stevestory
Posts: 13407
Joined: Oct. 2005
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| Quote | 12
Viola Lee
July 24, 2021 at 8:10 pm
I really hate to reappear, but here is a point I have made before that I think BA doesn’t get.
BA writes,
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And for quite a few years I myself have been mystified that leading mathematicians who work in theoretical physics, such as Peter Woit, have basically completely ignored Godel’s incompleteness theorem, and the insurmountable problem that it presents as to ever finding a purely mathematical theory of everything
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Godel’s Incompleteness Theorem’s are about purely mathematical axiomatic systems. Theoretical physicists are not trying to create a purely axiomatic system: they are trying to crate a descriptive system which maps completely to real-world phenomena, especially one which unifies general relativity and the quantum mechanics.
These are two different things. Godel’s Theorems says that there are undecidable propositions, and establishes this in an esoteric way. Here is a fairly good layman’s explanation: Link
However a theory about the physical world would be complete if it could explain and predict every possible real-world phenomena. However, if one were to consider the theory as a pure axiomatic system (which is not what the theoretical physicists is trying to do) the undecidable propositions that Godel’s theorem says must exist might not in fact map to any real-world phenomena, and thus be irrelevant.
The key idea here is between an purely abstract mathematical system, which is self contained and only looks to itself for its content, and a physical theory which maps mathematical content to real-world phenomena, and then looks to its fit with real-world phenomena for its validity.
Godel’s Theorem does not rule out the possibility of a theory of everything in the sense of a mathematical model which accurately describes, in an unifying way, general relativity and quantum mechanics.
Over and out. Take it away, BA, but keep it under 5000 words. Others may also have something to say about whether they think I’m right or not. |
Linky
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