Where do Quantum corrections matter?

[Galteeth]

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?

[Chalnoth]

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.

[Galteeth]

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!

[Galteeth]

Follow up question: Is it known that the solutions to the field equations give exact results?

[Chalnoth]

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

[Galteeth]

Exact in what way?

If the values of the inputs are known exactly, the results the equations give wil be exact results, not approximate.

[Chalnoth]

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.

[Galteeth]

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.

[Chalnoth]

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.