Trek science has been borderline at best, amusing most of the time and laughable at the worst of times. It was expressed quite well in the Authors Note in The Songs of Distant Earth which I just finished re-reading.
"However, this version was directly - and negatively
- inspired by the recent rash of space operas on TV and Movie screens. (Query: what is the opposite of inspiraten - expiration?)
Please do not misunderstand me: I have enormously enjoyed the best of Star Trek and the Lucas/Spielberg epics, to mention only the most famous examples of the genre. But these works are fantasy, not science fiction in the strict meaning of the term. It now seems almost certain that in the real universe we may ever exceed the speed of light. Even the closest star systems will always be decades or centuries apart; No Warp Six will ever get you from one episode to another in time for next weeks installment. The great Producer in the Sky did not arrange his program planning that way."
Smart man, Arthur C. Clarke. Just tell your stories and don't sweat getting the science right. If Trek had to deal with real world science we'd just now be getting from Earth of Alpha Centauri at 0.1 c. McCoy and Scotty would have passed away in the void between the stars and the rest of the command crew would be past retirement age.
Let Trek be Trek and don't expect it to be this weeks installment of Nova on PBS.