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

Dale
Mentor
2020 Award
THE TIME RATE OF CHANGES IN 'MECHANICAL MOMENTUM' CONSTITUTE FORCE IN MY USE OF THE WORD FORCE
From my understanding of your definition of "force" gravity in GR would be a "force" as would the centrifugal and Coriolis forces.

JesseM
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?
Can you please address my questions in post #12 about whether you are defining "momentum" relative to local inertial frames (in which case the effects of gravity are negligible thanks to the equivalence principle) or in some other way? Do you agree with my point there that any large-scale coordinate system in GR won't be an inertial one?

Shane,

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?

You have a way of asking questions that really irritates me. Take the above - why did you add the part I've underlined ? That means if I say 'no' to the question I'm implicitly agreeing with the rider. Are the electromagnetic effects in the rider supposed to be replacing the gravitation or in contrast to the gravitational effects ?

Ignoring the rider, I would say that gravity can change the mechanical momentun but it's frame dependent. As to whether Gravity ( not the modelled variety but the actual thing ) is a force - it's pretty obvious that it is in my frame of reference.

Something you might like to know is that gravity can be modelled as a force in close analogy to the EM field. As you know, the Lorentz force can be shown to arise purely by insisting on local phase invariance ( symmetry group u(1) ). Gravity can be shown to arise by insisting on local translational invariance. This is very neat because space and time translation have conserved currents, energy and momentum, which are the sources of gravity. This theory does not incorporate the equivalence principle as does GR, but if the EP is added to the gravitational gauge theory, we end up with the same field equations as GR.

The fact that GR incorporates the EP and is thus able to geometrize a force field into an acceleration field has no physical significance whatever. What is significant is whether gravitational mass and inertial mass are one and the same.

[edit : there's an explanation of TP gravity in arXiv:gr-qc/0312008v1 ]

Last edited:

Not in the [URL [Broken]

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 http://www.mth.uct.ac.za/omei/gr/chap6/node1.html 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.

I'm not entirely sure of the answer to this question, but I can provide my best take on it. Amazingly, momentum is one of the more abstract concepts in physics. With basic physics, it seems like such a simple concept. But at a certain point its definition changes, and changes, and then one might ask, what exactly IS momentum? My best answer to your question, and I could be wrong, is yes you can define momentum without reference to inertial frames in some cases, for instance in quantum theory particles have intrinsic angular momentum, and fields can store momentum. I don't believe that depends on inertial frames (once again I think I have that correct, but perhaps there are other perspective). There may be other cases where you cannot define momentum without respect to inertial reference frames, for instance the momentum of translation, everything would be relative to the inertial frame you are in. I'm reasonable certain there are more complex issues that I won't try to get into right now, as well. I'm sure there are better answers than mine, perhaps amongst items like Noether's theory,which is also quite abstract.

Last edited by a moderator:
Can you please address my questions in post #12 about whether you are defining "momentum" relative to local inertial frames (in which case the effects of gravity are negligible thanks to the equivalence principle) or in some other way? Do you agree with my point there that any large-scale coordinate system in GR won't be an inertial one?

I suppose there is one more thing I would add light carries momentum, but not mechanical momentum. So no, 'force' is imparted upon light if its direction is changed, although technically speaking the momentum is still changed.

Shane,

You have a way of asking questions that really irritates me.
I've noticed.
the above - why did you add the part I've underlined ? That means if I say 'no' to the question I'm implicitly agreeing with the rider. Are the electromagnetic effects in the rider supposed to be replacing the gravitation or in contrast to the gravitational effects ?
Could you please humor me and explain what you are referring to by 'rider' , so I can address your question?

Ignoring the rider, I would say that gravity can change the mechanical momentun but it's frame dependent.
Might agree, but still not sure what you mean by rider.
As to whether Gravity ( not the modelled variety but the actual thing ) is a force - it's pretty obvious that it is in my frame of reference.
Hmmm
If you could somehow fill your body with charged particles and stand next to an electric field, would it feel the same as gravity? Crazy thought of the day.
Something you might like to know is that gravity can be modelled as a force in close analogy to the EM field. As you know, the Lorentz force can be shown to arise purely by insisting on local phase invariance ( symmetry group u(1) ). Gravity can be shown to arise by insisting on local translational invariance. This is very neat because space and time translation have conserved currents, energy and momentum, which are the sources of gravity. This theory does not incorporate the equivalence principle as does GR, but if the EP is added to the gravitational gauge theory, we end up with the same field equations as GR.
Interesting.
The fact that GR incorporates the EP and is thus able to geometrize a force field into an acceleration field has no physical significance whatever.

no physical significance=no new testable predictions :zzz:
What is significant is whether gravitational mass and inertial mass are one and the same.
Agreed.

Last edited:
Might agree, but still not sure what you mean by rider

I mean the part of the sentence after the comma. I'm using the word in the sense of something 'tacked on'.

RIDER. A schedule or small piece of paper or parchment added to some part of the record; as, when, on the reading of a bill in the legislature, a new clause is added, this is tacked to the bill on a separate piece of paper, and is called a rider.

Source: Bouvier's Law Dictionary, Revised 6th Ed (1856)

I suppose it is rather obscure.

If you could somehow fill your body with charged particles and stand next to an electric field, would it feel the same as gravity? Crazy thought of the day.

You keep making associations between EM and gravity. Are you of the opinion that they are related ? Perhaps that gravity is actually the result of some electromagnetic phenomenon ?

JesseM

I'm not entirely sure of the answer to this question, but I can provide my best take on it. Amazingly, momentum is one of the more abstract concepts in physics. With basic physics, it seems like such a simple concept. But at a certain point its definition changes, and changes, and then one might ask, what exactly IS momentum? My best answer to your question, and I could be wrong, is yes you can define momentum without reference to inertial frames in some cases, for instance in quantum theory particles have intrinsic angular momentum, and fields can store momentum. I don't believe that depends on inertial frames (once again I think I have that correct, but perhaps there are other perspective).
The spin of particles in QM might be a special case that doesn't depend on a choice of reference frame, but I'm pretty sure that any textbook equation involving ordinary linear momentum of particles in QM, as well as any momentum stored by quantum fields, will be written with the assumption we are using an inertial frame (unless explicitly stated otherwise). Certainly the laws of quantum field theory are said to be Lorentz-symmetric, meaning they obey the same equations in the different inertial frames of special relativity.
shanesworld said:
I'm reasonable certain there are more complex issues that I won't try to get into right now, as well. I'm sure there are better answers than mine, perhaps amongst items like Noether's theory,which is also quite abstract.
Noether's theorem relates conservation of momentum to the fact that the laws of physics are invariant under spatial translation, but again I'm pretty sure this symmetry assumes inertial frames, in an arbitrary non-inertial frame the way a given physical system (a clock, say) behaves can vary with position.

Just saying "there are more complex issues" is very hand-wavey. If you want to say that gravity affects momentum, you need to actually have a clear definition of momentum in mind!
shanesworld said:
I suppose there is one more thing I would add light carries momentum, but not mechanical momentum. So no, 'force' is imparted upon light if its direction is changed, although technically speaking the momentum is still changed.
Light's momentum is still defined in the context of inertial frames--do you think any of the textbook equations for light's momentum such as p=hf/c would work in arbitrary non-inertial frames? And do you disagree that in a locally inertial frame in GR, by definition light would not be measurably deflected by gravity?

Last edited:
I mean the part of the sentence after the comma. I'm using the word in the sense of something 'tacked on'.
Ok, then 1) I might bring up that we are talking about a system where there is possibly some kind of combined effect, for instance the dynamics of a proton in gravitational field, where there may be an electric field present. 2) If you say No, then you ARE implicitly agreeing with the rider, there is no way around that in the context...(bearing in mind, the question is presented in the context of how this would be dealt with in GR specifically)
...

You keep making associations between EM and gravity.

These associations are for two reasons, 1) For the sake of analogy 2) We are discussing how the presence of combined effects would be addressed in GR, and perhaps in alternative frameworks.
Are you of the opinion that they are related ? Perhaps that gravity is actually the result of some electromagnetic phenomenon ?

NO, I have no affirmative or negative opinion on that matter at this point... it would seem natural to inquire if any such relations are present though...in itself that doesn't mean they are though; it also doesn't initially assume the negative. A unification approach would be one that sought to analyze each as different aspects of the same phenomenon, right?

Dale
Mentor
2020 Award

Noether's theorem relates conservation of momentum to the fact that the laws of physics are invariant under spatial translation, but again I'm pretty sure this symmetry assumes inertial frames, in an arbitrary non-inertial frame the way a given physical system (a clock, say) behaves can vary with position.
Noether's theorem is a very general result and does not require an inertial reference frame. In fact, it can be applied to very wierd coordinate systems. If a Lagrangian is invariant under a differential shift of some generalized coordinate you would then have conservation of the corresponding generalized momentum. This would not necessarily be equivalent to any component of momentum as defined in an inertial frame using orthonormal coordinates, but whatever the generalized momentum is would be conserved.

JesseM

If a Lagrangian is invariant under a differential shift of some generalized coordinate you would then have conservation of the corresponding generalized momentum.
But in an inertial frames the Lagrangian for any possible physical system will be invariant under a shift of the position coordinate, right? I imagine this wouldn't be true in general for arbitrary systems analyzed in arbitrary non-inertial frames?

Ok, then 1) I might bring up that we are talking about a system where there is possibly some kind of combined effect, for instance the dynamics of a proton in gravitational field, where there may be an electric field present. 2) If you say No, then you ARE implicitly agreeing with the rider, there is no way around that in the context...(bearing in mind, the question is presented in the context of how this would be dealt with in GR specifically)

Are you in any way related to Conway? :uhh: Anyway, what kind of combined effects? This sounds like a hodgepodge of your personal views of what MIGHT be discovered at some later date, sans math or citations, or even a clear mission. I've noticed that what began as (a fairly crudely and nastily put) question has evolved into something else entirely once you didn't receive the feedback you wanted/expected. As for #2... given how long you've been on conjecture and how short you've been (with others here) anything concrete, I wouldn't throw stones.

These associations are for two reasons, 1) For the sake of analogy 2) We are discussing how the presence of combined effects would be addressed in GR, and perhaps in alternative frameworks.

Alternate frameworks? Such as? That would be a "Beyond The Standard Model" bit, far removed from anything you're actually talking about. This is physics, so vague hints at a framework you have deigned not to share is singularly unilluminating.

NO, I have no affirmative or negative opinion on that matter at this point

Or, in common parlance: "I have no idea whatsoever", or, "I have a notion, AND an agenda."

... it would seem natural to inquire if any such relations are present though...in itself that doesn't mean they are though; it also doesn't initially assume the negative. A unification approach would be one that sought to analyze each as different aspects of the same phenomenon, right?

This is a deflection. Each time you're challenged by Dalespam, Vanadium, or Mentz you retreat to a slightly different position, from which you then begin to make similar "points". This fits some patterns I've seen here (and elsewhere), which end badly. If this is just a reflection of the same attitude that has you and Mentz at daggers-drawn, maybe you could discuss matters in a manner that seeks to provoke THOUGHT, not merely a reaction.

A very primitive side question here. From Kev's post no. 9:
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
Kev, could you give a link to show exactly what you are talking about? Most every website concerning GR displays general vector-tensor PDE's and it is impossible to find anything comprehensible as you have implicated.

is so beautiful it makes the rest of the thread a waste of time.

Last edited by a moderator:
A very primitive side question here. From Kev's post no. 9:

Kev, could you give a link to show exactly what you are talking about? Most every website concerning GR displays general vector-tensor PDE's and it is impossible to find anything comprehensible as you have implicated.

I beleive this will be useful. https://www.physicsforums.com/showthread.php?t=170293

EDIT: Heh, Kev is damned good isn't he? He's one of the guys/gals here who routinely spills concepts and math that make my noggin ache in a good way.

Last edited:
I mean the part of the sentence after the comma. I'm using the word in the sense of something 'tacked on'.

I suppose it is rather obscure.

You keep making associations between EM and gravity. Are you of the opinion that they are related ? Perhaps that gravity is actually the result of some electromagnetic phenomenon ?

Rider shouldn't be obscure to anyone... at least, no one who signs a contract in their life should be unaware of the concept. "The Doctrine of Stale Demand" aka Laches... now that is an obscure term of art. Rider actually makes sense, even without inserting it as a term of art. Ergo... you shouldn't be the one aplogizing...

Dale
Mentor
2020 Award

But in an inertial frames the Lagrangian for any possible isolated physical system will be invariant under a shift of the position coordinate, right? I imagine this wouldn't be true in general for arbitrary systems analyzed in arbitrary non-inertial frames?
With the caviat inserted in bold, I agree.

From Shanesworld post no.
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.

Consider: Two uncharged neutron stars are in binary orbit. They emit gravitational waves. They lose momentum.

It appears to this civilian that everyone, even the most expert, constantly make mistakes when using English, or 'natural' language. Maybe not with math, but constantly with natural language.

With the caviat inserted in bold, I agree.

This is my own lack of understanding here: there is no special meaning of "isolated" beyond the norm for a system in Relativity, right?

P.S. Caveat... I think you might be in the mood for caviar! If so, I recommend it be taken upon blinis, with creme freche and pepper vodka (none of the off-the-shelf **** either) and don't be afraid of sevruga or osetra, beluga isn't the only... um... fish in the sea. Ok, technically the fish is the sturgeon, but I give no respect to dinosaurs that masquerade as fish. :grumpy: Don't like caviar?... how about the same deal, but with salmon and some fresh chive?

P.P.S... Damn.. I think I'm hungry.

From Shanesworld post no.

Consider: Two uncharged neutron stars are in binary orbit. They emit gravitational waves. They lose momentum.

It appears to this civilian that everyone, even the most expert, constantly make mistakes when using English, or 'natural' language. Maybe not with math, but constantly with natural language.

Ok, you're right on the physics, but where do you see the mistake in the use of language? Remember that physics is a pastiche of past and present, including the language. People then demand it all "in 'english' not math", but so many of these concepts only start to make sense WITH the math. Math is the language of physics... it's not trite, but true.

Language is far more approximate, and limited, and less precise.

Dale
Mentor
2020 Award

This is my own lack of understanding here: there is no special meaning of "isolated" beyond the norm for a system in Relativity, right?
Correct.

P.S. Caveat... I think you might be in the mood for caviar!

Correct.

Ok, got it. I just wanted to make sure I wasn't going down the old "left hand path" on this one. As for caviar... I'm going to make a damned sandwich... I'm REALLY hungry!

Dale
Mentor
2020 Award
My wife has a lasagne in the oven, so fish eggs hold no appeal right now!

Just saying "there are more complex issues" is very hand-wavey. If you want to say that gravity affects momentum, you need to actually have a clear definition of momentum in mind!

Light's momentum is still defined in the context of inertial frames--do you think any of the textbook equations for light's momentum such as p=hf/c would work in arbitrary non-inertial frames? And do you disagree that in a locally inertial frame in GR, by definition light would not be measurably deflected by gravity?

Thanks for your insights. I disagree about that being hand wavy. 1) It is a fact, there are more complex issues. 2)I am not getting into them. QED

I wholly agree about having a clear definition of momentum in mind, in fact that is just the nature of the inquiry.

Do I think any textbook equations for light's momentum such as p=hf/c would work in arbitrary non-inertial reference frame? Yes. I'm pretty sure pushing the gas pedal on my car does not change the momentum of light.

From Shanesworld post no.

Consider: Two uncharged neutron stars are in binary orbit. They emit gravitational waves. They lose momentum.

It appears to this civilian that everyone, even the most expert, constantly make mistakes when using English, or 'natural' language. Maybe not with math, but constantly with natural language.

That is NOT from my post. Hmmm...maybe I'm not getting the From Shanesworld no. clause at the beginning?

Last edited:

Thanks for your insights. I disagree about that being hand wavy. 1) It is a fact, there are more complex issues. 2)I am not getting into them. QED

I wholly agree about having a clear definition of momentum in mind, in fact that is just the nature of the inquiry.

Do I think any textbook equations for light's momentum such as p=hf/c would work in arbitrary non-inertial reference frame? Yes. I'm pretty sure pushing the gas pedal on my car does not change the momentum of light.

So why are you here, talking about this, and expecting that you would get anything in return? "A cat for a hat, or a hat for a cat, but nothing for nothing."