Developments to unify quantum theory with General Relativity?

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Discussion Overview

The discussion revolves around recent developments in the unification of quantum theory with General Relativity, exploring the implications of incompleteness in physical theories and the philosophical aspects of mathematical logic in this context.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants note a perceived lack of progress in string theory and loop quantum gravity regarding the unification of quantum theory and General Relativity.
  • One participant suggests that an "incompleteness" in the unification scheme is inevitable, drawing a parallel to Gödel's work in mathematics.
  • Another participant expresses skepticism about the applicability of Gödel's incompleteness theorems to physical theories, arguing that physical theories cannot be proven incomplete in the same way as mathematical systems.
  • A participant challenges the reasoning that leads to the conclusion that physical theories might "not make sense," questioning the connection between mathematical incompleteness and the coherence of physical theories.
  • There is a discussion about the nature of axioms in mathematics, with a participant explaining that unprovable propositions can become axioms, which may not necessarily be true or false.
  • One participant proposes that a potential limitation in unifying theories could be similar to the Bell theorem, which might suggest that no theory can simultaneously satisfy certain properties related to quantum mechanics and general covariance.

Areas of Agreement / Disagreement

Participants express differing views on the implications of Gödel's theorems for physical theories, with no consensus on whether incompleteness can be proven in this context. The discussion remains unresolved regarding the relationship between mathematical logic and physical coherence.

Contextual Notes

Participants reference Gödel's theorems and their implications for mathematical systems, but the applicability of these concepts to physical theories is debated. The discussion highlights the complexity of defining coherence and completeness in the realm of theoretical physics.

mathman
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Have there been any recent developments in the attempt to unify the standard model of quantum theory with General Relativity? It appears the no progress has been made recently in string theory or loop quantum gravity.
 
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As time passes by it seems to me that a sort of "incompleteness" in this unification scheme is in order.
Just awaits for Godel of Quantum Gravity to prove it... :oldbiggrin:
 
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I am somewhat more optimistic. Godel was dealing in mathematics. I doubt if you can "prove" incompleteness for physical theories.
 
mathman said:
I am somewhat more optimistic. Godel was dealing in mathematics. I doubt if you can "prove" incompleteness for physical theories.
What will make you a pessimist?
Well a physical theory is constructed with maths, so the mathematics will be incomplete, and the physics won't make sense anyway, it's either inconsistent or incomplete.
 
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MathematicalPhysicist said:
Well a physical theory is constructed with maths, so the mathematics will be incomplete, and the physics won't make sense anyway, it's either inconsistent or incomplete.
This seems like a total non sequitur to me. How do you get from true but not provable propositions in an axiomatic system to propositions that “won’t make sense”?
 
Nugatory said:
This seems like a total non sequitur to me. How do you get from true but not provable propositions in an axiomatic system to propositions that “won’t make sense”?
Well "making sense" is with regards to classical logic.
It might make sense for someone using paraconsistent logic or some other non-conventional logic I am unaware of.
 
Nugatory said:
This seems like a total non sequitur to me. How do you get from true but not provable propositions in an axiomatic system to propositions that “won’t make sense”?
Godel does not have "true but not provable" propositions. It has unprovable propositions that become axioms as you extend the maths. The axioms are neither true not false. You can accept them as true, or you can accept various negations of them as true. E.g. the unprovable generalized continuum hypothesis may be accepted or rejected according to taste.

https://en.m.wikipedia.org/wiki/Continuum_hypothesis
 
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mathman said:
I am somewhat more optimistic. Godel was dealing in mathematics. I doubt if you can "prove" incompleteness for physical theories.
It could be something like the Bell theorem for local hidden variables in quantum mechanics. The theorem might state that no theory can simultaneously have properties of being (i) quantum, (ii) general covariant and (iii) obeying some additional property that currently everybody takes for granted.
 

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