Wavefunctions are functions (think f(x) = y) that take a system state as input and produce something like the square root of a probability as output. The “square root of a probability” takes the form of a set (vector) of complex numbers. These functions are called
I haven't read through all of this, but I'm sure you took a wrong turn, because at the end you're saying quantum wavefunctions are complex-valued because quaternions are how you should represent quantities in space-time, and that all this has something to do with spinors. And that's wrong in multiple ways.
A quantity is a spinor if it transforms in certain ways under rotations. A complex-valued object in space-time doesn't have to be a spinor; it can also be a scalar, vector, or tensor. Also, on the physics side, a large part of the significance of spinors is that they necessarily become fermionic when quantized.
I suggest reading some resources that don't try to reduce everything to Clifford algebras...
Check https://paperclip.substack.com/p/comments-on-understanding-wavefunction for a changelist.
I haven't read through all of this, but I'm sure you took a wrong turn, because at the end you're saying quantum wavefunctions are complex-valued because quaternions are how you should represent quantities in space-time, and that all this has something to do with spinors. And that's wrong in multiple ways.
A quantity is a spinor if it transforms in certain ways under rotations. A complex-valued object in space-time doesn't have to be a spinor; it can also be a scalar, vector, or tensor. Also, on the physics side, a large part of the significance of spinors is that they necessarily become fermionic when quantized.
I suggest reading some resources that don't try to reduce everything to Clifford algebras...