Implication of Goedel's theorems on physics

In summary, the conversation discusses the relationship between mathematics, physics, and Goedel's theorem. The physicist argues that mathematics is the foundation of many sciences, including physics, and that we can rely on experimentation to prove the noncontradiction of physics. The mathematician suggests that Goedel's theorem may apply to physics as an axiomatic system, but the physicist argues that physics is not an axiomatic system and thus the theorem does not apply. The conversation ends with the idea that we can still use a pragmatic approach in understanding and using physics without needing to prove its noncontradiction.
  • #1
aman
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I am a graduated mathematician.

Do you know that Kurt Godel proofed that it is not possible to proof that math is not noncontradiction?
Physicist and a lot of other sciences are based od math.
So, how can you proof that whole physics' is noncontradiction?You just believe in it as someone in God?
 
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  • #2
aman said:
So, how can you proof that whole physics' is noncontradiction?
You are currently using an artificial computing machine based on quantum theory and probably equipped with wireless communication technology that requires special relativity to understand (and general relativity if it has GPS). You have evidence literally in front of you that our understanding of the world is very, very good. If there's some obscure flaw in the logic of our theoretical models it'll eventually out itself when we try to build something and get contradictory results.
 
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  • #3
aman said:
So, how can you proof that whole physics' is noncontradiction?
By experiment.

In any case, I think your description above is a mischaracterization of his theorem. But for a correct characterization the answer to your question is still experiment.
 
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  • #4
aman said:
You just believe in it as someone in God?
All Gods believe in mathematics.
 
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  • #5
aman said:
So, how can you proof that whole physics' is noncontradiction?
I do not care because we may not be able to know whole physics, only little by little forever.
 
  • #6
One builds the edifice of Physics brick by brick and occasionally one finds that a section here or there needs to be rebuilt. Perhaps we will get to the end and perhaps we will discover the last brick does not fit. What to do?
 
  • #7
aman said:
So, how can you proof that whole physics' is noncontradiction?
Goedel's theorem is about axiomatic systems. Physics and other empirical sciences are not axiomatic systems so the theorem does not apply in any useful way.
 
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  • #8
I see no need to show that Physics is noncontradiction any more than my assumption that my car will get me from a to b tomorrow.
We have a present model for Physics that works (predicts) things more than adequately.
It’s not necessary to believe that there is any fundamental truth about the World so no god-like approach is necessary. We can be pragmatic.
 
  • #9
aman said:
Do you know that Kurt Godel proofed that it is not possible to proof that math is not noncontradiction?
Physicist and a lot of other sciences are based od math.
So, how can you proof that whole physics' is noncontradiction?
I have not read the article "Goedel and Physics" by John Barrow, I just know that it exists.

https://arxiv.org/abs/physics/0612253
 
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1. How do Goedel's theorems affect our understanding of the physical world?

The implications of Goedel's theorems on physics are primarily related to the limits of formal systems and the notion of completeness. These theorems show that no formal system, including mathematics and physics, can be both consistent and complete. This means that there will always be statements that cannot be proven or disproven within a given system, leading to uncertainties in our understanding of the physical world.

2. Can Goedel's theorems be applied to all branches of physics?

Yes, Goedel's theorems have implications for all branches of physics, including classical mechanics, quantum mechanics, and general relativity. This is because they are based on fundamental concepts of logic and mathematics, which are used in all areas of physics.

3. What are some specific examples of how Goedel's theorems have influenced physics?

One example is the uncertainty principle in quantum mechanics, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. This is in line with Goedel's incompleteness theorem, as it shows that there are limits to what we can know and measure in the physical world.

Another example is the limitations of the Standard Model in particle physics, which is a set of equations that describe the fundamental particles and forces in the universe. Goedel's theorems suggest that there may be aspects of the universe that cannot be explained by the Standard Model.

4. How do Goedel's theorems impact the search for a theory of everything?

Goedel's theorems have significant implications for the quest to find a theory of everything, which would unify all the fundamental forces and particles in the universe. These theorems suggest that there may be limitations to our ability to fully understand and describe the universe, and that a complete and consistent theory may not be attainable.

5. Are there any potential drawbacks to applying Goedel's theorems to physics?

Some scientists argue that the application of Goedel's theorems to physics may be limited, as they were originally formulated for mathematical systems and may not directly translate to the physical world. Additionally, some critics argue that the uncertainty and incompleteness suggested by these theorems may undermine the objective and deterministic nature of physics.

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