[jeffreyH (OP)]

No I haven't lost the plot. My question is as to whether the motion of objects towards a gravitational source is an indirect consequence of the action of the field rather than a direct one.

[Bogie_smiles]

I’ll go with it being an indirect consequence of the gravitational field, if we define the field as a quantification of the relative point by point values of the gravitational wave energy present in the field space.

[wolfekeeper]

Well, in relativity theory gravity is directly an inertial acceleration. I don't see how you can claim it's indirect.

[Bogie_smiles]

Well, in relativity theory gravity is directly an inertial acceleration. I don't see how you can claim it's indirect.

In General Relativity, I would have said that, according to the model, it is the curvature of spacetime that tells matter how to move (and the presence of matter that tells spacetime how to curve).


But in regard to the way the OP was written, the cause of motion towards a gravitational source involves the field, and the question is, is that motion a direct or indirect consequence of the action of the field.


In that context, the field doesn’t have action, it simply has point by point values at a point in time, so the effect of those values on objects in the field, i.e., motion, seems to be indirect, as I interpret it.

[PmbPhy]

No I haven't lost the plot. My question is as to whether the motion of objects towards a gravitational source is an indirect consequence of the action of the field rather than a direct one.

A massive object generates a field. The field then exerts a force on the object to make it move. Spacetime curvature has very little to do with it since the same thing happens in the absence of curvature.

In all cases you can refer to curvature as tidal forces. Spacetime curvature and tidal forces are he some thing expressed in  two different ways.

[jeffreyH (OP)]

I am thinking about Newton's first law and how it relates to both special and general relativity. Also the relation of Newton's first law with the distribution of energy and when this distribution is non uniform.

[PmbPhy]

I am thinking about Newton's first law and how it relates to both special and general relativity. Also the relation of Newton's first law with the distribution of energy and when this distribution is non uniform.

All three of Newton's law hold. The expression F = ma is not Newton's but Euler's expression. Newton defined force as being proportional to the change in momentum which in modern language means F =dp/dt. Newton's 3rd law always holds for contact forces. Even in non-relativistic mechanics it doesn't always work such as in the forces between charged particles, although momentum is still conserved.

[jeffreyH (OP)]

If we anchor the observer in an inertial frame then how does conservation of momentum relate to time dilation in inertial frames in relative motion to the observer's frame? Also, how do forces appear to our fixed observer?

[Bogie_smiles]

No I haven't lost the plot. My question is as to whether the motion of objects towards a gravitational source is an indirect consequence of the action of the field rather than a direct one.

A massive object generates a field.

Does that field equate to out flowing gravitational wave energy?

The field then exerts a force on the object to make it move.

Does the force that the field exerts on the massive object equate to the profile of the directionally inflowing gravitational wave energy arriving from distant massive objects?

[jeffreyH (OP)]

@Bogie_smiles Forget external fields. They would be drawing things away. Also they would likely have negligible effect if far distant. The gravitational field conditions the surrounding spacetime. It creates the conditions to change the inertia of objects. It creates conditions that are like inertial motion, with blue shift in the direction that an object will travel and redshift behind in its wake. Except that gravitation causes a gradient in inertia that is missing in special relativity. This is why inertial and gravitational mass are so directly connected. The gradient in inertia results in acceleration. The big question is why? Newton's laws don't ask why. I can't accept that.

[Bogie_smiles]

@Bogie_smiles Forget external fields. They would be drawing things away.

If you say that, then we have a different picture in our minds. I refer to a gravitational field like one PmbPhy referred to, one generated by a massive object. The massive object would be the source of gravitational wave energy emitted by the object, and that energy extends outward from the object at the speed of gravity, but the local object is a continuous source, so the out flow would maintain the continual presence of the field at the surface of the local object.

Is that what you would call an external field? That field would always be maintained by being refreshed by the inflowing wave energy that replaces the out flowing wave energy in a net exchange of energy where the local field and the inflowing distant fields converge.

The fact that it would seem to be drawing things away would not be a complete picture. There would also be the field/fields that are emitted by distant objects, and the gravitational wave energy from those objects is the out flowing gravitational wave energy of their external fields, which is inflowing gravitational wave energy absorbed by the object in our local frame. There are two components to the field, 1) one component is spherically out flowing energy from our object, and 2) the other is directionally inflowing energy to our object from distant sources.

The direction of motion of our object, relative to the surrounding distant objects, would be in the direction of the net highest inflowing wave energy at the surface of our local object.

Also they would likely have negligible effect if far distant.

Individually that is true, but as the radius of space from which the inflowing wave energy comes is increased, more and more distant objects are within the reach of gravity. The inverse square law applies to each distant object, but there are more and more distant objects as the distance increases.

The gravitational field conditions the surrounding spacetime. It creates the conditions to change the inertia of objects. It creates conditions that are like inertial motion, with blue shift in the direction that an object will travel and redshift behind in its wake. Except that gravitation causes a gradient in inertia that is missing in special relativity. This is why inertial and gravitational mass are so directly connected. The gradient in inertia results in acceleration. The big question is why? Newton's laws don't ask why. I can't accept that.

At present, spacetime is a macro gravitational effect quantified by the EFEs, but the micro effect, at the quantum level, i.e., quantum gravity, is an area of theoretical research associated with quantum mechanics that is considered a likely source of the solution to your question of how/why.

As I understand it form my layman perspective, a quantum solution to gravity will include a mechanical explanation for how the gradient is established by both the out flow and inflow of gravitational wave energy, and should answer the question of why; why inertial and gravitational mass are so directly connected.

I would look for the explanation to be based on the net gravitational wave energy at the surface of our local object, gravitational wave by gravitational wave, inflow and out flow converging right at the surface of the local object where the fields converge. There would be a directional effect since there is a distant source for each inflow of gravitational wave energy; each source would be from a different distance and each source would have a different mass, making the motion of our local object a net effect of all of the inflowing sources.

If the real answer is a quantum gravity solution, no matter how much we work with spacetime and the EFEs, I don’t see how we will be getting down to the how and why of the real connection between inertial and gravitational mass, which are two aspects that enter into quantifying relative motion, without the benefit of that quantum solution.

[PmbPhy]

Does that field equate to out flowing gravitational wave energy?

No. Gravitational waves only exist when the sources is accelerating.

[Bogie_smiles]

Does that field equate to out flowing gravitational wave energy?

No. Gravitational waves only exist when the sources is accelerating.

Agreed, but any two distant objects are almost always in relative motion, and where gravity is in play, both are experiencing acceleration.

[jeffreyH (OP)]

You would only get a significant amount of gravitational waves if an object had a large mass and was accelerating rapidly. Even then the distance between objects is important. An object with inertial motion has a gravitational field. It is the field that is important.

[Bogie_smiles]

You would only get a significant amount of gravitational waves if an object had a large mass and was accelerating rapidly. Even then the distance between objects is important. An object with inertial motion has a gravitational field. It is the field that is important.

To try to understand that, let me ask:
1) Does an object move in spacetime based on geodesics determined by the EFEs (i.e., based on the presence of surrounding massive objects as implied by the saying, (paraphrased) curved spacetime tells objects how to move, and massive objects tell spacetime how to curve?
2) Is it a special case when an object is accelerating, meaning accelerating objects emit gravitational waves, which contain information over and above the information contained in the geodesics?

Does that mean that when an apple falls from the tree, it emits gravitational waves due to the acceleration of gravity, but while hanging in the tree it has gravitational potential energy?

[PmbPhy]

Does that field equate to out flowing gravitational wave energy?

No. Gravitational waves only exist when the sources is accelerating.

Agreed, but any two distant objects are almost always in relative motion, and where gravity is in play, both are experiencing acceleration.

Objects don't radiate unless they're accelerating. Not merely because they're moving. The earth is accelerating in its orbit around the sun but the gravitational waves are so weak as to be virtually undetected.