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I don't remember where I read it, nor the exact wording, but there is a quote that is perfect for this. It went something like this, "Godel proved incompletenes
by brentr 18y ago
I don't remember where I read it, nor the exact wording, but there is a quote that is perfect for this. It went something like this, "Godel proved incompleteness. Anyone who thinks there is a theory of everything laughs in the face of Godel."
My point is that physics does not exist in a vacuum. It is built up from observational data found in nature and taken from experiments. If mathematics can't come to complete truth (Godel has proven this), then there is no hope for a theory of everything in something that uses mathematics as its language.
- DanielBMarkham 18y agoI'm with you about 80% of the way here. Godel showed (and guys tell me if I mess this up) that formal self-consistent systems have both statements that are true that cannot be proven and false statements that cannot disproved. In other words, complete systems are incomplete. This does not mean that complete systems cannot model reality to a high degree -- there's no reason why a ToE could pop out from some rotation or transmutation of mathematics. It just means there would be parts of it that would be incomplete -- the model itself could have a very high degree of fidelity. When applied to higher math and physics, this is another way of saying "you don't know what you don't know" ie, the models can work perfectly across all observation space and still be true to Godel.
- Asmodeus 18y agoIt will be incomplete in the sense that it will contain axioms with no formal proof. Technically speaking the TOE is this axiom. However, you can even prune these axioms by selecting for the simplest one that conflicts with the least data.
- sarehu 18y agoThat's complete nonsense. There's nothing about Godel's theorem that says the physical rules of the universe can't be described. You're babbling religiously.
- brentr 18y agoCheck out the following entry on Wikipedia related to Godel's Incompleteness Theorem and the Theory of Everything http://en.wikipedia.org/wiki/Theory_of_everything http://en.wikipedia.org/wiki/Theory_of_everything
- sarehu 18y agoWhat about it? All Godel's incompleteness theorem says is that there will be open questions about a universe describable by finitely many rules. The laws of physics don't need to provide answers to questions about whether computers in its universe will halt or whether planetary systems are stable.
- brentr 18y agoWhat do you mean "the laws of physics don't need to provide answers to whether planetary systems are stable"? Since when are planetary systems outside of physics? Your sentence "All Godel's incompleteness theorems says is that there will be open questions about a universe describable by finitely many rules" shows right there that there cannot be a theory of everything. How can you have a theory of everything yet still have open questions? That means that you have not answered everything.
- sarehu 18y agoIt's my understanding that a theory of everything describes the rules by which the universe operates. It doesn't say anything about emergent properties of these rules. For example, if everything in the universe obeyed Newtonian mechanics, I would say that Newtonian mechanics was a theory of everything. You would say that it isn't.
- mlinsey 18y agoTechnically, a "Theory of Everything" in physics is just a theory that relates the four known forces in the universe: gravity, electromagnatism, strong nuclear, and weak nuclear. The latter three (I believe) have already been unified. It's a "theory of everything" because it describes every force in the universe. That of course does not imply that the theory of everything automatically gets you a complete description of the universe. Even in the context of a single force, it can be difficult/impossible to come up with a closed form solution for how many different objects interact subject to that force. For example, the behavior of gravity is really well understood but that doesn't mean that we can come up with straightforward, closed form solutions for the n-body problem of a bunch of stars interacting with each other's gravitational pulls in space.
- gaika 18y agoOne counterexample for you: Conway's game of life has finite number of rules but you can construct universal turing machine with it that will have formally undecidable behaviour.
- ninguem1 18y ago"Theory of Everything" is not a theory for everything, literally. It is just a catchphrase used by physicists to mean a theory that encompasses the "Standard Model" (which describes particle physics) with General Relativity and gravitation, thus describing the whole physical universe (which, in the physicists narrow mind, is everything). So Godel has nothing to do with this.
- hhm 18y agoYou can have a theory of everything that is incomplete. There are no problems with that. And that's what people is looking for... ToE doesn't mean "a complete theory of physics", in the logical meaning of complete.