A Theory of Everything, for Everyone

Read this article in the Indiana Daily Student here....

Hilbert's tomb
Since a theory of everything would all the forces of matter, it would be elegant in how much information could be explained so simply. The math and physics behind theory would all have a function with everything else, and there would be nothing below it. As MIT Physics Professor Frank Wilczek put it, “You can recognize truth by its beauty and simplicity.” [3] But, during the 19th century, while physiologist Emil du-Bois Raymond proclaimed "ignoramus et ignorabimus" (or "we do not know and we will not know"), mathematician David Hilbert would write "For the mathematician there is no Ignorabimus, and, in my opinion, not at all for natural science either. ... The true reason why [no one] has succeeded in finding an unsolvable problem is, in my opinion, that there is no unsolvable problem. In contrast to the foolish Ignorabimus, our credo avers: We must know, We shall know.'"

Beyond what physics can tell us about how matter and forces work, there are issues with the way mathematical statements can actually explain the world. Is mathematics the language through which we describe nature or is it something that nature itself is made of? Is a theory of everything the end of knowledge the same way all biological organisms evolved from a single one? And what if there is no theory of everything? As 20th century American physicist Richard Feynman speculated, it is possible there is no theory that applies everywhere all the time.[1] Everything we observe will have something below it, and we’ll never get to any most fundamental theory.

Doing Gödel's work, son


We might be inclined to search for an answer in logic, a field that we think would prove the answers to all forms of reasoning, and, therefore, all knowledge. The most striking example of how we can prove/disprove these sorts of answers lie in Kurt Gödel's theorems that explain how there exist mathematical statements that can't be proven. And, one might think that, similarly, there are is physics information that can't be proven, either. The trouble with this is that, while Gödel's Incompleteness theorems only say for some fixed, recursively defined, axiom system there are statements you can't prove or disprove, that shouldn't matter for physics because you can just add new axioms when you want. Physics doesn't require a fixed-axiom system.

Save work on the Standard Model (on the fundamental forces and their interactions), theoretical physics hasn't had much success over the past few decades. There are things like string theory, loop quantum gravity, and similar theories, but, while they are ideas that could be true, we don't know.

The are epistemic problems with a theory of everything, as well. Why is it true that we can understand anything? Does finding out how the laws of nature work explain why they are the way they are? And, if we don’t know everything, how can we know anything?

References:
[1] http://nautil.us/issue/29/scaling/the-trouble-with-theories-of-everything
[2] http://www.pbs.org/wgbh/nova/physics/theory-of-everything.html
[3] http://ppp.unipv.it/collana/pages/libri/saggi/nuova%20voltiana3_pdf/cap4/4.pdf