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I know there are many questions on physics stack exchange devoted to the question of quantum gravity and reconciling GR and QFT, but don't mark this as a duplicate because my question is a bit more specific.
In the PSE page A list of inconveniences between quantum mechanics and (general) relativity? it was explained that the crucial problem in uniting general relativity and quantum mechanics comes when probing high-energy conditions at the Planck scale. However, this answer was not quite detailed enough for me, for I still do not fully understand why the theoretical frameworks clash at these conditions.
Can someone explain thoroughly (preferably conceptually and with minimal math) why general relativity and quantum mechanics implicitly do not work together to describe these high-energy interactions and a few examples of them.
I have a good conceptual understanding of both theories, but have little formal mathematical training.