And how does that thing work? I am incapable of understanding how that thing works.
Good point. That rules it out as plausible 23rd century technology.
I dunno - they put a LOT of effort into making the technology credible but futuristic in TOS - how else do you think much of it became reality? The TMP Enterprise always seemed to me to be a thing of absolute beauty and it remains the definitive Enterprise for me. The plans of the ship, for the most part, seemed credible, even though I'm not an engineer, although i admit that all the flashing lights and buttons have to give way to touch screen tech.
The JJprise just seems... less credible - like a fanboy's wet dream, although I'd be very interested to see what real engineers make of the designs.
Two really odd points are that the ship seemed to lose warp power, impulse power, thrusters, and emergency batteries all at once. And in the 21st century we use robotic drones to survey high radiation hot zones for a reason.