distances and at very large energy scales, both theories are found to be inadequate. Here is an illustration of such a scenario: the Heisenberg uncertainty principle states that the position and momentum of an object cannot be simultaneously determined. At the same time, general relativity states that momentum warps spacetime, which in turn determines how distances are measured. The consequences of quantum uncertainty effects and curved spacetime effects feeding back on each other are not yet known; neither quantum mechanics nor general relativity can tell the full story. What this tells us though is that we can expect surprising deviations from both quantum mechanics and general relativity in the right conditions. While these effects are insignificant on the scales we're ordinarily concerned with, they become relevant when we are attempting to describe the physics of particles with high enough energy to significantly bend spacetime, and perhaps even become black holes. Such a theory is necessary to make statements about what the physics of the early universe was like, just after the big bang. Once we have a quantum theory of gravity, (and we have candidates, such as loop quantum gravity and string theory) we will be able to start understanding the early universe to a level of detail we've never be able to before, and we're looking forward to being able to!

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