When Black Holes Collide

See also: What Happens When Black Holes Collide? - Kip Thorne

 

Inside Einstein's Mind

See Also: Inside Einstein's Mind | NOVA - PBS Documentary 

The LIGO and Virgo Gravitational-Wave Detectors

An artist's impression of two stars orbiting each other (left). The orbit shrinks as the system emits gravitational waves (middle). When the stars merge (right), there is a resulting powerful emission of gravitational waves. [Image: NASA]

The LIGO and Virgo gravitational-wave detectors have been hunting for signals from the collisions of neutron stars and black holes, which are dense objects formed from the remains of stars many times more massive than our Sun. When two of these objects orbit each other in a binary system, the emission of gravitational waves will gradually carry away some of their orbital energy, forcing them to get closer and closer together. This happens slowly at first, but as the orbit gets tighter the gravitational waves get stronger and the process accelerates until eventually the stars collide and merge, emitting in the last few seconds one of the most powerful outflows of energy in the Universe. See: What gravitational waves can tell us about colliding stars and black holes

The LIGO Hanford Control Room

LIGO's mission is to directly observe gravitational waves of cosmic origin. These waves were first predicted by Einstein's general theory of relativity in 1916, when the technology necessary for their detection did not yet exist. Gravitational waves were indirectly suggested to exist when observations were made of the binary pulsar PSR 1913+16, for which the Nobel Prize was awarded to Hulse and Taylor in 1993.

The Binary Pulsar PSR 1913+16:

See Also:

•  Advanced LIGO -- The Next Step in Gravitational Wave Astronomy

Energy Boost From Shock Front

Main Components of CNGS

A 400 GeV/c proton beam is extracted from the SPS in 10.5 microsecond short pulses of 2.4x1013 protons per pulse. The proton beam is transported through the transfer line TT41 to the CNGS target T40. The target consists of a series of graphite rods, which are cooled by a recirculated helium flow. Secondary pions and kaons of positive charge produced in the target are focused into a parallel beam by a system of two pulsed magnetic lenses, called horn and reflector. A 1 km long evacuated decay pipe allows the pions and kaons to decay into their daughter particles - of interest here is mainly the decay into muon-neutrinos and muons. The remaining hadrons (protons, pions, kaons) are absorbed in an iron beam dump with a graphite core. The muons are monitored in two sets of detectors downstream of the dump. Further downstream, the muons are absorbed in the rock while the neutrinos continue their travel towards Gran Sasso.microsecond short pulses of 2.4x1013 protons per

 For me it has been an interesting journey in trying to understand the full context of a event in space sending information through out the cosmos in ways that are not limited to the matter configurations that would affect signals of those events.

In astrophysics, the most widely discussed mechanism of particle acceleration is the first-order Fermi process operating at collisionless shocks. It is based on the idea that particles undergo stochastic elastic scatterings both upstream and downstream of the shock front. This causes particles to wander across the shock repeatedly. On each crossing, they receive an energy boost as a result of the relative motion of the upstream and downstream plasmas. At non-relativistic shocks, scattering causes particles to diffuse in space, and the mechanism, termed "diffusive shock acceleration," is widely thought to be responsible for the acceleration of cosmic rays in supernova remnants. At relativistic shocks, the transport process is not spatial diffusion, but the first-order Fermi mechanism operates nevertheless (for reviews, see Kirk & Duffy 1999; Hillas 2005). In fact, the first ab initio demonstrations of this process using particle-in-cell (PIC) simulations have recently been presented for the relativistic case (Spitkovsky 2008b; Martins et al. 2009; Sironi & Spitkovsky 2009).

Several factors, such as the lifetime of the shock front or its spatial extent, can limit the energy to which particles can be accelerated in this process. However, even in the absence of these, acceleration will ultimately cease when the radiative energy losses that are inevitably associated with the scattering process overwhelm the energy gains obtained upon crossing the shock. Exactly when this happens depends on the details of the scattering process. See: RADIATIVE SIGNATURES OF RELATIVISTIC SHOCKS

So in soliton expressions while trying to find such an example here in the blog does not seem to be offering itself in the animations of the boat traveling down the channel we are so familiar with that for me this was the idea of the experimental processes unfolding at LHC. The collision point creates shock waves\particle sprays as Jets?

Soliton

Solitary wave in a laboratory wave channel.

In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium. (The term "dispersive effects" refers to a property of certain systems where the speed of the waves varies according to frequency.) Solitons arise as the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described by John Scott Russell (1808–1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation".

So in a sense the shock front\horn for me in respect of Gran Sasso is the idea that such a front becomes a dispersive element in medium expression of earth to know that such densities in earth have a means by which we can measure relativist interpretations as assign toward density determinations in the earth.  Yet,  there are things not held to this distinction so know that they move on past such targets so as to show cosmological considerations are just as relevant today as they are while we set up the experimental avenues toward identifying this relationship here on earth.

 For more than a decade, scientists have seen evidence that the three known types of neutrinos can morph into each other. Experiments have found that muon neutrinos disappear, with some of the best measurements provided by the MINOS experiment. Scientists think that a large fraction of these muon neutrinos transform into tau neutrinos, which so far have been very hard to detect, and they suspect that a tiny fraction transform into electron neutrinos. See: Fermilab experiment weighs in on neutrino mystery

When looking out at the universe such perspective do not hold relevant for those not looking past the real toward the abstract? To understand the distance measure of binary star of Taylor and Hulse,  such signals need to be understood in relation to what is transmitted out into the cosmos? How are we measuring that distance? For some who are even more abstractedly gifted they may see the waves generated in gravitational expression. So this becomes a means which which to ask if the binary stars are getting closer then how is this distance measured? You see?

Measurement of the neutrino velocity with the OPERA detectorin the CNGS beam 

Ring World

Impact armor, a flexible form of clothing that hardens instantly into a rigid form stronger than steel when rapidly deformed (for example, by the impact of a projectile such as a bullet) - a technology which is quickly approaching reality; in fact being tested during the 2006 Winter Olympics as a product called d3o

Lest you forget "the concept" above is written in a story form of our past?

How is it possible for the human mind to see itself in some future?

We must ask ourselves about the value of the conscience "in moving backwards in time?" An "image" constructed(memory), while not having this ability to "move forward?"

Imagine that you give weight to the idea of human experience, limiting it, to the shades of darkness in our emotive responses. Yet, there is a time when happiness seems so effortless, that as we check how fast "time" has past, we wonder in amazement?

No need here to draw up Einstein's conclusions about a "pretty girl and the hot stove" again and again, as it should have sunk in by now? You are the observer and you color your world.



It's a brief image that I saw myself deploring the satellites in space. Yet, with it the fear of holding on to all that is the firm resolve of one's own focus. Of what is known. Of what we feel is safe? A satellite lost in space. My own fear, as I gazed into the black unknown, possibly lost forever.

It is part of "my" conscious mind that I would produce such imagery? No, my anxieties were manipuated into a picture form. I sent the insecurites of my own awareness of mind deep into the "creativity" of the subconscious mind.

You did not know you had such ability did you?:)

Imagine that I stand on the edge of the Grand Canyon "which I did," and that space spread out before me, is the space of the universe? Imagine indeed, how tight my grip as I look.

Science Fiction

Who is it that could not be touched by the fiction of science to have speculated about how we shall live in another time and place? It comes out when you create the circumstances for the mind to wonder, "creatively."


(Larry Niven's Ringworld, seen from space. Artwork by Harry Frank

Ringworld is a Hugo and Nebula award-winning 1970 science fiction novel by Larry Niven, set in his Known Space universe. The work is widely considered one of the classics of science fiction literature. It is followed by three sequels, and it ties in to numerous other books in the Known Space universe.

.

What gives the mind it capabilities to venture forward and we find technologies in the "sports world being demonstrated" to harness the "memories of the geometrics" which will save us?



If you understood the "lighthouse analogy" then why had you failed to realized the most "intense point" of impact/ highest energy particles delivered, arose from such geometrics involved? Hulse and Taylor? How was the binary stars revealed while the revolutions got closer?



Lest some forget too, it is well that the mind see's the value of the "gravity probe b" in such "geometric form" that it has placed a picture(nit it's schematics?) before us, which saids and acknowledges the nature and move to the non-euclidean geometries. Understandng the "lagrangian perspective" is then is a short step away?

Now what has transpired from the fiction of Ring World?


d3o Mesh is a perforated textured sheet which has been specifically designed for comfort and breathability for applications requiring good flexure and medium levels of impact protection and is suitable for all applications.

(dee-three-oh) is a specially engineered material made with intelligent molecules. They flow with you as you move but on shock lock together to absorb the impact energy.

It is okay to thnk about "the theoretical" and push forward the circumstances that allow one to speculate and drawn the new imagery of mind to new horizons. New lives. We do this all the time when we re-assess our lives in face of the directions we would like to go?


Plato:

Now you must remember, as a student and a older one at that, there will always be mistakes. Being granted this reprieve for a time(writing our fiction?), while we look at the question asked, what do I think? Hmmmm.... interesting question.

What is your story of creation? What hides underneath the story, what is it 's nature, that we may have "created the myth" and let one believe it is just a story?

Moore's Law Endangered?

Moore's Law(wikipedia 28 May 2006)

Moore's law is the empirical observation that the complexity of integrated circuits, with respect to minimum component cost, doubles every 24 months[1].

Clifford, in writing the brief article of interest, he relays another article here for consideration.

Spotting the quantum tracks of gravity wavesby Zeeya Merali

Their calculations show that as the gravitational force from a passing wave slightly changes the momentum of the entangled particles, it should knock them out of their pristine spin state. In principle, that effect could be detected, but it is so small that no one has found a way to pick it up, explains Yeo. He and his team suggest that the effect could be amplified using a process called "entanglement swapping", which allows pairs of particles that have never been in contact to become entangled. "Spin and momentum become entangled to a higher degree so that changing one produces an even larger change in the other," says quantum physicist Chris Adami at the Jet Propulsion Laboratory in Pasadena, California.

While it may have been some time that now passes it is worth the mention again that "spintronics" has this role to play, yet, in gravity probe B, the spherical valuations would only now make sense on a large cosmological plate?

So by analogy usng Grvaity probe B we gain perspective onthe relevances of change within that gravitational radiation?

A black hole is an object so massive that even light cannot escape from it. This requires the idea of a gravitational mass for a photon, which then allows the calculation of an escape energy for an object of that mass. When the escape energy is equal to the photon energy, the implication is that the object is a "black hole".

Yet, is is of some concern that when we travel down to such microstates, that we are able in fact to keep a pure and clean picture of what existed once, and had gone through the changes in "spin orientation and momentum?"

If the boundariesof the blackhole are indeed collapsing to supersymmetrcial proportions, then what use photon information if it cannot describe for us something that is going on inside?

#18

The distinction is important, since the term gravity waves is primarily used in fluid dynamics to describe fluid oscillations that have gravity as their restoring force

I noticed link did not work and I was looking for confirmation as to your statement. Not that you need it :)

So just to confirm source, I reiterate it here again. If any a expert, would they like to clean up reference(does it need to be)?

(Gravitational waves are sometimes called gravity waves, but this term should be reserved for a completely different kind of wave encountered in hydrodynamics.)

Also, "the effect" while in the throes of gravity waves just to clarify the thinking(ocean waves and such), effects of Hulse and Taylor different, while the entanglement issue speaks to energy release is defined by photons passage of time as is?

What is the fastest way for it to get here without being influenced. Lagrangian perspective[Edwin F Taylors least Action Principal] and "tunnel transport" and effects of lensing?

Of course thinking about the nature of the types of high energy level photon(gamma) and what they can traverse through, may be confusing, yet distinctive?

One of the physical device limitations described by Dr. Packan is that transistor gates, as further miniaturization is pursued, will become so thin that quantum mechanical “tunneling” effects will arise. These quantum effects will create leakage current through the gate when the switch is “off” that is a significant fraction of the channel current when the device is “on”. This could reduce the reliability of the transistors resulting in increased cost and decreased availability of more powerful chips

Developement of Disbelief

As you read, hold on to the thought about stringy/M theory developement.

Richard Denton:

I discovered that it was simply philosophy on its own that had played the very much larger role in the gradual erosion of belief.

This is a interesting statement to me since some scientists might think that to have even included this in our "developing perspective" might have showed immediate signs of weakness? Evil?

As if, math came out of all natural things, on it's own?

So how did such views change us if we did not think about them more critically?

See, I am not sure I like to think that there is "no God" that can be substitued by taking this power of belief outside of ourselves to religions and institutions. Crippling us, as to the empowerment we have for such changes in our own life?

While we had seen the topic of "stringevangelism" introduced, there wasn't this concerted effort to make string as a all empowering "theory of everything( what underlying reality was referred too?)", even though, some would try to "invoke" these Godly powers of discrimmination. As a facist group, that would censor any views contrary to their own, as to what seemed, "stringevangelistic?" :)

It then became the same institution, that it despises? Some might know who I mean here. If I stood up to it, could I change reality as well, as to that this group invokes into society?

Anyway while I used Jo-Annes thread, "A little Bit of Heaven," to highlight this quality of earthly senses?

Topo-sense

Plato:

This intuitive feeling that is generated once math processes are understood are realized in dynamical movement revealled in the brains thinking? Had to arrive from lessons it learnt previously? Pendulums, time clocks, great arcs, and gravity?

I sought to internalize Gr's momentums, with Mecuries orbital patterns, or Hulse and Taylors expanding awareness of other things(gravity). I started to ask myself if this internalization was wrong? Is Topo-sense wrong? As too, intuitive unfoldments of the subject, in regards to Genus figures(holes)? Would it perish too? Revelations, leading to maths used?

Internal developement would have revealled a greater core depth of the realities around us. Which are highly abstract, yet, could have lead to insight and convictions held in astronomy happenings in the cosmo(isomorphic relations?)? So this internalization developed conviction, with the basis of Gr's valuation of quantum mechanical things, to cosmological proportions?

Strings as a model then, that could lead to perspectives with "langangian valuations" not only in terms of supersymmetry(concentration of a all pervading "beginning" that we could resort too,) as I espoused in Andrey Kravtsov computer's model.

That such relations in our philosophical orientation of physics would endure in measure, culminate with "fineness" and valuations of gravity perspectives. Could you do this, without some model?

So, would the "counter of belief in God," be the lesson the valuation of what one holds by introducing atheistic valautions, AS TO ROADS LEADING TO "COMMON SENSE?"

While I used stringy comparison for examination, this leads back again to what models can be used to keep the human beings empowered, without stealing this away from them by such institutionalizations? Continued reflection, thwarted, as to no experimental valuations yet philosphically introduced. You remember the opening statement I used?

I thought about the choices we make then, and the convictions we have. Would this have been irrelevant in our assessments of our own characters? After all, it would be you who walked back into society to think about the Smolins and Susskinds who would debate the essence of the backgrond?? What is understood, and what stringy needs to do?

Harmonic Oscillation

This "math sense" has to become part of one's makeup? An inductive process. Experimentally challenged. Deductive.

If such a idea is held from weak to strong idealizations in terms of comological views, then you get this sense of "energy valuations" as well. If you calculate when the binary pulsar distances around each other, the value of that information has been released in the bulk. This information should become weaker, as the orbits get closer?

The theory of relativity predicts that, as it orbits the Sun, Mercury does not exactly retrace the same path each time, but rather swings around over time. We say therefore that the perihelion -- the point on its orbit when Mercury is closest to the Sun -- advances.

I would think this penduum exercise would make a deeper impression if held in concert with the way one might have look at Mercuries orbit.

Or, binary pulsar PSR 1913+16 of Taylor and Hulse. These are macroscopic valutions in what the pendulum means. Would this not be true?

Part of the Randall/Sundrum picture Sean supplied of the brane world perspectives needed for how we look at that bulk view. If you are to asume that space is not indeed empty, then what is it filled with? Gravitonic perception would make this idea of the quantum harmonic oscillator intriguing to me in the sense that "zero point", would be flat space time. Any curvature parameters would have indeed signalled simple harmonic initiations?

Omega valutions in regard to the what state the universe is in, would have been defined in relation to a triangulation.

The quantum harmonic oscillator has implications far beyond the simple diatomic molecule. It is the foundation for the understanding of complex modes of vibration in larger molecules, the motion of atoms in a solid lattice, the theory of heat capacity, etc. In real systems, energy spacings are equal only for the lowest levels where the potential is a good approximation of the "mass on a spring" type harmonic potential. The anharmonic terms which appear in the potential for a diatomic molecule are useful for mapping the detailed potential of such systems.

But indeed while we understand this large oscillatory factor in our orbits, does it not make sense to wonder how simple that harmonic oscillator can become when we are looking for extra dimensions?

I had a picture the other day of a music instrument of a wire stretched, and weights being applied respectfully. The string when strummed gave certain frequencies accordingly to different mass valuations. This is the early pythagorean instrument I had see a few years ago, that would have similarities with "gourds of water" as weight and levels changed.



Here we seen a torsion pendulum. The way the wire twists and it's resulting valuation.



So you see how simple experimental processes help to correct our views on the way we see things.

From a historical perspective views of scientists with this explanation support the harmonic oscillators as follows:

Let us see how these great physicists used harmonic oscillators to establish beachheads to new physics.

Albert Einstein used harmonic oscillators to understand specific heats of solids and found that energy levels are quantized. This formed one of the key bridges between classical and quantum mechanics.

Werner Heisenberg and Erwin Schrödinger formulated quantum mechanics. The role of harmonic oscillators in this process is well known.

Paul A. M. Dirac was quite fond of harmonic oscillators. He used oscillator states to construct Fock space. He was the first one to consider harmonic oscillator wave functions normalizable in the time variable. In 1963, Dirac used coupled harmonic oscillators to construct a representation of the O(3,2) de Sitter group which is the basic scientific language for two-mode squeezed states.

Hediki Yukawa was the first one to consider a Lorentz-invariant differential equation, with momentum-dependent solutions which are Lorentz-covariant but not Lorentz-invariant. He proposed harmonic oscillators for relativistic extended particles five years before Hofstadter observed that protons are not point particles in 1955. Some people say he invented a string-model approach to particle physics.

Richard Feynman was also fond of harmonic oscillators. When he gave a talk at the 1970 Washington meeting of the American Physical Society, he stunned the audience by telling us not to use Feynman diagrams, but harmonic oscillators for quantum bound states. This figure illustrates what he said in 1970.

We are still allowed to use Feynman diagrams for running waves. Feynman diagrams applicable to running waves in Einstein's Lorentz-covariant world. Are Feynman's oscillators Lorentz-covariant? Yes in spirit, but there are many technical problems. Then can those problems be fixed. This is the question. You may be interested in reading about this subject: Lorentz group in Feynman's world.

Can harmonic oscillators serve as a bridge between quantum mechanics and special relativity?

Lee Smolin saids no to this?

A Supersymmetrical Valuation of Where things Began

Of course "phase transitions" and "asymmetrical realizations" had to arise from developmental processes in the universe? One had to know, in what sphere such developemental would take place, and if we circumvented all these chinese boxes or Russina dolls to exemplifed allegorical comments about consciousness. It had to follow a Gr perspective, and, a quantum mechanical one? "Topo-sense" as to developing topolgical models within consciousness, as a well as, models in the developing universe as a GR sense? IMagine to then such toposense further develped from theidealizatin of quantum views such physicla actions taken from cosmological proportions and reduced to probability functions entailed in our mental structure, then indeed we had transgressed our limitation to a feeling?:)

The theory of relativity predicts that, as it orbits the Sun, Mercury does not exactly retrace the same path each time, but rather swings around over time. We say therefore that the perihelion -- the point on its orbit when Mercury is closest to the Sun -- advances.

Imagine for a moment about that such a "momentus occasion", as well we learn to see the developmental process of circles(orbits) and Mercuries orbital patterns (a daisey) and got this general sense of reduced orbital pattern decay of rotatng binary pulsar systems as revealled by Taylor and Hulse.

We got to know "information release" from the distances involved, and could calculated when they would combined? This is a "prediction then" based on, a viable measure, not only in terms of that distance valuation, but of how we might arrive at it other then in astronmical viewing. What would be revealled in LIGO application?

Atiyah's comments are important here I think.

If theory is the role of the architect, then such beautiful proofs are the role of the craftsman. Of course, as with the great renaissance artists, such roles are not mutually exclusive. A great cathedral has both structural impressiveness and delicate detail. A great mathematical theory should similarly be beautiful on both large and small scales.

Assymetrical views would have revealled mandalic interpretations very distinctive of conscious awareness, and unfoldment in design. This had to have a geometric and foundational perspective that arose from the expansitory valution of brane world idealizations? As well as, the deeper recesses of our own minds?

Finally, we also hope that this series furthers the discussion regarding the nature and function of 'the mandala'. In the spiritual traditions from which Jung borrowed the term, it is not the SYMMETRY of mandalas that is all-important, as Jung later led us to believe. It is their capacity to reveal the asymmetry that resides at the very heart of symmetry. By offering a new view about how consciousness itself is structured - in a fundamentally paradoxical fashion - and how these structurings are reflected in principles according to which the mandala is organized, we are able in this series to show how personality itself may be thought of as having an essentially 'liminocentric' design.

One had to be able to recognize this "model apprehension" and speak to it directly in experience. I could do that because of my explorations. Am I adapting to new methods of model developements? For sure. :)



"Luminousity" as enlightenment could possibly help push back the veil, if we could probably do this?

Observatories

What is Sun-Earth Day?

As I was reading Cliffords newest entry on Cosmic Variance site, his trip reminded me of the hike we took to see the Big Horn Medicine Wheel.

Now what is interesting about this is I am not one who has had much association with such places of observatories, but far up to the left of this wheel is one that seems very out of place.

Ironic in the sense that ole history about these "Medicine Wheels" could have brought such historical perspective to the science. Look at the universe, from a place where ancient artifacts gathered.

At the center of the wheel there is a raised central cairn, and several others on the periphery of the wheel. These have been alleged to have astronomical alignments. Astronomer John Eddy suggested that a line drawn between the central cairn and an outlying cairn at the Bighorn Medicine Wheel pointed to within 1/3 of a degree of the rising point of the sun at the summer solstice. The actual astronomical purpose of the design of these wheels remains controversial. The design may also have assisted in the performance of specific rituals and ceremonies that have been lost to us. The 28 spokes could indicate the lunar month, or the length of the female menstrual cycle.

But I am not going to join the speculative feature of this wonderment, but to bring forward the understanding that mountains that may look the same, may have other reasons like it does for Clifford and his views of home. That for him to look, and have something nagged his "observatory mind" would have been as simple as "cheez, it looks like home."

Well from a more suttle place, I bring forward the understanding that our perspective about cosmology, our understanding of the uniqueness of Omega? The implications of General Relativity, and how Alexanders Firedmann's eqaution is part and parcel of the understandng of a geometry. That helps lead the mind into the ability to see dynamicals of this universe. How would your obervation have changed with such paradigmal changes. In Toposense, is speak to that as well as relate that General Realtivity had it's saem consequence. Ask Sean about that one?

Now we engage the spacetime fabric. This dynamcial abiltiy would not be seen before without this geometrical prospensity. So having been taken over by paradigmal change, the visionistic approach is one based on geometrical design, where the uniqueness of such correlations in the views of where nature resides. Brings one closer to the very spots we call "home". This is a real place for clifford, and yet without inducing such mysticism, this is also a place I draw from.

Now you say this guy is nuts. But imagine the science that leads one to see such topolgical realizations would take cosmological priciples about this epxanding universe and find that in a Genus example of the spherical WMAP of creation, there are abilities of this universe to become, well, lets say like images of marbles on rubber sheets, and how did such isolated cases exist within the greater potential of this universe to unfold and one is lead to portions of objective collapses that help to bring a greater dynamcial view about this same cosmos.

What makes this different is I relate topo-sense as a real part of paradigmal change.

The theory of relativity predicts that, as it orbits the Sun, Mercury does not exactly retrace the same path each time, but rather swings around over time. We say therefore that the perihelion -- the point on its orbit when Mercury is closest to the Sun -- advances.

I encourage such changes when we learn( or are really a result of such learning). Who could not get this sense from, Mercuries Daisey, or Hulse and Taylor Binary star rotations that release "gravitation waves" that give us information about how close they are becoming. What's it's predictve date about coming together?

While I relate Mecuries orbital patterns, such sense is not limited to here. Other idealizations as well, that we might wonder indeed how vast this landcape idea, when you consider the >Lagrange points?:)

Without Gravitational Waves, Spacetime is Flat?

I know it is very difficult for some people to understand this translation to harmonical expressions(any horizon and what is to lie beyond?) and the way in which we would percieve this dynamcial nature, using the expressions of non-Euclidean geometries?



We understood this creation of positive and negtaive in context of each other did we?

Riemannian Geometry, also known as elliptical geometry, is the geometry of the surface of a sphere. It replaces Euclid's Parallel Postulate with, "Through any point in the plane, there exists no line parallel to a given line." A line in this geometry is a great circle. The sum of the angles of a triangle in Riemannian Geometry is > 180°.



It is a strange thing to wonder how the heck one get's to translating harmonical oscillations in context of what we see expounded by Taylor and Hulse. To understand that at some point, the rotation around each other in distance, will decrease in time, and the oscillations will increase? What does this signal?:)



You do not discard thnking about the cosmological nature, methods, that have been used to orientate the world view in such a way, where all of a sudden the complexity of this dynamical nature has moved your thinking to strength and weakness of those same gravitational wave explanations.

Working closely with the experimental group, we use astrophysical, particle physics and superstring theory combined with observations to study gravitation and the origin and evolution of our universe.

The beautiful consistency of the cosmological tests with the Lambda CDM theory for structure formation maybe is particularly impressive to me because I spent so much of the last 15 years studying alternatives; you can trace through astro-ph my history of proposals that were viable when submitted but soon ruled out by advances in measurements of the angular distribution of the 3K thermal background radiation. But the constraints from the cosmological tests are not yet much more numerous than the assumptions in Lambda CDM and related models; it's too soon to declare closure of the cosmological tests.

Where to Now?

Once you see parts of the picture, belonging to the whole, then it becomes clear what a nice picture we will have?:) I used it originally for the question of the idea of a royal road to geometry, but have since progressed.

If you look dead center Plato reveals this one thing for us to consider, and to Aristotle, the question contained in the heading of this Blog.

It is beyond me sometimes to wonder how minds who are involved in the approaches of physics and mathematics might have never understood the world Gauss and Reimann revealled to us. The same imaging that moves such a mind for consideration, would have also seen how the dimensional values would have been very discriptive tool for understanding the dynamics at the quantum level?

As part of this process of comprehension for me, was trying to see this evolution of ordering of geometries and the topological integration we are lead too, in our apprehension of the dynamics of high energy considerations. If you follow Gr you understand the evolution too what became inclusive of the geometry developement, to know the physics must be further extended as a basis of our developing comprehension of the small and the large. It is such a easy deduction to understand that if you are facing energy problems in terms of what can be used in terms of our experimentation, that it must be moved to the cosmological pallette for determinations.

As much as we are lead to understand Gr and its cyclical rotation of Taylor and hulse, Mercuries orbits set our mind on how we shall perceive this quantum harmonic oscillator on such a grand scale,that such relevance between the quantum and cosmological world are really never to far apart?

As I have speculated in previous links and bringing to a fruitation, the methods of apprehension in euclidean determinations classically lead the mind into the further dynamcis brought into reality by saccheri was incorporated into Einsteins model of GR. Had Grossman not have shown Einstein of these geoemtrical tendencies would Einstein completed the comprehsive picture that we now see of what is signified as Gravity?

So lets assume then, that brane world is a very dynamcial understanding that hold many visual apparatus for consideration. For instance, how would three sphere might evolve from this?

Proper understanding of three sphere is essential in understanding how this would arise in what I understood of brane considerations.

Spherical considerations to higher dimensions.

Spheres can be generalized to higher dimensions. For any natural number n, an n-sphere is the set of points in n-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is, as before, a positive real number.

a 1-sphere is a pair of points ( - r,r)
a 2-sphere is a circle of radius r
a 3-sphere is an ordinary sphere
a 4-sphere is a sphere in 4-dimensional Euclidean space
However, see the note above about the ambiguity of n-sphere.
Spheres for n ≥ 5 are sometimes called hyperspheres. The n-sphere of unit radius centred at the origin is denoted Sn and is often referred to as "the" n-sphere.

INtegration of geometry with topological consideration then would have found this continuance in how we percieve the road leading to topolgical considerations of this sphere. Thus we would find the definition of sphere extended to higher in dimensions and value in brane world considerations as thus:



In topology, an n-sphere is defined as the boundary of an (n+1)-ball; thus, it is homeomorphic to the Euclidean n-sphere described above under Geometry, but perhaps lacking its metric. It is denoted Sn and is an n-manifold. A sphere need not be smooth; if it is smooth, it need not be diffeomorphic to the Euclidean sphere.

a 0-sphere is a pair of points with the discrete topology
a 1-sphere is a circle
a 2-sphere is an ordinary sphere
An n-sphere is an example of a compact n-manifold without boundary.

The Heine-Borel theorem is used in a short proof that an n-sphere is compact. The sphere is the inverse image of a one-point set under the continuous function ||x||. Therefore the sphere is closed. Sn is also bounded. Therefore it is compact.

Sometimes it is very hard not to imagine this sphere would have these closed strings that would issue from its poles and expand to its circumference, as in some poincare projection of a radius value seen in 1r. It is troubling to me that the exchange from energy to matter considerations would have seen this topological expression turn itself inside/out only after collapsing, that pre definition of expression would have found the evoltuion to this sphere necessary.

Escher's imaging is very interesting here. The tree structure of these strings going along the length of the cylinder would vary in the structure of its cosmic string length based on this energy determination of the KK tower. The imaging of this closed string is very powerful when seen in the context of how it moves along the length of that cylinder. Along the cosmic string.

To get to this point:) and having shown a Platonic expression of simplices of the sphere, also integration of higher dimension values determined from a monte carlo effect determnation of quantum gravity. John Baez migh have been proud of such a model with such discrete functions?:) But how the heck would you determine the toplogical function of that sphere in higher dimensional vaues other then in nodal point flippings of energy concentration, revealled in that monte carlo model?

Topological consideration would need to be smooth, and without this structure how would you define such collpases in our universe, if you did not consider the blackhole?

So part of the developement here was to understand where I should go with the physics, to point out the evolving consideration in experimentation that would move our minds to consider how such supersymmetrical realities would have been realized in the models of the early universe understanding. How such views would have been revealled in our understanding within that cosmo?

One needed to be able to understand the scale feature of gravity from the very strong to the very weak in order to explain this developing concept of geometry and topological consideration no less then what Einstein did for us, we must do again in some comprehensive model of application.