Unified Field Theory as a Pipe Dream

Not much in physics bugs me--most likely because I am not very well-versed in sciences in general. I did not read that guy's book, I didn't attend that seminar, and to be completely honest, the answer to "did you do your homework?" falls somewhere between "uhm..." and "hahahahahaha! seriously!?!".

But one thing--above all others--does. It is the idea of the Theory of Everything. It has many guises--and many refer to it as Unified Field Theory these days. Unified Field Theory (a variation of the theory of everything which reduces all to field equations) is a type of field theory that would allow all that may be thought of as fundamental forces and elementary particles to be written in terms of a single field (thank you wikipedia!). This condenses all force, all matter--into one equation (complexity unknown).

Sure this sounds difficult, but possible, right?

Wrong.

Let me explain.

So there was this smart guy named Gödel--a mathematician. He axiomated an approach to logic and validation in the form of two theorems that reference eachother that established upper limits to all but the most trivial mathematical systems. These are called "Gödel's Incompleteness Theorems".

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" is capable of proving all facts about natural numbers. Basically, no theory or set of theories can prove everything about numerical processes.

The second incompleteness theorem shows that if this system is also capable of proving basic facts about the natural numbers, then one arithmetic truth the system cannot prove is the consistency of the system itself. Or, that if the system proves something about natural numbers, then the system cannot be proven to be true.

The ramifications of this should be startling--basically any theory that involves the natural numbers cannot be complete--it is either missing some element or it itself cannot be proven to be true--it is a theory that proves incompleteness reigns.

Any "Unified Field Theory" will certainly be a consistent, non-trivial mathematical theory--and therefore, by these, it must also be incomplete. Unified Field Theory brings us nowhere--good news for us physicists!

Q.E.D.