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I Godel's ITs & the Physical World: Is a ToE impossible?

  1. Nov 16, 2015 #1
    Both Hawking and Dyson have said that Godel's incompleteness theorems prove that it is impossible for us to formulate an absolutely fundamental Theory of Everything.

    Is that true? Do the theorems apply to the physical world as they apply to the realm of mathematics?
     
  2. jcsd
  3. Jan 9, 2016 #2
  4. Jan 9, 2016 #3
    I'm not convinced. I don't see why a supertheory couldn't be self-referential. But might be right. Perhaps a more detailed exposition would do it for me.

    I'd say that nothing can ever be proved in physics. We have math, phenomena, and a provisional link between them. But I could be wrong. That's really too simple. Maybe there is some way to show that no other theory would work.

    You would be interested in Kochen and Conway's Free Will Theorem, which I think deserves much more attention than it has received. It's in the same ballpark but is a thoroughly worked out "proof" instead of an informal lecture.
     
  5. Jan 9, 2016 #4
    My question isn't really about determinism and freewill.
     
  6. Jan 9, 2016 #5
    Geometry is built on axioms and I'm told it is complete; no theorems exist in the theory that cannot be proved by the existing axioms. And yet geometry can be described with mathematics which is incomplete. So does that make geometry complete or incomplete? I think geometry is complete since the math is limited to that necessary for a description of geometry. Likewise, I think the math used in physics is limited to only that used to describe the theorems of physics (whatever those turn out to be). Physics is not an effort to prove every theorem of math. It's an effort to find the smallest set of physical rule necessary to describe reality.
     
  7. Jan 10, 2016 #6

    Demystifier

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    Godel's theorems do not imply many things which people sometimes think they do. In particular, they do not imply that "it is impossible for us to formulate an absolutely fundamental Theory of Everything". I highly recommend to read the book
    https://www.amazon.com/Gödels-Theorem-Incomplete-Guide-Abuse/dp/1568812388
     
    Last edited by a moderator: May 7, 2017
  8. Jan 10, 2016 #7
    If you read that lecture you will see that Hawking absolutely does NOT say that GIT proves anything about physics.
     
  9. Jan 10, 2016 #8
    oh, you're right. apologies for being such an idiot.
     
  10. Jan 11, 2016 #9

    Demystifier

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    Or maybe you are not an idiot. In the last paragraph Hawking says
    "Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind. I'm now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery." (my bolding)

    Hawking is not clear how exactly he arrived at that conclusion, but it seems to be motivated by the Godel's theorem.
    Nevertheless, strictly speaking, that conclusion does not follow from the Godel's theorem.
     
  11. Jan 11, 2016 #10
    True, but Kochen-Conway showed that some things will never be predictable. Would that mean that an "absolutely fundamental TOE" is impossible?
     
  12. Jan 11, 2016 #11
    Distinguishing incomplete from complete is quite technical. Diophantine equations are incomplete, but it wasn't easy to prove that. I don't know whether geometry is complete. The first step would be to define geometry, and I wouldn't know how to do that. The old compass and straightedge stuff is almost surely complete.
     
  13. Jan 11, 2016 #12

    Demystifier

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    They didn't show that.
     
  14. Jan 11, 2016 #13
    Who says?
     
  15. Jan 11, 2016 #14
    How does things not being predictable lead to the impossibility of a TOE?
     
  16. Jan 11, 2016 #15
    Thanks. I was wondering how a mathematical theorem without experimental basis could lead to physical results.
     
  17. Jan 11, 2016 #16
    Such is their claim.
     
  18. Jan 11, 2016 #17

    Well, it depends on your definition of a TOE.
     
  19. Jan 11, 2016 #18
    Ok, you give me one and then show how it relates to predictability.
     
  20. Jan 11, 2016 #19

    You are the one who brought it up. I don't care.
     
  21. Jan 11, 2016 #20
    From what I can gather, they did not claim anything regarding whether determinism is true or not, they didn't say that some things will never be predictable.

    They just stated a relationship between particles and human free will IF certain conditions are true.
     
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