The Star Trek television series and films use the term "warp drive" to describe their method of faster-than-light travel. Neither the Alcubierre theory, nor anything similar, existed when the series was conceived—the term "warp drive" and general concept originated with John W. Campbell's 1931 science fiction novel Islands of Space. Alcubierre stated in an email to William Shatner that his theory was directly inspired by the term used in the show and cites the "'warp drive' of science fiction" in his 1994 article. A USS Alcubierre appears in the Star Trek tabletop RPG Star Trek Adventures. Since the release of Star Trek: The Original Series, more recent Star Trek spin-off series have made closer use of the theory behind the Alcubierre Drive incorporating warp bubbles/fields into the in-universe science.
Still violates the laws of physics
You and I are in two conventional spaceships traveling at 0.86c relative to each other. In my reference frame, you are traveling through time at half the rate I am. This is due to time dilation, not speed of light delay. After I experience one year on my ship, you will have experienced 6 months on your ship. In your reference frame, the opposite is true. After you experience one year on your ship, I will have experienced 6 months on my ship. This violates no laws of physics, because even though there is no universal "present," the limited speed of light ensures that causality is maintained.
Both of our ships have away shuttles with Alcubierre drives. These away shuttles can move arbitrarily fast, far in excess of the speed of light, without ever leaving their parent ship's reference frame.
After 60 years, my ship has a cyclospirosis outbreak because someone didn't wash their hands. The last pilot not suffering from explosive diarrhea hops in our away ship and instantaneously warps some distance in front of your ship (reminder: in my reference frame, you have only aged 30 years). He sends you a message explaining the situation. This message reaches you after you've only aged 30 years.
Swapping to your reference frame now. Causality must be preserved, so since you received that message after 30 years in my reference frame, you must receive that message after 30 years in your own. But in your reference frame, after 30 years of passed, my clock is only at 15 years. You decide to send your own away shuttle to warn us about this future outbreak. Your away shuttle arrives arbitrarily fast, sending us a message about a future cyclospirosis outbreak that arrives 45 years before that outbreak happens.
You can dress your FTL technology in whatever sci-fi bullshit you want. If you can get information to a destination faster than a photon could, you can break causality.
Here's the thing. If it's all vibrating strings in 10 dimensions then ????