Why is there a need to unify Quantum mechanics and General Relativity and what is meant by such a unification?
One could have asked a similar question of Maxwell: was there a need to unify electricity and magnetism? The need was intellectual, to get a mathematical model that described existing observations of electric and magnetic effects and be predictive of new situations/systems. And look where satisfying this need got us.
Physicists, who appeared as a different discipline from mathematics and philosophy from the appearance of Newton on the scene, have been actively pursuing theoretical models of unification.
Physics has developed different mathematical models for different ranges of the variables of space and time. These different models meld and emerge at the boundaries where both frameworks apply: classical mechanics emerges from quantum mechanics. Classical electromagnetism emerges from quantum electrodynamics. This happens seamlessly.
General relativity reduces to Newtonian gravitation in flat spaces . Special relativity reduces to classical mechanics for non relativistic phase spaces.
With the establishment of the standard model of particle physics , the path to unifying three of the known fundamental forces through GUT theories is well trodden. It really is impressive how weak and electromagnetic theories have been unified at the quantum level and there is real evidence for the unification of the strong force to the other two.
At present physics assumes that the underlying level of nature is quantum mechanical, and this assumption works. The difficulty arises with General Relativity, which works with the coordinates themselves on which the quantum mechanical effective field theories are built. The need for quantizing gravity rigorously arises when cosmological models are built and the variables are stretched to their limits.
At present the usual way of building quantum field theories gives only effective quantization of gravity, used in cosmologial models with good resuls. The mathematics though has infinities that cannot be brushed away or renormalized. The search is on for a quantization that is rigorous. String theories offer the possibility of embedding the standard model of particle physics and quantizing gravity, but they are still at a research stage.
Can we say then that some of the questions that a unification of General relativity and Quantum mechanics may answer are if the gravitational interaction between spacetime and matter and energy happens somehow directly or through a quantum gravity field or another undiscovered field(s) by means of real and/or virtual particles of that field. Also whether spacetime itself is also somehow quantized or not?
In effective field theories the standard way of building a model is used, having a graviton exchanged, the graviton building up the classical gravitational waves of general relativity. These cannot be unified with the existing SU(3)xSU(2)xU(1) current particle theory in an elegant manner.
As pointed out above, research in string theories offers a path for embedding the standard model , its elementary particles being vibrations of a basic unite , a string. The different particles are vibrations on this string and have the group symmetries of the standard model, and in addition a spin two graviton exists as a vibrational level to model the quantization of gravity. The future research will show if this is a good path for unifying all four known forces in a quantum mechanical underlying framework.