According to VenDell, there are three things that make up the cosmere: matter, energy, and Investiture. Each of these can be transformed into one another. While seemingly obvious, this can explain a lot of the strange phenomena we've seen in the various magic systems Brandon has created. Also, it brings to light some interesting questions about how the cosmere is different from our world.
Investiture => Energy
This transformation is the easiest to piece together. It explains how a lot of the cosmere's magic works: half of the surges (Adhesion, Gravitation, Division, Abrasion, and Progression), some aspects of Allomancy, and most Aons are at least partially dictated by this rule. Perhaps in Era 4 an e=mc^2-type equation would be in use.
Energy => Investiture
This one's harder to find examples of, but Lift definitely makes use of it: some of the chemical energy from her food turns into Investiture during cellular respiration instead of kinetic and heat energy.
Investiture => Matter
According to VenDell, God Metals are an example of this. But what kind of matter are they?
This is really what I wanted to get to with this post. The evidence presented in tLM kind of contradicts itself when talking about what trellium and harmonium are. I have a few theories:
1. Harmonium is a heavy alkali metal
This is a bit of a crack theory: the only real evidence for this is that Harmonium is silvery and reacts violently with water -- the two main properties of alkali metals. Perhaps in the cosmere, atoms work slightly differently, with Investiture assisting protons and neutrons packing in a way that makes Francium or Ununennium (the undiscovered Element #119) have stable isotopes. I have no idea where lerasium, atium, or trellium fit into this, though, and it also doesn't work because of another reason: the emission spectrum.
2. Matter doesn't work the same way in the cosmere
An atom's emission spectrum is dictated by how it emits photons when its electrons change energy levels. This creates several lines, which each correspond to a certain type of electron in the atom. I think. I don't quite understand how it works. Anyway, no currently known element has a full emission spectrum like the god metals do. I propose that "axi," which are stated a few times to be the fundamental particles of the cosmere, work radically differently from the fundamental particles of our universe. This would fit with some of the strange properties we've seen ordinary Earth objects having, most notably aluminum/ralkalest/aluminium being a sort of insulator for Investiture. Since no world we've seen has gotten far enough scientifically to develop a theory of atoms and whatnot, we have no idea what the cosmere could look like on an atomic/quantum scale.
3. God Metals aren't truly matter
My favorite theory coming out of this is that God Metals work in a way similar to Stormlight, and that they're both at an in-between spot; not truly matter and not truly Investiture. When Stormlight is put through a prism, it produces results very similar to when you use a spectrograph on God Metals. Neither of these work the way that we expect matter and light to work in our universe, but they seem to have the same basic properties as those things. Plus, VenDell explicitly said that God Metals are matter. I propose that he was oversimplifying a tad, and that God Metals aren't exactly matter -- but not a form of Investiture, either.
Let me know if you have any other theories.
Matter => Investiture
Sand mastery turns water into Investiture. Allomancy turns metals into Investiture -- at least, that's what I assume, since it seems like iron filings would be a tad hard to digest.
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P.S. Nerdy, most of this post was written before I started the haiku challenge, so it doesn't count. Also, it would be madness to post this whole thing in a haiku format.