why is general relativity not compatible with quantum mechanics?. can they ever be compatible?.

Phenomena that is descibed in a quantum manner has a particle mediating it/associated with it, like light has the photon. The gravitational force of GR doesn't yet have a workable particle theory associated with it. The 'graviton' is the proposed particle to join the Standard Model of particles but it doesn't yet work mathematically as it produces infinities, which are not allowed.  It also hasn't been discovered experimentally. This leaves scientists with two theories, which are applied depending on what's being studied. 

Edited May 26, 20223 yr by StringJunky

Quantized field theories can be 'modeled' by the typical Feynman diagrams with their interaction connections ( in simplistic terms ).
In QED and QCD, these interaction connections can be summed, the infinities cancel out, and you have a workable field theory.
If the same approach is attempted with gravity, the infinities generated by the summing, do not cancel out because gravity is self coupling.
IOW, it interacts with itself; gravity gravitates.
That makes the standard approach to a quantized field theory unworkable.

13 hours ago, QuantumStrangeness said:

why is general relativity not compatible with quantum mechanics?. can they ever be compatible?.

There are a whole lot of technicalities involved, but fundamentally it boils down to two basic issues - background independence, and time.

GR is background-independent, in the sense that it does not make reference to any underlying frame or system of coordinates; what’s more, it is the metric (system to measure space and time) itself that is a dynamic variable here. Gravity is geometry of spacetime. QM on the other hands is formulated as wave functions that explicitly depend on space and time, so it is background-dependent. Reconciling this is proving to be very difficult.

In GR, time is treated on equal footing as space, and thus forms spacetime. It’s a geometrical dimension, and a fundamental part of the world. Time in QM, however, is just another parameter appearing in the theory, and is not the same as space. 

Whether we’ll ever bring these together into a fully self-consistent model of quantum gravity that has the proper limits, is anyone’s guess. There are various attempts and candidate models at present, but none of them is universally accepted as being the ‘right’ one. It’s an area of active research, so we’ll see what happens.

On a side note, you can formulate quantum field theories in curved spacetime, but that’s not the same as quantum gravity.

17 hours ago, QuantumStrangeness said:

why is general relativity not compatible with quantum mechanics?. can they ever be compatible?.

The incompatibility happens only when gravity is strong. In most cases you can simply ignore gravity, and in others you can just incorporate it as you would other interactions (such as a gravitational potential affecting matter waves that travel at different heights and then interfere)

18 hours ago, QuantumStrangeness said:

why is general relativity not compatible with quantum mechanics?. can they ever be compatible?.

Most of the time, when we understand one system or nature, we can create a simple and smooth math from it. But for an unknown, you might get wrong anticipation. 

For example, a machine produces an output using collatz conjecture. You ask some experts determine the system and create a math from it. What will you expect the results? 

 

They will create different maths. Oddly every math will work just fine on certain level but not on others. 

 

This is how we deal with gravity.