How are self-replicating mines supposed to work?

Question

Standard replicators are able to replicate mundane materials and smaller not-too-complex machines. At one point, under the influence of a Cardassian anti-riot program, the replicators in DS9 are magically able to produce something like a self-targetting automatic phaser gun.

Normally, for more complex tasks, such as "building a powerplant" or "making major parts of a starship", very special and rare "industrial" replicators are needed. Apparently, an entire planet normally doesn't have more than half a dozen of these, and they are valuable enough for super secret security measures so the Maquis won't steal them (which they do anyway).

In either case, replication is the process of turning energy into matter.

In addition to their main power supply and thrust, the self-replicating mines contain a standard photon torpedo warhead, which means that they are able to release a considerable amount of energy (which is "gone" after the explosion) from a matter/antimatter reaction. The energy, and of course the antimatter must come from somewhere (regardless of the energy needed, can a replicator replicate antimatter at all?).

It seems improbable (if not impossible) that self-replicating mines could work at all. If you were able to replicate an energy cell containing the same amount of energy as the original one plus a considerable amount of matter/antimatter plus some other stuff, like a cloaking device then you would have the most perfect perpetuum mobile imaginable.

Answer 1

You're ignoring the fact that each mine contains a small amount of handwavium. In the Trek universe, it's apparently possible to extract reasonable amounts of energy from the vacuum itself and the mass is provided to the relevant mine by its neighbours (who then use the energy they've extracted to create more mass):

The replicator system was designed to accommodate a swarm detonation of up to twenty mines and still maintain the total shell. The replicator was a kludge of Cardassian and Starfleet types and included a raw-matter supply container able to contribute enough mass to build one-sixty-fifth of a complete mine. Mass for any one new mine was transported through the replicator's subspace emitters from as many mines away as was necessary. In a bucket-brigade system. As distributed over the entire shell, enough mass was stored to replace over 2,500 mines.

In the event the mass supply dwindled below 85 percent, the replicator sections were designed to extract particles from the zero-point vacuum domain to replenish the system. The threshold was set deliberately high because of the long lead time required to produce small numbers of particle pairs. - DS9: Technical Manual

Theoretically, the Cardassians could have overwhelmed the system by continually throwing things at the minefield but in practice, the mines can operate indefinitely, replacing broken mines and recharging themselves.

Answer 2

Replicators have been described a number of times to convert energy into matter. They don't need matter to replicate things at all, only energy... however, they can decompose matter into energy which can be stored for later use (when recycling is used).

As for the self-replicating mines... you might be forgetting one source of power the mines could use. Solar.

Keep in mind that Solar radiation is about 22 higher in space than it is on Earth. Furthermore, the sun is emitting an enormous amounts of power... ours has an output of 380 Yottawatts.

Now, keeping in mind that technology would evolve at faster than exponential pace in real life, let alone the Trek universe... the Federation would be able to have ridiculously efficient/powerful solar energy conversion technology which would be more than enough to power replicators.

And, arguably, it would be more efficient to use self-replicating mines that for example have a hull capable of using massive amounts of solar energy for replication and regular operations.

The mines were set inside a Bajoran solar system. Also, accumulation of power from surrounding space (background radiation) could have been used (as well as debris from older miner... though antimatter explosions would likely leave none behind - so perhaps the leftover mines might harvest the explosive energy from destroyed ones).

Bussard collectors on Federation ships were initially described as devices that generate necessary energy for the starship itself as its traveling through space - self-sufficient systems which would effectively negate the need for any kind of 'refueling' nonsense (in reality, each Federation ship has the needed technology to run indefinitely without refueling since it should be capable of replenishing its stores continuously on the go).