6 Degrees of Separation: Order from Chaos

[Shadowself]

You're killing me! (I'm gonna get indigestion from all this popcorn)

Have to stop and fix something to eat and another pot of coffee is in the making as well!

I promise today is the day I finish this.

[Shadowself]

So here it goes...

CTC's or Closed Timelike Curves:

If CTCs exist, their existence would seem to imply at least the theoretical possibility of time travel backwards in time, raising the spectre of the grandfather paradox, although the Novikov self-consistency principle seems to show that such paradoxes could be avoided.

In "simple" examples of spacetime metrics the light cone is directed forward in time. This corresponds to the common case that an object cannot be in two places at once, or alternately that it cannot move instantly to another location. In these spacetimes, the worldlines of physical objects are, by definition, timelike. However this orientation is only true of "locally flat" spacetimes. In curved spacetimes the light cone will be "tilted" along the spacetime's geodesic.

For instance, while moving in the vicinity of a star, the star's gravity will "pull" on the object, affecting its worldline, so its possible future positions lie closer to the star. This appears as a slightly tilted lightcone on the corresponding spacetime diagram. An object in free fall in this circumstance continues to move along its local axis, but to an external observer it appears it is accelerating in space as well—a common situation if the object is in orbit, for instance.

A closed timelike curve can be created if a series of such light cones are set up so as to loop back on themselves, so it would be possible for an object to move around this loop and return to the same place and time that it started. An object in such an orbit would repeatedly return to the same point in spacetime if it stays in free fall. Returning to the original spacetime location would be only one possibility; the object's future light cone would include spacetime points both forwards and backwards in time, and so it should be possible for the object to engage in time travel under these conditions.

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Okay then...I've highlighted in Blue the important things to recognize about CTC's.

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Next:

Now I know for fact that I have mentioned this in this thread. But I failed to recognize its significance.

1) The n-body problem

In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally.

Solving this problem has been motivated by the desire to understand the motions of the Sun, Moon, planets and the visible stars. In the 20th century, understanding the dynamics of globular cluster star systems became an important n-body problem.

The classical physical problem can be informally stated as:

Given the quasi-steady orbital properties (instantaneous position, velocity and time) of a group of celestial bodies, predict their interactive forces; and consequently, predict their true orbital motions for all future times.

Knowing three orbital positions of a planet's orbit, he was able to produce an equation by straightforward analytical geometry, to predict a planet's motion; i.e., to give its orbital properties: position, orbital diameter, period and orbital velocity. Having done so, he and others soon discovered over the course of a few years, those equations of motion did not predict some orbits very well or even correctly. Newton realized it was because gravitational interactive forces amongst all the planets was affecting all their orbits.

The above discovery goes right to the heart of the matter as to what exactly the n-body problem is physically: as Newton realized, it is not sufficient to just specify the initial position and velocity, or three orbital positions either, to determine a planet's true orbit: the gravitational interactive forces have to be known too. Thus came the awareness and rise of the n-body "problem" in the early 17th century. These gravitational attractive forces do conform to Newton's Laws of Motion and to his Law of Universal Gravitation, but the many multiple ( n-body) interactions have historically made any exact solution intractable. Ironically, this conformity led to the wrong approach.

Newton concluded via his third law of motion that "according to this Law all bodies must attract each other." The existence of gravitational interactive forces, is key.

The problem of finding the general solution of the n-body problem was considered very important and challenging.

In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prizeworthy. The prize was awarded to Poincaré, even though he did not solve the original problem. (The first version of his contribution even contained a serious error). The version finally printed contained many important ideas which led to the development of chaos theory.

https://en.wikipedia.org/wiki/N-body_problem

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So why is this important? It brings you to:


2) The Two-body problem



Any discussion of planetary interactive forces has always started historically with the two-body problem.

In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other. Common examples include a satellite orbiting a planet, a planet orbiting a star, two stars orbiting each other (a binary star), and a classical electron orbiting an atomic nucleus (although to solve the electron/nucleus 2-body system correctly a quantum mechanical approach must be used).

The two-body problem can be re-formulated as two one-body problems, a trivial one and one that involves solving for the motion of one particle in an external potential. Since many one-body problems can be solved exactly, the corresponding two-body problem can also be solved. By contrast, the three-body problem (and, more generally, the n-body problem for n ≥ 3) cannot be solved in terms of first integrals, except in special cases.

https://en.wikipedia.org/wiki/Two-body_problem

Which brings us to the:

3) The Three-body Problem


In physics and classical mechanics, the three-body problem is the problem of taking an initial set of data that specifies the positions, masses, and velocities of three bodies for some particular point in time and then determining the motions of the three bodies, in accordance with Newton's laws of motion and of universal gravitation, which are the laws of classical mechanics. The three-body problem is a special case of the n-body problem. Unlike two-body problems, there is no general closed-form solution for every condition, and numerical methods are needed to solve these problems.

Historically, the first specific three-body problem to receive extended study was the one involving the Moon, the Earth, and the Sun. In an extended modern sense, a three-body problem is a class of problems in classical or quantum mechanics that models the motion of three particles.

In 1911, United States scientist William Duncan MacMillan found one special solution. In 1961, Russian mathematician Sitnikov improved this solution.

The Sitnikov problem is a restricted version of the three-body problem named after Russian mathematician Kirill Alexandrovitch Sitnikov that attempts to describe the movement of three celestial bodies due to their mutual gravitational attraction. A special case of the Sitnikov problem was first discovered by the American scientist William Duncan MacMillan in 1911, but the problem as it currently stands wasn't discovered until 1961 by Sitnikov.

https://en.wikipedia.org/wiki/Three-body_problem

https://en.wikipedia.org/wiki/Sitnikov_problem

Thus...Configuration of the Sitnikov problem



Look familiar yet? Let me help you...



But that is not all...more to come with this equation and CTC's

[Shadowself]

In the post I just made: CTC's

As I noted in the last post I highlighted certain portions to be noted.

CTC's: In these spacetimes, the worldlines of physical objects are, by definition, timelike. However this orientation is only true of "locally flat" spacetimes. In curved spacetimes the light cone will be "tilted" along the spacetime's geodesic.



Let's look at the tomb from another view, in specific that portion...



you'll note not only 3 stars noted in 2 sections but a tilted view of three stars in section as highlighter here.



Well that's interesting...

In curved spacetimes the light cone will be "tilted" along the spacetime's geodesic.


But what about the Three-body problem? Specifically the Sitnikov problem


The system consists of two primary bodies with the same mass {\displaystyle \left(m_{1}=m_{2}={\tfrac {m}{2}}\right)} \left(m_1 = m_2 = \tfrac{m}{2}\right), which move in circular or elliptical Kepler orbits around their center of mass. The third body, which is substantially smaller than the primary bodies and whose mass can be set to zero {\displaystyle (m_{3}=0)} (m_3 = 0) moves under the influence of the primary bodies in a plane that is perpendicular to the orbital plane of the primary bodies.

The origin of the system is at the focus of the primary bodies. A combined mass of the primary bodies {\displaystyle m=1} m=1, an orbital period of the bodies {\displaystyle 2\pi } 2\pi , and a radius of the orbit of the bodies {\displaystyle a=1} a=1 are used for this system. In addition, the gravitational constant is 1. In such a system that the third body only moves in one dimension – it moves only along the z-axis.

Significance?

Although it is nearly impossible in the real world to find or arrange three celestial bodies exactly as in the Sitnikov problem, the problem is still widely and intensively studied for decades: although it is a simple case of the more general three-body problem, all the characteristics of a chaotic system can nevertheless be found within the problem, making the Sitnikov problem ideal for general studies on effects in chaotic dynamical systems.


Now...for those who may be unaware because they have not read this thread. I spent a significant amount of time describing the bottom half of the tomb ceiling and it's specific association to CHAOS THEORY...specifically dynamical systems in CHAOS THEORY. hence the title of the thread itself!


So does the N Body Problem or three-body problem, CTC's and traversable wormholes even have a reference point?



Check it:

The two-body problem in geometrodynamics

Abstract

The problem of two interacting masses is investigated within the framework of geometrodynamics. It is assumed that the space-time continuum is free of all real sources of mass or charge; particles are identified with multiply connected regions of empty space. Particular attention is focused on an asymptotically flat space containing a “handle” or “wormhole.” When the two “mouths” of the wormhole are well separated, they seem to appear as two centers of gravitational attraction of equal mass. To simplify the problem, it is assumed that the metric is invariant under rotations about the axis of symmetry, and symmetric with respect to the time t = 0 of maximum separation of the two mouths. Analytic initial value data for this case have been obtained by Misner; these contain two arbitrary parameters, which are uniquely determined when the mass of the two mouths and their initial separation have been specified. We treat a particular case in which the ratio of mass to initial separation is approximately one-half. To determine a unique solution of the remaining (dynamic) field equations, the coordinate conditions g0α = −δ0α are imposed; then the set of second order equations is transformed into a quasilinear first order system and the difference scheme of Friedrichs used to obtain a numerical solution. Its behavior agrees qualitatively with that of the one-body problem, and can be interpreted as a mutual attraction and pinching-off of the two mouths of the wormhole

https://www.sciencedirect.com/scienc...03491664902234

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I think the boys at CERN might think so...N Body and particle physics...and CTC's

Solving The N-Body Problem in (2+1)-Gravity

I'm going to image and present specific sections of this paper presented at CERN























And you get the gist....from here: http://cds.cern.ch/record/292146/files/9511207.pdf



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Now I would say gravitational movement would be extremely important in stabilizing a wormhole. What's more I've in fact taken three body's here... Aldebaran...Jupiter...and Earth to coordinate a specific system with a generating planet such as Jupiter. You know the freaky fluid that exists in it that would in fact be a marvelous generator for such a system set up.

As there is more to add later to this it is indeed the end of the impending proof of 99.999999% proof that this indeed is a sample of the unproven paradox theorem that is most possible and probably as to the placement of Orion as the Key to the equation.

I digress....hope you all understood all that as sometimes I'm not certain that I explain things well.

Source: https://www.youtube.com/watch?v=JwYX52BP2Sk

[Emil El Zapato]

"A closed timelike curve can be created if a series of such light cones are set up so as to loop back on themselves, so it would be possible for an object to move around this loop and return to the same place and time that it started. An object in such an orbit would repeatedly return to the same point in spacetime if it stays in free fall. Returning to the original spacetime location would be only one possibility; the object's future light cone would include spacetime points both forwards and backwards in time, and so it should be possible for the object to engage in time travel under these conditions."

And that is the big buzzkill. Among an uncountable infinity of possible locations the chance, is that old near zero probability, that one would return home. Under those conditions time travel is not only possible it is inevitable...

[Shadowself]

Ah! I found a video to describe the the Sitnikov problem

Note the center body and it's reference to Time. Note the fluid dynamics involved and you do indeed have this:

Source: https://www.youtube.com/watch?v=ckoMPBVHUD4


Explained very well here So much so you can actually see the wormhole dynamics displayed and reference to chaos theory::

Source: https://www.youtube.com/watch?v=lis6y6fqjtk

[Dreamtimer]

The fourth dimension is less than six degrees away, right?

Source: https://www.youtube.com/watch?v=eGguwYPC32I


To Infinity...and Beyond!

[Emil El Zapato]

I just saw Aragorn's lost wallet

One thing I learned recently is that some 'scientists' equate Degrees of Freedom and dimensions... I don't see it that way. It is similar to the concept of a 'vector measure' and 'magnitude measure'. They can be measured with the same units but they are very different in nature. hmmm, but also Einstein's 4th dimension, theoretically is a measure of time...simply put, it is a 'difference in time' that comprises the 4th coordinate. (but some scientists differ in their interpretation) suggesting that time is not a single dimension but rather an emergent property of multi-dimensionality...so in the end...I certainly don't know what is or isn't.

age really doesn't matter until one gets old anyway...He be born that way...

[Aragorn]

I just saw Aragorn's lost wallet

Was there anything left inside of it? Because the one I have now is pretty empty.

[Emil El Zapato]

no, nothing changed... lol...

[Aianawa]

Since we NZ is in lockdown again, i can research strongly and feel to research dear Shadowself's thread here, early ones especialllly, feels pearls there may be.

Keep going guys!

No wrong answers here. All taken into consideration. I'll be reading here for a few days. Then over the weekend I'll continue on.

Thanks for the great reply so far!

Consider this: Six degrees of separation...and Chaos. What's the connection?

Remember...no wrong answers here.

I'll leave this to ponder:

Source: https://www.youtube.com/watch?v=2rzxAyY7D7k


Enjoy!

Maybe so so much more important Now.

[Dreamtimer]

Makes one wonder who they'll see just around the corner...

[Aianawa]

Oh yes, indeed