[modest]

Discussion continued from:

SNe Ia, Implications, Interpretations, Lambda-CDM

Originally Posted by modest

It allows you to set the parameters of omega-m and omega-lambda and watch what happens to the sale factor over time. The theory behind Einstein's original cosmological constant is represented here as much as any current model. It all depends on the value of the omegas you choose. You will, however, find it impossible to model Einstein's original static universe. As the page points out:

This is the same conclusion Einstein came to about his own model without the help of a java applet. Lambda can be set just right to reach a balance at any given time, but, the balance can't be sustained as time rolls on. The end result is either collapse or expansion - with or without a cosmological constant.

Originally Posted by coldcreation

Einstein, with his masterful touch, created a beautiful symmetry (however stable or unstable it was) between lambda and gravity, where lambda was a kind of antigravity, a mirror image, a reflection in the well of gravity with a different sign, in balance, exact opposites yet somehow equal, somehow one, like a man and a woman locked in an eternal embrace, dancing in unison. There was no splitting-off to dance alone (or with someone else).

And yet the history of lambda throughout the 20th century was like that of a woman who would mysteriously come and go. Now, the prima maestra absoluta has returned, and is here to stay (for now), full of disgusting freedom, with a liberal application of new physics, decidedly unrestrained, dressed in modern camouflage and ready for the big kill (the Big Rip).

Originally Posted by Little Bang

The possibility that the universe is static must exist because I can't prove with 100% certainty that it doesn't. A sharpened pencil can be balanced on it's point for some small amount of time, but never for a thousand years. If I, as an innocent bystander, need to pick one way or the other to carry on with research that requires one or the other be chosen I am going to choose expanding space.

Originally Posted by coldcreation

Isn't it ironic that without a finely tuned balance between expansion and catastrophic collapse, you, as an innocent bystander, wouldn't even have a pencil to balance on its point (neither would anyone else). Indeed, the solar system has remained in balance like a pencil standing on its point for several billion years (plus or minus a few seconds).

(I would like to here, in your own words, using whatever theory of gravity you please, i.e., GR, Newtonian mechanics, variable G etc., how that fine tuning, like a pencil balancing on its point, is possible, while remaining on-topic if you can).

So too has the Local Group and the Virgo Supercluster (or Local Supercluster), the galactic supercluster that contains the Local Group, the Milky Way and Andromeda galaxies, remained in a quasi-stable self-gravitating equilibrium configuration for several Gyr. If anything, several clusters are moving toward the center of the Virgo cluster. In all probability, the entire Virgo Supercluster is being lured toward a gravitational anomaly dubbed the Great Attractor, near the Norma cluster, but the pencil still stands, and it will do so for many Gyr to come.

My point () is that, though the universe may in fact be expanding, there are still observed systems and subsystems where stable equilibrium configurations are observed (and have in all likely-hood remained that way for at least 10 Gyrs), whereas, according to your argument those systems should be categorically unstable, since your pencil goes bang after a fraction of a second, at best.

Originally Posted by Little Bang

To say that the solar system and the local group have remained static over the past 5 billion is a ludicrous piece of logic. There have been continuous changes over that time. My own words.

Originally Posted by PhysBang

Indeed, the idea that there is some sort of finely tuned stability or balance in the solar system or the galaxy is pure fantasy. You can find this idea in much of coldcreation's writings, if you care to look. It is an integral part in his fantasy about the cosmological constant and Lagrange points.

But it honestly is not worthwhile taking the time.

Originally Posted by coldcreation

OK, this discussion is become increasingly off-topic.

I will retaliated first though. I am not saying that the solar system has been stable for 5 Gyr. I wrote a few Gyr. The sun, if I recall, has only existed for 4.5 Gyr (whether there was a first generation progenitor I do not know). So littlebang is obviously correct (the straw man was 5 Gyr). However, he did not answer my question. How the fine tuning (like a pencil balancing, or oscillating rather on its point), observed in the solar system is possible.

Of course, the solar system is chaotic in a sense: it has instabilities associated with it and its constituents, and the trajectories of its constituents (say, the Earth) cannot be predicted for time periods exceeding 100 Myrs.

However,

I doubt the mass of the Sun will be decreasing by half any time soon. So it is structurally stable (probably, I would guess, for another 5 Gyr, give or take a Gyr or two). Hmm, sounds like a pencil on its point to me. What gives?

See On the stability of the solar system

Note this too:

Source, Large scale chaos and marginal stability in the solar system

The large chaotic variations from 0° to about 60° in the tilt of Mars, is not what I am talking about. It is the structure and its long term stability of the solar system in general, and its constituents specifically, that is of interest, not the tilt of the Earth or its ice ages (at least for the purpose of this off-topic discussion). The latter type of marginal stability (or marginal instability) is evident since small gravitational and mean motion resonance (etc.) interactions occur all the time. But again, there "is practical stability on a time-scale comparable to its age." (see above).

If you wish to continue this discussion on the stability and/or instability of gravitationally bounded systems, celestial mechanics - a truly fascinating field, tie it in with SNe Ia, lambda, dark, energy, the critical model and its finely tuned one to one expansion (the galaxies separate at a critical rate that prevents gravitational attraction from over-powering the expansion: also referred to as the the Einstein-de Sitter model), the fine tuning problem, the flatness problem, coasting expansion vs. accelerating expansion, i.e., cosmology. Or, begin a new thread on the topic: I will most definitely be there.

Recall, the subject of the stability of the solar system began with a discussion on the fine-tuning problem related to expansion (the favored Friedmann model, now defunct, in light of the SNe Ia data). Indeed, the fine tuning problem was more ubiquitous than appeared at first glance (not to mention thermodynamic or quantum states that appear also either stable, chaotic or both to one extent or the other.

I hope this is the proper method to continue a discussion into a new thread. If the ops edit this post I'll not be in the least offended.

I think there are at least 2 important things to consider when comparing the equilibrium of our solar system to the universe as a whole.

First, the elements of the solar system that are in dynamic equilibrium are a small fraction of its total mass at conception. Most of the system's mass has been swallowed by the sun or flung into deep space leaving orders of magnitude less mass in gravitational balance than was not in balance.

Out of a thousand comets thrown at the sun from the oort cloud, how many find themselves in a stable orbit. By the same token, how many universes out of a thousand would find themselves in static equilibrium?

Second, I'm not sure you can compare a local system of gravity to the expansion/collapse of the universe as a whole. General Relativity obviously allows a body to find a stable orbit around a mass for quite some time, but can this be translated to a homogeneous universe? The only mechanism to be analogous to centrifugal forces in the solar system that I can think of is the cosmological constant. As wikipedia's Cosmological Constant article points out:

It is now thought that adding the cosmological constant to Einstein's equations does not lead to a static universe at equilibrium because the equilibrium is unstable: if the universe expands slightly, then the expansion releases vacuum energy, which causes yet more expansion. Likewise, a universe which contracts slightly will continue contracting.

-modest

[coldcreation]

Very good modest.

I have a couple of preliminary points to make with respect to your two "important things to consider when comparing the equilibrium of our solar system to the universe as a whole."

You mention the that "the elements of the solar system that are in dynamic equilibrium are a small fraction of its total mass at conception." This is true. But the solar system is just one example a gravitationally bounded system that exhibits long-term stability of its constituents.

There are many other examples where dynamic equilibrium is observed in systems, the constituents of which are not a small fraction of total mass the system to the extent observed in the solar system, or even close, e.g., binary star systems (some of the most stable systems in the universe), certain globular cluster (some have very compact groupings of central stars, other not), certain galaxies: elliptical, spherical, barred galaxies, barred spirals, and certain spirals (where the bulge to disk mass ratio is small), galaxy clusters, and superclusters.

Thus the comparison should not be restricted to one system (the solar system) but to all self-gravitating bounded systems and subsystems in quasi-equilibrium configuration, so as not to limit the scope of the discussion.

A second point regarding the comparison (or extrapolation) of the dynamics of a "local system of gravity to the expansion/collapse of the universe as a whole."

Certainly, general relativity is the theory of gravity that best describes the dynamics of all gravitating systems. I think that as this discussion unfolds it will emerge that, indeed, the dynamics of all systems bounded under the influence of gravity (including the extrapolation to the entire quasi-homogeneous universe) are governed by the same natural laws, governed by Einstein's general postulate of relativity.

Therefore, (and this is the stance I will assume) the relation between massive bodies must be strictly similar or identical at all scales (where gravitation is the principle binding 'force'), including the 'scale' compatible with the Universe in its entirety.

A final point: you write "The only mechanism to be analogous to centrifugal forces in the solar system that I can think of is the cosmological constant." I wouldn't say that lambda and centrifugal forces are analogous (either in the underlying mechanism, in their operational mechanics or in their standard definitions). But they are perhaps related. It will be interesting to see how, if at all.


CC

[modest]

Originally Posted by coldcreation

You mention the that "the elements of the solar system that are in dynamic equilibrium are a small fraction of its total mass at conception." This is true. But the solar system is just one example a gravitationally bounded system that exhibits long-term stability of its constituents.

There are many other examples where dynamic equilibrium is observed in systems, the constituents of which are not a small fraction of total mass the system to the extent observed in the solar system, or even close, e.g., binary star systems (some of the most stable systems in the universe), certain globular cluster (some have very compact groupings of central stars, other not), certain galaxies: elliptical, spherical, barred galaxies, barred spirals, and certain spirals (where the bulge to disk mass ratio is small), galaxy clusters, and superclusters.

I hadn’t thought of that. In fact, it might be said that larger systems are in a kind of gravitational equilibrium for a longer period of time than smaller systems. A simple extrapolation where each is stable for less time than the next:

A pair of asteroids
A small moon / planet
A binary star
A globular cluster
A galaxy
A galaxy cluster
…
A universe of infinite size

would imply gravitational equilibrium over infinite time for our infinite universe. This reasoning is initially compelling but, I think, ultimately unsound.

If we take the above as true we are saying that an open and infinite universe would take infinite time to collapse to a singularity. Yet each finite region would certainly take a finite time to do so. I think the best we can say is how our visible universe is either expanding, contracting, or static; and, if anything, assume either the same or nothing about the rest of the infinite universe.

Therefore my reasoning above is maybe not so sound. Which leaves: what is the nature of the dynamic equilibrium in these larger systems?

A binary star is subject to my criticism of our solar system as a pencil-on-its-head. This is true if only because the vast majority of close approaches between stars will not result in a stable orbit. Most would either not be captured or be drawn too close and result in a nova, supernova, or some other merger event. When there is a very-nearly-perfect orbit it still isn’t a pencil on its head. The orbit will eventually fail. The same reasoning applies to galaxy clusters where we see collisions are frequent. These things look like a good examples of gravitational equilibrium but when seen over long enough time, I think the chaos and instability would show.

Originally Posted by coldcreation

Certainly, general relativity is the theory of gravity that best describes the dynamics of all gravitating systems. I think that as this discussion unfolds it will emerge that, indeed, the dynamics of all systems bounded under the influence of gravity (including the extrapolation to the entire quasi-homogeneous universe) are governed by the same natural laws, governed by Einstein's general postulate of relativity.

Therefore, (and this is the stance I will assume) the relation between massive bodies must be strictly similar or identical at all scales (where gravitation is the principle binding 'force'), including the 'scale' compatible with the Universe in its entirety.

I agree - it must be based on the same laws. I do not think; however, that the laws of motion (which help smaller systems reach a temporary dynamic equilibrium) can do so for the universe as a whole. I hope we could agree to rule out global-rotation as a means of countering global attraction. That is: a static universe isn’t kept from collapsing because everything is rotating about some center. Mach’s principle alone is probably enough to counter that idea. Observationally, we could notice different cosmic bodies don’t have variable transverse motion depending on distance as such an idea would necessitate. This is why I said:

Originally Posted by modest

The only mechanism to be analogous to centrifugal forces in the solar system that I can think of is the cosmological constant.

So - if the cosmological constant won’t enforce a global balance then nothing we know of will.

[coldcreation]

Originally Posted by modest

I hadn’t thought of that. In fact, it might be said that larger systems are in a kind of gravitational equilibrium for a longer period of time than smaller systems. A simple extrapolation where each is stable for less time than the next:

A pair of asteroids
A small moon / planet
A binary star
A globular cluster
A galaxy
A galaxy cluster

Do you have a source for this?

Originally Posted by modest

A universe of infinite size would imply gravitational equilibrium over infinite time for our infinite universe. This reasoning is initially compelling but, I think, ultimately unsound.

Note, though, that an infinite universe would not have a radius, or scale factor (no size), so by definition it could not become larger or smaller (i.e., it would not expand or collapse). However its constituents might all be moving away from one another (though in this context, I don't see how actual space would expand adiabatically). Just a thought...I could be wrong.

Originally Posted by modest

If we take the above as true we are saying that an open and infinite universe would take infinite time to collapse to a singularity. Yet each finite region would certainly take a finite time to do so. I think the best we can say is how our visible universe is either expanding, contracting, or static; and, if anything, assume either the same or nothing about the rest of the infinite universe.

I'm going to argue in favor of the static universe, shortly.

Originally Posted by modest

Therefore my reasoning above is maybe not so sound. Which leaves: what is the nature of the dynamic equilibrium in these larger systems?

Great question! I'm going to see if any recent publications cover this topic.

Originally Posted by modest

A binary star is subject to my criticism of our solar system as a pencil-on-its-head. This is true if only because the vast majority of close approaches between stars will not result in a stable orbit. Most would either not be captured or be drawn too close and result in a nova, supernova, or some other merger event. When there is a very-nearly-perfect orbit it still isn’t a pencil on its head. The orbit will eventually fail. The same reasoning applies to galaxy clusters where we see collisions are frequent. These things look like a good examples of gravitational equilibrium but when seen over long enough time, I think the chaos and instability would show.

But the close approach between stars resulting in a stable binary orbit is just one scenario to describe their origin. The other (and in my opinion more ubiquitous mechanism) is during the gravitational collapse of a gas cloud leading to the formation of many stars simultaneously, some of which will remain highly stable binary systems. These stars were not caught by chance association, they were form adjacent to each other and remain so.

Originally Posted by modest

I agree - it must be based on the same laws. I do not think; however, that the laws of motion (which help smaller systems reach a temporary dynamic equilibrium) can do so for the universe as a whole. I hope we could agree to rule out global-rotation as a means of countering global attraction. That is: a static universe isn’t kept from collapsing because everything is rotating about some center. Mach’s principle alone is probably enough to counter that idea. Observationally, we could notice different cosmic bodies don’t have variable transverse motion depending on distance as such an idea would necessitate...

I agree. Observations do not allow a rotating universe.

Originally Posted by modest

So - if the cosmological constant won’t enforce a global balance then nothing we know of will.

Not so fast. There is a solution to the cosmological constant problem that does enforce a global balance. However a slight modification of its standard definition (or the interpretation of what exactly lambda is) needs to be formulated. I have done this conceptually, i.e., qualitatively, not quantitatively. But I don't want this thread to be transferred to the Alternative Theory section of Hypography, so I don't know if I should elaborated on that physical mechanism here (even though it would appear smack on-topic). I've already hinted at it on several other occasions, without going into the full scope of the mechanism. After all, it does require a slight modification of Einstein's original cosmological term, i.e., it assumes a natural boundary condition associated with GR (one that can be tested, falsified, or confirmed, by observation if necessary).




CC

[modest]

Originally Posted by coldcreation

Do you have a source for this?

I’m not aware of any literature making this claim. As I stated, I don’t believe it’s a sound extrapolation. In addition to the reason in my last post (which focuses on extrapolating the trend to infinite) I’d also note that larger systems like galaxies can be less structured than smaller systems like solar systems. This would add to stability of some smaller systems and lower stability of some larger ones.

Originally Posted by coldcreation

Note, though, that an infinite universe would not have a radius, or scale factor (no size), so by definition it could not become larger or smaller (i.e., it would not expand or collapse). However its constituents might all be moving away from one another (though in this context, I don't see how actual space would expand adiabatically). Just a thought...I could be wrong.

I don’t know of any context where ‘scale factor’ relies on setting a radius of the universe. I’ve also never heard that an open universe precludes expansion.

Originally Posted by coldcreation

Not so fast. There is a solution to the cosmological constant problem that does enforce a global balance. However a slight modification of its standard definition (or the interpretation of what exactly lambda is) needs to be formulated. I have done this conceptually, i.e., qualitatively, not quantitatively. But I don't want this thread to be transferred to the Alternative Theory section of Hypography, so I don't know if I should elaborated on that physical mechanism here (even though it would appear smack on-topic). I've already hinted at it on several other occasions, without going into the full scope of the mechanism. After all, it does require a slight modification of Einstein's original cosmological term, i.e., it assumes a natural boundary condition associated with GR (one that can be tested, falsified, or confirmed, by observation if necessary).

If we agree that no process other than the cosmological constant can keep a static universe from collapsing then this is indeed what we’re left with. The nature of equilibrium in solar systems and galaxies are the laws of motion. This we agree cannot be the case for the universe at large. Therefore no matter how stable our solar system is, we cannot express that as a synonym for a static universe.

All we are left with is the cosmological constant. I believe that setting the cosmological constant to exactly offset gravity is balancing a pencil that will have no choice but to fall one way or the other. If (as you have expressed) the cosmological constant is zero, space is not expanding, and matter exists then GR demands the universe collapse into a singularity in the future. Any other expression of lambda does not fit into Einstein's field equations. Any other interpretation of lambda is not compatible with general relativity.

-modest

[modest]

Originally Posted by coldcreation

There is a solution to the cosmological constant problem that does enforce a global balance. However a slight modification of its standard definition (or the interpretation of what exactly lambda is) needs to be formulated. I have done this conceptually, i.e., qualitatively, not quantitatively. But I don't want this thread to be transferred to the Alternative Theory section of Hypography, so I don't know if I should elaborated on that physical mechanism here

If you do decide to start that thread in alternative theories perhaps we could work out a mathematical expression for it. I positively claim no great math skills - but I’d be willing to try.

Given my stance on the cosmological constant I hope you don’t take this as dubious or insincere or even worse - patronizing of me. I’m honestly curious to see what you’re thinking and try to work it out.

-modest

[coldcreation]

Originally Posted by modest

If we agree that no process other than the cosmological constant can keep a static universe from collapsing then this is indeed what we’re left with. The nature of equilibrium in solar systems and galaxies are the laws of motion. This we agree cannot be the case for the universe at large. Therefore no matter how stable our solar system is, we cannot express that as a synonym for a static universe.

I think what you are saying is that both Newton's and Kepler's laws of motion are sufficient in describing the equilibrium observed in the solar system. In other words, GR is not required, except for perihelion deviations etc. (if not, please explain). As it turns out, classical mechanics was not able do explain the observed stability (the fine-tuning) of the solar system. I would not exclude categorically classical mechanics from the debate, since to do so, would be to remove important considerations such as the work of Lagrange and others, thereby eliminating possible solutions to the current fine-tuning problem.

Hopefully in this discussion we can use one theory of gravity to describe dynamics (GR). I would prefer to interpret gravity as a curved spacetime phenomenon, as did Einstein, and proceed from there to see if the observed equilibrium is accounted for.

A brief historical note:

Herman Weyl (1917) wrote a paper expressing his views on axially symmetric static solutions to Einstein’s field equations. Weyl presupposed that two bodies are held together, at rest, by stresses counteracting the gravitational force—a concept enthusiastically criticized by Levi-Civita. Others continued to search for a resolution of the static two-body problem—not always realizing the need for stresses in order to maintain equilibrium, (this requisite is occasionally referred to as ‘strut’ or ‘rod’ between massive bodies). Einstein suspected that stability would require the presence of a true singularity of the field outside the two masses. Silberstein described the singularity as a mass-center or free particle (two bodies, two mass points). As it turns out, Silberstein was mistaken on the key concern of the two-body predicament, though Einstein’s stratagem was not entirely adequate either. It appears that Silberstein developed a one-center solution that did not depict the field of a spherically symmetrical source.


My point is, in a curved spacetime (according to the laws of general relativity) there is no justification (aside from stipulating initial conditions that lead to a form of 'natural selection' whereby planets would form at precisely right distance from the Sun, and attain a desired mass in accordance with a planet's velocity) for the maintenance of stability over large time-scales, with respect to N-body systems (i.e., three of more massive bodies).

As I understand it, the justification (inadequate as it is) comes from the equivalence principle, meaning that the Earth, say, has inertial motion equivalent to an object in free-fall. This implies explicitly that the Earth 'feels' no gravitational 'force,' and so laws of physics that govern local celestial mechanics can be approximated the same as in special relativity, or worse, Newtonian mechanics.

In sum: there is (still) a fine-tuning problem inherent in our understanding of the dynamics of the solar system. This problem needs to be resolved. It can be resolved. It is not beyond the reach of current physics to do so. However something remain amiss. My goal has been to set out and find that which is amiss. And I think I have done so (without new physics).

Originally Posted by modest

All we are left with is the cosmological constant. I believe that setting the cosmological constant to exactly offset gravity is balancing a pencil that will have no choice but to fall one way or the other. If (as you have expressed) the cosmological constant is zero, space is not expanding, and matter exists then GR demands the universe collapse into a singularity in the future. Any other expression of lambda does not fit into Einstein's field equations. Any other interpretation of lambda is not compatible with general relativity.

I understand your stance, and respect it. This is, after all, the mainstream view. However, there are drawbacks to considering lambda as a mathematical parameter, or even as an aspect of spacetime (a repulsive force, negative pressure, anti-gravity, dark energy, or whatever) that can either be positive, negative or zero.

My contention is (and I will eventually attempt to prove it, either here or in an off-shoot of this thread, when and if the time comes) that the value of lambda can only be zero. It cannot be positive or negative. It is thus not a parameter. Perhaps this interpretation of lambda will change the outcome of the field equations when applied to real systems, but it wont change fundamentally the field equations in and of themselves other than by limiting the scope of possibilities.

However, though limiting the scope of possibilities, the defining features of GR remain the same: the concept of gravitational 'force' is replaced by spacetime geometry. (Lambda, too, is treated exclusively as a spacetime geometry phenomenon - albeit Euclidean). Phenomena that are ascribed to the action of the force of gravity (i.e., free-fall and orbital motion) represent inertial motion within a curved geometry of spacetime in relation to Euclidean or Minkowski spacetime. The laws of physics still remain the same for all observers, whether accelerated or not. The principle of general covariance still holds, as does the equivalence between inertial and geodesic motion, along with the principle of local Lorentz invariance (requiring that the laws of special relativity apply locally - and now globally - for all inertial observers. Last but not least, the curvature of spacetime and its energy-momentum content are intimately inseparable, but always in relation to empty space. So curvature always has a positive value (not a positive or negative value). Note: whether one choses a positive or negative sign to identify curvature is a question of choice. I use 'positive' for convenience. So that all deviations from linearity are positive, i.e., curvature caused by the presence of stress-energy. Gravity does not therefore exist in two different varieties or flavors (like electric charge) on either side of zero curvature.


In other words, it may be premature to exclude an alternative interpretation of lambda for fear that it is not compatible with general relativity, when in all probability it is entirely compatible with not just GR but with classical mechanics as well.

Before moving on to cosmology, I would like your response to the observed local stability of such systems as the Earth-Sun-Moon 3-body problem. We can take it from there, further.



CC

[coldcreation]

Wait, there’s more.

A note regarding cosmology: Purists have yelped but Lambda does blow the cobwebs away. And more than a physicist has been sucked through the deep throat of their own Newtonian devise.

Stephen Hawking has an answer: “the correct approach…is to consider the finite situation, in which the stars all fall in on each other…we now know it is impossible to have an infinite static model of the universe in which gravity is always attractive” (1988 p. 5). The only ugly problem with this theory is that it’s wrong.

With astonishing versatility, Hawking was able to indulge at the same time in prudently constructed views harking back to the past. A humid feeling of dull gloom though emanates from his words. Recall, Newton had cleverly reasoned that an infinite universe has no center-point at which stars would collapse. Thus the nostalgic reveries and apocryphal problem to which Hawking makes allusion had already been posed and solved in the 17th century: one year before the Salem witch trials of 1692.

If the descriptive laws of physics in and around our solar system are anything like the laws of physics in the rest of the universe, should not the solar system be expanding or contracting (NOT): Or rather, should not the universe maintain an equilibrium between expansive and contractile propensities—as does our solar system—as do electrons and protons—and many other natural phenomena in the microcosm and macrocosm. Is not the entire universe governed by the same set of laws that govern its parts?

The answer according to the LCDM appears to be NO.



CC

[modest]

Originally Posted by coldcreation

I think what you are saying is that both Newton's and Kepler's laws of motion are sufficient in describing the equilibrium observed in the solar system. In other words, GR is not required, except for perihelion deviations etc. (if not, please explain).

No. I make no distinction between Newton’s laws of motion and GR’s equations of motion for my point above. Galaxies and planetary-systems (or any gravitational system in dynamic equilibrium) rotate. They rotate faster toward the center of gravity. That transverse motion is not seen in global observations of our universe. The motion is real in one system and absent in the other regardless of what laws or equations you use to describe it.

Originally Posted by coldcreation

As it turns out, classical mechanics was not able do explain the observed stability (the fine-tuning) of the solar system. I would not exclude categorically classical mechanics from the debate, since to do so, would be to remove important considerations such as the work of Lagrange and others, thereby eliminating possible solutions to the current fine-tuning problem.

It is impossible to include general relativity in a debate while excluding classical mechanics. The latter is part of the former.

Originally Posted by coldcreation

A brief historical note:

Herman Weyl (1917) wrote a paper expressing his views on axially symmetric static solutions to Einstein’s field equations. Weyl presupposed that two bodies are held together, at rest, by stresses counteracting the gravitational force—a concept enthusiastically criticized by Levi-Civita. Others continued to search for a resolution of the static two-body problem—not always realizing the need for stresses in order to maintain equilibrium, (this requisite is occasionally referred to as ‘strut’ or ‘rod’ between massive bodies). Einstein suspected that stability would require the presence of a true singularity of the field outside the two masses. Silberstein described the singularity as a mass-center or free particle (two bodies, two mass points). As it turns out, Silberstein was mistaken on the key concern of the two-body predicament, though Einstein’s stratagem was not entirely adequate either. It appears that Silberstein developed a one-center solution that did not depict the field of a spherically symmetrical source.

I see you get this from “The attraction of gravitation: New studies in the history of general relativity” (1993) where you’ve pulled out a few sentences from the two-body chapter.

Originally Posted by coldcreation

Weyl presupposed that two bodies are held together, at rest, by stresses counteracting the gravitational force—a concept enthusiastically criticized by Levi-Civita

and from the book:

Weyl (1917) assumed that the bodies were held at rest by stresses counteracting the gravitational forces, without going into any detail. After the paper was criticized by Levi-Civita, he elaborated on this and indicated how the stresses can be calculated (Weyl 1919b).

Originally Posted by coldcreation

Others continued to search for a resolution of the static two-body problem—not always realizing the need for stresses in order to maintain equilibrium, (this requisite is occasionally referred to as ‘strut’ or ‘rod’ between massive bodies).

and the book:

Within the next few years, a number of scientists attacked the static two-body problem, not always realizing the need for stresses to maintain equilibrium. (This requirement is now frequently stated as the need for a "strut" or "rod" between the bodies.)

The stresses here (you may well know) are not real. The rod or strut or line singularity is a mathematical tool used in the model to investigate a situation. If you calculate the stress on the rod you have useful information. When you remove the rod from the model the two bodies would accelerate toward each other - each freefalling until they collide.

If fact - the point the book is making with all this is very relevant to our conversation and is either missed or omitted by you.

It is implicit in these papers that in Einstein's theory bodies cannot be in equilibrium under the influence of gravitational forces alone...

Nevertheless, the importance of his [Weyl’s] proof that there is no static solution for two masses that are free to move was widely, though not universally, recognized.

The generally accepted result of Weyl and Levi-Civita’s work is that you need a force other than gravity to maintain an equilibrium. For instance: if two mass points are attracted gravitationally and repelled through electrostatic forces then an equilibrium can be accomplished. I believe the expression for this would be: M1 M2 = Q1 Q2.

Originally Posted by coldcreation

My point is, in a curved spacetime (according to the laws of general relativity) there is no justification (aside from stipulating initial conditions that lead to a form of 'natural selection' whereby planets would form at precisely right distance from the Sun, and attain a desired mass in accordance with a planet's velocity) for the maintenance of stability over large time-scales, with respect to N-body systems (i.e., three of more massive bodies).

As I understand it, the justification (inadequate as it is) comes from the equivalence principle, meaning that the Earth, say, has inertial motion equivalent to an object in free-fall. This implies explicitly that the Earth 'feels' no gravitational 'force,' and so laws of physics that govern local celestial mechanics can be approximated the same as in special relativity, or worse, Newtonian mechanics.

In sum: there is (still) a fine-tuning problem inherent in our understanding of the dynamics of the solar system. This problem needs to be resolved. It can be resolved. It is not beyond the reach of current physics to do so. However something remain amiss. My goal has been to set out and find that which is amiss. And I think I have done so (without new physics).

You must consider the original orbiting mass of the solar system - then calculate the odds that the current mass is still orbiting. When you look at it from that perspective you eliminate the problem you are troubled by.

If the solar system started with 8 or 9 planets fully formed and has ended up with the same then your objection would make good sense. But this is not the case. Most all the mass of our forming solar system has (in the past 5 billion years) lost orbital stability. We can only observe what remains. In other words: only by assuming the solar system has been a perfect system do we have fine tuning problems associated with a perfect system.

Originally Posted by coldcreation

My contention is (and I will eventually attempt to prove it, either here or in an off-shoot of this thread, when and if the time comes) that the value of lambda can only be zero. It cannot be positive or negative. It is thus not a parameter. Perhaps this interpretation of lambda will change the outcome of the field equations when applied to real systems, but it wont change fundamentally the field equations in and of themselves other than by limiting the scope of possibilities.

The case of lambda = zero is well investigated.

Originally Posted by coldcreation

Before moving on to cosmology, I would like your response to the observed local stability of such systems as the Earth-Sun-Moon 3-body problem. We can take it from there, further.

The earth and moon are more stable in their orbital dynamics than any matter that has so far failed to maintain orbit.

Originally Posted by coldcreation

If the descriptive laws of physics in and around our solar system are anything like the laws of physics in the rest of the universe, should not the solar system be expanding or contracting (NOT): Or rather, should not the universe maintain an equilibrium between expansive and contractile propensities—as does our solar system—as do electrons and protons—and many other natural phenomena in the microcosm and macrocosm. Is not the entire universe governed by the same set of laws that govern its parts?

The answer according to the LCDM appears to be NO.

Here is the problem. You want to say that any mass currently orbiting our star represents stability and therefore the universe can be static. You are connecting the dots by making assumptions and not investigating what's between the dots. You've outlined no comparison between orbital dynamics and the cosmological constant. You assume perfect stability in orbiting systems without considering that eventually they will all fail.

The laws of physics can be the same everywhere while many different situations present themselves. If the solar system looked like the universe (homogeneous and not rotating) would it be static? No. Therefore your analogy brakes down at the most simple level. Not because the laws of physics are different at different scales but because the universe doesn't look like or act like an orbital system.

-modest

[coldcreation]

Originally Posted by modest

Galaxies and planetary-systems (or any gravitational system in dynamic equilibrium) rotate. They rotate faster toward the center of gravity.

What's your source for that?

What about all the objects (gravitational systems in dynamic equilibrium) that do not rotate (or that rotate exceedingly slow): M84, M86, or M87. What about many of the dwarf galaxies surrounding the Milky Way: Maffei I and Maffei II? What about the non-rotating globular clusters?

Indeed about 75% of all galaxies observed in the universe are non-rotating (or very slowly spinning) elliptical type or spherical type galaxies: these galaxies are dynamically very stable. Only about 25% are the spiral, barred-spiral, or barred type rotating systems.

Note that the stars forming the bar shape of barred galaxies do not rotate faster toward the center of gravity, contrarily to your generalization above.

Let's consider the simplest case scenario of the primary bar structure. By accurately measuring the Doppler shifts at diverse positions on bars, astronomers have established that bars revolve as solid bodies. Meaning that the time it takes the bar to travel around the galaxy’s axis is the same for all point along the bar.

To convolute the issue further, the central region of bar galaxies is often characterized by a secondary bar in which may be found embedded a third bar, i.e., many barred spirals have a primary bar with a secondary bar nestled inside, the orientation of which can differ from the primary bar (Martin, Friedli, 1999 (Edited to add full refernce: Martin, P., Friedli, D. 1999, At the Hearts of Barred Galaxies, Sky and Telescope, March 1999, Vol. 97, Number 3, pp. 32-37)). This interesting and unanticipated fact shows that there are wide variety of intermediary scales and stages where equilibrium conditions are satisfied—a phenomenon frequently observed in the dynamical behavior of celestial bodies of the solar system, concerning widely different regimes of motion and scales, e.g., small objects, satellites, rings, etc. orbit large planets, which in turn orbit a larger object: the Sun. And at every scale there are specific distances, velocities, masses, mean motion resonance patterns and geometrical arrangements and relationships. So we find the patterns continue on scales consistent with planetary systems, groups of stars and galaxies themselves. I'm sure if we increase the scale to galaxy clusters, or even to that of superclusters, we will find the same pattern.

Originally Posted by modest

That transverse motion is not seen in global observations of our universe. The motion is real in one system and absent in the other regardless of what laws or equations you use to describe it.

I explained above that transverse motion is not a prerequisite to long-term stability.

Check this out, from Stability of rotating spherical stellar systems:

Abstract ?The stability of rotating isotropic spherical stellar systems is investigated by using N-body simulations. Four spherical models with realistic density profiles are studied: one of them fits the luminosity profile of globular clusters