Quantum Gravity and Special Relativity

[Meruem]

TL;DR

How do quantum gravity and special relativity are linked?

is there a equation that links quantum gravity and special relativity?

 

[Nugatory]

Special relativity applies the special case in which there are no significant gravitational effects (that's why it's called "special") while general relativity handles the more general case in which gravitational effects may be present (that's why it's called "general").

So no, there is no equation that links quantum gravity and special relativity because if gravity is involved special relativity is not.

 

[Demystifier]

In the presence of classical gravity, special relativity is valid locally, for any local inertial observer. One expects that a similar relation should also be valid in quantum gravity, but no one knows for certain.