How do gravitational fields interact?

[geordief]

Two massive bodies approach each other and their fields ,I imagine combine in some way so that a third object's worldline  is affected  (is different from what it would otherwise  have been )

 

What methods are used to  calculate the resultant gravity field from the 2 contributory  fields?

 

Also ,separately (but the two questions may be connected) have there been ,or are there any underway that try to show any quantum effects  when two bodies gravity fields interact? 

Is it possible to look at the behaviour of 2 very small objects  and search for quantum effects in the way they move wrt each other?

[swansont]

7 hours ago, geordief said:

 

Is it possible to look at the behaviour of 2 very small objects  and search for quantum effects in the way they move wrt each other?

“move” is a poor description to use here, since it suggests a classical trajectory. 

[Strange]

8 hours ago, geordief said:

Also ,separately (but the two questions may be connected) have there been ,or are there any underway that try to show any quantum effects  when two bodies gravity fields interact? 

Is it possible to look at the behaviour of 2 very small objects  and search for quantum effects in the way they move wrt each other?

There is this:

Quote

The proposed experiment will determine whether two objects — Bose’s group plans to use a pair of microdiamonds — can become quantum-mechanically entangled with each other through their mutual gravitational attraction. 

https://www.quantamagazine.org/physicists-find-a-way-to-see-the-grin-of-quantum-gravity-20180306/

I don't know if there is any more recent information available

[joigus]

10 hours ago, geordief said:

What methods are used to  calculate the resultant gravity field from the 2 contributory  fields?

The resultant gravity field is the sum of the fields in Newtonian gravity, both for force fields or for potentials (superposition principle for Newtonian gravity.) It's a good approximation if the fields are not very strong. "Very strong" means that the Newtonian potential divided by c² is << 1. In GR it's much more complicated (strong fields.) But even in the Newtonian case the resultant gravity field doesn't really solve the problem of motion if the three masses are comparable, as you are in the 3-body problem, which can only be approached numerically or perturbatively (by calculating incremental approximations from a simple particular solutions.) The reason is that any of the three bodies interact with the other two, and the equations cannot be separated.

I'm not sure I'm answering your question, I'm trying incremental approximations to your question.  

I hope it adds something significant.

I forgot: Mixing quantum mechanics and gravity is not possible as of today. Some people (Beckenstein, Hawking) have successfully combined both to do calculations, but it doesn't generalize very easily at all. Plus gravity generally is negligible in the very small world.

Edited June 4, 2020 by joigus
addition

[swansont]

1 hour ago, joigus said:

 

I forgot: Mixing quantum mechanics and gravity is not possible as of today. Some people (Beckenstein, Hawking) have successfully combined both to do calculations, but it doesn't generalize very easily at all. Plus gravity generally is negligible in the very small world.

Depends on how you mix them. There is no quantum theory of gravity, but QM effects owing to gravity could be observed. Atoms going through an interferometer where the paths diverge vertically would show an effect. Gravitational time dilation is seen in quantum states.

[geordief]

1 hour ago, joigus said:

The resultant gravity field is the sum of the fields in Newtonian gravity, both for force fields or for potentials (superposition principle for Newtonian gravity.) It's a good approximation if the fields are not very strong. "Very strong" means that the Newtonian potential divided by c² is << 1. In GR it's much more complicated (strong fields.) But even in the Newtonian case the resultant gravity field doesn't really solve the problem of motion if the three masses are comparable, as you are in the 3-body problem, which can only be approached numerically or perturbatively (by calculating incremental approximations from a simple particular solutions.) The reason is that any of the three bodies interact with the other two, and the equations cannot be separated.

I'm not sure I'm answering your question, I'm trying incremental approximations to your question.  

I hope it adds something significant.

I forgot: Mixing quantum mechanics and gravity is not possible as of today. Some people (Beckenstein, Hawking) have successfully combined both to do calculations, but it doesn't generalize very easily at all. Plus gravity generally is negligible in the very small world.

What if the 3rd object was massless? A photon,perhaps.

If the third object is massless , there would be no 3 body problem would there?

Swansont told me earlier (maybe be last year) that adding  gravitational fields was not simply adding them **.

I was hoping to learn a little more  of how they actually combined by this example

**If I understood you correctly it is "simply adding " if the 2 fields are weak  but not if they are strong.

 

[joigus]

38 minutes ago, swansont said:

Depends on how you mix them. There is no quantum theory of gravity, but QM effects owing to gravity could be observed. Atoms going through an interferometer where the paths diverge vertically would show an effect. Gravitational time dilation is seen in quantum states.

AAMOF, you're totally right. I was imprecise to the point of being incorrect with "mix." It was a really bad word choice. You can mix them, yes. Gravity cannot escape the quantum nature, of course. I should have said gravity cannot be formulated as a quantum theory.

3 minutes ago, geordief said:

What if the 3rd object was massless? A photon,perhaps.

A 3-body problem in which one of them is a photon is very simple. Even though with high speeds you must be careful, the photon wouldn't be very difficult to deal with. It's a 2-body Newtonian problem (which has an exact solution) plus a photon moving about. You can totally ignore the effect of the photon on the planets (I suppose you're assuming astronomical objects) and you could get fine details about the effects of the planets on the photon, which would be very small anyway.

[Markus Hanke]

On 6/5/2020 at 12:26 AM, geordief said:

Swansont told me earlier (maybe be last year) that adding  gravitational fields was not simply adding them **.

I was hoping to learn a little more  of how they actually combined by this example

GR is a nonlinear theory, so gravitational fields do not simply combine. What this means is that, when you have two valid solutions to the field equations and you combine them together, the result you get is generally not itself a valid solution. 

The only way to describe spacetimes where you have several gravitational sources of comparable “strength” (a relativistic multi-body problem) is to feed the entire setup into the field equations, and work out the appropriate solution from scratch. Unfortunately it turns out that this cannot be done in closed analytical form (i.e. with pen and paper), because the various unknowns in the equations do not neatly separate, as they would for other, simpler scenarios. It therefore has to be done via numerical methods, using computers with considerable computational power.

[geordief]

4 hours ago, Markus Hanke said:

GR is a nonlinear theory, so gravitational fields do not simply combine. What this means is that, when you have two valid solutions to the field equations and you combine them together, the result you get is generally not itself a valid solution. 

The only way to describe spacetimes where you have several gravitational sources of comparable “strength” (a relativistic multi-body problem) is to feed the entire setup into the field equations, and work out the appropriate solution from scratch. Unfortunately it turns out that this cannot be done in closed analytical form (i.e. with pen and paper), because the various unknowns in the equations do not neatly separate, as they would for other, simpler scenarios. It therefore has to be done via numerical methods, using computers with considerable computational power.

Are there setups where this computational approach is  100%  faithfull to the separate inputs?

So absolutely nothing is lost by combining the separate fields in this way other than the time and effort involved in the process....

 

I mean ,we are not talking about  approximations,no matter how close   provided the scenario is simple enough ,are we?

 

(Happy Lockdown Restriction Easing  Day!)

Edited June 8, 2020 by geordief

[Markus Hanke]

17 hours ago, geordief said:

Are there setups where this computational approach is  100%  faithfull to the separate inputs?

Sorry, I am not certain what you mean by this.

17 hours ago, geordief said:

So absolutely nothing is lost by combining the separate fields in this way other than the time and effort involved in the process....

It’s more like a conceptual shift...instead of treating the two bodies as separate entities and trying to ‘combine’ them somehow, you describe a single spacetime instead that has more than one gravitational source in it. There is no information lost in this, it’s just a matter of computational effort. Note that the computational resources required increase exponentially with the number and nature of gravitational sources, so if you have more than two ‘simple’ bodies, even powerful computers will take a long time to calculate this.

17 hours ago, geordief said:

I mean ,we are not talking about  approximations,no matter how close   provided the scenario is simple enough ,are we?

It’s not an approximation, but, like any computation in GR, it is an idealised scenario - at the very least, it will be assumed that the 2-body system is placed in an otherwise completely empty region of spacetime, without other distant sources, and without background curvature. Often, there will be more simplifying assumptions, since each symmetry we impose on the system substantially reduces the computational requirements. Basically, you want to keep it as simple as possible, or else you might be waiting a long time on your computer to finish crunching the numbers.

[geordief]

6 hours ago, Markus Hanke said:

23 hours ago, geordief said:

Are there setups where this computational approach is  100%  faithfull to the separate inputs?

Sorry, I am not certain what you mean by this.

By "inputs" I was referring  to the two "separate " gravitational sources and their  apparently(in my naivety?) independent  contribution to the  total field.

Now I am wondering  whether even the field of a symmetric one body system may be seen as an approximation in the extreme analysis  when account is taken of the fact that  any quantum effects are ignored because they are at present unknown.

[swansont]

On 6/4/2020 at 7:26 PM, geordief said:

Swansont told me earlier (maybe be last year) that adding  gravitational fields was not simply adding them **.I

I would guess that was Mordred commenting, or perhaps Markus.

Newtonian gravity obeys superposition; the failure to do so is thus small for weak fields, and only noticeable for strong fields. How you approach the problem depends on the details of the problem. If you don’t specify, you’re going to get the full GR treatment, but you don’t need to solve the GR equations if Newtonian gravity will suffice.

[Markus Hanke]

22 hours ago, geordief said:

By "inputs" I was referring  to the two "separate " gravitational sources and their  apparently(in my naivety?) independent  contribution to the  total field.

Now I am wondering  whether even the field of a symmetric one body system may be seen as an approximation in the extreme analysis  when account is taken of the fact that  any quantum effects are ignored because they are at present unknown.

Yes, in a sense the whole of GR is an approximation to a full theory of quantum gravity - more accurately, GR is the what is called the classical limit of such a theory. But within that classical domain, there is nothing stopping you from making it as accurate as you need to. The obvious limitation here is always computing power, since the less symmetric the problem becomes, the more elaborate the necessary calculations will be.

[joigus]

My interpretation of the question was more along the lines of @swansont, rather than @Markus Hanke's. Although I think Markus is totally right in his qualifications. And the reason is that the user said "how do gravitational fields interact," using the plural for "gravitational fields." The moment you consider different sources of gravitational field and ask yourself how they combine, it seems to me that you must be taking a Newtonian approach. Something like,

\[\boldsymbol{g}=\boldsymbol{g}_{1}+\boldsymbol{g}_{2}\]

In GR there is no useful way that I'm aware of in which you consider the gravitational field as made up of individual gravitational fields that can be tagged.

[geordief]

1 hour ago, joigus said:

My interpretation of the question was more along the lines of @swansont, rather than @Markus Hanke's. Although I think Markus is totally right in his qualifications. And the reason is that the user said "how do gravitational fields interact," using the plural for "gravitational fields." The moment you consider different sources of gravitational field and ask yourself how they combine, it seems to me that you must be taking a Newtonian approach. Something like,

 

g=g1+g2

 

In GR there is no useful way that I'm aware of in which you consider the gravitational field as made up of individual gravitational fields that can be tagged.

Well I think I have heard that a gravitational field interacts with itself.**

I also have heard that GR is a theory based on locality  ańd that a non local frame of reference does not apply.

** perhaps I was ascribing a physicality to the field itself whereas it is perhaps rather a property of matter?

 

 

 

[joigus]

1 hour ago, geordief said:

Well I think I have heard that a gravitational field interacts with itself.**

True. But that is in GR. In Newtonian gravity fields can be ascribed to point sources or densities of mass, and studied separately to a certain extent.

1 hour ago, geordief said:

I also have heard that GR is a theory based on locality  ańd that a non local frame of reference does not apply.

Also true. In GR frames of reference are local, not global ("global" is preferable to "non-local," for what I think you mean) "non-local" being generally reserved for other concept in field theories. Namely, couplings or interactions of the form,

\[\varphi_{1}\left(x\right)\varphi_{2}\left(x+d\right)\]

with \varphi_1 \varphi_2 being any field variables.

1 hour ago, geordief said:

** perhaps I was ascribing a physicality to the field itself whereas it is perhaps rather a property of matter?

Fields are better looked upon as distortions of space-time, rather than as a property of matter. "Matter" in modern field theory (QFT) rather being considered as excitations of fields. Most fields (Yang-Mills fields) requiring an "internal variable" (independent of space-time) and gravity being peculiar in the sense that these "distortions of space-time" are felt the same by all matter and radiation (equivalence principle.) That's why gravity can be considered as a distortion of space-time itself, while Yang-Mills fields are excitations of these internal variables that can be studied in terms of their space-time projections. All are local fields, and none are strictly linear. Even electromagnetism in QFT (quantum electrodynamics) has non-linear effects at sufficiently high energies.