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So from what i know transporters can convert matter into energy(or a stream of sub-atomic particles) before re-assembling the matter elsewhere using the same energy. why not simply take that transporter stream and use it directly to power star-fleet Technology instead of faffing about with anti-matter and dilithium. am i fundamentally misunderstanding how transporters work?

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    Remember that using the transporter also costs a lot of energy - I would bet it costs more than you'd get out of converting stuff into energy. – Vanguard3000 Jan 11 '18 at 19:31
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    The canonical example is in Voyager when Chakotay is ordered to recycle a gift he replicated for Janeway rather than, say, a chunk of rock picked up from their last away mission. It can only be assumed that when ordinary matter is converted to energy it isn't in a usable form. (Also, replicated matter is clearly different from "real" matter in some critical way.) [PS: in this context, "recycle" means "feed back into the replicator to recover the energy used in its creation".] – Harry Johnston Jan 11 '18 at 19:32
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    @HarryJohnston - In this instance it might also mean to return to being the "feedstock" that the replicators use to turn into other forms of matter. – Valorum Jan 11 '18 at 19:36
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    I think one reason would be that the anti-matter and dilithium have a semi-stable power output, such that it is close to our generators but on a much larger scale, while they would have to have either massive power storage, which is inefficient and difficult, or have a steady stream of matter on board to disintegrate in their transporters, also rather inefficient, so they are using what works in the most economic sense. – Daishozen Jan 11 '18 at 19:50
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    What would (does) power the transporters? – Wikis Jan 11 '18 at 20:36
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Transporters work, according to the Next Generation Technical Manual, by breaking an object down into a stream of matter (not energy), sending it elsewhere, and reassembling it. It takes energy to disassemble and reassemble an object. It also takes energy for everything else involved in that, such as scanning the object to be transported so that it can be reassembled, making the confinement beam so that the matter stream is not dispersed, and other things necessary for transport and reassembly.

The replicators use transporter technology to transform feedstock into objects, or reduce objects back into feedstock. According to the TNG Technical Manual, the stock for food replicators is made of sterile organic matter that is designed to require the least amount of quantum manipulation by the replicator, and therefore minimize the power used. The Technical Manual also states that there is a cost-benefit tradeoff for replication versus storage. For otherwise perishable foodstuffs and uncommon spare parts, it makes more sense to trade feedstock and energy for the finished product. For common spare parts, it makes more sense to simply store them.

In order for your scenario to work, the transporters would have to convert matter into energy, which is a rather vigorous reaction, and I'm not sure what they would have to look like to safely do that. And even if they did convert matter into energy, you couldn't both use that energy to transport and reassemble an object, because you'd use some of the energy up in reassembly and therefore not get the same object back out. A transporter like that would definitely justify Dr. McCoy's fears.

Since they've figured out how to harness the energy, annihilation of matter and antimatter appears to be the way to go for power generation in Star Trek. Doing that, there's definitely more than enough energy to run everything on the ship.

Note: I've shied away from explicitly referring to thermodynamics here, because the transporter violates physics in a number of ways, but the creators of the TNG Technical Manual tried not to do any more violence to physics than strictly necessary. The writers of some of the episodes didn't necessarily try as hard.

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