Correlating Newtonian Model with Einstein's GR

[Schmelzer]

Newtonian fine, the proportionality constant (say G) is experimentally measured. It's a standard experiment. How do you measure the related constant in GR?

In exactly the same way. One simply computes the GR prediction for the same experiment. For this, of course, the Newtonian approximation of GR will be sufficient, but you can, of course, also use full GR to compute it.

I was not clear enough; I was referring mainly to the 8pi, not the full 8$$\pi$$G. We are in agreement here.

Factors of 2$\pi$ appear in mathematics all the time, and some more factors 2 are nothing one would care about.

If it would be possible to get rid of them by some convention, similar to "we use units with $c,\hbar=1$", mathematicians would be happy to do it. But a "we use units with $2\pi=1$" makes not really sense.

 

[The God]

the Newtonian approximation of GR will be sufficient, but you can, of course, also use full GR to compute it.

Could you please provide a link where G is recovered by using GR only, without resorting to Newtonian. The standard experiment measures attraction force related quantity, say small deflection or torsion, in GR we have no such animal called attraction force, so what would be the qty available in GR for measurement?

Say we did not know about Newtonian at the time of GR, could we have discovered G (kind of G or some factored constant of G)?

 

[NotEinstein]

You do not understand 'made to'.
I never claimed that those derivations are wrong, I said that G (constant) is flicked from Newtonian, despite three apparent incongruencies as stated in #1 to #3.

#1: Because in the limits taken, spacetime comes flat (with only small perturbations), and this can be approximated with a separate space and time. In other words, exactly in the limiting case, the geometry of spacetime reduces to a theory without a spacetime geometry.
#2: I've already pointed out you can easily introduce a limited speed of light (and gravity) in Newtonian physics, which is (to my knowledge) exactly what was done, long before Einstein came along.
#3: Because in the limiting case, the perturbations of spacetime can be approximated by a force.

You do some maths, and when you are near about that Poisson' equation, you compare it with Newtonian existing Poisson's equation and get G, and then boast around that lo GR leads to Newtonian in limiting case.

One does not get G, one gets 8piG. And what else could one expect? Because they are describing similar things, and Newtonian physics can be derived from GR, either GR should be able to derive the value of G, or it must use it as a constant of nature, exactly as Newtonian physics does.

You read #62 again, the 'how' is not seeking the maths or procedural answer, it's referring to incompatibility. As I told you how a non force concept become force concept...

That is not a problem. The force is an approximation of a spacetime that is nearly flat.
And more important, the maths work. In fact, the maths of GR work better than those of Newtonian physics. If you are saying the two are incompatible, we must reject Newtonian physics completely, as GR is clearly superior in describing reality.

and how gravity moving at c, suddenly start moving with infinite speed....it cannot.

And as I've already said multiple times now, this indeed does not happen.

 

[NotEinstein]

Could you please provide a link where G is recovered by using GR only, without resorting to Newtonian. The standard experiment measures attraction force related quantity, say small deflection or torsion, in GR we have no such animal called attraction force, so what would be the qty available in GR for measurement?

Say we did not know about Newtonian at the time of GR, could we have discovered G (kind of G or some factored constant of G)?

If GR mathematically reduces to Newtonian physics in a limiting case, we can set-up an experiment within such a limited case environment to probe the value of the constant of nature that appears in GR. This is exactly what many of those (if not all) experiments that probe the G for Newtonian physics do: they are in such a limited case environment. Ergo, those experiments not only give the value of G for Newtonian physics, they also give the value of the constant for GR. And that turned out to be 8piG.

 

[The God]

And as I've already said multiple times now, this indeed does not happen.

Then keep hunting around till you find out the speed of gravity in Newtonian. You will stumble upon something sooner or later.

 

[The God]

The force is an approximation of a spacetime that is nearly flat.

Not even word salad.

 

[The God]

If GR mathematically reduces to Newtonian physics in a limiting case, we can set-up an experiment within such a limited case environment to probe the value of the constant of nature that appears in GR. This is exactly what many of those (if not all) experiments that probe the G for Newtonian physics do: they are in such a limited case environment. Ergo, those experiments not only give the value of G for Newtonian physics, they also give the value of the constant for GR. And that turned out to be 8piG.

Good you took some clues from Schmelzer. But you are usurping Cavendish experiment (and improvised versions) into GR. That is one more example of "made to".

 

[NotEinstein]

Then keep hunting around till you find out the speed of gravity in Newtonian. You will stumble upon something sooner or later.

First hit on my Google search: https://en.wikipedia.org/wiki/Speed_of_gravity#Laplace So it was already being attempted in 1805, a good century before Einstein did it. It appears you have put no effort into educating yourself on this at all! Just as with the derivation I linked...

Not even word salad.

Perhaps I was unclear in my formulation: the model with gravity as a force (Newtonian) is a good approximation of the model with spacetime when said spacetime is nearly flat (and at low velocities). The derivation I linked proves this.

Good you took some clues from Schmelzer. But you are usurping Cavendish experiment (and improvised versions) into GR. That is one more example of "made to".

So, because there is an experiment which gives the value of the constant of nature for GR, GR is forced to look like Newtonian physics, because that is also based on the same experiment. Seems perfectly consistent to me. I don't understand why you have such a problem with this? Why couldn't an experiment to measure the (apparent) gravitational attraction between two objects be used to provide input for two different theories?

 

[The God]

First hit on my Google search: https://en.wikipedia.org/wiki/Speed_of_gravity#Laplace So it was already being attempted in 1805, a good century before Einstein did it. It appears you have put no effort into educating yourself on this at all! Just as with the derivation I linked...


Perhaps I was unclear in my formulation: the model with gravity as a force (Newtonian) is a good approximation of the model with spacetime when said spacetime is nearly flat (and at low velocities). The derivation I linked proves this.


So, because there is an experiment which gives the value of the constant of nature for GR, GR is forced to look like Newtonian physics, because that is also based on the same experiment. Seems perfectly consistent to me. I don't understand why you have such a problem with this? Why couldn't an experiment to measure the (apparent) gravitational attraction between two objects be used to provide input for two different theories?

Not unclear, incorrect. But I will let that pass too.

Anyways read again the link's Laplace section, read it fully and find out what it says about the proposition. It explains why in Newtonian a finite speed could be an issue. It's clear that you did not read it fully. I am surprised that (instantaneous aspect of Newtonian is a fundamental problem with the theory) you are unaware of it, but attempting to educate (or troll) others.

PS: Not your fault, many Google (educated) autodidacts are experts here, you have already taken that role.

 

[Schmelzer]

Could you please provide a link where G is recovered by using GR only, without resorting to Newtonian.

No. Once it is not necessary to do this, why would somebody do it?

The standard experiment measures attraction force related quantity, say small deflection or torsion, in GR we have no such animal called attraction force, so what would be the qty available in GR for measurement?
Say we did not know about Newtonian at the time of GR, could we have discovered G (kind of G or some factored constant of G)?

Of course, we could have measured the gravitational constant, and of course using the same experiment. That there are no attraction forces is metaphysics, not physics. It is about how the animal is named, not about a real difference in the observable effects.
The Newtonian limit, or at least the version of it I prefer, uses harmonic coordinates. If you follow GR ideology, this is nothing but an irrelevant, arbitrary choice. But nothing prevents you to interpret these same harmonic coordinates to define the absolute Newtonian space and time, which defines inertial movement. And once you have inertial, force-free movement defined, you have all you need to define gravity as a force.

 

[NotEinstein]

Not unclear, incorrect. But I will let that pass too.

No, please correct me if I'm wrong! If you don't explain why it's incorrect, I cannot learn from it.

Anyways read again the link's Laplace section, read it fully and find out what it says about the proposition. It explains why in Newtonian a finite speed could be an issue. It's clear that you did not read it fully. I am surprised that (instantaneous aspect of Newtonian is a fundamental problem with the theory) you are unaware of it, but attempting to educate (or troll) others.

No, please explain to me what it says about the proposition.

But it is funny... Up until that Wikipedia-link you said Newtonian physics cannot incorporate a finite speed of gravity, but now that claim is suddenly reduced to "could be an issue". It's almost as if you didn't know about this...
You keep telling me to read more, and search for more, but every time I do, I find out about something else that you got wrong. Perhaps you should also start reading scientific material more fully?

PS: Not your fault, many Google (educated) autodidacts are experts here, you have already taken that role.

Is this another insult?

And I see you've dodged my question about experimental data being used for two different theories.

 

[The God]

No, please correct me if I'm wrong! If you don't explain why it's incorrect, I cannot learn from it.


No, please explain to me what it says about the proposition.

But it is funny... Up until that Wikipedia-link you said Newtonian physics cannot incorporate a finite speed of gravity, but now that claim is suddenly reduced to "could be an issue". It's almost as if you didn't know about this...
You keep telling me to read more, and search for more, but every time I do, I find out about something else that you got wrong. Perhaps you should also start reading scientific material more fully?


Is this another insult?

And I see you've dodged my question about experimental data being used for two different theories.

Read below from the link given by you only. I see no reason why I should engage you any further, since you do not read or comprehend your supplied links itself. You are being a drag only.


"From a modern point of view, Laplace's analysis is incorrect. Not knowing about Lorentz' invariance of static fields, Laplace assumed that when an object like the Earth is moving around the Sun, the attraction of the Earth would not be toward the instantaneous position of the Sun, but toward where the Sun had been if its position was retarded using the relative velocity (this retardation actually doeshappen with the optical position of the Sun, and is called annual solar aberration). Putting the Sun immobile at the origin, when the Earth is moving in an orbit of radius R with velocity vpresuming that the gravitational influence moves with velocity c, moves the Sun's true position ahead of its optical position, by an amount equal to vR/c, which is the travel time of gravity from the sun to the Earth times the relative velocity of the sun and the Earth. The pull of gravity (if it behaved like a wave, such as light) would then be always displaced in the direction of the Earth's velocity, so that the Earth would always be pulled toward the optical position of the Sun, rather than its actual position. This would cause a pull ahead of the Earth, which would cause the orbit of the Earth to spiral outward. Such an outspiral would be suppressed by an amount v/ccompared to the force which keeps the Earth in orbit; and since the Earth's orbit is observed to be stable, Laplace's c must be very large. As is now known, it may be considered to be infinite in the limit of straight-line motion, since as a static influence, it is instantaneous at distance, when seen by observers at constant transverse velocity. For orbits in which velocity (direction of speed) changes slowly, it is almost infinite. ."

 

[The God]

Yes, you deserve an answer for experimental data part. There is no problem in usage of experimental data for any number of theories, but please read what does that experiment measure. Ok I will help you a little bit, it measures something caused by gravitational "attraction force". GR does not recognise gravity as force; remember my "made up" comment?


PS : No, it was not an insult. It's a reality here, autodidacts are available dime a dozen in various internet forums. That is not a big deal, as long as they do not start pretending as experts.

 

[The God]

No. Once it is not necessary to do this, why would somebody do it?

Of course, we could have measured the gravitational constant, and of course using the same experiment. That there are no attraction forces is metaphysics, not physics. It is about how the animal is named, not about a real difference in the observable effects.
The Newtonian limit, or at least the version of it I prefer, uses harmonic coordinates. If you follow GR ideology, this is nothing but an irrelevant, arbitrary choice. But nothing prevents you to interpret these same harmonic coordinates to define the absolute Newtonian space and time, which defines inertial movement. And once you have inertial, force-free movement defined, you have all you need to define gravity as a force.

I know about your inclination for harmonic coordinates, not that it matters.

But you are giving a messy interpretation with force, force free, absolute space, absolute time, spacetime; I know you are sort of deep into GR alternative of yours, this post of yours is a blend of Newtonian, GR and your alternative take. And I think not many will share your view that "not attraction force" in GR is metaphysics not physics. It will change the very definition of geodesics, so called straightlines in curved spacetime.

 

[NotEinstein]

Read below from the link given by you only. I see no reason why I should engage you any further, since you do not read or comprehend your supplied links itself. You are being a drag only.

You're right, I was looking for answers in the wrong place. The correct explanation is actually the limit-taking process. By taking the limit to small velocities, you effectively set c to infinity. This makes the propagation of gravity instantaneous as well.
https://physics.stackexchange.com/a/187557

But as I've mentioned before, this part of the discussion is actually unnecessary: if they are incompatible, we simply reject Newtonian physics as GR is a much better description.

Yes, you deserve an answer for experimental data part. There is no problem in usage of experimental data for any number of theories, but please read what does that experiment measure. Ok I will help you a little bit, it measures something caused by gravitational "attraction force". GR does not recognise gravity as force; remember my "made up" comment?

GR does not have a gravitational force, but it does predict two massive objects will tend to move closer together, due to the bending of spacetime. There just happens to be a constant of nature involved there, a "strength" if you will, and these experiments can measure it. It turns out to be 8piG.

PS : No, it was not an insult. It's a reality here, autodidacts are available dime a dozen in various internet forums. That is not a big deal, as long as they do not start pretending as experts.

I'm still not sure what you meant with "you have already taken that role" then?

 

[Schmelzer]

I know about your inclination for harmonic coordinates, not that it matters.
But you are giving a messy interpretation with force, force free, absolute space, absolute time, spacetime; I know you are sort of deep into GR alternative of yours, this post of yours is a blend of Newtonian, GR and your alternative take. And I think not many will share your view that "not attraction force" in GR is metaphysics not physics. It will change the very definition of geodesics, so called straightlines in curved spacetime.

It makes no difference for the geodetic equation, if you write it down in harmonic coordinates, name some parts of it "gravitational force", and compare it with the Newtonian equation. If many will share or not does not matter. What matters is that people know how to do the Newtonian limit. Doing it in harmonic coordinates is standard. See C.M. Will, On the unreasonable effectiveness of the post-Newtonian approximation in gravitational physics, arxiv:1102.5192. It is simply not the only possibility, one is not obliged to use them according to GR ideology. But one can use them for all the computations.

The point of introducing my own interpretation of this use is to show you that there is no conflict. Switching to my interpretation of the Einstein equation does not change any physics, any observable predictions. Thus, it does not change the predictions for the experiment used to measure G in Newtonian theory. GR has different mathematics, but, once this math can be interpreted in terms of forces on a Newtonian background too, your objection that GR somehow has no forces, thus, something would be wrong this using the same experiment or so, fails.

 

[The God]

You're right, I was looking for answers in the wrong place. The correct explanation is actually the limit-taking process. By taking the limit to small velocities, you effectively set c to infinity. This makes the propagation of gravity instantaneous as well.
https://physics.stackexchange.com/a/187557

How do you effectively set 'c' to infinity? c is c, it is not even C. Another bloomer? See, do not rush to wiki or stackexchange everytime. Learn properly, make up your mind, then you will not be unclear. You are being so fickle minded.

But as I've mentioned before, this part of the discussion is actually unnecessary: if they are incompatible, we simply reject Newtonian physics as GR is a much better description.

You don't decide what is necessary or not. Reject Newtonian and get me G, that's the question I asked, you conveniently continued with your wikis and stackeys and retracted too. You can't.

GR does not have a gravitational force, but it does predict two massive objects will tend to move closer together, due to the bending of spacetime. There just happens to be a constant of nature involved there, a "strength" if you will, and these experiments can measure it. It turns out to be 8piG.

What bends between you and another person sitting infront of you? What is "strength" in GR? Another 'unclear' stuff?

Bye bye. You need to study quite extensively on basics of gravity, GR will come later. Why not take help from your free/unsolicited advisors on this thread, Origin and DaveC, may be they can lift you.

 

[The God]

It makes no difference for the geodetic equation, if you write it down in harmonic coordinates, name some parts of it "gravitational force", and compare it with the Newtonian equation. If many will share or not does not matter. What matters is that people know how to do the Newtonian limit. Doing it in harmonic coordinates is standard. See C.M. Will, On the unreasonable effectiveness of the post-Newtonian approximation in gravitational physics, arxiv:1102.5192. It is simply not the only possibility, one is not obliged to use them according to GR ideology. But one can use them for all the computations.

The point of introducing my own interpretation of this use is to show you that there is no conflict. Switching to my interpretation of the Einstein equation does not change any physics, any observable predictions. Thus, it does not change the predictions for the experiment used to measure G in Newtonian theory. GR has different mathematics, but, once this math can be interpreted in terms of forces on a Newtonian background too, your objection that GR somehow has no forces, thus, something would be wrong this using the same experiment or so, fails.

In Physics, the concept of force is not something which can be termed as mere semantics. You just cannot name some part of your harmonic coordinates based equations as force, force is a distinct entity in physics leads to acceleration and change in momentum and many other actions.

While I am fully aware of your extensive knowledge on the subject, if you acknowledge presence of force in GR, then how do you claim that a free falling frame or orbital motion frame is inertial?

 

[Schmelzer]

In Physics, the concept of force is not something which can be termed as mere semantics.

Indeed, and I don't reduce it to mere semantics. There is a difference between metaphysics and mere semantics. The ether interpretation presupposes a fixed affine background. Which has physical consequences, even if the equations are the same Einstein equations in harmonic coordinates one can use in spacetime GR too.

You just cannot name some part of your harmonic coordinates based equations as force, force is a distinct entity in physics leads to acceleration and change in momentum and many other actions.

Indeed, I cannot simply define gravitational forces in the spacetime interpretation. Because I would need, for this, a definition what would be a force-free movement. The inertial movement. This requires an additional structure - the background.

While I am fully aware of your extensive knowledge on the subject, if you acknowledge presence of force in GR, then how do you claim that a free falling frame or orbital motion frame is inertial?

I do not plan to do such things.

 

[The God]

Indeed, and I don't reduce it to mere semantics. There is a difference between metaphysics and mere semantics. The ether interpretation presupposes a fixed affine background. Which has physical consequences, even if the equations are the same Einstein equations in harmonic coordinates one can use in spacetime GR too.

Indeed, I cannot simply define gravitational forces in the spacetime interpretation. Because I would need, for this, a definition what would be a force-free movement. The inertial movement. This requires an additional structure - the background.

I do not plan to do such things.

1. Sure, there is a difference between metaphysics and semantics but than there is a difference between physics and metaphysics. You cannot do physics with 'force' while putting the force in metaphysics category. Can you?

2. Yes you are right and that's precisely was one of my points. We cannot define gravitational force in spacetime interpretation. The experiment to measure G, is around this very force and it's derivatives (torsion), clearly proving that this experiment cannot be recognised in spacetime interpretation. Surely in all the other theories which talk of additional background, your ether theory included.