So is it not just an energy wave detector, detecting an effect from a cause ?
It is an energy wave detector. The gravitational waves are a cause by which changes in the mirror distance can be detected. That is a cause producing a detectable effect. We can know when they are caused by gravitational waves and not local disturbances because (1) gravitational waves produce predictable, regular and opposite changes between the two different arms of the detectors, and (2) LIGO has two stations very, very far apart: one in Louisiana and one in Washington state. If both detectors pick up the trademark pattern of a gravitational wave at roughly the same time, then that rules out local vibrations as the cause. VIRGO, a similar gravitational wave detector in Italy, can provide further confirmation of the detection.
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