Summing gravity fields

[geordief]

I have heard that this is "notoriously difficult" and I think it must be done by computers (perhaps in the way that weather forecaster make millions of parallel calculations on ideally very small cells and ties them together)

 

I also imagine (from what I have learned so far) that it may be that it is the spacetime tensors that could be summed in order to produce the resulting global field.

 

Are there any alternative ways to do this process.?

 

 

[TakenItSeriously]

I've dealt with electromagnetic field solvers before.

 

https://en.m.wikipedia.org/wiki/Electromagnetic_field_solver

 

Though, Im not sure if they would be appropriate to use. I understand that they are based upon some kind of FEM analysts, but I'm assuming it must be dependent on anchoring a structure to some reference point which, I assume, wouldn't work for a gravity wave.

 

Edit to add:

I see your talking about gravity "fields" so, perhaps it could work as long as you establish an inertial reference frame to the massive object under study.

 

The two fields are based upon the same formulas, they are only different in magnitude.

Edited July 9, 2016 by TakenItSeriously

[ajb]

The problem with general relativity is that it is hightly non-linear. You cannot simply add two solutions to get another one.

[geordief]

The problem with general relativity is that it is hightly non-linear. You cannot simply add two solutions to get another one.

Is there such a thing as a "unit" gravitational field ?

 

Is it possible to model how one object with unit characteristics interacts with another object (again with unit characteristics) at a unit distance and ignoring external objects?

 

If this was possible could one build upon that ? Does everything get too complex practically immediately and so the task is handed over to computers?

 

I remember before the advent of supercomputers ,weather forecasters did their best nonetheless and I think it was said the skill was something of an "art"

Edited July 9, 2016 by geordief

[TakenItSeriously]

The problem with general relativity is that it is hightly non-linear. You cannot simply add two solutions to get another one.

But then wouldn't that make computer modeling a more practical solution?

 

Edit to add:

Or perhaps modeling two fields prevents establishing a single inertial reference frame?

Edited July 9, 2016 by TakenItSeriously

[ajb]

Is there such a thing as a "unit" gravitational field ?

Not really, we don't have a linear structure on the space of solutions.

 

 

But then wouldn't that make computer modeling a more practical solution?

Yes, and people do this.

 

 

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Edit: What people often do it take an exact solution and then consider adding a solution to the linearised equations. Then in an approximate sense the sum of these two solutions is a solution.

Edited July 9, 2016 by ajb

[geordief]

Not really, we don't have a linear structure on the space of solutions.

 

 

 

Am I going too far to say that gravity seems as intrinsically non deterministic as quantum theory?

 

Is it also inherently statistical? Would "chaotic" describe it better? (is that the same as "non-linear" ?)

[ajb]

Am I going too far to say that gravity seems as intrinsically non deterministic as quantum theory?

The theory of gravity is deterministic - as is quantum theory in the sence that given a state and the equation of motion I know what the state will be at any future time. It is just that the results of measurements are given in terms of probbailities.

 

 

Is it also inherently statistical? Would "chaotic" describe it better? (is that the same as "non-linear" ?)

It is not by itself statistical. If you consider a large number of particles interacting non-gravitationally say, then in principle you can describe their invididual motions. But in practice you cannot and so you pass to statistical methods.

 

This could be chaotic.

 

Also, you could think about the evolution of a Cauchy surface - I guess this maybe chaotic, I am not sure.

[TakenItSeriously]

Am I going too far to say that gravity seems as intrinsically non deterministic as quantum theory?

 

Is it also inherently statistical? Would "chaotic" describe it better? (is that the same as "non-linear" ?)

 

IMHO, I think that's probably a true statement if you look at string theory and quantum gravity loops. Both require extra dimensional solutions.

[geordief]

Is a Cauchy surface what you get when you set t=constant in the spacetime manifold?

[ajb]

Is a Cauchy surface what you get when you set t=constant in the spacetime manifold?

It is more technical than that, but yes.

 

You could think about GR in the space-time cut formalism as an initial Cauchy surface that evolves in time. I imagine due to the non-linear nature of GR that this evolution could be chaotic, but I am not sure as this is not close to my actual interests.