Actually Trek warp drive is a lot closer to being un-imaginary than you'd think. At least, depending on what model you're using. In 1978, NASA propulsion engineer and ST:TMP science advisor Dr. Jesco von Puttkamer wrote a production memo explaining warp drive in terms grounded in real physics -- and his model was based on essentially the same principle as the one that Alcubierre proposed in Classical and Quantum Gravity
16 years later. Since Alcubierre is a confessed Trekker, I wonder if he was aware of Puttkamer's warp model.
Never underestimate the power of science fiction to inspire real scientific and technological innovations.