Theory of Everything and Godel’s incompleteness theorem
Published by admin April 17th, 2008 in Authority, Doctors of Philosophy, cosmologyA commenter yesterday wrote regarding Max Tegmark’s mathematical universe that
maybe our universe is a mathematical object . . . but can we understand this object? Can we solve the equations? I seriously doubt it, we are already having troubles with Navier-Stokes, let alone Dirac coupled with Maxwell, and even with classical mechanics. I rest my case.
This makes sense to me. Furthermore, there seems to be a lot of research proving that a true theory of everything would violate Godel’s incompleteness theorem. Hawking makes a good case here:
We and our models, are both part of the universe we are describing thus a physical theory, is self-referencing like in Godel’s theorem. One might therefore expect it to be either inconsistent, or incomplete. The theories we have so far, are both inconsistent, and incomplete.
Wikipedia also cites many critiques of this view. As usual physicists are having fun with a pun. They’ve turned everything into a pun and exploit this fertile scholastic field they’ve created.
To me Godel’s theorem does not apply to physics. In physics all symbols and objects are context sensitive. Interpretation is proportional to interpreting Doctor’s authority. No object makes sense without doctoral interpretation. In other words, physics is not science. It is the old scholastic profession. Godel’s theorem does not apply to a field where practitioners seriously consider the possibility of a theory of everything. Also, physics theories are space-filling theories. If there is one theory of everything soon there will be many theories of everything. So, regardless of Godel’s theorem, a physical theory of everything is impossible. There will always be too many of them.
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I agree with you and Hawking and Godel and Chaitin that a Theory of Everything is a self referential impossibility.
We are all part of “The Matrix” known as our “Reality” and therefore find it impossible to establish a true meta-view of the architecture of this reality.
What we can achieve however is to enumerate a set of overarching physical and cultural principles that can help us unify our matrix and comprehend it at a local level.- eg symmetry, beauty, evolution, logic, quantum field theory, thermodynamics, entropy & information, networks, decisions, relativity etc.
This may then provide us with a means of testing the truth of the next russian doll level as in Tegmark’s mathematical universe or Frank Tipler’s Omega Pioint hypthesis.
Good luck & thankyou
david hunter tow
Thank you for your thoughtful comment.
I agree with you and Hawking and Godel and Chaitin that a Theory of Everything is a self referential impossibility.
I was reading a tutorial about Haskell programming language. Someone told me that it would help resolve my confusion about data types in physics. The tutorial gives this example about a recursive program:
Supposedly the same program would result in an infinite loop in non-functional languages such as C. In Haskell, as it’s lazy, it’s possible to create recursive programs and as long as you refer to a finite set of values the program will work. At lest this is what I thought it was. In a way this sounds like what you are suggesting: We may look for the Theory of Everything or define one, and we may never find it but as long as we stay local we’ll find out about our matrix and unify what we know. A sort of lazy Theory of Everything. Newton did something similar. He presented his definition of force as a Theory of Everything when he called it universal law of gravity. But his universal force can only be locally known (even if it existed.) We also do the same with pi. We only use the first few numbers. In the case of the universe, we do not know the geometric properties of the totality to form a ratio. We may be seeing a local manifestation of a mathematical object but we do not know the ratios that created what we see.
The totality is unknown to us. The entire existence from first man to the last, compared to the lifetime of totality, may be shorter than the lifetime of moth who lives but just a day. That moth will never know the seasons or weeks and may not even know the Moon, let alone galaxies. Can a moth cosmologist claim to know the universe and describe it as a Theory of Everything? No. I believe that the same is true for a human cosmologist. Therefore, your suggestion, if I understand it correctly, of yearning for the universal while remaining local seems like a pragmatic solution.
Thanks again.