Dynamic Equilibrium of the Universe and Subsystems

[modest]

Here are some binary systems that appear to defy the Newton's law of motion:... The violation seems to be a rule rather than an exception.

 

I didn't see the problem you're referring to in the abstract you quoted. I believed it was there so I spent 20 minutes reading the paper and news releases completely. Still not. I figured it might be hiding in the paper's data so I put the raw info in excel and solved it. The solution agrees with the paper and newton - i.e. there most certainly is nothing "defying newton's laws of motion". There is no such claim, no such description, no such observation in what you've linked above.

 

This is like the third time in a row you've claimed a source says or means something it clearly does not. It's just a bit frustrating.

 

-modest

[coldcreation]

I didn't see the problem you're referring to in the abstract you quoted. I believed it was there so I spent 20 minutes reading the paper and news releases completely. Still not. I figured it might be hiding in the paper's data so I put the raw info in excel and solved it. The solution agrees with the paper and newton - i.e. there most certainly is nothing "defying newton's laws of motion". There is no such claim, no such description, no such observation in what you've linked above.

 

This is like the third time in a row you've claimed a source says or means something it clearly does not. It's just a bit frustrating.

 

-modest

 

It is possible that I misinterpreted the observations. It wouldn't be the first time an interpretation of the evidence has been erroneous, by myself or others. And I'm sure it won't be the last.

 

I was under the impression that these low-mass stars should be orbiting at a much greater distance from one another than observed, i.e, that tight binary-pairs were usually more massive stars.

 

The study found companions to low-mass stars typically only 4 AU from their primary stars "surprisingly close together," (Nick Siegler, a University of Arizona) and that "More massive binaries have typical separations closer to 30 AU, and many binaries are much wider than this." I supposed my assumption was that this did not fit into the standard gravitational scheme (and I still think something is amiss). I will do more research so as not to jump to conclusions too quickly.

 

 

Even so, you seem to be avoiding my main point; namely that centrifugal force exactly cancels gravity, like balancing a pencil on its point. Regardless of initial conditions [of which we are not in agreement, since I suspect most of the cloud that condenses gravitationally into, say, a binary-pair, and thus close to 100% of the material is accounted for. So a large percentage of the original cloud does currently orbits in the form of binary stars, or in the case of the solar system, in the form of planets, the Oort Cloud and the Kuiper Belt] there are observed throughout the cosmos gravitationally bounded systems in quasi-stable equilibrium that will undoubtedly survive (without collapse and without diverging into the depth of space) for time-scales compatible with several Gyr.

 

The two-body problem is a good one to start with because of the ubiquity of such systems (about half of all nearby stars are binaries), because of the physical stability they display, and because of the difficulty of finding exact solutions for the problem. I know some have claimed to have solved the two-body problem, and indeed they have. But that is usually done by considering the dynamics of two non-spinning structureless point-particles with two mass parameters M1 and M2 moving under the influence of gravity (I guess that works if real bodies are spherically symmetric, but in the case of binary galaxies the problem is compounded). So we could state that the two-body problem in General Relativity (with respect to real systems such as binary galaxies) has no known analytical solution (analogous to the case of Newtonian mechanics where the finite three-body problem has no known analytical solution. I could be wrong here too.

 

The three-body problem, which I would like to delve into next, has no exact solution except under very special circumstances (eg when the three bodies are all on the same line, in equilateral triangle formation and a third which escapes me) called the restricted 3-body problem and the general 3-body problem.

 

Here is a good place to start, for those interested: The Three-Body Problem*By Mauri Valtonen, Hannu Karttunen where the two-body problem is discussed.

 

I am not suggesting that we will find, anytime soon, exact solutions for the three-body probelm, but the discussion is an important one, even qualitatively, since it relates to both the stability and chaosicity of objects here in the solar, the Galaxy, the Local Group and so on. As far as binaries are concerned we still do not have a basics understanding of the origin (formation processes) or of the most basic properties of such systems (something crucial in understanding stellar systems dynamics). So to assume their longevity is due to a precise cancelation of gravitational force and centrifugal force (making then stable) is premature, in my opinion.

 

Indeed, galaxies also come in pairs (binaries), as they do small groups (triplets) and large groups. So understanding the underlying physics of binary stars will surely help on other scales as well.

 

I noticed, too, that you avoided my point above about the barred structure present in a large portion of galaxies (stars forming the bar shape of barred galaxies do not rotate faster toward the center of gravity), probably since it did not fit into your scheme above (objects rotate faster toward the center of gravity). Clearly the center of gravity is located in the galactic nucleus, in the bulge component (even in barred galaxies), yet stars located both on the outer edge of the bar and those near the central core orbit once around the center of mass in the same amount of time.

 

 

So, again, the fine-tuning problem is still alive and kicking three centuries after it was first enunciated. My aim is to get to the bottom of the problem, i.e., to explain why gravitationally bounded stable- and quasi-stable equilibrium configurations exist almost everywhere we turn our telescopes (without having to rely on the finely tuned gravitational attraction balancing the orbital angular velocity associated centrifugal force, and without brushing the problem under the carpet with initial condition conjecture).

 

Fortunately, there is another model that explains the fine-tuning without the chimerical balance of two opposing 'forces.' It is a simple and more general geometric solution based on the interacting fields of gravitating bodies, where curved spacetime (gravity) alone is responsible for the observed equilibrium.

 

 

 

 

CC

[modest]

It is possible that I misinterpreted the observations. It wouldn't be the first time an interpretation of the evidence has been erroneous, by myself or others. And I'm sure it won't be the last.

 

I'm glad you would say so

 

I was under the impression that these low-mass stars should be orbiting at a much greater distance from one another than observed, i.e, that tight binary-pairs were usually more massive stars.

 

This was the first study finding binary stars at that mass - no one knew how distant they'd be from one another. They would have guessed further than 3 au because more massive stars are more separated than that.

 

The study found companions to low-mass stars typically only 4 AU from their primary stars "surprisingly close together," (Nick Siegler, a University of Arizona) and that "More massive binaries have typical separations closer to 30 AU, and many binaries are much wider than this." I supposed my assumption was that this did not fit into the standard gravitational scheme (and I still think something is amiss). I will do more research so as not to jump to conclusions too quickly.

 

I see. That's not the case. Masses don't need an exact distance to be in a 'stable' orbit. They need an exact distance, velocity, mass relationship. The astronomer was not surprised because these masses didn't fit that relationship. I don't know why you would assume that. They were simply surprised because the distances were smaller than they find in more massive systems. But, this would make sense wouldn't it. A planet (which is even less massive) is even closer. Obviously the formation mechanism (which isn't completely known) favors closer binaries in less massive systems. There's no problem there. The paper doesn't express a problem.

 

 

Even so, you seem to be avoiding my main point;

 

I'm doing my level best to address everything.

 

namely that centrifugal force exactly cancels gravity, like balancing a pencil on its point. Regardless of initial conditions [of which we are not in agreement, since I suspect most of the cloud that condenses gravitationally into, say, a binary-pair, and thus close to 100% of the material is accounted for. So a large percentage of the original cloud does currently orbits in the form of binary stars, or in the case of the solar system, in the form of planets, the Oort Cloud and the Kuiper Belt] there are observed throughout the cosmos gravitationally bounded systems in quasi-stable equilibrium that will undoubtedly survive (without collapse and without diverging into the depth of space) for time-scales compatible with several Gyr.

 

Once again you're making an assumption. Where do you get that a collapsing nebula is close to 100% equal to the mass of the protoplanetary disk plus star / stars? Where do you get that the accretion disk is close to 100% equal in mass to what ends up in orbit? If your claim that gravity is a force of balance is based on the above assumption then how should it be countered? Newton's and Einstein's equations say there is no indefinite equilibrium of bodies interacting gravitationally. That's it. That's my counter.

 

Indeed, galaxies also come in pairs (binaries), as they do small groups (triplets) and large groups. So understanding the underlying physics of binary stars will surely help on other scales as well.

 

Yes, galaxies are interacting gravitationally all the time just like binaries and planets and everything else. Your claim is that these are analogous to balancing a pencil on its head. The math says no and the images of galaxies colliding would tend to agree. So, I don't see how you're making headway.

 

I noticed, too, that you avoided my point above about the barred structure present in a large portion of galaxies (stars forming the bar shape of barred galaxies do not rotate faster toward the center of gravity),

 

Yes, I did avoid it - on purpose. You asked me for a source for what I said and I gave you Kepler's law. I didn't want to continue on that subject because it's tangent to the topic. My point was that systems in dynamic equilibrium rotate and the universe does not. That argument didn't depend on the speed of rotation. If you want to talk about it that's fine - but I don't see where it's going.

 

It's not just barred galaxies that have odd rotation curves. They all (or I guess nearly all?) do. You would expect the speed of rotation to decrease with distance from the galactic center. Instead the rotation curve is usually nearly flat. It's as if there is unseen mass that extends well beyond the perimeter of the visible galaxy. Either that or Newton's and Einstein's laws of gravity are wrong. I know you will reject the idea of dark matter and neither will you reject GR - so I don't see how focusing on galaxy rotation curves will be useful. Neither of our arguments depend on that observation and it will be a point of contention between us. I would just as well leave it alone.

 

 

So, again, the fine-tuning problem is still alive and kicking three centuries after it was first enunciated. My aim is to get to the bottom of the problem, i.e., to explain why gravitationally bounded stable- and quasi-stable equilibrium configurations exist almost everywhere we turn our telescopes

 

What else would you expect to see? Is there some way you could spot a failed gravitational system (besides galaxy mergers)? There's not going to be a sign post saying a solar system or binary star tried to form here but couldn't. Every time you see something in orbit it gives you no indication of how many failed orbits there were. And, I can't express the importance of this enough: everywhere you point your telescope you're looking at a system that will fail in its stability. There are no gravitational pencils that will stay balanced - including the universe.

 

 

Fortunately, there is another model that explains the fine-tuning without the chimerical balance of two opposing 'forces.' It is a simple and more general geometric solution based on the interacting fields of gravitating bodies, where curved spacetime (gravity) alone is responsible for the observed equilibrium.

 

Whatever it is - it isn't GR.

[coldcreation]

...Yes, I did avoid it - on purpose. You asked me for a source for what I said and I gave you Kepler's law. I didn't want to continue on that subject because it's tangent to the topic. My point was that systems in dynamic equilibrium rotate and the universe does not. That argument didn't depend on the speed of rotation. If you want to talk about it that's fine - but I don't see where it's going.

 

The subject of barred galaxies (notably the bar structure itself) is not tangent to the subject. It is directly related. If ever a pencil balanced on its point it is there, in the structure of the bar itself. But do they evolve? Sure (Hubble’s SBa, SBb and SBc (1926) or de Vaucouleurs SAB, etc. (1959)), just like everything else. Again, the fact that an extraordinarily large number of these stable arrangements exist, that many variations of these morphological types are observed, and therefore, that bars must both be easily formed and possess long-term life expectancy, encourages the belief that the associated dynamic mechanism is embedded in the heart and sole of the gravitational interaction. Because physics in the solar system must be the same as physics on intermediary scales, and specifically because of the role of gravity on compositional restriction, the relation of the barred formation profile to the purest and most orderly geometric structures must be comparatively obvious. Indeed it is!

 

As bars evolve into normal spirals, other systems are in the process of forming bars. This prototypical pattern of evolutionary trends is indeed complex. The evolutionary aspects of galaxy formation and progression are not beyond the scope of our current discussion.

 

It's not just barred galaxies that have odd rotation curves. They all (or I guess nearly all?) do. You would expect the speed of rotation to decrease with distance from the galactic center. Instead the rotation curve is usually nearly flat. It's as if there is unseen mass that extends well beyond the perimeter of the visible galaxy. Either that or Newton's and Einstein's laws of gravity are wrong. I know you will reject the idea of dark matter and neither will you reject GR - so I don't see how focusing on galaxy rotation curves will be useful. Neither of our arguments depend on that observation and it will be a point of contention between us. I would just as well leave it alone.

 

Rotational curves are just another example (in addition to barred galaxies) of how many gravitationally bounded systems defy Newton's law of motion (may as well throw in Kepler's laws too). This is part of the problem. So every time observations defy these laws something else is needed to amend the situation. It's funny how nonbaryonic dark matter (and supermassive black holes) seems to keep sticking its ugly head into the business of physics: a place where it has no business at all.

 

[i wrote the following in Hilton Ratcliff's thread] Applying Newton’s law of motion, Kepler’s third law planetary motion and the viral theorem (which asserts that for gravitating systems in statistical equilibrium, the gravitational potential energy must be twice the kinetic energy of the galaxies), it is shown that the mass of the Coma cluster exceeds the mass attributable to the visible parts of the galaxies by a factor of twenty or more—again, implying that most of the mass in the cluster is in the form of dark matter (Longair 1989).

 

Moving to even larger scales, the magnitude of the problem is even more precipitous within the largest agglomerations of matter known in the universe: superclusters. [The largest known structures in the universes are holes of empty space. The scale corresponding to these regions where the galaxy count is significantly low is about 30 to 50 times the scale of a cluster of galaxies (Longair 1993)]. Calculations have divulged that huge amounts of gravitating matter must be missing if the theory that outward centrifugal force is responsible for the balancing act with the inward attraction of gravity. Here, clearly stated, is the core principle the modern stance: it is separated totally from any direct dependence on the stimulus of nature—the discrepancy between gravity and velocity yield baffling forms of missing dark matter. Gravity along with missing mass and centrifugal force are set up as three distinct polarities. Newtonian mechanics seems to work well when applied to the solar system. But going up the scale of masses to galaxies, to clusters of galaxies, superclusters and ultimately the mass density of the universe as a whole, the less compelling and the more uncompromisingly large the deviation from reasonable interpretation.

 

There is obviously another solution to the problem. BTW, general relativity is not wrong, it just needs to be determined its boundary conditions (where the math stops and nature takes over). That boundary condition can be easily identified (by observation) and interpreted (analytically).

 

 

What else would you expect to see? Is there some way you could spot a failed gravitational system (besides galaxy mergers)? There's not going to be a sign post saying a solar system or binary star tried to form here but couldn't. Every time you see something in orbit it gives you no indication of how many failed orbits there were. And, I can't express the importance of this enough: everywhere you point your telescope you're looking at a system that will fail in its stability. There are no gravitational pencils that will stay balanced - including the universe.

 

You're assuming there are many failed orbits. Do you have a source for that assumption?

 

 

 

So, again, the fine-tuning problem is still alive and kicking three centuries after it was first enunciated. My aim is to get to the bottom of the problem, i.e., to explain why gravitationally bounded stable- and quasi-stable equilibrium configurations exist almost everywhere we turn our telescopes (without having to rely on the finely tuned gravitational attraction balancing the orbital angular velocity associated centrifugal force, and without brushing the problem under the carpet with initial condition conjecture).

 

Fortunately, there is another model that explains the fine-tuning without the chimerical balance of two opposing 'forces.' It is a simple and more general geometric solution based on the interacting fields of gravitating bodies, where curved spacetime (gravity) alone is responsible for the observed equilibrium.

 

Whatever it is - it isn't GR.

 

Sure it is GR.

[modest]

The subject of barred galaxies (notably the bar structure itself) is not tangent to the subject. It is directly related.

 

Somehow when I wrote that it was tangent I just knew you'd think it's key. Yep, I had that funny knowing feeling about that.

 

If ever a pencil balanced on its point it is there, in the structure of the bar itself. But do they evolve? Sure (Hubble’s SBa, SBb and SBc (1926) or de Vaucouleurs SAB, etc. (1959)), just like everything else.

 

In fact, they come and go and come and go - I'm trying to figure how that's a pencil on its head... No. I can't figure how this is an example you wanna go with.

 

Again, the fact that an extraordinarily large number of these stable arrangements exist, that many variations of these morphological types are observed, and therefore, that bars must both be easily formed and possess long-term life expectancy,

 

The bar is by all accounts temporary. Much more temporary than the galaxy. How is that stable?

 

As bars evolve into normal spirals, other systems are in the process of forming bars. This prototypical pattern of evolutionary trends is indeed complex.

 

It seems you know how temporary they are which begs the question: why are you using them as an example?

 

Rotational curves are just another example (in addition to barred galaxies) of how many gravitationally bounded systems defy Newton's law of motion (may as well throw in Kepler's laws too).

 

For our purposes, they are one and the same. The bar exists because of the flat rotational curve and without the flat rotational curve the bar couldn't be.

 

But, I have that knowing feeling once again. This conversation is about to go all wrong. It's going to turn into - 'does dark matter exist' when It really doesn't have to go there. I don't need dark matter to make my argument. And, you don't need to disprove dark matter to make yours. So, this is about to get ugly for no reason.

 

This is part of the problem. So every time observations defy these laws something else is needed to amend the situation.

 

Something 'else' is by definition needed to explain galaxy rotation curves. Observation plus GR doesn't do it. You either need dark matter or you need to put GR in the trash. Those are the only two accepted realities to the situation.

 

It's funny how nonbaryonic dark matter (and supermassive black holes) seems to keep sticking its ugly head into the business of physics: a place where it has no business at all.

 

Hey - I tried to keep it out of the discussion. I think it obviously does belong in physics, but we don't need to focus on that.

 

 

There is obviously another solution to the problem. BTW, general relativity is not wrong, it just needs to be determined its boundary conditions (where the math stops and nature takes over). That boundary condition can be easily identified (by observation) and interpreted (analytically).

 

The irony is that a tight boundary condition to GR would only make the situation worse. You would need more dark matter in that case. Besides, you can't just toy with GR like that.

 

What else would you expect to see? Is there some way you could spot a failed gravitational system (besides galaxy mergers)? There's not going to be a sign post saying a solar system or binary star tried to form here but couldn't. Every time you see something in orbit it gives you no indication of how many failed orbits there were. And, I can't express the importance of this enough: everywhere you point your telescope you're looking at a system that will fail in its stability. There are no gravitational pencils that will stay balanced - including the universe.

 

You're assuming there are many failed orbits. Do you have a source for that assumption?

 

I must be drunk. I'm saying there's no way to know something and you're asking me to prove what that something is? Honestly? I.. I don't.. Wait, what?

 

I'm saying you can't see the failed orbits therefore you don't know how many there are/were. You want me to source how many there are/were? I can't make any kind of sense out of that.

 

-modest

[coldcreation]

Somehow when I wrote that it was tangent I just knew you'd think it's key. Yep, I had that funny knowing feeling about that.

 

All things are related in some way or another: often in ways more deeply than presumed (or assumed). After all, barred galaxies are very common in the cosmos (about half of all disk galaxies have bars: de Vaucouleurs & de Vaucouleurs 1964) and it is well known that the bars themselves are stable structures. It is interesting to theorizes just how these gravitationally bounded systems relates to other systems bounded under the sole influence of gravity. Tangent? I think not.

 

 

In fact, they come and go and come and go - I'm trying to figure how that's a pencil on its head... No. I can't figure how this is an example you wanna go with.

 

You see modest, the vision of a new world I've attempted to outline (here at Hypography and in other places) is a vision of a world relatively freed from the tragic and apocalyptic scenarios today found in every textbook on cosmology. Certainly there is no need to beautify nature—but to transfer the beauty and elegance into a fresh cohesive dialogue that most accurately represents her—one that is in tune with her intricacies, one that only describes our universe, the universe, whose order was only a phase in a continuous process of change.

 

 

The bar is by all accounts temporary. Much more temporary than the galaxy. How is that stable?

 

The fact that bars exists is in and of itself remarkable. Just how stable or transient they are no one really knows for sure. Simulations are lacking, limited and inconclusive at best. Though bars do occur naturally in N-body simulations of rotating stellar disks and are observed in nature to be intrinsically stable, but that doesn't mean, of course, that they are not responsible for evolutionary change in their host galaxies (Kormendy 1982). Bars remain the flattest and most triaxial stellar systems known in the cosmos.

 

• Once formed' date=' stellar bars are quite robust; they typically persist for the duration of N-body experiments with no more evolution than might be expected from two-body relaxation. But a bar can interact with the galaxy it lives in, and both the bar and its host may change as a result. Over time, bars in disk simulations rotate more slowly as gravitational torques transfer angular momentum from the bar to the surrounding material (e.g. Sellwood 1981). They also grow somewhat longer, and this is a natural consequence of their slowing down, since bars tend to end at the CR, which moves out as Omega_b decreases. [/quote'] Source.
  

   

  If these structures were not stable they would be destroyed as quickly as they form (if they would even form at all), both in simulations and in the real world.

   

   

  It seems you know how temporary they are which begs the question: why are you using them as an example?

   

  Everything is temporary, but that by no means excludes the fact that systems reach stability configurations and remain stable for extended periods of time. It is therefore interesting (nontrivial) to see just how stability is maintained for that duration.

   

  To not introduce these structures [barred galaxies] into a discussion on the stability of gravitating systems would be to neglect (perhaps conveniently) a large portion of observational data.

   

   

  For our purposes, they are one and the same. The bar exists because of the flat rotational curve and without the flat rotational curve the bar couldn't be.

   

  Precisely. That is why it is important to understand the operational mechanism involved.

   

   

  But, I have that knowing feeling once again. This conversation is about to go all wrong. It's going to turn into - 'does dark matter exist' when It really doesn't have to go there. I don't need dark matter to make my argument. And, you don't need to disprove dark matter to make yours. So, this is about to get ugly for no reason.

   

  I don't think we need to elaborate any further on nonbaryonic DM unless it becomes inevitable. For now, that is not the case.

   

   

  Something 'else' is by definition needed to explain galaxy rotation curves. Observation plus GR doesn't do it. You either need dark matter or you need to put GR in the trash. Those are the only two accepted realities to the situation.

   

  Dumping GR is obviously out of the question. Why would you exclude the possibility that there might be a third (or more) acceptable "realities to the situation"? And why would that something 'else' have to be CDM (something, to date, outside of physics)?

   

  My ultimate goal is the annulment of the divorce between science and nature. To achieve this goal a very slight modification, or extension, needs to be attached to GR: the boundary condition. But this condition does absolutely not take away from the beauty, the symmetry, or the generality of Einstein's general postulate of relativity. Quite the contrary: it adds all of the above.

   

  My assumption here is that the exact laws that govern quasi-stable and stable gravitating systems can be derived from GR (surely it would be an ignominy if this were not the case) and that historically the interpretation of GR leaves something to be desired. It is for the latter reason that solutions to the problems (e.g., rotational curves) has been lacking (without CDM).

   

   

  Hey - I tried to keep it out of the discussion. I think it obviously does belong in physics, but we don't need to focus on that.

   

  Oh good.

   

   

   

  The irony is that a tight boundary condition to GR would only make the situation worse. You would need more dark matter in that case. Besides, you can't just toy with GR like that.

   

  The situation could hardly get worse than it is right now. More DM is not required. In fact, the only dark matter fused into the mix is baryonic DM. Physicist have been toying with GR since its inception. Black holes, dark energy and the big bang itself are the results of toying with GR (radically).

   

   

   

  You're assuming there are many failed orbits. Do you have a source for that assumption?

   

  I must be drunk. I'm saying there's no way to know something and you're asking me to prove what that something is? Honestly? I.. I don't.. Wait, what?

   

  My point is that it should not be assumed there were many failed orbits during the formation process of gravitating systems. An asteroid impact (or many of them) on the surface of the moon is not evidence in favor of your claim. Au contraire. It is evidence that objects coalesce and subsequently remain stable in specific orbits (that, yes, do vary with time depending on many factors, often external to the system under consideration).

   

   

  I'm saying you can't see the failed orbits therefore you don't know how many there are/were. You want me to source how many there are/were? I can't make any kind of sense out of that.

   

  I didn't think so.

   

  Again, the fact that gravitating systems are capable of long-term stability (for time-scales of say 5 Gyr or more) is direct evidence that there is a mechanism operational in the combined fields of all massive bodies (particularly and manifestly in Lagrange points and the immediate environs of such). The fact that a finely tuned ad hoc mechanism for balancing gravitational ‘attraction’ with an outward centrifugal ‘force’ requires the theoretical inclusion of something outside of physics (viz dark energy, negative pressure and/or nonbaryonic dark matter) to explain the observed equilibrium occurring in systems that would otherwise be orbiting to quickly or too slowly, if at all, to be accounted for through natural means, is evidence that the physics of gravitation needed to be complemented, needed to be defined in terms of a real physical mechanism operational in the field, not one that could only explain occurrences within the free-open unlimited range Newtonian gravity (were gravity is an 'attractive force') or mathematical aberrations of GR (viz supermassive black holes).

   

   

   

  CC

[coldcreation]

“This Principle alone is sufficient to determine the laws of equilibrium in every circumstance; because in composing successively all the forces two by two' date=' we should attain a single force, which will be equivalent to all the forces, and which by consequence should be null in the case of equilibrium, if in the system there is no fixed point; but if in the case there is one, the direction of this unique force must pass through the fixed point” (Lagrange, La Composition des Force, Méchanique Analytique, 1788, p. 6) [my translation']

 

 

In Théorie des fonctions analytiques (1796), more than one hundred years before Albert Einstein and Hermann Minkowski, Joseph-Louis Lagrange referred to dynamics as a “four-dimensional geometry.” Without doubt, such illustrations aimed at their audiences, with physical intent, were certainly not geometric in any ordinary sense; but unquestionably they were geometric in their concern with planimetric space of gravitating systems, and in the fundamentals of their relationship with matter. He believed now another basic factor was to be understood and exploited: space. He saw the understanding of space as a legacy left by the invention of Newton. In Lagrange’s system imbued with the notion of dynamic continuity, is stressed the importance of unbroken rhythms and completed movements by circular field lines; now with the spatial factor introduced.

 

It is difficult to overestimate the importance of the Lagrange discovery. Not only does it confine the number of possible structures that can exist, it demonstrates a regularity and pattern among those systems that do exist. The Lagrange system reveals how interacting gravitational fields of massive bodies generate periodicity, just as the Pauli principle generates the periodicity among atomic elements in the case of electrons orbiting atomic nuclei—as in the Mendeleev periodic table of elements—and the systematic pattern among quark clusters that represent the subsistence of a profound layer of reality on the smallest scales. (The forces that cluster quarks together are not yet fully understood but some of the patterns and features have already been identified). Our ability to recognize that Nature forms regular patterns at all scales (from quarks to superclusters) and limits the number of available structures, rather than giving way to disorganized chaos, is essential if we are to make any progress at all in cosmology.

 

 

 

CC

[coldcreation]

There exist in the visible universe a huge number of gravitating systems (from the smallest planetary systems to the giant super clusters of galaxies). In each system there are a series, often a multitude of bodies, each in its own gravitational potential well, each immersed within a curved spacetime ‘trough’ or depression, the ‘depth’ of which depends on the mass of the object, in accord with GR. Too, within the multitude of massive bodies and their gravitational wells are a series of ‘peaks’ in the manifold. These peaks are usually characterized by particular points (and curved surfaces: to be discussed further) in the combined fields of two or more bodies; called Lagrange points.

 

The remarkable feature of the field described above should be first visualized in a 2-dimensional setting (this view will ultimately fail to provide the full breadth of the exposé: for that the 4-dimensional landscape, or spacescape should be used). In a 2-dimensional setting, let us begin with a flat plane, which represents an ideal Euclidean spacetime (ideal because there is always some residual ground energy that is irreducible so space would never be totally empty or flat). Now introduce stars, planets, galaxies, galaxy clusters, and superclusters. Each object is embedded in its own gravitationally curved spacetime well, each with its own unique depth depending on the mass of the object or system.

 

Now let us turn our attention toward the other end of the field curvature: the space between objects and the space surrounding objects or systems. The Lagrange points are the peaks of the field that separate the potential wells of massive bodies. Contrary to the differing depths of the gravitational wells of each object, the Lagrange points (particularly L1) all posses the same value. The gravitational curvature is equal to zero (since a particle place on L1 experience no acceleration).

 

This too is in accord with GR, however it places a limit (not on the depth of a gravitational well), on the 'height' (or peak) of combined (or interacting) gravitational fields. That my friends must be equal to zero curvature: what would be described as "empty" field free space (or a field free point).

 

Earlier renderings of the combined fields of gravitating systems had the peaks scattered about with differing values just as the gravity wells themselves; each with its own value, where a perfect balance between centrifugal force and the attraction of gravity are finely tuned by some initial condition (or an assumed 'natural selection' process).

 

 

The significance of this is crucial.

 

Let's see if anyone can figure out why...

 

 

 

 

CC

[modest]

Sorry for my recent truancy. I will answer your concerns above. I'm just a bit stifled by some odd circumstances at the moment.

 

In the meantime, this might be of interest to this topic and your theory:

http://hypography.com/forums/news-brief/14339-nasa-baffled-unexplained-force.html

Pioneer anomaly - Wikipedia, the free encyclopedia

 

-modest

[coldcreation]

Sorry for my recent truancy. I will answer your concerns above. I'm just a bit stifled by some odd circumstances at the moment.

 

In the meantime, this might be of interest to this topic and your theory:

http://hypography.com/forums/news-brief/14339-nasa-baffled-unexplained-force.html

Pioneer anomaly - Wikipedia, the free encyclopedia

 

-modest

 

You might know too that, unexpectedly, SOHO reached it’s halo orbit around the Sun-Earth L1 point six weeks ahead of schedule (on February 14, 1996), with enough fuel left over to sustain the orbital position for more than a decade—over twice the length of fuel-time anticipated preceding the launch (Martens 2001).

 

 

CC

[modest]

In the meantime, this might be of interest to this topic and your theory:

http://hypography.com/forums/news-brief/14339-nasa-baffled-unexplained-force.html

Pioneer anomaly - Wikipedia, the free encyclopedia

 

You might know too that, unexpectedly, SOHO reached it’s halo orbit around the Sun-Earth L1 point six weeks ahead of schedule (on February 14, 1996), with enough fuel left over to sustain the orbital position for more than a decade—over twice the length of fuel-time anticipated preceding the launch (Martens 2001).

 

CC

 

I guess so far there's nothing anybody has put forward that will predict these anomalies. As the news article points out, it may be in unbound orbits only that this happens. I certainly wouldn't say, yet, that this 'interesting data' could contribute to an equilibrium. However, if and when a successful theory explains what's going on - it certainly isn't impossible considering the pioneer data. We are a long way off from saying that though - It may just as well have nothing to do with gravity at all.

 

-modest

[coldcreation]

I guess so far there's nothing anybody has put forward that will predict these anomalies. As the news article points out, it may be in unbound orbits only that this happens.

 

These "anomalies" are not really anomalies. They are predicted by the Lagrange equations. The news article's supposition that this phenomenon may occur in unbounded orbits is erroneous. Clearly, if one couples the data from the SOHO mission with the other supposed anomalies (which at first appear unrelated) the fact that this happens in gravitationally bounded systems is obvious.

 

 

I certainly wouldn't say, yet, that this 'interesting data' could contribute to an equilibrium. However, if and when a successful theory explains what's going on - it certainly isn't impossible considering the pioneer data. We are a long way off from saying that though - It may just as well have nothing to do with gravity at all.

 

Au contraire. It has everything to do with gravity.

 

The fact that Kepler’s third law is violated when an object is in orbit around L1 is well known. But the fact too that the inverse square law is violated along the same line connecting two bodies is not known in physics. Kepler’s third law basically states that the closer an object (a planet) to the sun, the faster it travels in its orbit. An object placed in the halo orbit around L1 make a revolution around the sun in the same interval as the earth: a minor violation but a violation nevertheless of the third law. So why is the inverse square law violated? It is violated because instead of the field diminishing in intensity inversely to the square of the distance - which under normal situations tends to zero as distance tends towards infinity - the field curvature between two objects tends to, and attains zero at L1: only 1.6 million kilometers away in the case of the earth-sun field.

 

Like so many unnoticed or other seemingly inconsequential observations and events, usually ignored, this small deviation from the time schedule (a full six week discrepancy in the case of SOHO), hailed as a successful endeavor because it was ahead of schedule, may hold an important clue as to the strength, intensity and the geometrical structure of the gravitational field between home base, planet Earth, and our companion star, the Sun. Recall that calculations are based on the inverse square law, where the continuous gradation of the Earth’s field extends and weakens in every direction, including toward the Sun, declining inversely as the square of the distance. At 1.6 million km (L1) the field of the Sun takes over, i.e., on the other side (Sun-side) of L1 any probe or particle placed there would begin its acceleration toward the Sun.

 

It is my contention, here, that a divergence from this law is involved along the path leading towards the inner Lagrange point L1. If the two intrinsic fields (the Earth’s and the Sun’s) cancel at L1, the value of the field is zero at that point. The gradient in the Earth’s field, consequently, begins close to the Newtonian value, but the closer the ship moves toward the Sun, the greater the deviation from the inverse square law. In other words, the further removed an object from Earth, along the Sun-Earth (or Moon-Earth) lines, the weaker the field becomes, until its value approaches zero at L1.

 

So in answer to you above remarks, the observations that show a deviation from Newtonian mechanics (as well as from general relativity) - such as the "anomalies" cited above, and too, the rotational curves of stars orbiting galaxies (nearly flat rotational curves), the bar structure of certain galaxies, the observed equilibrium of such systems and many others - are a result of classical Lagrangian dynamics.

 

In another way, the same phenomena responsible for the stability associated with, say, Jupiter and its Trojan satellites, or the stability of quasi-stable halo orbits around the L1 or L2 points (include here; mean motion resonance patterns as a source of equilibrium) are responsible for the "anomalies" observed across a wide spectrum of gravitating systems. Indeed, what has been called a restricted 3-body problem is actually a very general N-body problem. In fact, it is not a problem at all, when Lagrangian dynamics are taken as general rather than restricted. It is thus GR combined with the Lagrange geometric scheme that will (and does) provide the solution. How? There is a generalization of the Lagrange formula, and a restriction on GR (the boundary condition I wrote about earlier) to be made. The combination of both determines the dynamics of self-gravitating systems.

 

The key to this argument lies in the structure and intensity of the gravitational field curvature at various points distributed throughout the combined fields of massive bodies (the relation between the gravitational wells and the 'peaks' of the field - which attain a zero value for gravitational curvature, say, at L1 and L2 saddle points and a more complex structure at L4 and L5). Note, this view is in general opposition with the standard interpretation of the field according to which the 'peaks' in the filed are at different potentials. That is what makes all the difference in the world (in the universe).

 

If you would like a more in-depth analysis for this mechanism, I can provide it.

[modest]

These "anomalies" are not really anomalies. They are predicted by the Lagrange equations.

 

I certainly don’t see how. The Euler-Lagrange equation will give you or will reduce to Newton’s second law. In various circumstances it is more convenient or easier to solve Lagrangian mechanics, however, this is an issue of math - the results are the same. The pioneer and other anomalies (and let’s even add galaxy rotation or dark matter to the list) these anomalies do not agree with Newtonian predictions and therefore necessarily don’t agree with Lagrangian mechanics. From wiki’s ‘Lagrangian’:

 

Using this result, it can easily be shown that the Lagrangian approach is equivalent to the Newtonian one.

If the force is written in terms of the potential [math] \vec{F} = -\nabla V (x)[/math]; the resulting equation is[math] \vec{F} = m \ddot{\vec{x}}[/math], which is exactly the same equation as in a Newtonian approach for a constant mass object.

A very similar deduction gives us the expression [math] \vec{F} = d\vec{p}/dt[/math], which is Newton's Second Law in its general form.

 

Also, wiki’s page on the Euler-Lagrange equations supports the same thing in more detail.

 

The news article's supposition that this phenomenon may occur in unbounded orbits is erroneous.

 

You are probably right. I believe Anderson was pointing out the ‘unbound orbit’ commonality because this is something we’ve never seen (as far as I know) in a bound or ‘stable’ orbit of which we have many, many more well-observed examples. I was mentioning this unbound thing because I thought you’d take to it. The satellites we put in stable orbit exactly comply with the known laws of motion and gravity while a couple / few that we’ve sent into unstable or unbound orbits might have a very tiny bit of extra force pulling them back toward the system. Is something trying to enforce an equilibrium? I’d say no, but I thought you’d like the idea.

 

Clearly, if one couples the data from the SOHO mission with the other supposed anomalies (which at first appear unrelated) the fact that this happens in gravitationally bounded systems is obvious.

 

It looks most likely that we had different ideas of bound. Anderson was talking about a bound orbit where the orbit repeats itself over and over - basically what we’ve defined as ‘stable’ in this thread. If we presume for a moment that the anomaly is real and further presume it only happens in an unbound orbit then that could lend itself to your ideas of what’s going on.

 

It may just as well have nothing to do with gravity at all.

Au contraire. It has everything to do with gravity.

 

I’m saying that most likely the anomalous velocities are not caused by gravity or at least no directly so. The culprit could easily be one of the following:

• observational errors
  
• computational errors
  
• unaccounted for mass
  
• drag from interplanetary medium
  
• gas leak
  
• coulomb force
  

 

The fact that Kepler’s third law is violated when an object is in orbit around L1 is well known. But the fact too that the inverse square law is violated along the same line connecting two bodies is not known in physics. Kepler’s third law basically states that the closer an object (a planet) to the sun, the faster it travels in its orbit. An object placed in the halo orbit around L1 make a revolution around the sun in the same interval as the earth: a minor violation but a violation nevertheless of the third law.

 

This does not violate Kepler’s third law because his laws do not apply here. His are two body solutions only. They couldn't accurately give solutions to a situation where three bodies are significantly affecting each other's mass gravitationally.

 

So why is the inverse square law violated? It is violated because instead of the field diminishing in intensity inversely to the square of the distance - which under normal situations tends to zero as distance tends towards infinity - the field curvature between two objects tends to, and attains zero at L1: only 1.6 million kilometers away in the case of the earth-sun field.

 

No. The inverse square law of gravity:

 

[math]F = G \frac{M_1 \times M_2}{r^2}[/math]

 

Says that the sun attracts the earth with a force that is 1. proportional to the product of the masses. and 2. inversely proportional to the square of the distance between them. This means that as the earth gets further away from the sun the force decreases according to the inverse square law. What you want to do is add a satelite to get between the masses and feel some forces of its own. This is a third mass that doesn't fit in the equation above which you can see only has M1 and M2. You can of course describe a third mass at the point L1 using Newtonian mechanics and Newton's law of gravity which I'll do if you like. The equation above (in non-relativistic circumstances) is not violated and the inverse square law holds.

 

If the two intrinsic fields (the Earth’s and the Sun’s) cancel at L1, the value of the field is zero at that point.

 

Ture. Well, depends what you mean 'value of the field'. It would be flat. But, any object there would have potential gravitational energy compared to the sun and the earth.

 

The gradient in the Earth’s field, consequently, begins close to the Newtonian value, but the closer the ship moves toward the Sun, the greater the deviation from the inverse square law. In other words, the further removed an object from Earth, along the Sun-Earth (or Moon-Earth) lines, the weaker the field becomes, until its value approaches zero at L1.

 

Not exactly. You wouldn’t say the gradient in the earth’s field - but in the total field. The earth plus the sun. It is true that the ‘gradient’ in the field (or the change in potential as GR would prefer) is zero at L1. There is no gravitational force because the vectors cancel. The distinction that needs made, however: Earth’s field is not weakening at a greater than expected rate. Earth is affecting space time at L1 just as much as if the sun were not there. The reason space time is flat at L1 is because the sun effectively ‘bends’ it the other direction.

 

So in answer to you above remarks, the observations that show a deviation from Newtonian mechanics (as well as from general relativity) - such as the "anomalies" cited above, and too, the rotational curves of stars orbiting galaxies (nearly flat rotational curves), the bar structure of certain galaxies, the observed equilibrium of such systems and many others - are a result of classical Lagrangian dynamics.

 

As I sourced above, Lagrangian dynamics predicts nothing different from Newtonian mechanics.

 

It is thus GR combined with the Lagrange geometric scheme that will (and does) provide the solution. How? There is a generalization of the Lagrange formula, and a restriction on GR (the boundary condition I wrote about earlier) to be made. The combination of both determines the dynamics of self-gravitating systems.

 

What boundary condition? You mean to combine… actually, I’m not going to argue with you here. Let me just say that I think you should start by looking at cases where the Euler-Lagrange equation is already used in conjunction with general relativity. Look into how the GR laws of motion are derived. See if you can or would do it differently and if so how and what result do you get.

 

peace,

-modest

[snoopy]

Very interesting debate

 

It took me some time to read it all.

 

Cold Creation I take it you are arguing for a flat spacetime and a position of the planets based upon Lagrangian points ?

 

I seem to to remember some author arguing the same reason...

 

It was a book I read sometime ago it might have been Roger Penrose but I am not sure..

 

However the fine tuning problem may just be either an imagined problem ie there is no fine tuning occurring or may just be a gap in our knowledge which may at some future time be explained.

 

Look and you shall find...

 

The problem with this reasoning it is basically a tautology I could point to winter and summer, day and night as signs of deep equilibrium in the universe the more I look the more I find....

 

This sits a little uneasy with me and I prefer to view the universe a s some happy accident...

 

But incredibly interesting especially the bit about the space probe.

 

Peace

;)

[coldcreation]

Coldcreation I take it you are arguing for a flat spacetime and a position of the planets based upon Lagrangian points?

 

Hello snoopy. Flat spacetime no. I am saying that Lagrange points are far more important than suspected in the maintenance of equilibrium, for all gravitating systems. And, that spacetime is flat (ie., curvature is equal to zero) at the inner Lagrangian points.

 

The position of the planets are not based on L-points (though there are objetcs that occupy L4 and L5 positions of certain planets), but the equilibrium observed is related. The best way to view the problem is in the curved spacetime context. The Euclidean connection is that all peaks (L1 particularly) in the combined field of gravitating systems are at the same potential value of curvature (the same 'height') equal to zero. The value (for curvature: gravity) of these points are not variable like the potential wells of massive bodies (the 'depth' of which depends on the gravitating mass density).

 

However the fine tuning problem may just be either an imagined problem ie there is no fine tuning occurring or may just be a gap in our knowledge which may at some future time be explained.

 

Modern physics has generally attributed the equilibrium or fine-tuning to the supposed ‘fact’ that the velocity of each planet is precisely adjusted in order to maintain their orbits. It is assumed that this velocity was a result of the initial conditions prevalent during the formation of the solar system, but current science is unable to explain how this happened or how it is maintained. It is assumed that this was an intrinsic feature of the protoplanetary disk from which the accretion of the planets occurred. According to theory, without the exact velocity distribution, the solar system would not exist; the planets would either have collapsed into the Sun, or would have been freed from the confines of the Suns gravitational field and vanished into intergalactic space.

 

Modest, I will get back to your post soon...

 

 

cheers

 

 

CC

[snoopy]

Hello snoopy. Flat spacetime no. I am saying that Lagrange points are far more important than suspected in the maintenance of equilibrium, for all gravitating systems. And, that spacetime is flat (ie., curvature is equal to zero) at the inner Lagrangian points.

 

I meant that the Universe taken as a whole has a flat spacetime, not that the space around gravitating objects is flat.

 

Modern physics has generally attributed the equilibrium or fine-tuning to the supposed ‘fact’ that the velocity of each planet is precisely adjusted in order to maintain their orbits. It is assumed that this velocity was a result of the initial conditions prevalent during the formation of the solar system, but current science is unable to explain how this happened or how it is maintained. It is assumed that this was an intrinsic feature of the protoplanetary disk from which the accretion of the planets occurred. According to theory, without the exact velocity distribution, the solar system would not exist; the planets would either have collapsed into the Sun, or would have been freed from the confines of the Suns gravitational field and vanished into intergalactic space.

 

Yes I know, the current explanation isnt great is it ?

But it nevertheless remains the fact that not all solar systems discovered by interferometry are so fine tuned...

There have been instances where Jupiter size planets orbit their parent stars at the proximtiy of Mercury. They could not have formed at that distance and so must have travelled inwards creating havoc as they went.

 

The fact also remains that intelligent beings need a stable planet and solar system to evolve in.

 

So it is no surprise really that we are in an extremely stable system of planets, the real surprise would be if we had evolved in a planetary system that wasnt fine tuned and full of chaoctic orbits.

 

Also there is evidence that the earths moon was created when a planet struck the proto earth and melded with it to form the earth-moon system we now know.

You have to ask where the fine tuning was then ?

Without the moon the earths orbit would not be so stable and the earth might be in danger of even flipping over.

More possible fine tuning ?

Personally I dont think so, I think if you look to find fine tuning of the Universe you will surely find it it is after all everywhere...

From the small to the large.........

Physics is littered with bodies of evidence of fine tuning.

 

Its like the universe was created but it might just be as I have said one big happy accident and there is no fine tuning occuring.

 

Peace

:winter_brr:

[modest]

The best way to view the problem is in the curved spacetime context. The Euclidean connection is that all peaks (L1 particularly) in the combined field of gravitating systems are at the same potential value of curvature (the same 'height') equal to zero. The value (for curvature: gravity) of these points are not variable like the potential wells of massive bodies (the 'depth' of which depends on the gravitating mass density).

 

For this to be true you'd have to say all bodies of equal mass at any Lagrange point have equal potential gravitational energy to some reference. That can't be true. The point L1 between two orbiting stars may have very high potential if it is in a gravity well. The stars may be near a super-massive black hole. That L1 from our reference wouldn't have the same potential as our earth-sun L1. We can confirm this with gravitational lensing. All the galaxies of a cluster make one gravitational lens. The Lagrange points don't make holes in the lens.

 

I don't see any reason why general relativity would be wrong on this. The Lagrange point is where the field is flat - not zero. Besides, null geodesics continue to diverge after L1 all the way to infinity.

 

-modest