Is Newton's Law a Result of Constant Volumetric Expansion?

[MDEarl]

Food for thought…an open question to the board:

A spherical volume defined as V ≡ 4/3 Π R ³ undergoes constant accelerated volume expansion generated by its mass M. The simplest equation for this is:
Av = d²V/dt² = CE x M . The two equations lead to instantaneous volume velocities of 4Π R² (dR/dt) and CE M t + Vo (Vo= initial velocity). Setting them equal to each other, then solving for dR/dt yields a radial velocity of dR/dt = (CE M t + Vo)/( 4Π R²). With some work, using classical constant acceleration equations found in any H.S. text and differentiating dR/dt, Radial acceleration = AR= - (CE M)/ (12 Π R²). This is Newton’s law (with CE = 12 Π G). Without any presuppositions, a constant volumetric expansion yields Newton’s law, is this just coincidence? Any relationship to the expanding universe?

 

[Chalnoth]

Food for thought…an open question to the board:

A spherical volume defined as V ≡ 4/3 Π R ³ undergoes constant accelerated volume expansion generated by its mass M. The simplest equation for this is:
Av = d²V/dt² = CE x M . The two equations lead to instantaneous volume velocities of 4Π R² (dR/dt) and CE M t + Vo (Vo= initial velocity). Setting them equal to each other, then solving for dR/dt yields a radial velocity of dR/dt = (CE M t + Vo)/( 4Π R²). With some work, using classical constant acceleration equations found in any H.S. text and differentiating dR/dt, Radial acceleration = AR= - (CE M)/ (12 Π R²). This is Newton’s law (with CE = 12 Π G). Without any presuppositions, a constant volumetric expansion yields Newton’s law, is this just coincidence? Any relationship to the expanding universe?

Right, for the most part the expanding universe is deeply within the classical limit of General Relativity, and so it has to follow Newton's Laws. At least as long as you're only considering matter. The difference arises when you start to consider radiation, which doesn't gravitate at all in Newtonian gravity, but was critical in determining the rate of expansion in the early universe.

 

[Naty1]

I'm not sufficiently conversant with GR to know if you take your favorite version of Einstein's field equations, and eliminate all the terms escept mass [ignore pressure,radiation,etc] what pops out...How close does one get to GMm/r[sqrd]??

 

[Chalnoth]

I'm not sufficiently conversant with GR to know if you take your favorite version of Einstein's field equations, and eliminate all the terms escept mass [ignore pressure,radiation,etc] what pops out...How close does one get to GMm/r[sqrd]??

In the appropriate limit, the Einstein field equations reduce to Newtonian gravity plus an extra force term proportional to $1/r^3$, as well as additional higher-order terms.

 

[MDEarl]

I'm not well-versed in einstein's field equations either. My point is, the classical calculation that i proposed works out perfectly as a sort of "reverse" Newton's law. that is...by describing an expanding volume produced by a mass, an acceleration (spacial expansion) field is produced which decreases as R increases as per Newton. Would we notice it if we are part of such an expansion? Certainly we would be accelerated at the surface of a massive object (equivalency principle). Could this strange Newtonian "force" of gravity be actually a common volumetric expansion of all things.The reason we don't expand into other objects would be relative motion. By the way, in that calculation that I did, it turns out that the radial velocity is exactly the Newtonian escape velocity!

 

[Chalnoth]

I'm not well-versed in einstein's field equations either. My point is, the classical calculation that i proposed works out perfectly as a sort of "reverse" Newton's law. that is...by describing an expanding volume produced by a mass, an acceleration (spacial expansion) field is produced which decreases as R increases as per Newton. Would we notice it if we are part of such an expansion? Certainly we would be accelerated at the surface of a massive object (equivalency principle). Could this strange Newtonian "force" of gravity be actually a common volumetric expansion of all things.The reason we don't expand into other objects would be relative motion. By the way, in that calculation that I did, it turns out that the radial velocity is exactly the Newtonian escape velocity!

Well, you have to bear in mind that the matter density on large scales in the universe is uniform. So the acceleration actually increases with distance. But yes, you can very much use Newton's laws to derive the Friedmann equations, as long as you aren't worried about things other than normal matter (as Newtonian gravity only deals with normal matter).

 

[Naty1]

In the appropriate limit, the Einstein field equations reduce to Newtonian gravity plus an extra force term proportional to 1/r 3 , as well as additional higher-order terms.

Thank you...Is there any physical significance [interpretation] to these additional terms??

 

[Chalnoth]

Thank you...Is there any physical significance [interpretation] to these additional terms??

Maybe there's a better explanation, but basically it's just saying that within General Relativity, the gravitational force gets stronger at small distances than in Newtonian gravity. There may be a slick geometric description of precisely why, but that's all I've got.

 

[MDEarl]

I'm finally back. The suspicion that I have regarding the universe has not been resolved in my mind for many reasons. I question the very foundation of gravity, because it seems that there is a major disconnect between Newtonian gravity and GR.
GR, as far as I have seen, has been only proven with regard to Newtonian, localized concentrated mass situations (gravitational lensing, precession of mercury, etc.) If anyone knows of any test of GR which applies to the cosmos, please let me know.
I think it is presumptuous to assume GR works in regard to the universe in general, which differs in so many ways from localized gravity (expanding at an accelerated rate rather than contracting for starters)...and if you think about it, testing theories of universal expansion is an approximate science at best. I suggest that if the logic of the early 20th century was wrong, an entire culture based upon a flawed premise now exists. The "physical significance to these additional terms" referred to by NAty1 seem to complicate the issues, so that simple minds such as mine feel inadequate.
I cannot but believe that gravity is based upon simpler principles than what current cosmology proposes. That's why I am interested in exponential expansion, and feel that it explains both GR and cosmic acceleration. The key difference is that it is true that "matter density on large scales in the universe is uniform" (per Chalnoth), and that causes a completely different effect than the constantly accelerated expansion of my original post.

 

[w4k4b4lool4]

I'm not well-versed in einstein's field equations either. My point is, the classical calculation that i proposed works out perfectly as a sort of "reverse" Newton's law. that is...by describing an expanding volume produced by a mass, an acceleration (spacial expansion) field is produced which decreases as R increases as per Newton. Would we notice it if we are part of such an expansion? Certainly we would be accelerated at the surface of a massive object (equivalency principle). Could this strange Newtonian "force" of gravity be actually a common volumetric expansion of all things.The reason we don't expand into other objects would be relative motion. By the way, in that calculation that I did, it turns out that the radial velocity is exactly the Newtonian escape velocity!

Interesting idea; various people have thought about this, and in fact it dates back to the early days of GR (Eddington?). There have been various criticisms. Anyway, my concern is the following: I don't see how you get (e.g. planetary) orbits out of this "volumetric expansion" ... (?)

 

[w4k4b4lool4]

Also, the equation you wrote down implies that objects of different masses will end up having difference sizes, and so it's difficult to understand how to make sense of your particular equations. For example, I hold an apple in one hand and a metal replica in the other. Relative to me, the sizes of both are the same and stay the same, but the gravitational field of each is different.

 

[MDEarl]

intreresting response w4... I just returned and have to go out for a while, but I am sure I can convincingly address your points when I get back, - since I gave this a lot of thought, and can't quite remember what eddington said, but as I recall, he differed from my thoughts and I resolved that to my satisfaction quite some time ago. Eddington and friedmann et al were all bucking einstein because of his steady-state mindset. will return later.

 

[Chalnoth]

If anyone knows of any test of GR which applies to the cosmos, please let me know.

Well, the strongest test of GR on the largest scales is the cosmic microwave background, the physics of which behave precisely as we would expect from GR. There are other tests as well studying things on smaller scales such as galaxy clusters and the like, and GR being correct on those scales continues to match the data better than alternative models.

 

[MDEarl]

back again.
--------------------------------------------------------------------------------
"Also, the equation you wrote down implies that objects of different masses will end up having difference sizes, and so it's difficult to understand how to make sense of your particular equations. For example, I hold an apple in one hand and a metal replica in the other. Relative to me, the sizes of both are the same and stay the same, but the gravitational field of each is different."
As it turns out, The apple and the replica create different gravitational fields which exist beginning at the surface and extend outward agreeing with Newton's law. That space is defined by the equations, and essentially are produced in that manner because the mass is constant relative to an increasing volume, producing a decreasing ρ (proportional to 1/R^3), resulting to an acceleration field which decreases in magnitude as R increases (by 1/R^2).
That is consistent with Newton, wherein the gravitaional field of the more massive object "pulls harder" than the less massive, regardless of volume. We just don't notice because of the weakness of the force.
I mention that the Newtonian field begins at the surface, because internal to the object, ρ may be considered constant, (as with the cosmos in general) and that produces a completely different result.

 

[MDEarl]

w4, I think a more difficult aspect to accept is that if all elements expand equally (volumetrically), that we would not notice. But Ʃ Δv = ΔV , and it is conceivable. I believe that you concur from your statement.

Revolutionary motion, as you mention, w4, was a problem with me, but i have resolved that by considering that the expanding space provides a simpler path for objects to traverse, just as spacetime produces orbital revolution. If an object enters an expanding space, its velocity and direction are affected, consistent with both Newton and GR. From my limited knowledge of GR, it is a geometric description of a bent spacetime ... I think that the expansion field that comes out of the equations that I submitted is in fact "spacetime".

i googled "eddington" about his grav theory, but don't see a resemblance...but i do think that an expanding Earth has crossed every physics student's mind at one time or another. The only thing is that these particular equations, from my searches, have never been presented before.

 

[MDEarl]

Well, the strongest test of GR on the largest scales is the cosmic microwave background, the physics of which behave precisely as we would expect from GR. There are other tests as well studying things on smaller scales such as galaxy clusters and the like, and GR being correct on those scales continues to match the data better than alternative models.

Chalntoth,
The CMBR seems to be one of the most controversial issues in cosmology today. It was my impression that no one can explain it, and there are many theories. I have to agree that GR is better than alternative models, but my point is that no model is "spot on". GR works for smaller scale phenomena (galaxy clusters etc.)but how do we know how closely? I recently googled the Hubble constant, and found a range of values (depending upon the method used) that astounded me. The FLRW model for the universe was supposed to predict a contracting universe: it doesn't. and a constant was added to make it fit. I guess what I am saying is that there is something wrong.

 

[MDEarl]

Sorry, I meant Chalnoth

 

[Chalnoth]

Chalntoth,
The CMBR seems to be one of the most controversial issues in cosmology today. It was my impression that no one can explain it, and there are many theories.

Huh, what? That's just flat-out wrong. The CMB is an incredible verification of the standard model of cosmology. It remains our best measurement of the ratio of dark matter to normal matter to date, and it is next to impossible to come up with an alternative gravity theory which fits the CMB without dark matter.

As for dark energy, dark energy had little to no impact on the universe at the time the CMB was emitted, so the existence (or not) of dark energy doesn't change at all most of the behavior of the CMB. What it does change are the details of the expansion since the emission of the CMB, but this just impacts how we perceive it not how it was emitted. So the effect of the accelerated expansion on the CMB is minimal.

Most of the impact of the accelerated expansion comes in with the formation of structure later on. There's a lot of ongoing work to determine exactly how structures have formed over the history of the universe, and that research can give us quite a lot of insight into the nature of dark energy, and can also distinguish between dark energy and at least some types of modified gravity.

I have to agree that GR is better than alternative models, but my point is that no model is "spot on".

As near as we have been able to determine experimentally so far, General Relativity is indeed spot-on. No deviation from GR has yet been detected at all.

 

[Chalnoth]

Sorry, I meant Chalnoth

You can edit your own posts.

 

[George Jones]

I have closed this thread.

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