I've always enjoyed the science fiction genre, and there are many books shows available. Especially I like works where the physics are credible. The Enceladus series by Brandon Q. Morris is such a work. Also The Expanse show seems pretty great in that regard.
Recently I have watched Star Trek: Enterprise and loved the plots, the characters and their development, the recurring arch enemies and the general uplifting spirit. But from the physics side I needed to chuckle quite often. Some people just take the science to be fictitious and don't bother; but I prefer credible science fiction and complain a lot.
First off: Why does always something explode on the bridge when they get hit? On a navy warship the bridge is exposed, that could happen as well. But they have a CIC which is a bunker inside the ship. Enterprise does not have a window on the bridge, so why is it located at the edge of the hull? In The Expanse, the MCRN Donnager seems to have a combined bridge and CIC well protected in the ship. In the fight nothing explodes in the CIC. And even the railgun hit is unspectacular, as it should.
The armament with the energy weapons looks reasonable. I have no idea what a phase cannon is supposed to be. Is is a laser? Or rather an ion cannon? Not sure what the phase is there. The photon torpedos sound peculiar, but I a lot of photons certainly generate heat and destroy things. I just wonder how those photons are created. As the drive seems to run on antimatter, perhaps they just have an annihilation and produce tons of gamma rays. Then they would be antimatter warheads, which is physically possible though the containment field is an engineering problem for the quantities needed to generate a sufficient yield.
The warp drive itself is okay. There seems to be a possibility to obtain a solution to Einstein's field equations of general relativity such that one could travel faster than light. My understanding is that one creates a tidal wave in spacetime curvature and then “just” surfs it. It seems to just require a lot of engineering and tons of energy. These are the things that I can live with in science fiction: The warp drive is built upon something which cannot be completely ruled out. The way that it is presented in the show is a bit too optimistic, though.
What I find annoying is that radio communication seems to be instant over arbitrary distances. Captain Archer can just have a video conference with Admiral Forrest without any latency. This does not make sense, even with a warp drive. In The Expanse they explicitly restrict themselves to the solar system and have signal delays. This gives for a couple very dramatic scenes where the admirals have to plan with information that is twenty minutes old. And then various things go bad because other factions have the information earlier.
Another strange moment was where the Enterprise approached a dormant space ship that has been floating there for a while without any sort of propulsion. One person on the bridge said “it stands still”, which does not make sense without a reference frame. And as they were in void between various stars, there is no such reference frame. If they said “it does not accelerate” or “it lost propulsion”, I'd be perfectly happy. But there just is no objective frame of reference in deep space.
The transporter supposedly disassembles all the atoms and puts them back together. Also there was a scene where they discussed how consciousness travels with that, that one briefly exist in both places and that one might also be a clone and the original gets killed. They hinted at quantum entanglement for the consciousness. Indeed Roger Penrose has described (“Road to Reality”, “Emperor's New Mind”) how our laws of physics are deterministic on a classical level and completely random on the quantum level. Quantum entanglement could provide for some form of a free will. I found that an interesting reference, assuming that it was intentional.
In The Expanse they did gravity with constant acceleration, that is completely doable except that we just cannot get enough fuel into a rocket to do so just yet. On Enterprise they just had mystical “gravity plating” that did the job. I can totally understand that having a lot of scenes with weightlessness are hard to film. It just feels like they have added some magic such that they don't have to worry about gravity at all.
All the time travel thing is okay. From my understanding of general relativity it is plain impossible to propagate information backwards in time, so I just consider everything fiction. But they have that little changes in actions have drastic consequences, just as it should be.
In the third season there are the “sphere builders” who come from a different dimension. That's not how dimensions work. They can come from a different region of space. And there could be additional dimensions that we do not have any way of detecting yet. But then space just has hidden dimensions and they live in a different position along that dimension. It would be like people have only lived on the surface of earth and we would call avians being from a different dimension because they are not on the ground but into a direction that we cannot go along.
Given all that, I still liked the character development. There were Vulcans like T'Pol or Soval who significantly changed their beliefs during the four seasons. Also Trip, Shran and Degra surprised me over and over again. So even if one is picky with the science, it still is a nice show.