Physical Mechanism of Gravity - the Spatiotemporal Ground-State

[coldcreation]

I'm not aware of these "Trojan" objects, do you have a link.

 

Time is not a *solution* to gravity, but there is undeniable interplay. Afterall, why else would gravity be measured in terms of meters per second squared?

 

In this post there is a link that explains the situation very well, regarding objects located at the Jupiter-Sun L4 and L5 points.

 

Yes, space and time are inseparable one from the other. Time is thus linked to the physical mechanism of gravity.

[modest]

That measurement is acceleration due to gravity, not gravity itself.

 

Force is measured by its effect - always.

 

-modest

[freeztar]

That measurement is acceleration due to gravity, not gravity itself.

 

Yes, you are correct, gravitational acceleration. Though, without gravitons, there can be no direct measurement.

[Little Bang]

CC, I have painted myself into a corner. We have shown the collision of electromagnetic energy can create an electron positron pair (the Stanford linear accelerator experiment) and by extension a proton negatron pair. We can explain gravity as a function of a slowing clock. The observed red shift as a function of the expansion of space at C and a point from which all the energy of the universe can come. The problem is that I can not find a way for time to ever reach zero which would release all that energy.

[modest]

The problem is that I can not find a way for time to ever reach zero which would release all that energy.

 

Do you want time to reach zero as in T=0, as in follow the scale factor back in time to T = 0? Or, do you want time dilation to be infinite as you alluded to in your last post? Time dilation is infinite at the cosmological horizon.

 

-modest

[Little Bang]

Time is a variable and how fast time runs is totally dependent upon the strength of the gravity well in which it is measured. Suppose that we could measure how fast or slow time moves on every proton in the universe and average those times. We would then have an average time for the present day universe. Now let's go back in time to when the universe was only one percent of it's present size. The average time there would be 99% slower than today. Now we go back to the instant before the Big Bang (assuming there was one) the gravitational field strength would have been approaching infinity. How do I turn gravity off so that the Big Bang can happen? One way would be if time did completely stop.

[freeztar]

Yes, but the point that I was making was that gravity and acceleration are not the same thing (and no, the equivalence principle in relativity does not say they are the same thing) .

 

You are correct, gravity and acceleration are not the same thing.

I didn't even mention the equivalence principle.

 

The strength of a gravitational field is typically measured in newtons, not in m/s/s.

 

Of course, once mass is factored in. Note that the equation for a newton is [math]{kg}*{m}/{s}^2[/math]. ;)

My original point was that time is factored into gravity.

 

EDIT: I can't believe I forgot to say this, but also; that statement you listed is not really true.

Remember, I said "directly" measure.

I can know precisely the gravitational pull of an object without ever having to know it's acceleration.

 

What is the gravitational "pull" of a fortune cookie? :hyper:

 

There is no need for gravitons (the actual existence of such particles has not been determined yet in any case).

 

Of course.

I really think we are on the same page here.

 

So, rather than continue to distract from the topic, I suggest we focus on CC's ideas. What do you think of them?

[modest]

Time is a variable and how fast time runs is totally dependent upon the strength of the gravity well in which it is measured. Suppose that we could measure how fast or slow time moves on every proton in the universe and average those times. We would then have an average time for the present day universe. Now let's go back in time to when the universe was only one percent of it's present size. The average time there would be 99% slower than today.

 

I have 2 problems with this LittleB. Craig pointed out the first: what you are saying is only true from the perspective of someone outside the universe. As I fall into a gravity well, my clock doesn't slow - not from my perspective. Why would the evolution of the universe be any different?

 

My second problem is the mechanics of the thing you describe. Gravitational time dilation exists between frames of differing spacetime geometry. I know from everything I've read that the global geometry of the universe shouldn't change over time. I'm unable to prove this true - it's certainly a gray area for me. But, I could give you 10 sources saying that a homogeneous universe that follows GR does not change its geometry over time. If this is true then we can't think of this kind of time dilation gravitationally.

 

I think your perspective on this is clever. But, ultimately not really the correct way to look at it.

 

-modest

 

//edit: this belonged in the 'bang or no bang' thread - sorry

[modest]

Anyways, regarding CC, he is right about one aspect of the Lagrange points. Any object in a stable Lagrange point will tend to stay there; in fact, even if you move it a little, it will actually drift back into the Lagrange point (if it is unstable, the slightest nudge will push it away...).

 

You're half right.

 

I should also note, from a quick glance, that another thing that he tends to do is references his own threads,

 

For the benefit of those who have not followed everything previously established, maybe

 

http://hypography.com/forums/astronomy-cosmology/14212-dynamic-equilibrium-universe-subsystems-6.html#post213579

:D

 

-modest

[Little Bang]

I owe CC an apology. Apparently there are stable Lagrangian asteroids. Could there be a stable Lagrangian asteroid that does not have spin?

[Little Bang]

Modest, I did not fully explain your question. I was not referring to T=0. If we look at the theoretical singularity before the BB, time is still running but so slowly as to be almost immeasurable.

[coldcreation]

Check this out.

Jupiter-Sun Lagrange points, by Petr Scheirich, 2005

 

The L4 and L5 zones are filled with asteroids (green dots)

 

Note, particularly, what is transpiring at L1 and L2 (the position and flow of objects is represented by pink dots) directly opposite the sun from Jupiter, and between Jupiter and the sun. These locations are not devoid of matter. Quite the contrary. Interesting!

 

 

 

CC

[Little Bang]

Excellent find CC. what do the green dots represent?

[coldcreation]

Excellent find CC. what do the green dots represent?

 

The Trojans move around these points much as a marble oscillates around the bottom of a smooth bowl. This movie shows the Trojans as they orbit around the Sun with Jupiter. The Trojans are in green' date=' and the Hildas (another asteroid group) are shown in red.[/quote']

 

Check this one out...

 

This movie is the same as the previous one' date=' but with the frame rotating so that Jupiter stays in place[/url']. This shows how the Trojans move about the Lagrange points.

 

 

CC

[Little Bang]

Wow, even more interesting.

[coldcreation]

The illustration below represents a saddle point (or Lagrange L1 point region: L1 is at the center), from here and enhanced with different colors.

 

 

 

 

The lines of force are shown in blue. M1 and M2 are located to the left and right, more or less centered inside the red contour lines (which are spherical shells, gravitational wells). We are looking at a cross section of a plane of a two-body system. L4 and L5 are not considered in this diagram.

 

Notes:

 

1. There is no arrow at L1 since there is no gravitational force at that point, i.e., the fields of M1 and M2 cancel at L1. Directly at this junction, L1, a test particle at rest will experience no net acceleration—consequently, the net gravitational force is zero at L1. Note that the cancellation of the gravitational force field at L1 is not due to the balance between an attractive force and the centrifugal acceleration away from the orbital axis. It is due to the equivalence of the value of curvature at this intersection.

 

2. This saddle point is a hyperbolic point on a 3D surface (and 4-D when time is added to the mix). It is thus a point or area with 'negative' Gaussian curvature.

 

3. When M1 and M2 are of identical mass there is a plane (a flat disc) perpendicular to the M1-L1-M2 line where all the lines of force located on this plane point towards L1, i.e., a test particle placed on this plane will gravitate towards L1 (not towards M1 or M2 unless it is displaced off the plane). What we have, in effect, is a Lagrangian plane, or Lagrange surface, similar to the membrane connecting double bubbles (see here).

 

4. When M1 and M2 are of unequal mass there is a curved plane (or surface) between the two bodies, the lines of force on which point towards L1.

 

Conclusions:

 

Depending on the scale and complexity of this system, objects such as particles, stars or even galaxies, may move along the Lagrange plane towards L1 where interactions or hadronic collisions are possible and even likely. In the case of interacting stars (at L1) the result would be explosive, to say the least. Some of the material left over from such a collision would gravitate ballistically towards M1 or M2. The result would be seen as 'jets' of relativistic plasma consistent with synchrotron radiation produced in a shock-region where infalling material compresses the magnetic field and accelerates the relativistic particles. Strong linear polarization would also be observed.

 

Some of the material would remain poised in an unstable or chaotic orbit around L1 (see illustration here).

 

These remaining 'objects' would be recognized as active galactic nuclei, `radio halos', compact radio sources or X-ray sources. These objects may also possess characteristics of binary AGN X-shaped radio sources (see the third illustration in this post). Active galaxies located at these types of saddle points may be seen to eject large volumes of relativistic plasma over several dynamical timescales.

 

Saddle points are thus far from empty voids. They may be the sight of very active phenomena, always lined up along an axis and flanked by massive bodies or aglomerations (M1 and M2).

 

 

To be continued...

 

 

 

CC

[coldcreation]

Lagrange predicts that L4 and 5 are stable while L1, 2, and 3 are not. This prediction got verified when the trojan asteroids were found at Jupiter's 4 and 5 points. It got verified again with human missions to L1 and 2.

 

Given that, what do these images show and how is Lagrangian mechanics key to the situation or question? Lagrange's method is equivalent to Newton's second law in any situation. Neither give a mechanism for gravity.

 

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).

 

 

Here we get right down to the core of the physical mechanism of the gravitational interaction. What is the relationship between Lagrange points, general relativity, and the physical mechanism of gravity?

 

 

A quick recap: In all gravitating systems, there are present areas, or points, of relative maxima and minima of the field curvature, potential, strength, force, intensity or dynamic stress. The maxima are located at the center point of massive bodies, and minima located where the effective relative gravitational potential vanishes (here we include saddle points, which by definition may not be minima, but where nevertheless the local potential is reduced to zero, i.e., combined gravity fields cancel to zero). These extrema of the combined fields of massive bodies are not polar opposites (some region attractive and others repulsive). The opposite of gravity is not spacetime curvature with a different sign (nor is it negative pressure), it is spacetime without curvature. So we could say that it is the tension in space between and around material objects that results in the gravitational field curvature. Gravity is a departure from linearity.

 

 

The opposite of gravity is NO gravity.

 

 

In another way, when reflecting upon gravity (spacetime curvature) we cannot neglect another important aspect of the field: where the gradient is flat. The field structure surrounding these points is often hyperbolic, i.e., in the case of saddle points (L1) the lines of force point outward along the M1-L1-M2 line and inward in a perpendicular direction (see illustration in previous post). Interestingly, massive objects can collect at the minima as well, and remain there in a quasi-stable equilibrium configuration. Interestingly, too, this field-free state can be associated (inextricably linked even) with Einstein's cosmological constant, lambda (more on this to come).

 

Space itself is not the ‘nothing’ once suspected, that could expand or contract endlessly, that could curve to infinity in the deep end or diverge to a false vacuum in the shallow end. Spacetime has very specific qualities; properties that do have limits and that do play a key role in the maintenance of equilibrium. Massive objects cannot collide (under ordinary situations) or fuse like globs of goo in a lava-lamp because they were orbiting too slowly: L1 prevents that. Objects do not wander off aimlessly into extragalactic space (again under ordinary situations) because their velocity was slightly too quick to maintain stability: L2 and L3 prevent that, with a little help from L1.

 

The motion, locations and values of the peaks and wells throughout N-body systems are far from random. For any given resonance in Hamiltonian systems there are always pairs of stable and unstable periodic resonant orbits (the latter of which may function as halo orbits). In two-body systems there are five Lagrange points, L1 – L5. In three-body systems (e.g., the earth-sun-moon system) there are ten, etc (and that is not including the possibility that there are also L-points created between the moon and sun, however stable and significant they may be).

 

Resonance contributes to the formation of deep and shallow wells and peaks in the manifold potentials throughout the entire solar system phase space forming a complex, evolving structure. These overlaying multiple gravitational resonances generate both chaos and order. Gravitational resonances contribute both large and small orbital changes while providing protection zones from large perturbations. The stability and longevity of all gravitating systems results from the dynamics of gravitational mean motion resonance patterns created naturally as a result of an interplay between maximum and minimum gravitational potentials in the combined fields of orbiting massive bodies. Mean motion resonances may lead to large changes in the orbits of one or more massive objects, or may enhance orbital stability, depending on the characteristics (mass, density, distance, velocity, complexity) of the gravitating N-body system. Laplace was the first to find solutions to the Newtonian problem of stability of celestial objects (or lack thereof) and recognized the importance of such resonance patterns in the stability process.

 

 

Earlier renderings of the field 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 (or centripetal acceleration of an object moving around a circle) and the attraction of gravity (gravitational acceleration) were finely tuned by some initial condition. The problems with this interpretation are many; one of which is that the more numerous the components of the system, with its increasing intrinsic complexity and chaoticity, the more the system becomes unstable, and the natural symmetry is replace by artificial symmetry (e.g., GR needs to be supplemented with nonbaryonic cold dark matter).

 

 

So the violence that haunted Newtonian mechanics (with its attractive gravitational force) has been replaced by Einstein's general postulate of relativity (at its most lyrical stage: before lambda was looked upon with utter contempt) intermixed with the joyous geometry of Lagrange dynamics leading to exquisitely balanced self-gravitating configurations. So far, so cool.

 

 

In contrast to curved spacetime, the points of zero curvature (the Minkowski manifold) act as if the vacuum were repulsive (at least from one view-point), without truly being so (just as massive objects act as if they were attractive (again, from at least one point of view)). There is a net balance that occurs naturally between massive bodies, the surrounding field and the ‘peaks’ in the field called L-points (here we include saddle points). That is, to say that field-free space is repulsive would be inaccurate, just as gravity being an attractive force is inaccurate. The correct way of describing gravity and field-free space consists of combining three concepts: massive objects, field, vacuum, or equivalently, matter, curvature and gravity-free space (L-points), where the latter corresponds to a fundamental ground-state associated with the ultimate limit of malleability (curvature-free) of pure spacetime. Gravity is thus the curvature of spacetime (in the presence of matter) that would otherwise be flat (or very nearly so).

 

In this sense, the Lagrange points (again, particularly L1) play a crucial role in the stability or equilibrium of self-gravitating systems as well as, and more generally than previously assumed, the equilibrium of systems in relation to other systems often far removed spatiotemporally, i.e., rather than being a restricted phenomenon associated with two- or three-body systems, there is a general, ubiquitous, contribution to systems of any number of bodies.

 

 

 

The conclusions follow:

 

The state described by the Minkowski manifold is irreducible: Space cannot be emptied further, flattened further, stretched further than the 'standard zero condition' - to paraphrase Eddington's words regarding Einstein's cosmological constant - will allow. There exists a fundamental state, ubiquitous in spatiotemporal extent, within which all constituents (such as, elementary building blocks and nest of forces; defined as elementary particles, atomic nuclei, atoms, molecules, ions, and field, such as electromagnetic fields: along with the properties energy, entropy) subsist and within which all events and phenomena transpire.

 

The mechanism behind the gravitational interaction is obligatorily linked to 'empty' space, the substratum or ground-state. This same mechanism (as we will see below) is responsible for the underlying symmetries of the real world. So generalities regarding this state (or four-dimensional field-free surface) cross the boundary of applicability of GR to the domain of quantum mechanics (since, like massive gravitating bodies, particles are embedded within the same 4-D spacetime manifold).

 

Gravitational systems remain in stable and quasi-stable equilibrium configurations due to the interplay, or stress, between massive bodies and Euclidean or Minkowski space (which in the presence of objects is compressed, curved), a kind of surface tension.

 

Lambda (Einstein’s cosmological constant) can be explicated in physical terms, its mechanism along with that of gravity can be confirmed without the introduction of new physics or ad hoc assumptions (more on that to come).

 

The inexorable concept that the force of gravity would pull on every particle in the universe causing it to collapse under its own weight is done away with. The weight of the observational evidence supports the idea that quasi-equilibrium configurations are generated naturally via the interplay between areas, zones or points of local (or relative) maxima and minima gravitational field potentials: the minima being consistently equal in relative field potential value: zero. Thus the natural zero minimum value is fundamentally constant. In other words, the zero value of gravity is associated with a fundamental constant of nature.

 

Prior to the introduction of this fundamental limit it was thought that spacetime could be curved indefinitely, not just in the direction of maximum gravitational potential (in say, a supermassive black hole), but too in the opposite direction: on the other side of the Euclidean plane (in reduced dimension, of course) was just another type of curvature (often erroneously called a false vacuum, negative pressure, dark energy, lambda, the cosmological constant, antigravity, or vacuum energy density). The effect of this state in relation to gravity was always the same: it acted in opposition to the attractive effects of gravity, i.e., as a repulsive force.

 

The spurious contention that lambda is a repulsive force, dark energy, or negative pressure has to be abandoned immediately if celestial mechanics is to advance further or if we are to understand the evolution of the cosmos. Two of the problems with this state are that it can never be detected empirically, thus the term ‘dark’ energy, and it always requires new physics (something that is not physics). More on this to follow...

 

The combined concepts of general relativity with the Lagrange principle results in the elucidation of the mechanism not only of lambda but also of gravitation itself.

 

So what causes spacetime curvature, i.e., what is the physical mechanism of the gravitational interaction?

 

 

 

 

Chandra X-ray Image of Stephan's Quintet (detail) reworked and enhanced beyond its original splendor with artificial colors by Coldcreation. From here.

 

Chandra X-ray Image of Stephan's Quintet' date=' Close-up. The shock-heated gas in Chandra's X-ray image of Stephan's Quintet has a temperature of about 6 million degrees Celsius. The heating is produced by the rapid motion of a spiral galaxy intruder located immediately to the right of the shock wave in the center of the image. Scale: 2.9 x 2.3 arcmin[/quote']

 

 

 

I have made it a point throughout this thread to show that there is arguably a characteristic dynamical pattern related to a specific mechanism operational at all scales and at all energy levels (i.e., present in active galactic nuclei, barred galaxies, galaxy-QSO associations, galactic clusters, as well as here in the solar system): that pattern is associated with the local minima (add saddle point regions) of gravitational potential, and is consistent with a geometric dynamical explanation of formation, ordered structural characteristics, long-term stability or sustainability of systems bounded under the sole influence of gravity. It is from this classical Lagrangian starting-point that the mechanism behind the gravitational interaction must be considered, in association with general relativity, and from the ground-state up, if resolution to the problem is to be attained.

 

To understand gravity we must first consider spacetime in the absence of gravity, then ask ourselves; what changes when gravity is introduced? Or; how is spacetime modified when massive objects are introduced into the field? And likewise; what changes when a massive object is removed from the field? Note that in each of these questions there emerges a need to compare gravity with a space free-of-gravity, to compare spacetime curvature with flat space, Essentially we need to compare the local maxima and the local minima of the gravitational field potential for any given space, where the local minima is naturally, and always, equal to zero potential.

 

 

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:

 

 

 

That, and a further discussion of the actual mechanism behind the gravitational interaction are the topic of the rest of this thread...

 

 

 

 

CC