One subject near-and-dear to my heart is science fiction, with extreme emphasis on the science. Star Wars is not what I would call science fiction. It is swords and sorcery with fantastic, impossible weapons and “space ships” that fly and maneuver like airplanes.. even in the airlessness of space! It doesn’t care about physics, not even its own. It doesn’t even understand that a parsec is a distance, not a speed. It is “science” fiction only because somebody dropped it in the genre and was too lazy to fish it out. Star Trek is also not science fiction. It uses science-ish words in a generally self-consistent manner, but it abuses them to hand-wave impossible technology like “warp” drives into existence. It is about as plausible science-wise as Neon Genesis Evangelion. A more appropriate name might be bafflegab fiction.
And just to short-circuit any heated "discussion" about the relative merits of the above as they pertain to entertainment, I happen to like Star Wars, Star Trek, and Neon Genesis Evangelion. I'm not saying that they're in any way "bad". However, for the purposes of this topic they are hereby declared to be "not-science fiction". Not what I'm looking for and not what I'm here to discuss. I cite them only because they are well-known examples of the sort of "science" fiction that I'm trying to get past.
No, what I’m looking for here is science-themed anime (or manga, or books) based on real science. What I mean by science-themed is that science or technology or engineering must be a central element of the plot, character(s), and/or setting, and nothing important to the plot or setting of the story should contradict generally-accepted, real-universe physical laws as science currently understands them. It may extend them, or speculate at the edges of that body of knowledge, but it must not contradict their core.
Tools and devices used must at least be theoretically possible to create and operate in the real universe, and ideally practically so. Space ships made out of unobtanium or requiring energy equal to the mass of the universe to function for example are not practical and would be disallowed. Likewise things like “psionics” or “superpowers” would be considered to be just different pronunciations of “magic” and likewise excluded from the category.
Note however that applications of Clarke’s 3rd law are allowed, even encouraged, provided the “magic” can be explained using science and fabricated with real-world engineering techniques. In other words, no wizards, unless they’re really cyborgs with their own wifi-controlled nanite swarms. "Telepathy" between normal humans is allowed, if they've had the appropriate hardware surgically implanted.
If you’re still not clear on the concept, take a look at this page (Mohs Scale) I’m looking for a 5 or 6 on the “Mohs scale”.
Examples of anime that might make the cut:
Dennou Coil (basically AR, just with really advanced hardware, and we already have stuff like pokemon go and Minecraft Earth)
Sword Art Online, "Aincrad" arc (fantasy on top, yes, but a “hard” core of plausibly real-world technology underneath)
Ghost in the Shell
Space Brothers (borderline, could be considered simply slice-of-life or drama, but a focus on science and engineering as central to the setting and plot development saves it.)
Note that I’m making no claims as to the entertainment quality of any of the above, just stating that they have reasonably solid basis in real-world physics and engineering. IOW, they could be real in an alternate timeline or at some point in the foreseeable future.
I've seen all of the above. If anyone has any others to recommend I’d love to hear about them. Many places, even book and movie stores, have “science fiction and fantasy” sections. Ugh. Do a google search on “science fiction” and you’ll get Star Trek, Star Wars, Dune, etc. at the top of the list. With so many not-science topics obscuring the field it is hard to find the “real” science fiction that I’m after here.