My apologies, yet I do so love playing devil's advocate.

The crux of your explanation above is a reasoning why space travel as it occurs in Science Fiction, such as Star Trek is particularly complicated. As the compliment of a space vessel approached light speed their chronometers would slow down in relation to those more stationary by comparison on Terra. Would they ever actually exceed the speed of light? Physics answers, "no." It would be strange to return and see everyone you knew dead from having aged as you, a crew member aboard the star ship had experienced time the same but with a differing speed and distance. The concept of a "warp drive" is a bit more than difficult to fully explain with mankind's understanding of physics. One thing that is also a constant, in addition to change; it is that the more we learn, the more we realize that we do not know. It is impossible for anyone to know all that there is to know.

Warp drive aside, can anyone explain why I might be wrong and how LIGO can work. The way it looks to me is that if LIGO works, it breaks relativity, and vice-versa. I’m not saying LIGO scientists are fakers, just that it bothers me and I’d like to understand.

“I do so love playing devil's advocate.” - Noted.

There are a myriad of articles regarding LIGO and not one that I have perused addresses well your query. I see no reason why you could not contact the California Institute of Technology, specifically at the LIGO Laborotory. The phone number and contact address is simple to find online. I would be interested in hearing their reply.

The official LIGO stuff does not go in to enough detail to address this question. If you can find an example, I’d be grateful.

I wonder if they ever get any questions on resonance cascades. ;)

^ Part of keeping up ones GPA lies in knowing which questions to avoid asking. Know what I mean, GR?

Quite

(That said, I am still somewhat curious if any "laypeople" have ever asked them such silly questions, or if they've shared any witticisms amongst themselves on similar topics)