General Relativity Revisited (What if gravity actully is a force?)

  • #1
General Relativity Revisited (What if gravity actually is a force?)

I will admit a few things. First, I suppose I am posting on here because the chances of provoking some discussion, and recieving some feedback are likely better than a few other places I would try. On the other hand, I am hopful of recieving some well informed responses, if I am lucky; I'm often surprised. That aside, perhaps I'll at least have the delight of communicating some ideas, and getting some benificial feedback.

I basically understand what is meant by now when I hear about gravity not being a force. In other words General Relativity (GR) opts to model this phenomenon in terms of a curvature of the space-time fabric. I understand that this model works extremely well, and that it is, perhaps, even the best we have currently, or very close to it.

Yet, it hardly seems fair that now Gravity basically falls down into the category of a pseudo-force, while the electromagnetic interactions still get to sit on that noble pedestool of being a real force. Granted, that is a rather 'emotional' type of statement, but there is a 'reason' I have this sense of dissatisfaction with GR.

Let's talk about force. My current understanding of force is that it is, literally, is the change in mechanical momentum of a system over time. Noted, there are other forms of momentum which are not mechanical, such as those which may be stored in electromagnetic fields, but force particularly does NOT pertain to those changes, rather it purely belongs to the changes in 'Mechanical momnetum.' Are we to believe that gravity can not itself be the source of changes in the mechanical momentum of a system? The anticipated, typically educated, answer goes something like, "Well, according to the equivalence principle of GR, it cannot." In other words a body following its natural path under the influence of gravity cannot "feel" this effect.

I understand that is a nice idea. But, as romantic as it is, and as much as that makes sense 'in a way,' I am not satisfied. Why should we believe, a priori, that gravity cannot impart mechanical momentum on a body, and that this is soly up to the electromagnetc interactions? The equivalence of gravitational and inertial mass? Pshhhhhaw.

I know that the response to my 'a priori' question might go something like this. The effects of the predictions of GR have been experimentally measured through and through, and Gravitational lensing proves that the presence of mass curves the fabric of space time etc...why are you even going on? Well, for one, I have an inquisitive spirit, and I also believe that scientific theories are meant to be probed and questioned; someone like Richard Feynmann might say that is the nature of the game.

More importantly, let's rewind. GR succesfully models gravitation in terms of curvature in space-time, and through some means (that few of the brightes physicist could possibly reproduce) arrives at that formulation from, well I'm not even completely certain right now, but let's just say Special Relativity, and incorperating the equivalence principle, roughly speaking. But people, THIS IS A MODEL. There are many models that make succesful predictions in their appropriate realms. What if the bending of light by gravitational fields had been discovered prior to GR's creation? If I were not already biased by the beutifully compelling concept of space curvature, my conclusion would NOT be that such 'lensing' proves spacetime is curved.

I would simply take that to be definitive proof that the GRAVITATIONAL FIELD INTERACTS WITH THE ELECTROMAGNETIC FIELDS (afterall light is an electromagetic field propogatin in the form of a wave and gravity bends that, right?) The funny thing is that the converse of that statement is (and such symmetries are all to present in the the world) the Electromagnetic Field interacts with the Gravitational field. For some reason though, I never hear it put so simply. Instead we must do the space time is curved dance, never mind Occam's Razor. (Side note: I would almost expect, on such simple grounds, there to be way more research, and grants funding said research into how the Electromagnetic field interacts with the Gravitational Theorem, than I'm aware of currently, yes...with repect from the Scientific establishement and all.)

Why not entertain the idea that gravity IS a force and could hence contributes to the mechanical momentum of a system, just as electromagnetism can. Said symmetry alone to me is very intriguing. Perhaps this effect is so small we simply haven't yet measured it, but that basically makes sense considering how weak the Gravitational field is compared to the Electromagnetic field. If there is anyone that has any input or feed back on this, or is aware of current research going on that is related, please let me know. Thanks.


(BTW- I bring this up as an effort to provoke discussion on the topic, and not to claim conlusions based on any experimental knowledge, proprietary material, or sensitive information.)
 
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Answers and Replies

  • #2
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Force causes acceleration, acceleration is a change in momentum. So gravity can be modelled either as a force field or an acceleration field. If the equivalence principle is true, a gravitational force field is an acceleration field.

There is atheory of gravity that does not assume the equivalence principle, but gives the same predictions as GR if the EP is assumed. It also has no spacetime curvature.

It doesn't actually matter if you model gravity as a force field or an acceleration field.

You still fall down when you trip.:biggrin:
 
  • #3
Force causes acceleration, acceleration is a change in momentum. So gravity can be modelled either as a force field or an acceleration field. If the equivalence principle is true, a gravitational force field is an acceleration field.

There is atheory of gravity that does not assume the equivalence principle, but gives the same predictions as GR if the EP is assumed. It also has no spacetime curvature.

It doesn't actually matter if you model gravity as a force field or an acceleration field.

You still fall down when you trip.:biggrin:

Hmmm, interesting thought, but not entirely what I was getting at. Here's an thought that could interest you. Acceleration is not neccesarily a change in momentum, for intance there must be a 'mass' present. By analogy an electric field causes an acceleration of charge, however is not an acceleration field because the same charge can have a different mass and therefor accelerations will be different. Anyway thanks for your thoughts.
 
  • #4
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Acceleration is not neccesarily a change in momentum..
I think it is.

...for instance there must be a 'mass' present.
There always is. What else can be accelerated ?


By analogy an electric field causes an acceleration of charge
Are there any massless charged particles ?
however is not an acceleration field because the same charge can have a different mass and therefor accelerations will be different
Which is why the Lorentz force is a force, not an acceleration

Anyway thanks for your thoughts.
They were entirely wasted since you've dismissed them.
 
  • #5
I think it is.


There always is. What else can be accelerated ?



Are there any massless charged particles ?

Which is why the Lorentz force is a force, not an acceleration


They were entirely wasted since you've dismissed them.


Actually I did NOT dismiss them. I don't know what would make you assume that. I actually said they were interesting explicitly, but that I didn't believe it was exactly hitting the nail on the head as far as my inquiry, and even said something I thought would interest you. I'm sorry if your upset by such. If anyone has any other view points or information I envite you to share it. Thanks.
 
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  • #6
Are there any massless charged particles ?
From a theoretical stance,YES; I believe it is important to analyze such concepts, just as we have the theoretical machinery to treat a massive electrically neutral body, we should just as well be able to deal with a massless electrically charged particle in principle.
 
  • #7
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From a theoretical stance,YES; I believe it is important to analyze such concepts, just as we have the theoretical machinery to treat a massive electrically neutral body, we should just as well be able to deal with a massless electrically charged particle in principle.
Massless particles travel at the speed of light and cannot be accelerated.

...and even said something I thought would interest you.
Might interest me ? That's patronizing coming from someone who thinks massless charges exist and can be accelerated.

The truth is, mate, in your waffly piece you haven't actually said anything worth discussing.

If you search this forum you'll find a lot of hot-air about gravity being a force or a pseudo-force or whatever. It isn't important, it's just semantics.

...could hence contribute to the mechanical momentum of a system, just as electromagnetism can

This statement seems completely off the wall. When you drop something does its momentum in your eyes not increase ?

If you want to know about similarities between the gravitational field and electric field there's a wealth of literature on the subject on the internet.
 
  • #8
Massless particles travel at the speed of light and cannot be accelerated.

You are missing the point. Please post elsewhere, and stop cluttering my thread.
 
  • #9
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Actually I did NOT dismiss them. I don't know what would make you assume that. I actually said they were interesting explicitly, but that I didn't believe it was exactly hitting the nail on the head as far as my inquiry, and even said something I thought would interest you. I'm sorry if your upset by such. If anyone has any other view points or information I envite you to share it. Thanks.

I am not sure of the answer to your question, but here are some thoughts to add to the pot. In the Newtonian context, an body in circular orbit has the gravitational force balanced by an equal and opposite centrifugal force. One problem with this definition is that Newtonian physics also states that a body continues in a straight line if no forces are acting on it. If the centrifugal force exactly cancels out the gravitational force, then the orbiting body should be moving in a straight line and not in circle. This is at the root of banishing centrifugal force as a real force. In GR, both gravitational force and centrifugal force are treated as pseudo forces and the orbiting particle simply follows a geodesic (which is the equivalent of a straight line in curve space), when no forces are acting on the particle. For a point particle it is difficult to prove if no forces are acting on it or if all the forces are cancelling each other out. For a large orbiting body, not all the composite parts of the orbiting body can follow their individual geodesics simultaneously and as a result the orbiting body can be torn apart by tidal forces at the Roche limit. Those tidal forces are real enough! When a particle is forced to deviate from its geodesic the gravitational force becomes real. I am not sure how one would go about proving that there are no forces acting on a body in freefall other than defining force as something that is measured by an accelerometer and when something is in freefall an accelerometer will show a zero reading. Maybe Mentz is right and maybe it is just a case of interpretation and either viewpoint is correct. It might also be worth noting that the GR equations for orbital motion contains terms that look like Newtonian gravitational force opposed by centrifugal force, but there is an additional term that that is unique to GR as well. At the moment there are a couple of other threads going on in this forum, where we can not even agree if the gravitational force acting on a horizontally moving particle is independent of the particle's kinetic energy or not.
 
  • #10
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I understand that is a nice idea. But, as romantic as it is, and as much as that makes sense 'in a way,' I am not satisfied. Why should we believe, a priori, that gravity cannot impart mechanical momentum on a body, and that this is soley up to the electromagnetc interactions?
Sorry you're not satisfied. Do you actually think that gravity does not impart momentum ?
The equivalence of gravitational and inertial mass? Pshhhhhaw.
Pshhhhhaw to you too.

You haven't understood a single word I've written, and you're talking nonsense.

Your problem is you don't understand the subject you're talking about, but you have prejudices which you are arrogant enough to think override centuries of thinking.
 
  • #11
Your problem is you don't understand the subject you're talking about, but you have prejudices which you are arrogant enough to think override centuries of thinking.

My problem is that I have done much advance study in the area, and that you continue to harrass and provoke arguments. As I said, please stop posting here, that will simply lead to further reports.
 
  • #12
JesseM
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Yet, it hardly seems fair that now Gravity basically falls down into the category of a pseudo-force, while the electromagnetic interactions still get to sit on that noble pedestool of being a real force.
Not in the Kaluza-Klein theory which attempts to explain electromagnetism in terms of 5-dimensional spacetime curvature (with the extra spatial dimension wrapped into a microscopic circle so we don't notice it). As I understand it this approach has in some sense been incorporated into string theory, which attempts to unify all four forces (and thus can't treat them as fundamentally different sorts of things).
shanesworld said:
Let's talk about force. My current understanding of force is that it is, literally, is the change in mechanical momentum of a system over time.
Can you define "momentum" without reference to inertial frames? After all momentum is usually treated as a function of velocity in inertial frames. But in GR there are no global coordinate systems in large regions of spacetime (like a region that's large enough to observe the bending of light by a star) that satisfy the requirements of an "inertial frame", though you can talk about locally inertial coordinate systems in any small region where the curvature can be treated as negligible (thanks to the equivalence principle). Such a local inertial frame can be defined on the tangent space to a point in GR which I believe is how the momentum vector would normally be defined in a GR context. And in such a local inertial frame I'm pretty sure the light won't experience any change in momentum.
 
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  • #13
Vanadium 50
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Please post elsewhere, and stop cluttering my thread.

It's not "your thread". Everyone is free to participate.
 
  • #14
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My problem is that I have done much advance study in the area, and that you continue to harrass and provoke arguments. As I said, please stop posting here, that will simply lead to further reports.

I wasn't going to post here again, but you've talked me into it. I am not harassing you, I'm having a discussion which means I am allowed to ask you questions - which you have ignored.

You seem to have an objection to curved space, because you think it models gravity in a way that deprives it of its force-like nature. That isn't true. As you have said 'it's a model' - so why are you taking it literally ? In my first post I pointed out that gravity can be modelled as a force, and that with the added assumption of the equivalence principle, these models make the same predictions as GR.

If the EP is assumed to be false, the models do not make predictions that agree with observation. The EP is supported by experiment and observation, and is NOT a 'romantic' idea !
 
  • #15
D H
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In the Newtonian context, an body in circular orbit has the gravitational force balanced by an equal and opposite centrifugal force.
That is true only if you look at the orbit from a perspective of a rotating frame in which the planet is not moving.
One problem with this definition is that Newtonian physics also states that a body continues in a straight line if no forces are acting on it. If the centrifugal force exactly cancels out the gravitational force, then the orbiting body should be moving in a straight line and not in circle.
There is no problem. The planet is not moving in this frame. Stationarity is the trivial case for Newton's first law.

If you are going to pick on Newtonian physics, do it right.
 
  • #16
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Massless particles travel at the speed of light and cannot be accelerated.
Even if their speed is constant, they can change direction, which is an acceleration. And since massless particles can still have momentum, you could also still talk about a force on them starting from the definition F=dp/dt.

I find it strange that you and shane's comments quickly became so adversarial.

Shane,
To help drive home Mentz comments, note that Newtonian gravity can be rewritten as a metric theory. Does this no longer make gravity a force in Newtonian mechanics? just because we can write it with other mathematical representations?

Basically, to answer your question "What if gravity actually is a force?" we need to first come to some agreement on what you even mean by this. In trying to progressively make the question more precise, it is quite likely that will answer the question itself. Either way, this discussion needs to be had, otherwise people will only be talking past each other instead of with each other.
 
  • #17
Dale
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I understand that this model works extremely well, and that it is, perhaps, even the best we have currently, or very close to it.

Yet, it hardly seems fair that now Gravity basically falls down into the category of a pseudo-force
I would just like to point out that "works extremely well" is the one and only scientific criterion for judging a theory. It doesn't matter if it is "fair" or any of your other complaints; scientifically they are all completely irrelevant. The only scientific concern is that it accurately predict the results of experiments.
 
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  • #18
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JustinLevy said:
Even if their speed is constant, they can change direction, which is an acceleration. And since massless particles can still have momentum, you could also still talk about a force on them starting from the definition F=dp/dt.
Point taken - for now:smile: ( Angular momentun is an axial vector. The field would be doing work on a massless object ... hmmm).

But we don't know of any massless charged particles.

I find it strange that you and shane's comments quickly became so adversarial.
The guy did not understand what I said and lectured me. The phrase 'something you might like to know' is just polite for 'you've got it wrong (fool) because ...' followed by an elementary lecture.

I was actually saying this

To help drive home Mentz comments, note that Newtonian gravity can be rewritten as a metric theory. Does this no longer make gravity a force in Newtonian mechanics? just because we can write it with other mathematical representations?
but perhaps not as elegantly. Let's see if he ignores you as well because of his 'unsatisfaction'.
 
  • #19
JesseM
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I would just like to point out that "works extremely well" is the one and only scientific criterion for judging a theory. It doesn't matter if it is "fair" or any of your other complaints; scientifically they are all completely irrelevant. The only scientific concern is that it accurately predict the results of experiments.
While true, it is also true in the history of physics that "elegance" of some kind has often been a motivation for physicists when looking for new theories, and it doesn't seem unreasonable to hope a "theory of everything" would put all four fundamental forces on the same footing.
 
  • #20
Dale
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While true, it is also true in the history of physics that "elegance" of some kind has often been a motivation for physicists when looking for new theories, and it doesn't seem unreasonable to hope a "theory of everything" would put all four fundamental forces on the same footing.
True, but such considerations are philosophical rather than scientific, which is why I emphasized the word "scientific" in my post. E.g. in the SR vs. LET debate, both are equally valid scientifically since each predicts the same experimental results in all cases, but SR is generally preferred on philosophical grounds like Occham's razor. You can certainly use philosophical or aesthetic considerations to select between two theories which have equal experimental validation, but you cannot reject an experimentally validated theory on mere philosophical grounds.
 
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  • #21
JesseM
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True, but such considerations are philosophical rather than scientific, which is why I emphasized the word "scientific" in my post.
Well, are the intuitions that physicists may use when searching for new testable scientific theories not part of "science"? Was Einstein being scientific when he came up with the hunch that the equivalence principle should be a feature of any relativistic theory of gravity? It's just a question of word-definitions I suppose, but I wouldn't say that such things are purely "philosophical" (though I agree that if you have two complete theories which make precisely identical experimental predictions, then any reasons for preferring one over the other are 'philosophical')
 
  • #22
Cleonis
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I basically understand what is meant by now when I hear about gravity not being a force.

Here are some of my thoughts on that issue.

Let me first give two different definitions of 'force'. The first one only works in the context of newtonian physics, the second definition is designed to work well both for newtonian and relativistic dynamics.

I - When an object accelerates with respect to the local inertial frame it is being impelled by a force.

II - A force is an interaction between two objects so that the two object tend to change momentum with respect to their common center of mass. There is a corresponding potential energy that is released when the objects are free to move down the potential gradient. The tendency to move down the potential gradient is called 'being influenced by a force'.


We can regard the center of mass of the Solar system as the origin of an inertial coordinate system. In terms of newtonian dynamics there is only there is only a single, global, inertial frame. The orbiting motions of the celestial bodies are then attributed to newtonian gravitational force.
(More generally, we know of course that the Solar system is orbiting the center of mass of our Galaxy, we can always scale up to a larger context.)


As a general rule of physics we have that we must always take a global perspective, in the sense that we must always maximize the information content.
When thinking about a binary system there is no point in selectively looking at a single member of that system, you have to consider the system.

When a proto-stellar cloud contracts to form a star then it is conversion of gravitational potential energy that provides the energy for the star to heat up and ignite. It's equally standard in newtonian and relativistic physics to think in terms of gravitation as a potential well.


In all, whether gravitation is categorized as 'a force' is purely a matter of how you choose to define the concept 'force'.

It appears that some people retain the newtonian definition of force when thinking about General Relativity. With that mismatch set up you get that striking result: "Hey, gravitation is not a force!". As described above, that "implication" is artificial: an obsolete definition is used.


Among the fundamental changes brought on by GR there is the concept that local inertial frames can accelerate with respect to each other. Example: an orbiting satellite does not accelerate with respect to its local inertial frame, but it does accelerate with respect to the inertial frame that is co-moving with the common center of mass of the satellite and its primary. Generally, in terms of GR what is valid locally may very well not be valid globally, and vice versa.
 
  • #23
Dale
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Well, are the intuitions that physicists may use when searching for new testable scientific theories not part of "science"? Was Einstein being scientific when he came up with the hunch that the equivalence principle should be a feature of any relativistic theory of gravity?
The point is that what the OP is doing is not scientific. The OP is not using "intuition" or "hunches" to develop a new testable theory which resolves experimental deficiencies in a previous theory. He is simply complaining that an experimentally verified theory doesn't conform to his aesthetic ideals and personal preconceptions. That is clearly not scientific and not related to what Einstein did.
 
  • #24
Point taken - for now:smile: ( Angular momentun is an axial vector. The field would be doing work on a massless object ... hmmm).

But we don't know of any massless charged particles.


The guy did not understand what I said and lectured me. The phrase 'something you might like to know' is just polite for 'you've got it wrong (fool) because ...' followed by an elementary lecture.

I was actually saying this


but perhaps not as elegantly. Let's see if he ignores you as well because of his 'unsatisfaction'.


I will adress Mentz's comments one final time and then focus on the rest of the commenters which do not propose to assume things about me which they could not possibly know, which is mostly everyone. For starters I do not have a problem with space-time curvature or GR. It is indeed one of my favorite theories. However, as an educated person in general I believe you SHOULD question current theories in science. They, afterall are SCIENTIFIC theories, not dogmas. I'm sure both Richard Feynmann and Albert Einstein would appreciate such tactics, among many other notable Physicists, which I might add were more than prone to question the dominant theories of the day, to which I shall note even Einstein himself worked on revisions of GR, exemplified by such items as Einstein-Cartan Theory. To Mentz NEVERMIND (EDIT). Here's and olive branch, feel free to post here. I've been lecturing about not assuming things about people, but have noticed that in doing so it is equally impossible for me not to be assuming things about people myself, so I have not been independent of the problem I no longer mind if you post here. I hope you do. Questioning is part of the sciences, so by that logic, you have the right to question me.
 
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  • #25
Even if their speed is constant, they can change direction, which is an acceleration. And since massless particles can still have momentum, you could also still talk about a force on them starting from the definition F=dp/dt.

I find it strange that you and shane's comments quickly became so adversarial.

Shane,
To help drive home Mentz comments, note that Newtonian gravity can be rewritten as a metric theory. Does this no longer make gravity a force in Newtonian mechanics? just because we can write it with other mathematical representations?

Basically, to answer your question "What if gravity actually is a force?" we need to first come to some agreement on what you even mean by this. In trying to progressively make the question more precise, it is quite likely that will answer the question itself. Either way, this discussion needs to be had, otherwise people will only be talking past each other instead of with each other.


I'm not exactly clear on your question about gravity no longer being a force in Newtonian mechanics, however I find it strange that Ments's and my own comments became adversarial, mostly because to my Knowlege what I said to Ments was not what I read he took it as.

Let's revamp. It is well known that Maxwell's formulation of the Electromagnetic equations imply, through Poyntings hypothesis, and various conservation of momentu, that there is momentum stored in electromagnetic fields. Consider a system through which no energy or momentum may enter or leave (closed system). Imagine that there is no mechanical momentum present (or in other words motion of matter, to start, (initial conditions). While there is no mechanical momentum present to start, the momentum stored in the electromagnetic fields may infact be converted to mechanical momentum, while the overall momentum change in the system is still zero. Conservation of momentum is maintained for the closed system. Now, consider we take the constraint for this being a closed system away. Alternatively, now the momentum stored in the electromagnetic fields may be radiated away instead of transfered to mechanical motion. There may also (third possibility) be a combonation of said processes present. Conservation of momentum is still maintained, however the net momentum entering the system must be the same as the net momentum coming into the system, (this is just my attempt to put the tensoral continuity equation for momentum in classical electrodynamics in common speach, for those familiar with the Maxwell's stress tensor you may catch my drift.) The point is momentum is conserved. Momentum can be stored in fields. Momentum can be stored in mechanical forms. These two forms of momentum may be interchanged through a plethora of mechanisms in more kinds of systems than you or I could dream up in a lifetime, but the basic principle in this theory still remains. YET ONLY THE TIME RATE OF CHANGES IN 'MECHANICAL MOMENTUM' CONSTITUTE FORCE IN MY USE OF THE WORD FORCE. (For those of you who follow, the Maxwell stress tensor, combined with the Poynting vector, may be generalized into a single 4*4 tensor which, neglecting non electrodynamic effects in a system, IS exactly the Stress-Energy Tensor which would be used in GR, yet it is perfectly viable to discuss this tensor outside of the topic of GR. However My question remains: in gravitational theory, does Gravity itself have the capability of contributing to changes the mechanical momentum in a system, or is that entirely up to electromagnetic effects? If gravity can contribute to such effects then Gravity IS a Force. If gravity cannot contribute to such effects, then it is not a force. I'm always reading, and hearing that in GR gravity is not a force, so I am tempted to take this to mean that gravity can only contribute to changes in non-mechanical momentum in a system?, which would imply that allowing for gravity to contribute weakly to the changes in mechanical momentum in a system would be a revision to GR, THAT WOULD BE TESTABLE, would it not? Does anyone have any insights that may clarify. Thanks
 
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