Why can’t gravity be quantized using the same approach that worked for electromagnetism?
Electromagnetism was successfully incorporated into quantum mechanics through quantum electrodynamics (QED), treating the electromagnetic field as a quantum field whose interactions are mediated by photons.
Why can’t we apply the same mathematical reasoning to gravity, quantizing the gravitational field and introducing gravitons?
What exactly breaks down when we try? Is it a fundamental incompatibility between general relativity and quantum mechanics, or mainly a mathematical problem we haven’t solved yet?