The challenge of representing quantum gravity with elementary particles arises from the fundamental differences between gravity and the other fundamental forces described by quantum field theories. While the other forces, such as electromagnetism or the strong and weak nuclear forces, are mediated by elementary particles (photons, gluons, etc.), gravity is unique in several aspects:
Gravitons: In a quantum field theory, particles are associated with force-carrying particles, called gauge bosons. For example, the electromagnetic force is mediated by photons. However, the theoretical particle associated with gravity is called a graviton. Gravitons would be the hypothetical particles responsible for transmitting the gravitational force. Unfortunately, a consistent and complete theory of quantum gravity, including a well-defined graviton, has not yet been achieved.
The strength of gravity: Gravity is incredibly weak compared to the other fundamental forces. For example, you can easily pick up a pen against the pull of Earth's gravity, even though the entire Earth is exerting a gravitational force on it. This extreme weakness of gravity poses a challenge for understanding and measuring its quantum effects.
The nature of spacetime: In general relativity, spacetime is not just a fixed background; it is dynamic and can be influenced by matter and energy. This is in contrast to the other forces, where spacetime is usually assumed to be fixed and unaffected by the presence of particles. Incorporating this dynamic nature of spacetime into a quantum framework is a significant theoretical challenge.
Due to these unique aspects of gravity, the development of a consistent and complete quantum theory of gravity, including the representation of gravity in terms of elementary particles, has proven to be a formidable task. Various approaches, such as string theory or loop quantum gravity, are being explored to address these challenges, but a definitive resolution is still a subject of ongoing research and investigation.