Matter cannon is a physics concept used as a weapon in Stephen R. Donaldson's Sci-fi series, The Gap Cycle. The actual implementation and use as a weapon is completely fictional; however, the underlying theory and operational details are realistic. In essence, the weapon is described in terms of a set of viable concepts that have not been properly assembled to explain how or if the weapon could work in the real world.
Matter cannon Wikipedia
Donaldson describes the concept of matter cannon primarily in terms of chaos theory; in particular, he describes matter as organized or frozen energy, likening matter to order as organized or frozen chaos and likewise chaos as a fluid state of order. Based on the theory that any form of order can be created from any form of chaos, he explains that there must therefore be a manner to arrange a form of chaos which naturally falls into a predetermined form of order under certain conditions.
Based on this assumption, the possibility to create organized forms of energy which collapse into matter under the correct conditions must also exist. Matter cannon uses a controlled beam of light-constant energy which collapses when encountering physical matter, producing either pairs of protons and electrons or neutrons. Effectively, neutrons or pairs of ionized hydrogen and free electrons are created temporarily traveling at the speed of light for just a few picoseconds by the collapse of a beam of quarks and energy traveling at the speed of light. If the proper conditions are not met, the beam simply disperses; matter cannon fire has a limited effective range.
Due to charge conservation, it would be impossible for matter cannon to produce either individual protons or electrons; only neutrons or proton-electron pairs could come into existence by any means.
Matter cannon is mainly used as a ship-to-ship weapon in space. Donaldson dismissed the usefulness of matter cannon fire for orbital strikes on bodies which hold atmosphere: the beam can only penetrate at most several meters before either dispersing completely or completely depositing hydrogen gas into the atmosphere with an impressive but harmless shock wave. For similar reasons, matter cannon fire is not useful as a sidearm; although the massive energy requirements limit even a large portable matter cannon to a few charges at best.
Matter cannon as a ship-to-ship weapon in space is effective precisely because nothing can reasonably withstand the impact of mass traveling at light-constant speeds, even for a few picoseconds. Matter traveling at the speed of light effectively has infinite momentum, and thus infinite mass; further, special relativity suggests that time dilation effects would increase the effective mass infinitely at the speed of light. Therefore, several micrograms of hydrogen or neutron matter impacting the side of a ship at the speed of light would have the same impact as several hundred billion teragrams and more of neutron star matter impacting the side of the ship at near-light speeds.