Final answer:
A Pulsar Timing Array measures gravitational waves by tracking variations in pulsar signals, which are influenced by the warping of spacetime from passing waves, in accordance with general relativity. Initial indirect evidence came from a pulsar's orbital period decrease, and direct detection was made by instruments like LIGO.
Step-by-step explanation:
A Pulsar Timing Array can be used to measure gravitational waves by detecting the tiny fluctuations in the timing of pulsar signals caused by passing waves. Pulsars are highly regular astronomical clocks, and gravitational waves can slightly alter spacetime, changing the arrival time of their signals on Earth. This effect is incredibly subtle, requiring precise measurements.
The historic indirect proof of gravitational waves was observed from a pulsar, PSR1913+16, discovered by Joseph Taylor and Russell Hulse, which showed a decrease in orbital period, indicating energy loss consistent with the emission of gravitational waves. This observation supported the predictions made by general relativity about the existence of gravitational waves.
Later on, instruments like LIGO directly detected these waves, validating the indirect findings and confirming the hunch that massive celestial events, like the mergers of black holes or neutron stars, could produce detectable gravitational waves.