Final answer:
LIGO is one tool being used to search for gravitational waves and the graviton. Gravitational waves are detected by measuring the shift in the relative positions of two masses caused by the waves. While LIGO has not directly detected the graviton, the presence of a gravitational wave would suggest its existence.
Step-by-step explanation:
The search for gravitational waves and the detection of the graviton have been ongoing challenges for scientists. LIGO (Laser Interferometer Gravitational-Wave Observatory) is one tool being used to search for gravitational waves. The detectors at LIGO are designed to measure the slight shift in the relative positions of two masses caused by gravitational waves. While LIGO has not directly detected the graviton, the presence of a gravitational wave would suggest the existence of the graviton according to wave-particle duality.