What is the value addition of GR?

[controlfreak]

What are the value additions of GR ? What does it give more than "SR + Newtonian Gravity" gave? Just want to see if someone has listed the same.

I understand it gives a beautiful framework/idea for defining geometry of space time based on mass+energy sources and drafting law of motion of objects as geodesic equations instead of gravitational potential, force law and acceleration vectors like defined in Newtonian Gravity.

But apart from the nice way of reformulating the field equations, force law, Equations of motion in terms of geometry, did it explain/predict stuff which cannot be explained through the original gravitational field equation, force laws and SR like the bending of light due to gravity.

 

[PWiz]

This appears to be a very generic question. GR gave a wealth of new insights into topics such as gravitational waves, shifting orbital precessions, redshifting of EM waves as they travel away from gravitational potential wells, and pretty much wrecked the idea of gravity being a "force", alongside forcing us to rethink about performing calculations which would otherwise be elementary in the Newtonian framework (and I haven't even pointed out 10% of the ideas [introduced or tweaked] that GR contributed to yet). You can read plenty more by a quick Google search

EDIT: Unlike SR, not all calculations in GR are "tweaks" of non-relativistic formulae.

 

[PAllen]

Also, there is really no such thing as SR + Newtonian gravity. Its action at a distance in incompatible with SR, and this was immediately seen by physicists after 1905. Thus many were working on a resolution, some of which worked well enough (e.g. Nordstrom's second theory), but conflicted with experiment. GR won out because of match over time with observations (elegant logical basis was nice, but would have been irrelevant if there was conflict with observation).

 

[pervect]

What are the value additions of GR ? What does it give more than "SR + Newtonian Gravity" gave? Just want to see if someone has listed the same.

Newtonian gravity, with instantaneous action at a distance, isn't really compatible with special relativity. Which is why GR was developed in the first place, to have a theory of gravity that was truly compatible with special relativity rather than just a make-do hack that would work in limited circumstances.

I understand it gives a beautiful framework/idea for defining geometry of space time based on mass+energy sources and drafting law of motion of objects as geodesic equations instead of gravitational potential, force law and acceleration vectors like defined in Newtonian Gravity.

But apart from the nice way of reformulating the field equations, force law, Equations of motion in terms of geometry, did it explain/predict stuff which cannot be explained through the original gravitational field equation, force laws and SR like the bending of light due to gravity.

[/quote]

Yes. Aside from the theoretical considerations, GR has predicted a lot of observed phenomenon, the harvard tower experiment for gravittional time dilation being one of the more famous. In a similar vein, see the scout rocket experiments. Timekeeping has gotten so precise that we need to routinely adjust for these effects.

Some of the other effects, such as increased light bending, perihelion precession, the shapiro effect, and most recently frame dragging (gravity probe B), are more in the nature of minor corrections but have been observed accurately enough to confirm them. GR has had a great impact on cosmology, as well - it did not quite predict Hubble expansion, but was instrumental in explaining it.

 

[phinds]

What are the value additions of GR ? What does it give more than "SR + Newtonian Gravity" gave?

Uh ... the right answer when you do cosmological gravitational calculations, as opposed to the wrong answer.

 

[Nugatory]

Some of the other effects, such as increased light bending, perihelion precession, the shapiro effect, and most recently frame dragging

The precession is particularly interesting (well, at least to me) because it was observed in the orbit of Mercury shortly after Newton. It puzzled people for the next two centuries, until GR was discovered and we could say "Aha! So that's what's going on!".

 

[atyy]

What are the value additions of GR ? What does it give more than "SR + Newtonian Gravity" gave? Just want to see if someone has listed the same.

I understand it gives a beautiful framework/idea for defining geometry of space time based on mass+energy sources and drafting law of motion of objects as geodesic equations instead of gravitational potential, force law and acceleration vectors like defined in Newtonian Gravity.

But apart from the nice way of reformulating the field equations, force law, Equations of motion in terms of geometry, did it explain/predict stuff which cannot be explained through the original gravitational field equation, force laws and SR like the bending of light due to gravity.

For things like the orbit of mercury, GR and be thought of as SR + "Newtonian Gravity modified" - the important point is that Newtonian Gravity without modification is not compatible with SR.

For things like the accelerated expansion of the universe, GR goes beyond SR + "Newtonian Gravity modified", because the background is no longer flat spacetime.

 

[controlfreak]

Thanks for the responses.

1. I see the "action at a distance" problem was resolved
2. Mercury's orbit was explained well
3. Gravitational time dilation is a good one apart from increased light bending and other such experiments got confirmed

But from what I get from your responses, apart from the different stuff related to how Gravity acts on light, the theory found most use in explaining or bringing about breakthroughs in cosmology I suppose and I see there are additional experiments created to confirm GR. I understand GR is the most correct theory until now but my question was more related to what additional value it brought in explaining things around us and providing breakthroughs in understanding more about the universe and resolve things which have been puzzling us like say Mercury's orbit. For instance solving actual physical problems which weren't resolved (and could never have been resolved through existing physics) or adding accuracy to existing solutions.

I understand that there is a competitor theory called Brans-Dicke theory which also uses Metric Tensor based approach. But is there any other theory which had tried explaining these above effects without invoking curvature but modifying Newtonian theory, incorporating the constancy of speed of light and maximum speed of transmitting change ... but retaining flat space time?

@Nugatory - To explain Mercury do we necessarily need GR or is it just that it was a slick tool which could churn out answers easily. I am not aware of the nitty gritties of the calculation and hence curious. Like for instance the results of double slit experiments cannot be explained without quantum mechanics - it was not a slick tool but just that the normal classical approach was just plain wrong and wouldn't work whatever you do.

 

[robphy]

Possibly useful
https://en.wikipedia.org/wiki/Alternatives_to_general_relativity#Early_theories.2C_1686_to_1916
"Early Theories..."

 

[Mentz114]

To explain Mercury do we necessarily need GR or is it just that it was a slick tool which could churn out answers easily. I am not aware of the nitty gritties of the calculation and hence curious. Like for instance the results of double slit experiments cannot be explained without quantum mechanics - it was not a slick tool but just that the normal classical approach was just plain wrong and wouldn't work whatever you do.

Definately not a slick tool. The equations for the orbits of planets come from a strict calculation which allows no room to fiddle anything. The amazing thing is that the exact closed solution was not found until about 2002. GR is definitely needed to explain the anomalous precession of the orbit of Mercury.

 

[russ_watters]

Thanks for the responses.

1. I see the "action at a distance" problem was resolved
2. Mercury's orbit was explained well
3. Gravitational time dilation is a good one apart from increased light bending and other such experiments got confirmed

But from what I get from your responses, apart from the different stuff related to how Gravity acts on light, the theory found most use in explaining or bringing about breakthroughs in cosmology I suppose and I see there are additional experiments created to confirm GR. I understand GR is the most correct theory until now but my question was more related to what additional value it brought in explaining things around us and providing breakthroughs in understanding more about the universe and resolve things which have been puzzling us like say Mercury's orbit. For instance solving actual physical problems which weren't resolved (and could never have been resolved through existing physics) or adding accuracy to existing solutions.

You forgot to mention time dilation and the Harvard tower experiment. Without understanding GR's impact on the timekeeping ability of clocks, GPS would be difficult or impossible to make work.

Whether you consider all of these things important or not is really up to your personal preference, but most science types consider the 1-2 punch of SR and GR to be among the greatest discoveries in the history of science. Enough to make Einstein a rock star on the order of Galileo or Newton.

 

[PAllen]

...

I understand that there is a competitor theory called Brans-Dicke theory which also uses Metric Tensor based approach. But is there any other theory which had tried explaining these above effects without invoking curvature but modifying Newtonian theory, incorporating the constancy of speed of light and maximum speed of transmitting change ... but retaining flat space time?

As I mentioned earlier, Nortdstrom's second theory was the best attempt of this type. However, it gave no deflection of light and a much too small perihelion shift for Mercury. (Note, there are formulations of Nordstrom's second theory that use a non-flat metric, but it was originally formulated with Minkowski metric, and that is the formulation most closely meeting your desire).

I would not consider the so called Post-Newtonian expansion approach in GR as meeting your criteria because it still uses non-flat metric, rather than the flat Minkowski metric.

@Nugatory - To explain Mercury do we necessarily need GR or is it just that it was a slick tool which could churn out answers easily. I am not aware of the nitty gritties of the calculation and hence curious. Like for instance the results of double slit experiments cannot be explained without quantum mechanics - it was not a slick tool but just that the normal classical approach was just plain wrong and wouldn't work whatever you do.

As noted, correctly predicting the perihelion and light deflection is what defeated all reasonable pure SR based approaches.

 

[pervect]

I'm not quite sure of the intent of the question, really. Percentage-wise, the biggest inaccuracy you'll get by not using GR comes with high velocities, the error being 2:1 for light deflection. Other effects show up mostly when you need high precisision, such as (for instance) trying to get centimeter resolution out of GPS.

 

[pervect]

If I may draw a colorul analogly, asking "why does GR need a curved space-time" is rather like saying "why do we use a globe to get accurate maps for the Earth". The answer in both cases is that the underlying geometry isn't flat. The formal mathematical details are somewhat involved, but that's the basic principle. Note that by the time you have SR, you already have (well, should have) the fundamental idea that the geometry of space and time is intertwined, into the geometry of space-time, as measured by the Lorentz interval. GR just describes the fundamental geometry of space-time near massive objects. The geometry is what it is, trying to do away with GR conceptually is rather like trying to get a working theory for navigating around the Earth with a flat Earth.

 

[controlfreak]

Let me put this differently.

There are three uses for any theory.

1. Reformulation : One use of a new theory could be an effective reformulation of an existing theory to help solve problems in an easier way which otherwise would have been cumbersome if done in the original manner like say some problems could be solved easily if we choose a different coordinate system (say polar coordinates instead of cartesian) or some problems get solved easily through the Lagrangian formulation. So in this case the idea is to take an existing theory and reformulate it for easier use but not modifying the "algorithmic complexity or algorithmic content" resident in the theory.
2. Revision: Another use of a new theory would be to explain phenomenon which otherwise cannot be explained by existing theories. It removes an inconsistency/gap between existing theories and observations by modifying existing theories, like what quantum mechanics did. This means that the existing theory has a certain "algorithimic content" to it but that doesn't match up with the "algorithimic content" of nature as observed through experiments. There is something more which is present in nature, which is not present in the existing theory. That gap or impedance mismatch is corrected by revising the theory. This is a more fundamental use than just reformulation.
3. Interpretation: Another use of a new theory is that it helps gain greater insight into why things are the way they are. It doesn't help problems to be solved in an easier way or remove inconsistencies between existing theory and observations. It helps in understanding nature in a more graspable manner for the human mind. It is a new way to articulate mathematical symbols so that it helps us gain greater insight into the "heart' of the theory.

Now for a thought experiment or a thought situation analysis:

If suppose we assume light speed is not constant and there is no speed limit in the universe, then we would not have the space time concept as propounded by SR. But even in that situation, a geometric reformulation of Newtonian gravitational field will make sense because of the equivalence of inertial and gravitational mass. In that context GR would just be useful as a reformulation tool rather than revision. But as experiments have vouched for constancy of the speed of light, it was imperative that the Newtonian or gallilean mechanics needed to modified and so SR came about to set that right. But with the revised mechanics, Newtonian gravity didnt work well and hence GR apart from its effective reformulation which was nevertheless useful as reformulation and interpretation tool, also incorporated SR into Newtonian theory of gravity by revising it. So it in a way it did all three.

My question was if suppose I am not interested in the geometric reformulation but only interested in modifying Netwtonian theory to incorporate SR could we have come up with another way of theorizing the same thing without bringing geometry into it. Why I say that is in formulating classical electrodynamics field theory, they didnt have the ability to redefine geometry due to the fact that force was not proportional to the inertial mass (ofcourse there was magnetism caused due to a moving charge and quantum mechanics later which really made it all clumsy and so inspite of the nice inverse square parallel with gravity exemplified by gauss law because of the other things which happened in EM , it developed in a completely different way and no one attempted to write field equations using metric tensors in that case). But again I suppose if there was no quantum behaviour in the world and assuming there was no SR and no magnetism, then we would have two forces dictated by inverse square laws one depending on charge and one on mass. In electrodynamics masses don't cancel out and hence a geometric formulation might not make sense but in the other it will make sense.

In essence Newton could have attempted a geometric reformulation of his theory before Maxwell equations just that he would have dealt with a curved 3 dimensional space, curved due to the presence of mass. If suppose he had done that then, after SR came about due to maxwell's equations, then we just needed to have changed that geometric reformulation to include SR by extending the formulation from 3D space to 4D minkowski space time and curving that. In a way I am revising history to understand the value GR brought to the world or rather splitting GR into two theoretical components if you will - one the geometric formulation of gravity and the other - the inclusion of the constancy of the speed of light. Both are if you will linearly independent theoritical components. This makes me wonder if we can always create a theory of gravity which can include SR but not be a geometric formulation. I wonder if someone has attempted that.

 

[harrylin]

[..]
My question was if suppose I am not interested in the geometric reformulation but only interested in modifying Netwtonian theory to incorporate SR could we have come up with another way of theorizing the same thing without bringing geometry into it.
[..] In a way I am revising history to understand the value GR brought to the world or rather splitting GR into two theoretical components if you will - one the geometric formulation of gravity and the other - the inclusion of the constancy of the speed of light. Both are if you will linearly independent theoritical components. This makes me wonder if we can always create a theory of gravity which can include SR but not be a geometric formulation. I wonder if someone has attempted that.

I find your question puzzling, as GR was originally presented as principle theory as well as field theory - and nevertheless it had a geometric formulation. Geometry is unavoidable in SR and GR because length measurements depend on the used reference system. How could you avoid geometry in an alternative formulation? Probably you should clarify that before meaningful answers can be given.

 

[Mentz114]

..
..
This makes me wonder if we can always create a theory of gravity which can include SR but not be a geometric formulation. I wonder if someone has attempted that.

SR is a geometric theory so it would seem a natural thing to extend it to be 'general' and include gravity. One of Einsteins key insights was the existence of a special state of motion - i.e. free fall. In this state the faller feels 'weightless'. The problem with a non-geometric (dynamic) theory is getting rid of the force of gravity in this state. GR handles this with the concept of geodesic motion. This is profoundly different from Newtons dynamic gravity.

 

[controlfreak]

Geometry is unavoidable in SR and GR because length measurements depend on the used reference system.

Geometry is unavoidable in SR as SR redefines the stage. But then GR is about Gravitational force/field like Maxwell's equations is about EM force/field. Both are classical forces (I am not bring in QM here - let us leave it out of the discussion now). It so happened that in case of gravitational force it is proportional to Gravitational Mass which "miraculously" was also equal to the inertial mass and so Gravitational Field theory could be formulated in a geometric way while EM field theory couldn't be - this has nothing to do with SR. Even if there we no SR, GR could be articulated in a geometric way - for instance Newton could have done it but it wouldn't have accounted for SR but that will have come later. When I mean geometric way, I mean how Einstein articulated the field in terms of the modifications in the geometry of space and all objects irrespective of their masses traveled in straightlines/geodesics in that newly formulated space. In other words, he mathematically absorbed gravity into the space formation and that formulation though incorporated SR has nothing to do with SR but to do with the fact that Gravitational Mass and Inertial Mass are same and that was the beautiful "elevator" thought which inspired Einstein.

That is not true in the case of EM as EM field or force was proportional to charge and not mass ,and so masses and charges don't cancel out and so EM field theory couldn't be formulated in an elegantly geometric way like Gravitational field theory could be. So if suppose Gravitational mass is not equal to inertial mass, then this nice geometrical formulation wouldn't be feasible. What I am saying is for a moment, let us not assume that fact (GM=IM) and formulate the field theory like how we had done for EM where (Q was not equal to IM) and let's see where we get.

 

[Mentz114]

So if suppose Gravitational mass is not equal to inertial mass, then this nice geometrical formulation wouldn't be feasible. What I am saying is for a moment, let us not assume that fact (GM=IM) and formulate the field theory like how we had done for EM where (Q was not equal to IM) and let's see where we get.

What you get is a theory which is GR when GM=IM is assumed, and one which gives incorrect predictions when GM is assumed not equal to IM.

This comment is based on the Field Theory Gravity which according to Feynman, Deser and others is GR.

See
Field Theory of Gravitation: Desire and Reality
Yurij V. Baryshev

here http://arxiv.org/abs/gr-qc/9912003

 

[controlfreak]

SR is a geometric theory so it would seem a natural thing to extend it to be 'general' and include gravity.

No it is not because SR was a geometric theory that Einstein found it natural to make GR as gravitational theory. SR's geometry insight is different from GR's geometry insight. SR geometry insight is about adding a 4th dimension and mixing time with space because of the constancy of speed of light which played havoc with the time dimension. GR's geometry insight is about baking a force into geometry - completely different inspirations and that Einstein was able to bake the force into geometry only because gravity was such a force which can be baked into geometry because GM=IM. If Einstein had lived in Newton's time, he would have done it then. And then SR would have come about and then GR would have been modified to incorporate SR. Unfortunately the order of formulations were different and hence Einstein did both at one shot - geometric formulation of gravity and incorporation of SR in gravity.

 

[Mentz114]

No it is not because SR was a geometric theory that Einstein found it natural to make GR as gravitational theory. SR's geometry insight is different from GR's geometry insight. SR geometry insight is about adding a 4th dimension and mixing time with space because of the constancy of speed of light which played havoc with the time dimension. GR's geometry insight is about baking a force into geometry - completely different inspirations and that Einstein was able to bake the force into geometry only because gravity was such a force which can be baked into geometry because GM=IM. If Einstein had lived in Newton's time, he would have done it then. And then SR would have come about and then GR would have been modified to incorporate SR. Unfortunately the order of formulations were different and hence Einstein did both at one shot - geometric formulation of gravity and incorporation of SR in gravity.

That is your opinion but I don't agree with it.

Einstein realized that to reproduce the physical fact of free-fall, geometrisation of forces was necessary. He specifcally sought out a theory which allowed him to do this.
And the result is awesome ( in the older sense).

 

[controlfreak]

What you get is a theory which is GR when GM=IM is assumed, and one which gives incorrect predictions when GM is assumed not equal to IM.

I am not contending that GM is not equal to IM. I am saying create a theory where GM might or might not be equal to IM and you get a theory. In that overarching generic inverse square law theory (which incorporates SR) when you make GM=IM you will get the current GR and it will make right predictions. But then because as GM might or might not be equal to IM we cannot use that fact apriori and so we cannot go the geometric way and will be forced to think differently like classical relativistic EM as Q is not equal to IM.

Einstein realized that to reproduce the physical fact of free-fall, geometrisation of forces was necessary. He specifcally sought out a theory in which allowed him to do this.

Exactly. That means if Einstein was born in Newton's time and had no idea of maxwell or constancy of speed of light, still he would have gone ahead with program of geometrisation of gravitational forces and would not have waited for SR to dawn upon him the idea to geometerize as the inspiration to geometerize came from GM=IM and not SR.

 

[Mentz114]

I am not contending that GM is not equal to IM. I am saying create a theory where GM might or might not be equal to IM and you get a theory. In that overarching generic inverse square law theory (which incorporates SR) when you make GM=IM you will get the current GR and it will make right predictions. But then because as GM might or might not be equal to IM we cannot use that fact apriori and so we cannot go the geometric way and will be forced to think differently like classical relativistic EM as Q is not equal to IM.

FTG is such a theory. It does not assume IM=GM.

Exactly. That means if Einstein was born in Newton's time and had no idea of maxwell or constancy of speed of light, still he would have gone ahead with program of geometrisation of gravitational forces and would not have waited for SR to dawn upon him the idea to geometerize as the inspiration to geometerize came from GM=IM and not SR.

Sorry my crystal ball is not working so I cannot check this speculation.

 

[controlfreak]

FTG is such a theory. It does not assume IM=GM.

Thank you for the pointer - very helpful. This is what I was thinking about - a theory which doesn't curve the underlying stage - Minkowski spacetime but still gives answers. I found a forum answer of yours on this topic - https://www.physicsforums.com/threads/gravity-on-the-minkowski-spacetime.383877/ - Quite helpful. They name GR as geometerodynamics while the theory I was asking for is named as gravidynamics and seems to be something which has been pursued from the time of Poincare. Interesting.

Sorry my crystal ball is not working so I cannot check this speculation.

Fair enough :-) I was just wondering about the plausible origin of the inspiration for geometrization as geometerization of field is not always possible and is only natural where the source of the field is equivalent to the source of inertia. Ofcourse it is anyone's gauss and not an useful line of thought anyway.

 

[Mentz114]

Thank you for the pointer - very helpful. This is what I was thinking about - a theory which doesn't curve the underlying stage - Minkowski spacetime but still gives answers. I found a forum answer of yours on this topic - https://www.physicsforums.com/threads/gravity-on-the-minkowski-spacetime.383877/ - Quite helpful. They name GR as geometerodynamics while the theory I was asking for is named as gravidynamics and seems to be something which has been pursued from the time of Poincare. Interesting.

Your questions are relevant but most of them have been asked and answered.

Fair enough :-) I was just wondering about the plausible origin of the inspiration for geometrization as geometerization of field is not always possible and is only natural where the source of the field is equivalent to the source of inertia. Ofcourse it is anyone's gauss and not an useful line of thought anyway.

Fair enough. In fact you are in good company with such speculation because T. Padmanabhan also comes up with what he thinks would have happened if QFT had been invented before Einsteins day.

 

[harrylin]

Geometry is unavoidable in SR as SR redefines the stage. But then GR is about Gravitational force/field like Maxwell's equations is about EM force/field. Both are classical forces (I am not bring in QM here - let us leave it out of the discussion now). It so happened that in case of gravitational force it is proportional to Gravitational Mass which "miraculously" was also equal to the inertial mass and so Gravitational Field theory could be formulated in a geometric way while EM field theory couldn't be - this has nothing to do with SR. Even if there we no SR, GR could be articulated in a geometric way - for instance Newton could have done it but it wouldn't have accounted for SR but that will have come later. When I mean geometric way, I mean how Einstein articulated the field in terms of the modifications in the geometry of space and all objects irrespective of their masses traveled in straightlines/geodesics in that newly formulated space. In other words, he mathematically absorbed gravity into the space formation and that formulation though incorporated SR has nothing to do with SR but to do with the fact that Gravitational Mass and Inertial Mass are same and that was the beautiful "elevator" thought which inspired Einstein. That is not true in the case of EM [..]

Quite so; but that doesn't really answer my question. According to Einstein's formulation of GR, the gravitational field shortens a meter stick when it is held parallel to the field lines (of course, this is not including elongation or compression due to weight). Given that result which directly follows from SR + EP, how could one avoid geometrical descriptions altogether?

let us not assume that fact (GM=IM) and formulate the field theory like how we had done for EM where (Q was not equal to IM) and let's see where we get.

Do you mean that you want to see a theory according to which meter sticks are unaffected?
BTW, the whole "GM=IM" assumption discussion doesn't make sense to me, given that mass is a physical concept. A rabbit is a rabbit, no matter how you measure it.

 

[controlfreak]

how could one avoid geometrical descriptions altogether?

I am not asking to avoid geometry altogether as that doesn't make any sense but the idea of geometerization of a force/field or specifically the curving of the Minkowski space time by a field. This link will be useful to clarify - https://www.physicsforums.com/threads/gravity-on-the-minkowski-spacetime.383877/

BTW, I find the whole "GM=IM" assumption discussion nonsensical, given that mass is a physical concept. A rabbit is a rabbit, no matter how you measure it.

" A body at rest gives way before the action of an external force, moving and attaining a certain velocity. It yields more or less easily, according to its inertial mass, resisting the motion more strongly if the mass is large than if it is small. We may say, without pretending to be rigorous: the readiness with which a body responds to the call of an external force depends on its inertial mass. If it were true that the Earth attracts all bodies with the same force, that of greatest inertial mass would move more slowly in falling than any other. But this is not the case: all bodies fall in the same way. This means that the force by which the Earth attracts different masses must be different. Now the Earth attracts a stone with the force of gravity and knows nothing about its inertial mass. The "calling" force of the Earth depends on the gravitational mass. The " answering" motion of the stone depends on the inertial mass. Since the " answering " motion is always the same all bodies dropped from the same height fall in the same way it must be deduced that gravitational mass and inertial mass are equal."

- A. EINSTEIN, The Evolution of Physics.

 

[controlfreak]

Fair enough. In fact you are in good company with such speculation because T. Padmanabhan also comes up with what he thinks would have happened if QFT had been invented before Einsteins day.

Infact there is another interesting way to look at this theoretical picture. That is through the origin of magnetism. Magnetism is a force which originates due to charge movement which implies there is something interesting happening there. In fact we can even consider magnetism as not a real fundamental force but just a mathematical correction to coulomb's law needed to account for relativity considerations to motion when a charge moves. So if we take coulomb's law and SR we can possibly come up with a field theory which doesn't need to treat magnetism as a separate force and vector like Maxwell has done. In fact that is what has been done by Einstein in his GR where he has used Newton's Inverse Square law for Gravity and Lorentz SR and came up with a comprehensive field theory without necessity for an introduction of a new vector - Gravito Magnetic Field B but he had it kinda easy because GM=IM. But on the other hand, if you go the other way around, instead of going Einstein way we can go the Maxwell way for articulating Gravity and include another vector/field called Gravito-Magnetism and have a parallel set of equations for Gravity like in the case of EM.

The two obvious differences are :

1. The source of force/field is equivalent to source of inertia in case of Gravity
2. The force is only attractive and not repulsive in case of Gravity

But then the point 1 will not affect the field equations or force law and would only affect the equations of motion when we get down to calculating acceleration. The only change would be due to point 2. And when I googled stuff I found we already had those kinds of laws (GEM laws - https://en.wikipedia.org/wiki/Gravitoelectromagnetism) and there are certain negative signs in the Gravity equations as against Maxwell due to possible the strictly attractive nature of Gravity and absence of positive and negative masses and the convention that field is treated positive for a positive charge in EM. If Maxwell's equations are written with the convention field is negative for a positive charge (like how gravitational field is negative for positive mass - there is no negative mass - it is upto us to assign the signs) then we have exactly the same equations similar to Maxwell's. This has been further refined into a new theory called Lorentz Invariant Theory of Gravitation which was what I was exactly looking for - https://en.wikiversity.org/wiki/Lorentz-invariant_theory_of_gravitation. The equations are simple and straightforward similar to Maxwell's equations instead of indulging in geometrization of space time which GR did and also incorporates SR for free (Maxwell's equations included SR in the form of B - Magnetism without his knowledge of SR and hence Maxwell's equations were automatically Lorentz Invariant and infact prompted Einstein to make gravitation laws so). The thing is possibly if we start with these LITG equations (which are very similar to Maxwell) instead of GR possibly it would be easier to come up with a QFT for gravity like it was done for EM in case of QED as there is a parallel. In fact if QFT was invented before Einstein possibly he would have tried to go the LITG way but then that is just crystal ball gazing in the past :-)

 

[controlfreak]

To summarize :

Given a fundamental force (Gravity, Electrical) originating from a fundamental source (mass,charge) dictated by an inverse square law (Newton theory of gravity, Coloumb's law) if we have to incorporate relativistic considerations (Lorentz Invariance) then we can go two ways to articulate the same mathematically:

• Einstein Way - Bake the force into the geometry of space time and make the laws Lorentz Invariant
• Maxwell Way - Create an ancillary (mathematical) field (Magnetism) to account for relativistic effects and make the laws Lorentz Invariant

That means :

1. We can go Einstein Way to explain EM like how Kaluza-Klien did which forms the basis of string theory.
2. We can go Maxwell way to explain Gravitation like how many from Heaviside to Fedosin were and are trying to do in the form of LITG or GEM.

Now which path to take to achieve the below:

• Quantize Gravity - Possibly LITG has a better chance as there is a parallel in QED
• Unify Gravity and EM - Possibly string theory but not so sure

This discussion helped me to clear my mind and come to the above clarity. Thanks for the responses.

 

[Vanadium 50]

The only person who has mentioned Maxwell is you, and your statement above is simply incorrect. Those two theories are not mathematically equivalent.

 

[Dale]

There are three uses for any theory.

1. Reformulation : One use of a new theory could be an effective reformulation of an existing theory to help solve problems in an easier way which otherwise would have been cumbersome if done in the original manner like say some problems could be solved easily if we choose a different coordinate system (say polar coordinates instead of cartesian) or some problems get solved easily through the Lagrangian formulation. So in this case the idea is to take an existing theory and reformulate it for easier use but not modifying the "algorithmic complexity or algorithmic content" resident in the theory.
2. Revision: Another use of a new theory would be to explain phenomenon which otherwise cannot be explained by existing theories. It removes an inconsistency/gap between existing theories and observations by modifying existing theories, like what quantum mechanics did. This means that the existing theory has a certain "algorithimic content" to it but that doesn't match up with the "algorithimic content" of nature as observed through experiments. There is something more which is present in nature, which is not present in the existing theory. That gap or impedance mismatch is corrected by revising the theory. This is a more fundamental use than just reformulation.
3. Interpretation: Another use of a new theory is that it helps gain greater insight into why things are the way they are. It doesn't help problems to be solved in an easier way or remove inconsistencies between existing theory and observations. It helps in understanding nature in a more graspable manner for the human mind. It is a new way to articulate mathematical symbols so that it helps us gain greater insight into the "heart' of the theory.

So, I don't know if there is an authoritative classification, but personally I would not classify 1 and 3 as a new theory.

I would classify 1 as a reformulation of the existing theory. In other words, I would not describe Lagrangian mechanics as a different theory than Newtonian mechanics, but just a reformulation of it.

I would classify 3 as an interpretation of the existing theory. For example, I wouldn't call MWI and Copenhagen different theories, but just different interpretations of quantum mechanics.

Only 2 constitutes a genuinely new theory, and GR does that. Any reformulation or reinterpretation is incidental.

 

[controlfreak]

Only 2 constitutes a genuinely new theory, and GR does that.

Well that may be one way of looking at the word "theory" but then I see that you understand what I was saying. And we are in agreement that GR does all three functions, incidental or not.

Those two theories are not mathematically equivalent.

I am not sure what are you referring to here. I didnt say Maxwell's theory is mathematically equivalent to GR. And it is a big thread and not sure what specific point you are referring to as you haven't quoted any sentence of mine. I only pointed out the fact that LITG explains gravity with equations similar to Maxwell's equations and also incorporates SR. These links will help clarify - http://serg.fedosin.ru/muen.htm , http://serg.fedosin.ru/gmen.htm. In that manner I had said the phenomenon of Gravity can be explained/articulated using two mathematically different forms - one form as given by GR and another as given by LITG which looks similar to Maxwell's equations.

 

[ShayanJ]

I am not sure what are you referring to here. I didnt say Maxwell's theory is mathematically equivalent to GR. And it is a big thread and not sure what specific point you are referring to as you haven't quoted any sentence of mine. I only pointed out the fact that LITG explains gravity with equations similar to Maxwell's equations and also incorporates SR. These links will help clarify - http://serg.fedosin.ru/muen.htm , http://serg.fedosin.ru/gmen.htm. In that manner I had said the phenomenon of Gravity can be explained/articulated using two mathematically different forms - one form as given by GR and another as given by LITG which looks similar to Maxwell's equations.

GravitoElectroMagnetism is not equivalent to GR. GR is highly non-linear while GEM is linear. In fact you even can derive GEM from the non-relativistic limit of linearized GR for a stationary source(Gravitation by Padmanabhan,section 6.4.1).
So what you say is wrong and I'm really wondering where you got it from. Even the links you yourself presented explain that those equations are valid under some conditions and approximations.

 

[controlfreak]

GravitoElectroMagnetism is not equivalent to GR. GR is highly non-linear while GEM is linear. In fact you even can derive GEM from the non-relativistic limit of GR for a stationary source(Gravitation by Padmanabhan,section 6.4.1).
So what you say is wrong and I'm really wondering where did you get it.

Thank you for your response. You are right.

Infact I was just contemplating about the similarities in the force/field laws in the static world between Electrostatics and Newton's Law of Gravity (Gravitostatics) and was wondering if instead of going the GR way is it possible to come up with a theory of gravitation similar to the form Maxwell did for EM which explained the change in Electrostatic force laws when the source (charge) started moving. When charge started moving magnetism arose and I felt that when mass moved something similar has to occur and its just that the Gravito Magnetic force would be so weak it wouldn't be observed easily like how magnetism gets observed easily. Maxwell was able to capture that in his EM equations and which also satisfied Lorentz Invariance. I felt if he could do it for charge, we can come up with a similar approach for mass sources as well. Then I googled and got to these links like GEM and LITG. But then it has also been mentioned GEM/LITG are alternatives to GR in weak field approximation like you have pointed out and hence not fully equivalent to GR. But if we generalize Maxwell's equations for strong fields and make it Non Linear and apply the same approach to GEM or LITG will we get an equivalent theory?

 

[Dale]

was wondering if instead of going the GR way is it possible to come up with a theory of gravitation similar to the form Maxwell did for EM

As has already been mentioned to you several times, many people have tried, but none has succeeded in obtaining such a theory which is consistent with observation.

Since you have essentially already exhausted this route, perhaps you might consider an alternative approach to your question. Perhaps consider what it would take to geometrize Newtonian gravity. See Newton Cartan gravity.