The finite speed of gravitational interactions and waves, as described by general relativity, does not necessarily imply the quantized nature of the gravitational field in the same way that the finite speed of light is associated with the quantized nature of the electromagnetic field.
In quantum field theory, the electromagnetic field is quantized, meaning it is composed of discrete packets of energy called photons. The quantization of the electromagnetic field is essential for understanding phenomena such as the photoelectric effect and the behavior of light in various experiments.
However, the quantization of the gravitational field is still an open question in physics. The current framework of general relativity describes gravity as a classical theory, where the gravitational field is a continuous and smooth entity, not composed of discrete quanta like photons.
Efforts have been made to develop a theory of quantum gravity that would reconcile general relativity with quantum mechanics. Various approaches, such as string theory and loop quantum gravity, propose different ways to quantize gravity. However, a complete and experimentally confirmed theory of quantum gravity is still elusive.
The finite speed of gravitational interactions and waves, similar to the finite speed of light, arises from the geometry of spacetime as described by general relativity. It means that changes in the gravitational field propagate at a finite speed, limited by the speed of light. This finite speed has been experimentally confirmed by observations of gravitational waves.
While the quantization of the gravitational field is an active area of research, it is important to note that the finite speed of gravitational interactions and waves does not, by itself, provide evidence for the quantized nature of gravity. It is a feature of general relativity, which is a classical theory of gravity, and the question of whether gravity is truly quantized remains an open and challenging problem in theoretical physics.