Where do Quantum corrections matter?

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Discussion Overview

The discussion revolves around the relevance of quantum corrections in the context of General Relativity (GR) and their implications at both small and large scales. Participants explore whether these corrections are significant in extreme environments like black holes and if they could influence gravitational behavior at larger distances.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants suggest that quantum corrections to the equations of relativity are likely important at very small scales, such as near black holes.
  • Others argue that at large scales, gravity behaves linearly, which implies that small-scale quantum effects would not significantly impact large-scale gravitational behavior.
  • A participant notes that while linearity suggests a lack of dramatic effects from small-scale changes, there remains a possibility of unknown factors influencing gravity at large distances.
  • Follow-up questions inquire about the exactness of solutions to the field equations in GR, with some participants clarifying that exact results are contingent on precise input values.
  • It is mentioned that for simple systems in GR, exact solutions exist, but this does not hold universally for all scenarios.
  • A participant requests further elaboration on the conditions under which exact solutions apply, indicating a desire for deeper understanding.

Areas of Agreement / Disagreement

Participants express differing views on the significance of quantum corrections at large scales, with some asserting their irrelevance due to linearity in gravity, while others remain open to the possibility of unknown influences. The discussion on the exactness of field equation solutions also reveals varying interpretations and conditions.

Contextual Notes

Limitations in the discussion include the dependence on specific definitions of "exact," the conditions under which GR solutions are considered, and the unresolved nature of the relationship between quantum effects and gravitational behavior at different scales.

Galteeth
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Caveat: layperson question.


I know we don't have a unified theory of GR and quantum fields. From what I have read, it appears to be generally assumes that quantum corrections to relativy's space warping equations probably matter at very small scales, like in black holes.

Is it thought that they also matter at large scales, sort of like chaos?
 
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Galteeth said:
Caveat: layperson question.


I know we don't have a unified theory of GR and quantum fields. From what I have read, it appears to be generally assumes that quantum corrections to relativy's space warping equations probably matter at very small scales, like in black holes.

Is it thought that they also matter at large scales, sort of like chaos?
Nope. Chaos theory is used to model non-linear dynamical systems. At large scales, gravity is linear. Linearity basically means that if you produce some change in the system, the response to that change is a simple multiple of the input. That is, if I change a system by an amount X, and the result is a change Y, and then change the system by an amount 2X, the result will be a change of 2Y. When you have linearity, there really isn't any room for changes in small-scale behavior to have dramatic effects upon large-scale behavior.

That said, I will grant that it is possible that there is some change of which we are currently unaware that may cause changes to gravity at large distance scales. But it seems extremely unlikely for the above reasons.
 
Chalnoth said:
Nope. Chaos theory is used to model non-linear dynamical systems. At large scales, gravity is linear. Linearity basically means that if you produce some change in the system, the response to that change is a simple multiple of the input. That is, if I change a system by an amount X, and the result is a change Y, and then change the system by an amount 2X, the result will be a change of 2Y. When you have linearity, there really isn't any room for changes in small-scale behavior to have dramatic effects upon large-scale behavior.

That said, I will grant that it is possible that there is some change of which we are currently unaware that may cause changes to gravity at large distance scales. But it seems extremely unlikely for the above reasons.

Thanks!
 
Follow up question: Is it known that the solutions to the field equations give exact results?
 
Galteeth said:
Follow up question: Is it known that the solutions to the field equations give exact results?
Exact in what way?
 
Chalnoth said:
Exact in what way?

If the values of the inputs are known exactly, the results the equations give wil be exact results, not approximate.
 
Galteeth said:
If the values of the inputs are known exactly, the results the equations give wil be exact results, not approximate.
In General Relativity, for simple systems, yes, this is the case. But not in general.
 
Chalnoth said:
In General Relativity, for simple systems, yes, this is the case. But not in general.

Could you elaborate on that a bit? Or direct me to a resource that does?

Also, i wanted to thank you for taking the time to answer my questions.
 
Galteeth said:
Could you elaborate on that a bit? Or direct me to a resource that does?

Also, i wanted to thank you for taking the time to answer my questions.
Well, two cases I know of that are solved exactly in GR are spherically-symmetric systems, and a homogeneous, isotropic universe. There may be others, I'm not certain.
 

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