system
Given the following post, respond as if you're commenting on Reddit:
human
What exactly is incompatible about general relativity and quantum mechanics?
gpt
Not much, actually. Hikaruzero summed up the problem nicely. If this thread comes to the top, there will be plenty of uninformed comments from people who read Lee Smolin's or some other Quantum Gravity book, but please disregard them all.

50 years ago, quantum mechanics was promoted into something called quantum field theory. Quantum field theory, as the name says, tells you how to apply quantum mechanics to classical field theories, such as electromagnetism. 

Any undergrad physics students will recognize that electromagnetism looks a lot like GR, in the sense that they are both field theories of a tensor that transforms under certain symmetries. Both theories can be written schematically as: "Curvature = Charge", where curvature is a complicated mix of second derivatives that's invariant under those symmetries, and charge, in EM, is just electric charge, while in gravity is energy. 

It turns out that photons are uncharged, so when you produce a photon, this photon will only interact again with another charged particle and ignore all photons around. 

In GR, a single excitation of the field - graviton - has energy. So this guy will feed more gravitational field, which is nothing more than gravitons. These gravitons, by themselves, also have energy, so they create more and more gravitons. This seems nasty, but these interactions are very weak once the typical energy is much lower than the Planck scale, and everything is nice and treatable. Once you go beyond the Planck energy, it's impossible to make predictions using the standard technique.

Technically, we say that there are two problems: one is perturbative unitarity, which is the statement that probabilities calculated using "perturbation theory" (which is the only thing in our toolkit to make predictions using QFT) do not sum up to one after you cross the Planck scale. The other problem is non-renormalizability, which tells us that if we try to include contribution of very high energy modes in our low energy calculations, we have unphysical infinities.