The phrase "that can't be explained by science" is meaningless.
Yes, exactly. It's a fundamental misunderstanding of what science
is, this notion that it's some fixed, unchanging dogma. It's the exact opposite of that, and I hate it when fiction misrepresents it that way. The entire purpose of science is to
grow -- to examine things that are beyond current science and figure out how they work. If something is real, then science can observe it, describe it, codify its workings, and formulate testable theories of how and why it works that way.
A couple of centuries ago, if you'd told scientists about relativity and quantum physics, they'd have dismissed them as impossible flights of fancy. Today, they're the foundation of modern physics. Because they were real, science grew to encompass them, which is the entire point of science. The only things that are permanently "beyond science" are things that don't actually exist, that are just superstition and fraud. "This can never be explained by science" is a smokescreen used by charlatans who know their claims can't hold up to scrutiny.
Therefore, in a hypothetical universe where psionics or magic or ghosts or gods existed, they would be a real, observable part of the physics of that universe, and thus there would be branches of science that studied them and figured out their workings. There are a number of fantasy universes that depict magic being studied and worked with as a scientific discipline, for instance Larry Niven's
The Magic Goes Away universe, Diane Duane's Young Wizards/Feline Wizards universe, and Jim Butcher's
The Dresden Files. Duane in particular treats magic and physics as effectively interchangeable and inseparably intertwined. Magic is part of that universe's physics, as everything within a given universe would have to be.
This is what I like about
Ghostbusters -- unlike a lot of popular fiction, it doesn't perpetuate the toxic lie that science is a finite discipline unable to encompass new knowledge. It portrays a world where ghosts are real and scientists have developed workable, effective means to study and contain them using existing technology. They're not something fundamentally apart from the physics of that world, they're part of the physics of that world and can be interacted with through physical means. That's the only way it could work. If something is part of the universe, it's part of the laws of that universe, not some completely disconnected thing. You can't have it both ways.
In the Trek universe, psionics is a proven and understood science. We saw from the start in "Where No Man Has Gone Before" that they had codified tests of esper ratings and the ability to measure psionic ability. That's an artifact of TOS being created in a time when science and science fiction took claims of telepathy and psionic powers somewhat seriously; in the case of SF, that was largely due to the pervasive influence of John W. Campbell, who was a firm believer in such things. So TOS's writers assumed the psychic research that was trendy at the time would pan out and be advanced further in the future. But within the context of the fictional world, it's all real and understood by science. Psionic energy can be scanned. Disembodied consciousnesses are known to exist as energy patterns, and can be technologically swapped between bodies ("Return to Tomorrow," "Turnabout Intruder") or stored in inanimate objects (Sargon's globes, Vulcan katric arks) or specific types of energy matrix ("Lonely Among Us," "Coda"). Incorporeal entities are commonplace, many with abilities we would describe as godlike.
Pretty much everything that's part of traditional myth and superstition has a physically real, scientifically understood counterpart in the Trek universe. Future science has expanded to incorporate and demystify it. So what's left?
