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Is it possible to create a neutron out of pure energy, i.e. not by bringing a bunch of already-existing quarks together? (A quick calculation using E = mc2 shows the energy required would be about 1.5 e-10 J.)
Would an equivalent antiparticle always need to be created?
There is nothing pure in energy.
is often understood as the ability of a physical system to do work on other physical systems.2 Since work is defined as a force acting through a distance (a length of space), energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length.
Energy in the elementary particle level needs a carrier, either a gauge boson, i.e. photon for electromagnetic interactions, a W/Z for weak, gluon for strong, or particles in general as seen in the standard model.
A neutron is a combination of three quarks . A complicated system of conservation laws rules in the microcosm, in addition to energy conservation: from baryon number conservation to charge conservation to lepton number, to color conservation. The three quarks of the neutron have to be balanced with three antiquarks to keep the conservation laws. Thus the carrier that will allow the generation of a neutron cannot generate it singly, even if it is a gluon or gluons of enough energy. It would have to generate the antiquarks too.
No, because of electron neutrino that remains in hypothetical "complete" decays of neutron.
For example: $n \to e^+ e^- \bar{\nu}_e \to \gamma \;\gamma\;\bar{\nu}_e$
