[tierradelfuego]

Hey, Cold --

"I'm still getting my ducks in a row too. It's not easy."

Yes, I agree ... but I have been waiting a year and a half! :-)

I am glad to read your recent postings. You are finally revealing more details on your broad cosmological model (and by "broad", I include the nuclear/subatomic ramifications), in which I believe you have significant insights. But I am dying to read at least a sketch or an outline of your overall picture! Let's get on with it! Naysayers be damned! :-p

I love the idea that the Lagrange points have much overlooked significance, particularly with respect to Arp's work. Dark matter, dark energy -- pfft! "I fart in their general direction!" There are many objects out there that are screaming for a new explanation -- quasi-stellar objects, objects with discordant redshifts, some of the peculiar galaxies, some of the objects that are incorrectly thought to be gravitationally lensed images of other objects, ... anything else? And you are on track for saying something more significant, for which I only have a couple of bits and pieces from your previous postings.

To the current dispute ...
It seems to me that if one accepts Einstein's equivalency principle, then one should not have a problem with your assertions about a saddle point at L1. That is the precisely the gist of the issue. When someone argues against your point that you are somehow lacking in respect for the centripetal acceleration of M2 towards M1, I would argue the opposite, and in fact, an argument against your point lacks an understanding of the equivalency principle, and hence, its significance to what you are trying to emphasize. Einstein said in GR -- no difference. No difference. No difference. ...

My qualm -- with respect to a two-body problem (say, Sun-Earth), are you ignoring the solar system's galactic centripetal acceleration (let's assume an ultra-simple model in which the solar system is orbiting a central galactic mass)? So is not L1 merely an approximate saddle point, hence, L1 is not flat with regard to L1's galactic orbit? And so on ... Milky Way's orbit within the local cluster, etc?

However, as one changes to larger and larger frames of reference, does not the Lagrangian points with respect to the objects involved get "flatter" in some "absolute" sense, in the sense of an absolute frame of reference (to the degree that one can employ that concept in a post-Einsteinian cosmology)? And could that be what you are hinting at? For example, in a simple "cluster" of galaxies in which a small galaxy is rotating about a much more massive galaxy, can't the Lagrangian points be described as being "flatter" than the Sun-Earth Lagrangian points? Or the solar system's Lagrangian points with respect to a simple Milky Way model? And the "flatter" a Lagrangian point, the more significant it is within your "cold matter creation model" (my short-hand term)? Just guessing here as to where you are going, but the "flatter" the point, the more prolific its "ability" in matter creation? Hence, the active regions at the Lagrangian points around galactic clusters?

Am I on the right track?
If so, did I guess too much or reveal too much?

I think that I see bits and pieces of the whole picture. I am dying to read an explanation from you for how your model explains the discordant redshifts. I cannot conceive at all how this would be -- but, hey, I should not feel too bad, it's your model, not mine. ;-)

--Tierra

[coldcreation]

Originally Posted by modest

It sounds like what you’re saying is that the key to the physical mechanism of gravity can be found in the equivalence principle of GR. That is to say: there is a significant reason gravity and inertial acceleration share physical and mathematical descriptions. To demonstrate the link between the two you are looking at Lagrange points where the force given by the gravitational field is exactly equal to the inertial force of rotation. You are perhaps thinking that an investigation into the nature of this equality could be useful in understanding what’s behind GR.

Certainly the Einstein equivalence principle is the drum and bass of the gravitational theory that signals a departure from linearity. In other words, gravity is a ‘curved spacetime’ phenomenon; the effects of gravity are equivalent to the effects of living in a curved spacetime. A consequence of EEP is that the laws governing experiments or observations must be independent of velocity in a free-falling frame of reference (Lorentz invariance). All bodies, without exception, fall with the same acceleration in the same gravitational field, and physics in a freely falling frame of reference is independent of location and the velocity of the frames. And so, yes, it is key to elucidating the physical mechanism of gravity.

Originally Posted by modest

If this is indeed a correct characterization - I would suggest simplifying your perspective. Lagrange points do have an equality of gravitational and inertial forces that are reflected in the weak equivalence principle. However, a simple orbit does as well.

It has been known since the advent of general relativity that it is impossible to discover by experiment whether a given system of coordinates is accelerated, or whether its motion is straight and uniform and the observed effects are due to a gravitational field. The implication of the equivalence principle “shatters the concept of inertial systems, as soon as gravitation enters in.” (Einstein 1940, 1954, p.330).

So the simple perspective is equivalent to trying to find the answer to the problem by using the wrong approach.

Originally Posted by modest

On this page:
Field Equations & Equations of Motion
The equation of motion, a geodesic, is found for a circular orbit by setting the gravitational force equal to the centrifugal force . It would be easier to investigate this situation rather than a three body solution if I have correctly understand your intent.

Easier, for sure, but to pursue this path further would be no different than hunting dogs barking at the base of a tree where they erroneously think their quarry is hiding.

My ambition is to do away with the centrifugal force in this context.

Originally Posted by modest

My problem is: I’m not sure if this kind of inquiry can get a person past the description which I’m sure you’ve heard. When you are accelerating in a rocket - you accelerate through space and feel weight as a result. When you stand on a planet - space moves (because of curved time) through you and you feel weight because of it. So, the equivalence principle seems to describe mass curving spacetime as the mechanism for gravity. The math that is built on that principle (general relativity) works well.

It follows from Einstein's equivalence principle, that the degree (or gradient) of gravitational field curvature is directly proportional to the inertial mass of a massive body (or gas cloud), not because the mass itself produces the gravity field, but because the spacetime manifold contours itself (there is a displacement from linearity) accordingly and proportionally to the mass of an object in relation to a hitherto trivial or inconsequential lower-threshold: spacetime with a Minkowski signature.

Each gravitational well potential is gauged not solely on mass, but on the degree of displacement from a linear metric that has a unique relative value for all times and all local minima of combined fields..

It is deduced that the acceleration of a freely falling object can be interpreted as having nothing to do with its mass.

Understandably, gravity is not an attractive force between objects (it is not a real force at all) but a curved spacetime phenomenon where space between objects (as well as other key locations in the combined fields of massive bodies) is less curved (relative to the standard zero condition there is less deviation from linearity) than in other parts of the field; since the gradient tends to, and attains, the local zero potential along the M1-M2 line. Furthermore, space between objects is curved hyperbolically (viz L1 Lagrange-Euler saddle points) as opposed to quasi-spherically in the surrounding vicinity of massive bodies. These geometrically opposed fields act seemingly against one another. One is the result of tension and stress, the other due to a cancellation of the interacting gravitational fields.

Accordingly, let’s be very clear: An apple is not pulled towards the earth, but neither is it pushed from outer space. The latter (where space is seen as a repulsive force) is just as viable observationally (i.e., we are equally entitled to view the situation as such) as the former to describe gravity. But conceptually it fails in the same way as considering gravity an attractive force generated by mass.

An apple experiences no force at all during its free-fall. It is thus neither lured from below nor shoved from above. So, why on earth (pun intended) do objects plummet in a gravitational field? Implicitly, general relativity describes this phenomenon correctly (without providing a mechanism): the apple follows the path of least action. It follows the geometrical shape of the curved field, falling ‘down’ the slope or gradient of the spacetime manifold.

What follows is that removed from the concept of Newtonian gravitation is (1) the notion of intrinsic ‘force’ that causes objects to accelerate towards an origin O, located at the center of massive bodies. (2) Gravitationally bounded systems in long-term quasi-stable configurations are not maintaining orbits due to the mutual attraction of massive bodies counter-balanced by a fictitious finely tuned centrifugal ‘force.’


It can also be deduced that gravitational curvature is not the 'stretching' of spacetime, but actually a 'compression' of spacetime, since any curvature in the surface results in greater area (not less, as would be the case if spacetime were stretched). This is an important distinction to be made (and to be debated further if need be), since it would appear to imply that the origin of the tension or stress associated with gravity, and more importantly, responsible for curvature (gravity), resides not at the core of massive objects but in the vacuum itself, i.e., the mechanism of gravity bares the hallmark thus of a stress on the spacetime manifold itself, it is directly related to a property of the vacuum itself, as a structural quality of the spacetime manifold. For this reason I see it as essential the relation of local minima (Lagrange points in general) in the grand scope of GR.

An analogy, albeit limited, would be the tension associated with the surface of water (surface tension), as mentioned above in this thread. The indentation and stress surrounding the tip of an insects appendage when gliding upon the surface of a pond is meaningless without regard of the original flat surface from which the deviation from linearity and stress are derived. The weight of the insect determines the depth on the indentation, but it is the surface tension, present wether the insect is there or not, that carries the weight. Surely that original surface is more than a simple starting point from which a measurement can be made. Certainly, it is more than a mathematical artifact, for sure it is more than nothing.

To remove this fundamental ground-state from the picture, would be to ignore the foundation within which all of physics must be based, the stage or foundation within which all interactions, events, happening and phenomenon transpire.

Originally Posted by modest

In short - If we are looking for a reason mass curves spacetime then I don’t see how we’re getting there by looking at areas in the gravitational field that are equal in gravity and inertial acceleration. But, that certainly doesn't mean it can't be done. I'm just giving you my perspective on what you're saying as best I understand it.

We're not looking for the reason mass curves spacetime, we're looking for the reason spacetime is curved in the presence of mass, rather than remaining flat (Euclidean). This is no play on words. In the former it is implicit that 'something' inherent in mass generates gravity. In the latter it is left open other possibilities. In another way, we need to know the exact properties of spacetime both in the presences of mass-energy and in its absence.

Originally Posted by modest

We at least agree the two spots are not the same which means L1 cannot and must not have flat spacetime. Which, by the way, you still haven't acknowledged.

I would hope we both agree that there is a spot between M1 and M2 where the gravitational fields of each body cancel (the gradient is flat), i.e., that there exists a point, a saddle point (surrounded by a field, the geometric structure of which is hyperbolic) located between M1 and M2 where the gravitational field gradient is equal to zero.

There are many references that state this location to be at L1, perhaps for simplicity or lack of rigor.


When we examining this point where the effective potential drops to zero, we find a smooth surface, not a sharp peak. This means that from L1 to the surface of M1 or M2 there is a gradual transition in the gradient that tends from a local minimum value of zero to whatever it might be on the surface of a celestial object. The fact emerges: the gravitational field curvature gradient is different along the M1-L1-M2 line than the potential at, say, an angle 90 degrees. It follows that the field surrounding M1 (and M2) is not spherically symmetrical.

So regardless of the location where an object would remain at rest du to the fictitious centrifugal force, there is an interaction taking place amid the combined fields that is entirely geometric in origin and structure, that impels us to reassess the age-old notion that e.g., the gravitational force of the Moon pulls on the surface of the Earth causing the tides to rise, and that on the other side of the Earth centrifugal force is responsible. The geometric argument reduces the two fictitious effects to one real effect: spacetime curvature.

This will appear nonintuitive for the newcomer, who may argue that gravity has to be greater in the direction of the Moon, not less, otherwise how would the tides rise when the Moon is overhead?

The answer is simple as it is elegant: If indeed the structure of the field is responsible for the rise and fall of tides here on earth then this tells us something more about our beloved G-spot (or lack of G-spot). It tells us that gravity is less intense along the M1-L1-M2-L2 line than it is in all other directions. Less, not more intense. (Less is best)

The binding mechanism associated with the gravitational interaction geometric in origin, and it is directly associated with a weakness in the field, or at the very least, a weakness in the potential between bodies. Thanks to the cancelation of the field between bodies and the resulting field structure in the immediate (and not so immediate) vicinity.

Obviously that's not all. There is something else to be derived from this geometrical conjecture.


To be continued...



CC

[Little Bang]

It seems rather strange that no theory has ever explained mass, charge, gravity, and inertia. I don't have a theory that explains everything but I can suggest a relationship between every one of the four. Gravity is the result of time running slower as a particle falls, inertia is the result of time running faster as a particle is accelerated, mass is related to time(frequency) via f = MC^2/h, and I'd bet my bottom dollar that charge is related to frequency as a result of a waveform or waveforms being turned back in on themselves forming a spinning woveform, something like a dog chasing it's tail. That's my story and I'm sticking to it. Albert spent the last forty years of his life search for a connection between EMR and gravity. He had it all along and I don't understand why he didn't see it. TIME

[modest]

Originally Posted by modest

We at least agree the two spots are not the same which means L1 cannot and must not have flat spacetime. Which, by the by, you still haven't acknowledged.

Originally Posted by coldcreation

While I appreciate you correcting my English, what I was actually going for was: "by the bye" which does sound a little ridiculous when you say it three times really fast. But, I would submit that "any road" (also an acceptable substitute for apropos) is even more ridiculous.



-modest

[coldcreation]

Originally Posted by modest

While I appreciate you correcting my English, what I was actually going for was: "by the bye" which does sound a little ridiculous when you say it three times really fast. But, I would submit that "any road" (also an acceptable substitute for apropos) is even more ridiculous.



-modest

Sorry, my bad.


I'll be back.

[coldcreation]

Originally Posted by Tierradelfuego

Hey, Cold --

"I'm still getting my ducks in a row too. It's not easy."

Yes, I agree ... but I have been waiting a year and a half! :-) I am glad to read your recent postings. You are finally revealing more details on your broad cosmological model (and by "broad", I include the nuclear/subatomic ramifications), in which I believe you have significant insights. But I am dying to read at least a sketch or an outline of your overall picture! Let's get on with it! Naysayers be damned! :-p

Hello Tierra, welcome back. It's been a long time, for sure.

Thanks for your post. Certainly some of the concepts discussed here may be applied to a broad cosmological picture. Particularly since gravity is likely responsible for the existence of the beautiful agglomerations of material, with their wispy tendrils and compact entrails, observed throughout the cosmos. Particularly too since all of these simple and complex, hot or cold, compact or spars, active or passive, stable or unstable, large and small gravitating structures are embedded within the vacuum continuum of space. It is possible that once the mechanism responsible for the gravitational interaction has been identified cosmological implications may surface, along with the nuclear/subatomic ramifications, if any. Let's wait and see.

Originally Posted by Tierradelfuego

I love the idea that the Lagrange points have much overlooked significance...

More generally than Lagrange points I think the properties of 'empty space' (or field-free space, local minima) relative to (and in relation with, via the field) that which occupies space, that have been overlooked to some extent, or at the very least, have been looked at ambiguously at times (particularly the concept of curved spacetime). It is this relation that can be perceived in studying the attributes of maxima and minima (along with saddle point regions), and visa versa.

Originally Posted by Tierradelfuego

To the current dispute ... It seems to me that...understanding...the equivalency principle [is significant] to what you are trying to emphasize. Einstein said in GR -- no difference. No difference. No difference. ...

Sorry for quote-mining. I have attempted to respond to this in a reply-post to modest (see above). There is a big difference between the concept of spacetime curvature and the concept of gravity as an attractive force balance by centrifugal 'force.'

Originally Posted by Tierradelfuego

My qualm -- with respect to a two-body problem (say, Sun-Earth), are you ignoring the solar system's galactic centripetal acceleration (let's assume an ultra-simple model in which the solar system is orbiting a central galactic mass)? So is not L1 merely an approximate saddle point, hence, L1 is not flat with regard to L1's galactic orbit? And so on ... Milky Way's orbit within the local cluster, etc?

The fundamental nature of the Sun-Earth saddle point is not modified by the central galactic mass, aside from slight perturbations in its structure, any more than by the presence of the Moon. One thing is for sure, there are saddle point areas between the solar system and other nearby stellar systems, between the spiral arm and the inner galactic region, between the Galaxy and its companions, between the Local Cluster and the core of the Local Supercluster, between the latter and other distant clusters, and so on.

Originally Posted by Tierradelfuego

However, as one changes to larger and larger frames of reference, does not the Lagrangian points with respect to the objects involved get "flatter" in some "absolute" sense, in the sense of an absolute frame of reference (to the degree that one can employ that concept in a post-Einsteinian cosmology)? And could that be what you are hinting at? For example, in a simple "cluster" of galaxies in which a small galaxy is rotating about a much more massive galaxy, can't the Lagrangian points be described as being "flatter" than the Sun-Earth Lagrangian points? ...

Surely, as the scale under consideration increases and the density decreases, the gravitational field gradient becomes smoother, flatter. There however some very massive objects (and groups of) that likely have steep gradient fields. Note too that even though the field around a saddle point is less intense, the trajectory of a test particle will be in accord with the structure of the saddle point area (large or small, steeply inclined or not).

As far as "flatter" in some "absolute" sense: Flat is flat. There is no flatter. For this reason the distinction between local minima and global minima, relative minima and absolute minima is blurred. So there is no "absolute frame of reference." The closest we can get to an absolute frame of reference is the local (or relative) minima of any given system. Those minima or surfaces would be equivalent to a flat Minkowki spacetime (at least at one point in the field).

Topologically, we have a situation that would appear as a series of troughs, peaks, valleys and planes. Sea level is unattainable, even in an empty universe: There remain residual fluctuations of the lowest possible energy state, the ground energy state) in accord with the laws of nature, i.e., the physical laws.

It could be argued that the absolute zero value of gravitational potential (at infinity) represents by definition an ultimate limit inherent in nature (an absolute minimum value of spacetime curvature) precisely because it is unattainable. It could be argued too that local (or relative) zero value of gravitational potential (located at certain Lagrange points).


Before moving on to a "post-Einsteinian cosmology" (if at all we will: I'm not sure what that means) there are several points to retain:

One-Body (M1): The field of a single object is trivial (but interesting in that it is the simplest case of a gravitational field). If this (say a perfectly spherical star) were the only object in the universe (the Lone Star State ) the field is spherically symmetrical, the gradient of curvature (the gravitational potential) is everywhere the same on its surface. The gradient of curvature falls off inversely and proportionally with the square of the distance away from the objects, in all directions.

Two-Body System (M1, M2): The fields (or gravitational wells) of these each of these objects is no longer spherically symmetrical. The gradient of curvature (the gravitational potential) is NOT everywhere the same on the surface of M1 or M2. The inverse square Law would seem not no hold along the M1-L1-M2 line, since the local gradient falls of to zero near L1. The geometric structure of the combined fields between M1 and M2 is hyperbolic, i.e., there is a saddle shaped structure (in reduced dimension) of the field in the vicinity of L1, or H (see H above). In addition, there are other locations in the combined fields of a co-rotating system where material can coalesce and remain there without accreting onto M1 or M2. Thus there is a potential for the formation of a stable N-body system inherent in the combined field of a rotating two-body system. The pattern created when these areas are occupied is typical of Lagrange dynamics. Upon careful examination, this pattern can be seen in a wide variety of locations inside and outside of the solar system.

Three-Body Systems and N-Body Systems: Upon careful examination, too, alterations of this pattern can be seen in a wide variety of locations outside of the Galaxy. A two-body system can very easily become a three- or four-body system. These alterations of the original patterns occur for a variety of reasons: depending on material flow, material availability, physical scale of the system and especially because once enough mass collects in particular zones (say at L4 and/or L5) the gravitational well of the new body (or group of objects) interacts with the field of M1 and M2, creation new L1 points and new L4 and L5 zones, where more material can collect, and so on increasing in complexity. Examples of some of these systems are reproduced above. They range in location from local stellar clusters (e.g., Pleiades), galactic nuclei, active galactic nuclei, barred galaxies, barred spiral galaxies, associated objects (e.g., quasars) thought to be gravitationally lensed (e.g., Einstein Cross), to galaxy clusters and galactic superclusters.

Originally Posted by Tierradelfuego

I think that I see bits and pieces of the whole picture. I am dying to read an explanation from you for how your model explains the discordant redshifts. ...

Note Tierra: These patterns (seen reproduced throughout this thread) can be observed in systems that are known to be associated, as well as in systems that display discordant redshifts (I have intentionally avoided these: the Einstein Cross being the exception). The ubiquity of such Lagrangian systems suggests that the physical mechanism involved must be directly related (inextricably attached) to the concept of gravity (spacetime curvature) as described by general relativity (thus cosmology); and so must also be attached to the fundamental laws of nature (the physical laws).





CC

[modest]

Originally Posted by coldcreation

Sorry, my bad.


I'll be back.

I honestly didn't mind

Awaiting your return,

-modest

[coldcreation]

Originally Posted by coldcreation

It has become increasingly apparent that the laws of nature (to which the physical mechanism of gravity must be attached) are most eloquently expressed in terms of a minimum principle (as opposed to a maximum principle) that opens the way to a quasi-complete understanding of a particular phenomenon or aspect of nature (notably that of gravitation).
...

The conclusions follow: ... see above.


So, in setting a limit to the gravitational field curvature (the local minima) and recognizing the dynamical importance of such, three things are accomplished and a fourth eliminated:

CC

Continued from above:

So, in setting a limit to the gravitational field curvature three thing are accomplished and a fourth eliminated:

1. Gravity (spacetime curvature) can now be understood in terms of stress or tension in an otherwise flat, Euclidean, gravity-free spacetime that carries with it the propensity to depart from linearity in the presence of massive bodies.

2. The mechanism behind the cosmological constant (lambda) is elucidated in physical terms: it describes the properties of a state where the gravitational spacetime curvature in the combined field of massive objects cancels out, decreases to zero (at Lagrange points), a gravity-field-free state, the pure and natural absolute vacuum state.

3. The velocity of objects in orbit is not due to a finely tuned initial condition with a cancellation of gravity and centrifugal force. Objects in orbit (stars around a galaxy, etc.) can remain in orbit whether they are moving more quickly or more slowly than would otherwise be allowed under the mainstream Newtonian view. Nonbaryonic dark matter, supermassive black holes, BHs, and other speculative ‘exotic’ reveries are no longer needed to explain rotational curves that defy conventional wisdom. Likewise, the inexplicable fine-tuning between the outward thrust of pressure to counter the gravitational pull in cases where rotational velocities are too slow or nonexistent is no longer required.

4. Lambda is no longer considered a parameter the value of which can be positive, negative, or equal to zero depending on a particular model, but is now considered the absolute zero of spacetime curvature. An undetectable repulsive force (or negative pressure) has been removed from the vacuum, thus, eliminating the need for new physics.


Why bring Einstein's cosmological constant (lambda) into the mix?

That will be the subject on the next few posts...

[modest]

I believe my two main critiques have been worked out.

1. Lagrange points do not have zero potential
2. Spacetime is not flat at L1

Which leaves only the question of stability. From quotes like this:

Originally Posted by coldcreation

With this in mind, my distaste for centrifugal force (namely the way it artificially balances, or cancels precisely, the gravitational force, leading to a fine-tuning problem inherent in celestial mechanics) can be satisfied. I don't have to swallow it.

It looks like you are saying L-points are stable in your way of thinking. I insist only L4 and L5 are stable. And, that is not a permanent stability as it relies on the stability of M1 and M2 where GR’s equations of motion do not allow permanent stability. So, I think it would be good to expand on that just a bit. I hope I’m not sidetracking you too badly here, but the quote above looks wrong to me. It would be a fine tuning problem to settle something at L1 or L2 by my way of thinking.

-modest

[snoopy]

Hi everyone,

I would just like to say that I believe a final theory of gravity would explain its fractal nature... why galaxies look like they do , terrain of planets and trees for example.

I am not sure your theory can do this.

If you are using the gravitational langrangian then you must also use the matter lagrangian with increasing powers of curvature.

The couplings ci are dimensionless and in matrix elements the expansion will
be of the form 1 + Gq2ci.

In a theory where gravity is the only low
energy interaction, a point particle would be expected to have di of order
G. However for interacting theories or composite particles the coefficients
can be much larger. In matrix elements of the energy momentum tensor, di
play the role analogous to the charge radius..

This leads to ever more complexity and you end up with an unworkable theory

or a theory that looks like +...+...+ etc ad infinitum
ie you end up with infinties unless you just keep it simple and avoid complex gravitiational situations.

Just some thoughts.

Peace