The Peculiar Math That Could Underlie the Laws of Nature (quantamagazine.org)

xanthos writes: A fascinating article in Quanta magazine introduces us to Cohl Furey and the eight dimensional mathematics called octonions that she is using to model the interactions of strong and electromagnetic forces.

"Proof surfaced in 1898 that the reals, complex numbers, quaternions and octonions are the only kinds of numbers that can be added, subtracted, multiplied and divided. The first three of these "division algebras" would soon lay the mathematical foundation for 20th-century physics, with real numbers appearing ubiquitously, complex numbers providing the math of quantum mechanics, and quaternions underlying Albert Einstein's special theory of relativity. This has led many researchers to wonder about the last and least-understood division algebra. Might the octonions hold secrets of the universe?"

"In her most recent published paper she consolidated several findings to construct the full Standard Model symmetry group for a single generation of particles, with the math producing the correct array of electric charges and other attributes for an electron, neutrino, three up quarks, three down quarks and their anti-particles. The math also suggests a reason why electric charge is quantized in discrete units -- essentially, because whole numbers are."

Comments

Another step in our understanding of Everything

[mykepredko]

Great article and illustrates how as we try to understand reality (for lack of a better word): we first find that our current level of physics can't explain what we observe so we need to go to the next level. That next level needs the appropriate mathematical tools which often end up being already invented and looking for a practical application.

From the perspective of using a branch of mathematics that is new to the field, there's a lot of similarity between this story and using mathematics to predict crime: https://science.slashdot.org/s...

I believe we need to promote and retell these stories to students so that they can look beyond the simple and search for mathematical analogues that allow them to understand and model the physical world in different ways.

Re:cart before the horse?

[Pfhorrest]

So... you're telling me that reality is defined by an abstract algebra concept?
I thought we were using abstract algebras to *model reality*--not the other way around.

Yes. Reality will be defined by some mathematical structure or another. We can invent mathematical structures to describe any possible way that reality might be. Whatever way it turns out that reality is, whichever mathematical structure accurately describes it defines its properties.

One might even say (as Max Tegmark more or less does) that concrete existence, the kind of existence that applies to rocks and trees and such, is just a special case of abstract existence, the kind that applies to mathematical structures like numbers and triangles. All mathematical structures "exist" in that abstract sense, and the things that "exist" in a more concrete sense are just the things that are part of the same mathematical structure of which we are a part, i.e. of our physical reality.

Similar to how, as David Lewis puts it, "'actual' is indexical", i.e. in a multiverse of possible worlds (which, NB, would all be part of the concrete world we're talking about above), the "actual world" is just the one that we happen to be part of, and not ontologically different from any of the other possible worlds. We might likewise say that "'concrete' is indexical"; concrete reality is just the abstract structure of which we are a part, and not ontologically different from any other abstract structures.

It's still an empirical question to figure out which possible world (configuration) of which abstract structure we are a part of. But whatever the answer will turn out to be, there's some possible math that will describe it.

Re: Clueless editor about singularity

[Tomahawk]

If the square is negative you're imagining things. A square root being negative is just reality.