Has it been observed? Is it just theoretical? Is it one of those simple-but-profound things?
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Regular chemical reactions also produce energy from mass. Whenever something is burning, for example, a tiny amount of its mass and the mass of oxygen it’s reacting with gets converted into energy – heat and light. Likewise, endothermic chemical reactions that consume energy convert it into a tiny amount of mass.
If you want a fairly extreme example then colliders like CERN produce all kinds of particles from the kinetic energy of a collision
Pair production! It’s been a while, but if I remember correctly, it’s when a high-energy gamma particle passes by a nucleus, splitting the gamma into an electron and a positron.
First off, matter is simply a _form_ of energy, and _mass_ is a property of energy. All energy has mass, by E = mc², and all mass is energy. This goes so far as it being possible to create a black hole from light alone, called a _Kugelblitz_ (German for “ball lightning”, but not the same).
Or from a slightly different perspective, anything that changes the energy of an object also changes the mass. The underlying reaction can be nuclear, chemical, (de-)compression, falling down the stairs, … . Energy is technically never converted into mass; but you can convert it to matter, so lets talk about that:
The most purest form of what you ask for is the creation of antimatter (and along with it, equal amounts of matter). You effectively put enough energy into a small space and it can form (anti)matter. This has been achieved in several labs, CERN likely being the best known one.
Positrons, that is, anti-electrons, are sometimes even created this way by nature on our planet, by extreme lightning or cosmic rays hitting the atmosphere. This is not to be confused with “beta^^+ decay”: an atom shooting out a positron; this if anything releases energy, not uses it to create more matter.
You can also fuse or split atoms in cases where it is not energetically favourable, meaning that it will use energy instead of releasing some in total. With fission, his happens all the time in nuclear reactors whenever a neutron is absorbed in a way not intended for the reaction (that is, most of them). We can also do it on purpose.
Fusion is generally a bit tricky as you need quite extreme conditions to fuse atoms to begin with, and doing it with quite heavy ones is even harder. But this is for example what we do when we create new elements by shooting very heavy nuclei (gold, lead, and the like) into a piece made from another heavy element. In nature, it happens inside collapsing dying stars and colliding neutron stars, the extremely energetic explosions we call _Supernovae_. So there is a lot of energy (as compression, heat, light, …) around to work with.
Both fission and fusion can convert energy into mass. It just depends on the elements. For example if you fuse iron atoms with deuterium atoms you get cobalt which have higher mass then iron and deuterium combined. This fusion does require energy input.
Most of these events happens in supernovaes. So we have not directly observed any of it. But we can see the effects of this and compare the composition of older and newer stardust to see exactly how this happens. But we can also create matter using energy in our labs. This is the primary purpose of particle accelerators. They are basically machines bulit to focus a lot of energy into a tiny area and observe what strange particles gets created. These particles have mass which far excedes the mass of the input particles.