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This is an unusual parallel, but both "Star Trek" and "Star Wars" have unusual, fictional, seemingly magical crystals that rest in the hearts of both franchises' most recognized technologies.
Dilithium crystals have been explained in detail at /Film in the past, as part of the site's Trekspertise series. Briefly, dilithium crystals are a necessary engine component of all Starfleet starships. Starfleet vessels are powered by the energy produced by matter/antimatter explosions. Said energy passes through dilithium crystals, which, according to Rick Sternbach's and Michael Okuda's invaluable "Star Trek: The Next Generation Technical Manual," has a unique molecular structure that is useful for redirecting energy into plasma streams. A dilithium crystal is porous to antihydrogen, and once the crystals have been subjected to a high-frequency electromagnetic field, antimatter can pass through it without sparking a reaction.
It's all very technical, which is the way Trekkies like to roll. Dilithium crystals don't produce energy of their own, but they are incredibly useful in the "Star Trek" universe. They are also said to be very rare, and remain one of the few natural resources in "Star Trek" that still needs to be located and mined out of the ground, rather than replicated.
Kyber crystals, meanwhile, are just as spiritual as dilithium crystals are mechanical. According to Star Wars.com, kyber crystals have a vague psychic quality that connects them to the Force. Kyber crystals are the "lens" that allows lightsabers to work. A Force-attuned Jedi mentally links with a specially selected crystal, making said Jedi mentally in control of their own weapon. The crystals are also rare and are mined from (mostly) the ice caves of the planet Ilium.
But which crystal is more "powerful?" Let's explore that notion a little.
Dilithium crystals aren't powerful, but do share one quality with kyber crystals
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Of course, one could immediately point out that comparing dilithium crystals to kyber crystals is a little like comparing apples to oranges. The starship crystals from "Star Trek" don't produce any power of their own, and are only powerful in the sense that they're unique and useful to the fictional technologies of Starfleet.
Indeed, dilithium crystals, while used in all the vessels constructed by Starfleet, aren't used by every space-faring species on "Trek." Romulans, for instance, power their engines using miniature, artificial singularities. Without powerful magnetic fields and a direct injection of antimatter into their unique porous matrix, a dilithium crystal is essentially inert. Kyber crystals, in comparison, possess qualities that make them able to be weaponized by Jedi with psychic abilities. They are also used in the Death Star as part of the station's massive weapons systems, so kyber crystals seem to have power of their own.
There was a recent wrinkle in "Star Trek" history, however, that brought the properties of these two fictional crystals together. In the third season of "Star Trek: Discovery," there was a galaxy-wide cataclysm called The Burn, which caused all active dilithium crystals — and the ships that housed them — to simultaneously explode. The Burn was caused by a mental outburst by a young Kelpien named Su'Kal (Bill Irwin) whose mother was pregnant with him when she was forced to move into a cave lousy with dilithium. The unborn child somehow developed a psychic link to the crystals, and when he threw a tantrum, it caused all the dilithium in range of his brain to explode. So, like kyber crystals, dilithium also seems to have some kind of ill-defined psychic quality.
Kyber crystals not only possess psychic qualities, but can also be used for weapons
Lucasfilm
Space.com once wrote extensively about kyber crystals, explaning a little more about the way they function in "Star Wars." They pointed out that a lightsaber gets its color from the psychic energies of the Jedi that is using it. Sith, who operate using the Dark Side of the Force, are able to "bleed" their crystals, corrupting them with dark psychic energies, causing them to turn red. This is why we witnessed a lightsaber changing color mid-battle in the TV series "The Acolyte." Crystals can also be healed and mentally purified, something that Ahsoka once did in "Star Wars: Rebels." Unlike dilithium crystals, kyber crystals are more than a mere mineral.
/Film has written before that kyber crystals are actually semi-conscious — both organic and inorganic — and possessed of a group mind, making them in tune with the psychic Jedis and Siths. They're kind of alive. They were once worshiped, and ancient Jedi made statues out of the substance. They were mined out of existence after the events of "Star Wars: Episode III — Revenge of the Sith" when the Empire came into being. And in addition to the crystals being used in the Death Star, the old Ilium caves were also repurposed to build the even larger Starkiller base in "Star Wars: The Force Awakens."
So it seems that kyber crystals are clearly "more powerful," in that they seem to produce their own power and are used for various pieces of "Star Wars" weaponry. Dilithium crystals, while inert, are used for more responsible, peaceful means — primarily to get to other planets quickly.
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