Exploring Branes: The Evolution of Superstring Theory

[sol2]

D1 to D5 Brane

http://www.sukidog.com/jpierre/strings/stringbh.gif

How the heck did you get to D5? You had to be able to determine the gravtion scalable feature in terms of these branes? From weak to strong. Certain particle situations then become realistic under such considerations.

From a one dimension recognition weak field gravitational measure would have satifsied the particle nature at it's minimum energy consideration? This would be distinctive?

One of the most dramatic recent results in string theory is the derivation of the Bekenstein-Hawking entropy formula for black holes obtained by counting the microscopic string states which form a black hole. Bekenstein noted that black holes obey an "area law", dM = K dA, where 'A' is the area of the event horizon and 'K' is a constant of proportionality. Since the total mass 'M' of a black hole is just its rest energy, Bekenstein realized that this is similar to the thermodynamic law for entropy, dE = T dS. Hawking later performed a semiclassical calculation to show that the temperature of a black hole is given by T = 4 k [where k is a constant called the "surface gravity"]. Therefore the entropy of a black hole should be written as S = A/4. Physicists Andrew Strominger and Cumrin Vafa, showed that this exact entropy formula can be derived microscopically (including the factor of 1/4) by counting the degeneracy of quantum states of configurations of strings and D-branes which correspond to black holes in string theory. This is compelling evidence that D-branes can provide a short distance weak coupling description of certain black holes! For example, the class of black holes studied by Strominger and Vafa are described by 5-branes, 1-branes and open strings traveling down the 1-brane all wrapped on a 5-dimensional torus, which gives an effective one dimensional object -- a black hole.
http://www.sukidog.com/jpierre/strings/bholes.htm

D5 considerations would have asked us to consider four of space and one of time?

 

[sol2]

http://www.space.com/images/h_space_membranes_010412_02.gif

"The [Ekpyrotic] scenario is that our current universe is [a] four-dimensional membrane embedded in a five-dimensional 'bulk' space, something like a sheet of paper in ordinary three-dimensional space," Turok told SPACE.com. "The idea then is that another membrane collided with ours, releasing energy and heat and leading to the expansion of our universe."

http://www.space.com/scienceastronomy/astronomy/bigbang_alternative_010413-1.html

Branes reside in the hidden dimensions, known as ``the bulk.'' While matter and light stick to the branes, gravity traverses both branes and bulk. The hidden dimensions cannot be seen because only gravity can go there

.

 

[sol2]

Are Brane Intersection UNiversal?

This question was once asked?

Intersection is a strange word if you do not consider it in light of the photon?

The finding announced today supports a theory of gamma-ray production posed by Prof. Avi Loeb of Harvard University and Prof. Eli Waxman of the Weizmann Institute in Rehovot, Israel. Not unlike a black hole, the sheer mass of a cluster serves as a gravitational drain, drawing in matter at speeds of up to a thousand miles per second. Electrons in this flow are accelerated, with an additional boost from magnetic fields, to near light speed and collide with microwave light, the afterglow from the big bang known as the cosmic microwave background.

These microwave light particles, or photons, are bumped up to the gamma-ray photon energy level. The gamma rays form a halo around the galaxy clusters. Other scientists, however, have suggested that the bulk of the gamma-ray background is produced not by this mechanism but by quasar-type galaxies, called blazars, each powered by a supermassive black hole. This background was discovered by NASA's second Small Astronomy Satellite (SAS-2) in the early 1970s.

Scharf and Mukherjee's new research compared a catalog of 2,469 galaxy clusters with the Compton database. Using sophisticated statistical techniques, they showed that the sky surrounding the most massive clusters was systematically brighter in gamma rays than other regions.

"The more massive the cluster (and greater the gravitational potential), the brighter the gamma-ray halo," said Mukherjee. "The enhancement observed was very similar to that predicted by the Loeb-Waxman theory."

The result announced today also supports the theory of the cosmic web. Scientists say that matter in the Universe forms a cosmic web, in which galaxies are formed along filaments of ordinary matter and dark matter like pearls on a string. Clusters form at the intersection of these filaments. The electrons that fuel the gamma-ray production rush into clusters along these rivers or filaments of matter connecting galaxies and clusters. Thus, gamma rays serve as probes to the early structure-forming epoch of the Universe.

Gamma ray halos around clusters also provides a means to measure intergalactic magnetic fields. Two of the three variables to measure magnetic fields are known: the mass of galaxy clusters and the distribution of the microwave background. The third variable is electron efficiency, which can now be measured by virtue of gamma-ray production.

The Gamma-ray Large Area Space Telescope (GLAST), scheduled for launch in 2006, should resolve gamma-ray haloes around galaxies with unprecedented clarity. GLAST could measure intergalactic magnetic fields and watch the formation of structure in the universe through its gamma-ray eyes, the scientists said.

For more information, go to:

http://www-glast.sonoma.edu/news/08_13_02.html

So what if this energy is all spread out in the CMB at a early stage?

How would you tell and not consider the significance of the spaces inbetween as we look? So there is no supersymmetry?

Heaven forbid, what shall we cal this http://www-glast.sonoma.edu/index.html WE all know very well we had been taking a serious look at describing how the formation of the universe from then to now, and look how wonderfull we have built this view of reality. Imagine, it's all wrong? :rofl:

 

[sol2]

I needed it to be a little clearer so I went for a definition.


Special relativity and Lorentz invariance

In order to account for the structure of space and time at the Planck scale, LQG breaks Lorentz invariance and posits that certain well known effects of special relativity such as length contraction and time dilation cannot occur below the threshold of the Planck scale. It also predicts that the speed of photon propagation in vacuum may be dependent on the photon's wavelength, and not constant as demanded by special relativity (where it is denoted by c). It is not clear whether an approximate Lorentz invariance can be recovered in LQG at long distances and whether LQG can explain the plethora of successful experimental tests of special theory of relativity. LQG proposes a privileged reference frame associated with the spin foam, and therefore it is natural to expect that it may suffer from the usual problems of the old-fashioned theories of luminiferous aether. Nevertheless, LQG is formally a local gauge theory of the self-dual subgroup of the Lorentz group.

Time

Additionally, in LQG, time is not infinitely continuous but discrete and quantized, just as space is: there is a minimum moment of time, Planck time, which is on the order of 10−43 seconds, and shorter intervals of time have no physical meaning. This carries the physical implication that relativity's prediction of time dilation due to accelerating speed or gravitational field, must be quantized, and must consist of multiples of Planck time units. (This helps resolve the time zero singularity problem: see subsection "Big Bang")

http://www.wordiq.com/definition/Loop_quantum_gravity

 

[sol2]

Brane World and the House of Cards

A couple of things popped into my mind about the issue of time and space.

In LQG Time is counted as discrete and space is counted a discrete also. I understand that LQG is doing work in speical relativity, and see where the Glast work might be of sigificance.

At the same time M theory has moved past SR to GR and accepted these measures in a cosmological way, and further have accepted features of time that allow this continuous nature to be expressed.

So we see the differences here, about how we can interpret the nature of reality from discreteness and from a continuous point of view in M theory, that if you accept the graviton nature of quantization of those gravity waves, you accept certain features about brane world.

I have looked at Glast and see where the potential exists now, and it is pretty clear, but we had not ventured into Brane world, and further attempts a dismantling brane world theories would have to speak to supersymmetry as it has been attacked here in this forum and other places.

We would have to have a responsible discussion, in light of the features Smolin points out that can falsify the brane world logic, so how shall we do this to save us all from delusional states

So what is the nature of the geometry in brane world? Will such intersection points allow us to speak to the theoretical graviton as we do with the issue of gamma ray radiation?

Are there such intersections in brane world that would have spoken to the holographical reality? It might be easier for some to visualize these hidden dimensins and such points arising from a intersection point?

Warped Geometry of Brane WorldGary N. Felder, Andrei Frolov, Lev Kofman

We study the dynamical equations for extra-dimensional dependence of a warp factor and a bulk scalar in 5d brane world scenarios with induced brane metric of constant curvature. These equations are similar to those for the time dependence of the scale factor and a scalar field in 4d cosmology, but with the sign of the scalar field potential reversed. Based on this analogy, we introduce novel methods for studying the warped geometry. We construct the full phase portraits of the warp factor/scalar system for several examples of the bulk potential. This allows us to view the global properties of the warped geometry. For flat branes, the phase portrait is two dimensional. Moving along typical phase trajectories, the warp factor is initially increasing and finally decreasing. All trajectories have timelike gradient-dominated singularities at one or both of their ends, which are reachable in a finite distance and must be screened by the branes. For curved branes, the phase portrait is three dimensional. However, as the warp factor increases the phase trajectories tend towards the two dimensional surface corresponding to flat branes. We discuss this property as a mechanism that may stretch the curved brane to be almost flat, with a small cosmological constant. Finally, we describe the embedding of branes in the 5d bulk using the phase space geometric methods developed here. In this language the boundary conditions at the branes can be described as a 1d curve in the phase space. We discuss the naturalness of tuning the brane potential to stabilize the brane world system.

http://arxiv.org/abs/hep-th/0112165

 

[sol2]

Brane World Interactions and Hyperspace

Brane World Cosmology Comes Down to Earth

How many dimensions are there? That’s not easy. Sure, we have three spatial dimensions plus time. And the physics of the four-dimensional framework of space-time is all encapsulated in Einstein’s general theory of relativity, a hugely successful paradigm. But cosmology raises many questions that go beyond the textbook presentation of general relativity. For example, when we run the universe backwards we reach a state of extreme matter and energy density right after the big bang. What theory can we use to describe the universe at the earliest times, when gravity needs folding into quantum theory? And at low energies, when the universe has expanded dramatically due to inflation, how can we account for the puzzles of dark energy and dark matter that weigh in at 97% of the rest mass of the universe?

In the low-energy limit these correspond to the textbook Einstein equations. Coauthor Misao Sasaki (Osaka University) had this comment for Science Watch: "We’ve derived the gravitational equations as seen by an observer on the brane. They look like the Einstein equations but they have two additional terms, which arise from the fifth dimension. One of these terms contains all the information on five-dimensional gravity, and that’s what has excited the interest of the researchers who are citing our work. If this term could be proved experimentally it will give us clear evidence that we are living in a brane-world.

http://www.sciencewatch.com/july-aug2002/sw_july-aug2002_page6.htm

 

[sol2]

Two...Two Branes Are Better then One

Additional spatial dimensions may seem like a wild and crazy idea at first, but there are powerful reasons to believe that there really are extra dimensions of space. One reason resides in string theory, in which it is postulated that the particles are not themselves fundamental but are oscillation modes of a fundamental string.

http://www.edge.org/3rd_culture/randall03/images/randall200.jpg

In cosmology, for instance. Alan Guth's mechanism whereby exponential expansion smooths out the universe works very well, but another possibility has been suggested: a cyclic universe, Paul Steinhardt's idea, wherein a smaller amount of exponential expansion happens many times. Such a theory prompts you to ask questions. First of all, is it really consistent with what we see? The jury's out on that. Does it really have a new mechanism in it? In some sense, the cyclic idea still uses inflation to smooth out the universe. Sometimes it's almost too easy to come up with theories. What grounds your theories? What ties them down? What restricts you from just doing anything? Is there really a new idea there? Do we really have a new mechanism at work? Does it connect to some other, more fundamental theoretical idea? Does it help make that work? Recently I have been exploring the implications of extra dimensions for cosmology. It seems that inflation with extra dimensions works even better than without! What's so nice about this theory is that one can reliably calculate the effect of the extra dimension; no ad hoc assumptions are required. Furthermore, the theory has definite implications for cosmology experiments. All along, I've been emphasizing what we actually see. It's my hope that time and experiments will distinguish among the possibilities.

http://www.edge.org/3rd_culture/randall03/randall03_p6.html

 

[Mike2]

As I understand it, space is filled with a "quantum foam" where every sort of virtual particle spontaneously pops into existence and then annihilate each other. The higher the energy of those particles, the less time they spend in existence. But wouldn't those virtual particles have to include every dimensional type of brane/particle? And wouldn't such a foam have to include every type of interaction between every dimensional type of brane? Isn't this the same as saying that the quantum foam is space, and space IS the interaction of every dimension? And isn't the interaction of every type of dimension the same as quantum geometry? Thus, it would seem that M-theory is quantum geometry, right? Or has somebody already gone this route?

Originally Posted by Mike2

It may be that the nature of the interation between branes of differing dimension in M-theory is not like the interation of differing dimensions in quantum geometry/gravity. Perhaps the nature of the interaction between different branes in M-theory is that one branes serves to fix the type of boundary conditions of the other. Whereas the nature of the interactions of different dimensions in quantum geometry/gravity is more like a path integral where each dimensional object is given its own amplitude and phase, and these mix with the amplitude and phase for objects of different dimension. Comments anyone?

But now that I thing of it, as I recall, it is the boundary conditions that create the quantum levels. So the intersection of branes serving to set boundary conditions for other branes may be equivalent to to the interaction of differing dimensions as in quantum geometry. So M-theory may still be equivalent to other approaches to quantum geometry.

 

[sol2]

Look

deeper...

...deeper...

...deeper...

I wanted to make sure I did not confuse the name of Andrey Krasnov with Kirrill Krasnov that Baez is related to in literature.

Why I wanted to add this here has to do with above posted, and how the intersection of photons held in regard to LQG's attempt at discribing the issues of Glast. from the SRian approach.

http://wc0.worldcrossing.com/WebX?14@92.YyIIcXeLrlD.0@.1ddf4a5f/57

http://www.sandlotscience.com/Moire/images/moire_intro.gif​

I wanted to add this animation to help people recognzie the similarity that has made me aware of how this intersection is a vital recognition of how we can see the evolution of the early universe to now.

We talk about cosmic strings here in the animation as a way of seeing the consolidation of event and structure in that universe. What was important for me was to recognize how supersymmetry might arisen from brane realizations, and again, the moire effect was most strange if we had considered this "intersection," of the graviton, as if the photon was to travel through these waves.

to here and touch the smile.

down...

the way...

all...

Look

 

[pelastration]

Intersections (like cutting properties) is imo the main problem. Ask yourself: Why would there be a Universal Sissor cutting everything in pieces?
A unifying approach needs to be: Unifying! Not separating.

If you are interested you can download my powerpoint presentations at ANPA (Cambridge UK). There were two presentations.
1. 3.6 Mb: [PLAIN]http://www.mu6.com/ANPA/pelastration1.ppt[/URL]
2. 1.2 Mb: [PLAIN]http://www.mu6.com/ANPA/pelastration2.ppt[/URL]

 

[sol2]

Intersections (like cutting properties) is imo the main problem. Ask yourself: Why would there be a Universal Sissor cutting everything in pieces?
A unifying approach needs to be: Unifying! Not separating.

If you are interested you can download my powerpoint presentations at ANPA (Cambridge UK). There were two presentations.
1. 3.6 Mb: [PLAIN]http://www.mu6.com/ANPA/pelastration1.ppt[/URL]
2. 1.2 Mb: [PLAIN]http://www.mu6.com/ANPA/pelastration2.ppt[/URL][/QUOTE]


I will be looking at your presentations. Can you put links to site presenting these two ppt presentations, as they did not download for me

I am bringing you to the very top post of this thread. Would you not agree that such scissors would have meant discrete pieces?

Topology is the branch of mathematics concerned with the ramifications of continuity. Topologist emphasize the properties of shapes that remain unchanged no matter how much the shapes are bent twisted or otherwise manipulated.

Imagine the membranes doing all kinds of things but never tearing.The bubbles should be able to do this in bubble eversions?
http://oldsite.vislab.usyd.edu.au/gallery/mathematics/diffeo/diffeo.html

Greg Egan is very helpful here As well, Helicoid visualizations.

From the Planck epoch to now the standard model has to assume that such a path(model) would materialize? What do two complete rotations mean?

http://viswiz.imk.fraunhofer.de/~nikitin/ax_3.gif

http://wc0.worldcrossing.com/WebX?14@208.lWSbctOOtqi.20@.1ddf4a5f/69

 

[pelastration]

I will be looking at your presentations. Can you put links to site presenting these two ppt presentations, as they did not download for me

Sol, I put them as webpages.
Here are the links (images contain some black dots):

First day: http://www.mu6.com/ANPA/pelastration1.htm

Second day: http://www.mu6.com/ANPA/2/pelastration2.htm. Here some pages are repeated + reactions added on questions during the first presentation. Some images (i.e. QM box eperiments) were explained verbally and not eplained on the slide. For the Alain Aspect experiment I had not the time to make an image.

 

[pelastration]

I am bringing you to the very top post of this thread. Would you not agree that such scissors would have meant discrete pieces?

Imagine the membranes doing all kinds of things but never tearing.The bubbles should be able to do this in bubble eversions?
http://oldsite.vislab.usyd.edu.au/gallery/mathematics/diffeo/diffeo.html

Greg Egan is very helpful here As well, Helicoid visualizations.

From the Planck epoch to now the standard model has to assume that such a path(model) would materialize? What do two complete rotations mean?

Thanks for the links.

Sure, Universal Scissors would create discrete pieces but they would loose history. If cut what would connect them gravitational?
Don't you think conservation of history (information) is essential?

Yes the 720° belt trick can be done with pelastrated holons. Lou Kauffmann showed the trick during the ANPA meeting. Fun. Lou looks into a special algebra for pelastrations.

 

[sol2]

Thanks for the links.

Sure, Universal Scissors would create discrete pieces but they would loose history. If cut what would connect them gravitational?
Don't you think conservation of history (information) is essential?

Yes the 720° belt trick can be done with pelastrated holons. Lou Kauffmann showed the trick during the ANPA meeting. Fun. Lou looks into a special algebra for pelastrations.

If cut what would connect them gravitational? Don't you think conservation of history (information) is essential?

The information is always there in the bulk. You never lose it. It just gathers in spots, sometimes stronger then other locations, and we see where all these holes start to look like swiss cheese universe.

Might Lou looked at math of topos theory?

 

[sol2]

Sol, I put them as webpages.
Here are the links (images contain some black dots):

First day: http://www.mu6.com/ANPA/pelastration1.htm

Second day: http://www.mu6.com/ANPA/2/pelastration2.htm. Here some pages are repeated + reactions added on questions during the first presentation. Some images (i.e. QM box eperiments) were explained verbally and not eplained on the slide. For the Alain Aspect experiment I had not the time to make an image.

You work very quickly and thank you for putting into html pages.

Your mention of Alain Aspect is a good sign to me that you are headed in the right direction. My little story will bring together a lot of what you are doing and seeing. Your framework will be complete as far as I see it, once you incorporate the final information.

From light to dark, and back again, and what begins and ends is very interrelated and contain seeds of each other. If you have a shadow and light and inbetween, a line, how shall we describe this line? For you, I know the image will materialize Good work. Maybe, you can give the image a complete rotation?

 

[pelastration]

If cut what would connect them gravitational? Don't you think conservation of history (information) is essential?
The information is always there in the bulk. You never lose it. It just gathers in spots, sometimes stronger then other locations, and we see where all these holes start to look like swiss cheese universe.

You mean ALL information? Holons contain ALL information of all previous combinations. Each particles has it's own history. I.e. each electron in the universe has a different layer-history than the other electrons, since it's origin is different. I don't believe such topological information of each particle is conserved in the traditional 'bulk'. And where would it be stored?

 

[sol2]

You mean ALL information? Holons contain ALL information of all previous combinations. Each particles has it's own history. I.e. each electron in the universe has a different layer-history than the other electrons, since it's origin is different. I don't believe such topological information of each particle is conserved in the traditional 'bulk'. And where would it be stored?

Prior Geometry and Holons One membrane peak (active) penetrates a passive peak. Since the membrane is non-breakable a new double layered area is created.

We call this local zone a HOLON. A holon contains history of the parents.


Slide('7')Piror Geometry and Holons
http://www.mu6.com/ANPA/pelastration1.htm

Holons (Koestler) may be: galaxies, stars, planets, humans, animals, plants, cells, DNA, genes, molecules, atoms, nuclei, particles.

Slide 14

I needed to understand how you were seeing. There were other defintions you had?

It would indeed be hard to see from a path integral approach. From a LQG perspective, and discreteness, how would you separate the coverings from the parent...hmmmm. I have to think about how you are relating history to parents.

One thing that immediately strikes me is that you have given boundaries with shape and color. The penetration and covering of other possibilties, in terms of the growth potential of families is a psychological relationship you have mathmatically developed into a wonderful creation.

Let's look at Bohr's atom. If we use liminocentric structures like you have when you partition your penetrations, to circles then what has this told you about these penetrations? Help me here

One of the interesting things to me is that if we have a enornmous amount of energy, something must happen, if energy is released. Now how might we look at this? In two ways. One in which you see just energy pervading the universe, or another, in how you might percieve the graviton in that bulk?

You might see something "pinching off" and with that, correllations of graviton association? The "point" as a boson, would leave the 3 brane reveal itself, as a wavelength of spectrum. Still the parent is at the core? And the parent connected to pervading bulk by its history.

Does this make sense?

 

[pelastration]

It would indeed be hard to see from a path integral approach. From a LQG perspective, and discreteness, how would you separate the coverings from the parent...hmmmm. I have to think about how you are relating history to parents.

The parents are the history. They are inside the child.
The slide 8 (First powerPoint: Holons and Duality) shows that. Two different parts of the membrane are joined in the holon B(A). Slide 11 shows the further holon C(ba). That contains the original B(a). That's layering history. Whatever more combinations are made by C(ba) in larger - more complex - towers, there will be always C(ba) involved. Call C(ba) an electron. So wherever that electron goes ... i.e. being part of a Cu-atom inside a molecule - it will contain the topological history of the membrane parts by which it was created. Another electron may be for example: D(ac), etc.

Let's look at Bohr's atom. If we use liminocentric structures like you have when you partition your penetrations, to circles then what has this told you about these penetrations? Help me here

Surely I want to help but I don't get the question. You mean the circles? These are a traverse cutting of the holon so you can see the layers from another side.
These local topological penetrations (creating holons like electrons ) will circle around the nucleus of an atom, not really different from Bohr's atom, only they are still attached (like by a belt) to the membrane. The 720° rule plays here.

One of the interesting things to me is that if we have a enornmous amount of energy, something must happen, if energy is released. Now how might we look at this? In two ways. One in which you see just energy pervading the universe, or another, in how you might percieve the graviton in that bulk?

.
Let's simplify and say that the membrane is spacetime (although the membrane is pre-geometry, timeless).
To me the spacetime membrane is the interconnective elasticity which is observed as "gravity".
Everything (holons) is restructured membrane. Everything, so what we call: energy and what we call: matter. It's just a different level of layering. We can say here that the curvature of spacetime creates matter: which confirms Einstein's idea that spacetime influences matter (indeed it creates matter). And when spacetime moves also matters moves with it (since it's on the spacetime brane).

In powerpoint 2 (slide: 14 ) you can see the dynamics: How membrane layers in a holon can be deformed.
The bold red lines are first levels of sub-holons (complex), the blue lines are the next level (more complex), and the purple line symbolize the three level (more, more complex). There can be much more levels.
The higher holon-towers become, the more the basic membrane 'feels' 'heaviness' = matter-like. That implies that there is more rigidity but also that the membrane 'bends' (like Einstein's rubber sheet). Matter curves spacetime.

We can see here that indeed everything is vibration, like Kaku and other string physicists say, but it's the fundamental membrane that vibrates (the fundamental hollow string). Combined vibrations create particles (various energy types and matter types).

You might see something "pinching off" and with that, correllations of graviton association? The "point" as a boson, would leave the 3 brane reveal itself, as a wavelength of spectrum. Still the parent is at the core? And the parent connected to pervading bulk by its history.

Pinching off is a nice human interpretation. ;-). But it's all on-the-brane. Nothing can leave the brane since everything is made by the brane and still part of the unbreakable membrane. Indeed holons will vibrate in a very specific way (depending of their internal structure), meaning: how the parent parts of the membrane are structured inside each holon.

 

[sol2]

Planck Epoch to Grand Unification

I am giving you this http://superstringtheory.org:8080/forum/stringcosmo/getpost.jsp?post=18 to direct your attention to the method, in which my attempts are to move forward concept building, and list the structure with how I am approaching this. People in this forum are unknowing partners in the continued developement. I appreciate the interaction and hope I am reciproicating what I am learning.

Now to me, if you present me with the Planck epoch, you have to understand what this means, and where "emergent realities" might come from.

In the last post I supply a thread, I deal specifically with what is called pearls and chains, because it reveals the cosmic string development effects from Planck epoch. So this leaves you with a taste in one's mouth of the era and the manifestation that arises to our current universe and realization.

So I traced the "history," back to Parent/Child, and here I am speaking to the effects produced by the cosmic strings, and the "cooling nature" in that universe, as a consistent feature.

You have to understand what the bulk means. It is "history" and represents the gravitons. This is a fourth dimensional(all of space) result of the 3 brane world. The history remains consistent throughout all the epochs and universe to now. The Fifth dimenison, is with time.

What we want to know then, is if the M really stands for membrane, or Mother ?

You see if you look at the Planck epoch, and the idea of pure energy, how do bubbles form? There is a leading thought here in terms of the creation of the universe and it is all encapsulated in the bubble M theory.

Yet alongside of this developing universe(child) the mother still exists in this (graviton)Sea, from which it too was born. So no matter how weak the graviton is in our current universe, it is still connected to the mother's embryonic womb from which the children came.

It has to have a "basis" from which to develope, and conceptually, this would have to have a vibratory nature(quantum harmonic oscillator?), and the only thing that I know that can show this is "energy".

If there are no gravitational waves, the spacetime fabric is flat.

The KK tower then becomes specific for me about particle identification.

This is about the duality that emerged, and it's logic. Line of shadow or line of light. For me then your examples of became features of solidity and sound.

I developed the lines and they can be broken or unbroken, yang and Yin respectively.

I will stop here, as it leads into other things.

Your model would have to be consistent with the history?

How can "energy" be born out of the complete blackness? Is it as simple as going to sleep(darkness) and waking up on the other side?

But it's all on-the-brane. Nothing can leave the brane since everything is made by the brane and still part of the unbreakable membrane

Yes, one thing can leave the brane. The EM spectrum is the face of the brane which can't leave. Yet the face, has to exist by it's definition, by what is in the bulk.

 

[sol2]

HIgher Sphere

Imagine for one moment that a bubble arises out of dirac's sea. This bubble is a summmation of brane worlds?

The Dirac sea is an interpretation of the negative energy states that comprises the vacuum In physics, a vacuum is the absence of matter (molecules, atoms...) in a volume of space. A partial vacuum is expressed in pressure units. The SI unit of pressure is pascal (Pa). It can also be expressed as a percentage of atmospheric pressure using the bar or barometer scale.


Degrees of vacuum
atmospheric pressure = 760 torr or 100 kPa
vacuum cleaner = around 300 torr or 40 kPa
mechanical vacuum pump = around 10 millitorr or 1.3 Pa
near Earth outer space = around 10-6 torr or 130 μPa
pressure on the Moon = around 10-8 torr or 1.3 μPa
interstellar space = around 10-10 torr or 13 nPa

The Dirac sea of particles and antiparticles is part of the foundation of modern quantum theory.

Paul Adrien Maurice Dirac
Paul Adrien Maurice Dirac, (August 8 1902 - October 20 1984) was a physicist and a founder of the field of quantum physics.

BiographyDirac was born in Bristol, Gloucestershire, England. In 1926 he developed a version of quantum mechanics, which included “Matrix Mechanics” and “Wave Mechanics” as special cases.

In 1928, building on Pauli's work on nonrelativistic spin systems, he derived the Dirac equation, a relativistic equation describing the electron. This allowed Dirac to formulate the Dirac sea and predict the existence of the positron, the electron's anti-particle; the positron was subsequently observed by Anderson in 1932. Dirac explained the origin of quantum spin as a relativistic phenomenon.

The "sea" has an infinite background charge and may play a role in the perceptions of spacetime

In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional manifold called spacetime (alternatively, space-time). A point in spacetime may be referred to as an event. Each event has four coordinates (t, x, y, z); or, in angular coordinates, t, r, θ, and φ. structures.
Dirac studied the electron in complex spacetime

In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional manifold called spacetime (alternatively, space-time). A point in spacetime may be referred to as an event. Each event has four coordinates (t, x, y, z); or, in angular coordinates, t, r, θ, and φ.
, Dirac published the Dirac equation. With the Dirac formalism, electron description is a particle to the proton. After others (including Hermann Weyl, Robert Oppenheimer, and Igor Tamm) disproved this possibility, Dirac predicted a new particle, the positron. If negative energy is transformed into a positive energy state, the energy is perceived as a positron. Positron is the antiparticle of electron. Positrons are produced through pair production (bipolar coupling).

In relativistic quantum mechanics, Dirac's equation admits both positive and negative energy states. So, what is there to prevent a fermion from constantly radiating away energy, resulting in lesser and lesser energy, resulting in a huge instability? Dirac proposed almost all the negative energy states are filled by a sea of negative energy fermions. In modern treatments of quantum field theory, the Dirac sea is subtly introduced by having different definitions for the occupation number for positive and negative frequency decompositions.

The model of a negative energy "sea" of electrons has critics.

http://encyclopedia.thefreedictionary.com/Dirac sea

This bubble encloses all possible dimensions? M stands for mother, and out of the waters of this world, the children(universes) are born?

I stumbled upon the words of Sakharov in relation to Dirac's Sea.

For some of us who had gather at a earlier time, the effective electron-positron questions all of a sudden presenrted other solutions as to how we could percieve dynamical movement.

On that point we can only conjecture. Sakharov suggested accounting for the effects of general relativity by introducing the concept of an "elasticity of space," analogous to the well-known curvature of space-time. The answer could also lie in the proper treatment of the so-called Dirac sea of particle-antiparticle pairs. The question of general relativistic effects, however, is a valid concern that legitimately challenges the interrelated ZPF concepts of gravity and inertia.

http://www.calphysics.org/haisch/sciences.html

Link was added from a post of Self Adjoint's http://arxiv.org/PS_cache/gr-qc/pdf/0403/0403052.pdf .

 

[sol2]

Engineering with Brane Perspective's

Beyond Einstein seems a catching phrase to me too. Yet we find a lot of evidence of this thinking all over the place. What do the new ideas espouse? Have we really grasped the significance?


BEYOND E=mc2


A first glimpse of a postmodern physics, in which mass,
inertia and gravity arise from underlying electromagnetic processes

Even if our approach based on stochastic electrodynamics turns out to be flawed, the idea that the vacuum is involved in the creation of inertia is bound to stay. Perhaps even bolder than the concepts themselves are their implications. If inertia and gravity are like other manifestations of electromagnetic phenomena, it might someday be possible to manipulate them by advanced engineering techniques.

http://www.calphysics.org/haisch/sciences.html

Sometimes we might need visual aids. So, I thought I would add this in relation to the question, on how would we see these dimensions, if we accept the gravitons in the bulk?

http://micro.magnet.fsu.edu/featuredmicroscopist/deckart/images/soap01small.jpg

Karl E. Deckart

 

[sol2]

Zitterbewegung and Dirac

Update on an Electromagnetic Basis for Inertia, Gravitation,
the Principle of Equivalence, Spin and Particle Mass Ratios

Both of the approaches above (together called the RHP approach for convenience) assume classical electrodynamics
operating in flat spacetime. Einstein’s field equations for general relativity (GR)
Gµ = 8Tµ (7) describe how curved spacetime geometry (Gµ ) is produced by the presence of matter or energy as described by the energy-momentum tensor (Tµ). Nickisch and Mollere have considered the possibility that electromagnetic fields, including that of the zero-point fluctuations, can be treated as a distortion in the spacetime of the charge. A massless charge would behave like a photon, following a null geodesic, but in a spacetime
defined by electromagnetic fields. A photon, in the absence of any energy or matter other than the zero-point fluctuations, will follow an unperturbed flat spacetime trajectory. However unlike the spacetime of a photon,
the spacetime of the massless charge is defined by the distortions of the zero-point fluctuations, producing a geodesic description of zitterbewegung. Additional electromagnetic fields may produce a non-zero-mean drift
of the zitterbewegung that is also accounted for in the geodesic motion. These non-zero-mean effects “accumulate” into a stretching of the particle’s spacetime, and this stretching is perceived by external observers
to be inertia.

http://www.arxiv.org/PS_cache/gr-qc/pdf/0209/0209016.pdf

 

[Mike2]

Update on an Electromagnetic Basis for Inertia, Gravitation,
the Principle of Equivalence, Spin and Particle Mass Ratios
If mass is due to this acceleration against thermal photons, then where does that leave the calculation of mass as vibrations in string theory?

 

[selfAdjoint]

This is Haisch, Rueda, and Puthoff, a way-out team of physicists trying to get new physics from the ZPE. Not even Sarfatti takes them seriously.

 

[sol2]

Update on an Electromagnetic Basis for Inertia, Gravitation,
the Principle of Equivalence, Spin and Particle Mass Ratios
If mass is due to this acceleration against thermal photons, then where does that leave the calculation of mass as vibrations in string theory?

For me just trying to grasp the significance of the brane theories is really quite a feat, but one thng is known within that theory, and that is the photon as a boson, is connected to the brane/branes.

If we change around the question in regard to glast, how photon interactions are showing us discrete features by the path integral approaches in regards to gamma ray detectors, how would you measure the photons interaction with the bulk/gravitons?

Do you accept the feature of the energy as telling you, by its' very existence that the history sits along side of the mass features, as signs of what had existed before. What indicators allow you to decide, what matters could become from those signature particles?

So even in the Planck epoch, what signatures would tell the universe to become the way it is?

You know I have a lot of questions also and they help me to focus. Becuase you asked a question yourself, other factors, detail the responds. Not always direct I know. I am sorry, but I too am learning.

https://www.physicsforums.com/showthread.php?goto=newpost&t=38773

Specifically elemental considerations on the moon cannot help us see what signatures can arise from the Planck epoch? Yet things end up the way they do, and we have to ask ourselves? Why iron?

So we have detailled the beginning in the Planck epoch to now. What in that history to now, is consistent?

If you accept the continuity and flow of time in regrads to 4 dimensional spacetime, we are lead to see in other ways, then the way the world allows us to see just the moon.

Acceptance of the unification of electromagnetism with gravity, how would you approach seeing?

The bubbles arise out of this sea and low and behold, everything we need is within that bubble. It encapsulates everything. So some like to extend this vision of bubble dynamics like Pelastrian does, and if we prodcue certain commentators in the links we supply, how would you, in accepting certain conditions, see what they are sayng, above and beyond Einstein, with these bubble technologies?

The Higher Sphere is choosen then not just for detailing casimere dynamics or bubble pressures outside influenced by boudaries, but the dynamcis of the geometry, is very telling then? You see?

Early universe detectors in gamma rays help us much closer to the temperature of that early universe, but is still a long ways from the essence of the Planck epoch. So we have to look at it in other ways

Being more then the pure antagonist, we look for ways in which we can use that light switch in producing more neuron synapse connectors, like those pearl and chains, in the cosmic strings. Who knows, this might be God's brain we are seeing inthe cosmos? :rofl: The chemistry would be very musically inclined.

 

[sol2]

This is Haisch, Rueda, and Puthoff, a way-out team of physicists trying to get new physics from the ZPE. Not even Sarfatti takes them seriously.

Go with me here for a minute.

Thrown a blanket over all of them(Sarfartti included), and what the heck are they doing? The blanket( a part of the bubble) saids, there are different shapes evolving from what they propose.

You have to apply this to all thinking. It is a paradigmal/model grokked?

If you take everything out of space, what is left? The blanket saids something would it not, as you are doing this?

 

[selfAdjoint]

Whenever I hear the phrase paradigm change, I reach for my textbooks.

 

[sol2]

Whenever I hear the phrase paradigm change, I reach for my textbooks.

As you should.

Strings, loop, and twistors all of are new paradigms, right? Or maybe my definition is different then yours?

Because you do no accept Kuhn, does not make the issue of paradigms go away. If you like, let's call them models. You accept models, and it changes the way you see? Is that better? :uhh:

 

[selfAdjoint]

From the Kuhn POV, strings, twistors, and even LQG are "normal science". Theory continuously connected to existing theory. The paradigm is quantization and both strings and LQG are within it. C^{* algebras on Hilbert spaces. Closure of the algebra. A paradigm shift would be at right angles to quantization. Many fakers and many cranks have claimed it, but not one has brought it off.}

 

[sol2]

If you noticed, my post previous to yours was http://superstringtheory.com/forum/metaboard/messages12/33.html

Its all in the "timing"?

Time and memory shape our perceptions of our own identity. We may feel ourselves to be at history's mercy, but we also see ourselves as free-willed agents of the future. That conception is disturbingly at odds with the ideas of physicists and philosophers, however, because if time is a dimension like those of space then yesterday, today and tomorrow are all equal.

http://www.sciam.com/singletopicissue/

What's normal science when you find numbers that arise, that are the same in other places? Coincidence? A cosmic wormhole that connects the same numbers and time? So what would be different of Self Adjoint from the person he was before?

Sol,

I don't think Kuhn is ever more in error than in this description of what he calls normal science. Either there is no normal science in his sense, or he just doesn't have any grasp of how real science goes along.

In real life physicists, both theorists and experimenters, are hungry for "physics beyond the standard model". The media hype over misundrstood "FTL" experiments and muom magnetic moment is just the tip of an iceberg of intense hunting for new facts and theories.

I don't know what world Kuhn is describing, but it's not this world.

Regards,

Yes I see what you mean. What's Normal?

Sol,

Let's see..

It is like, in some sense of developing the logic would you not say and we recognize the procedures then to the validation of things. I believe I have shown that even amidst the constants, there is always room for a mystery, or we would not have those who forge ahead.:)

This is a statement of faith, a faith that most present day physicists would subscribe to. Most of them would believe that "lateral thinking" will be necessary to move beyond the present unsatisfactory situation (The Standard model with its 19 or so arbitrary parameters and General Relativity, with its problems and neither of them having anything to do with the other).

I do not believe you will find the new physics on these boards. Most of the folks who post new theories do not have enough knowledge or mathematical skill. Like it or not, to know which crazy idea is the right one takes a lot of training.

Common sense isn't any help either. It's just the high mass, low speed approximation, and the fact that it's the physics we grew up with doesn't count.

Of course we are talking about something almost two years ago.

You see it is very difficult for me to express something mathematically yet I know, it is the substance of discerning the hills from the valleys:) You know like talking about some sub structure to space. Why things gravitate

What is the organizing principle amidst the matters? So I say a String is Energy, and then I say, a String Curves,

Olias asks the question about the "Higgs"(a professor crosses the room?) in string theory.

We know this fundamental question is looming on the horizon in terms of experimentation. So how much closer are we to the Planck epoch and "what lies beneath." So what is this organizing principal and low and behold, we have to accept certain fundamental theories, about the existing theories and gravitational waves, have yet to be proven?

There is a paradox that arises for me.

From the early universe, if such plasmatic conditions existed, and the bubbles formed from this epoch, would we recognize supergravity?

If energy is suppose to reveal this feature in terms of high energy consideration ,in terms of the gravitons in the bulk, then how "thick" indeed, is the gravitons in the bulk period. So you see, we have to assume something about the gravitational collapse?

Olias, has a very keen eye for such anomalies, like that card(six of red spades) he did not miss it the first time:)

http://news.uns.purdue.edu/images/taleyarkhan.r.jpg
Rusi Taleyarkhan

They haven't given up, and it might provides answers as long as this process continues to work? Energy in, energy out(graviton one of its forms) so how would we use this feature? Gravitational collapse maybe?


http://news.bbc.co.uk/olmedia/1570000/images/_1573450_mast150.jpg

Controlling the eddies and whirls of the writhing plasma so that it can burst into life as a miniature Sun has been a formidable, and so far only partially met, engineering challenge.

"If we follow the Mast idea and not the Jet one, we could imagine a string of medium-scale fusion reactors instead of a few very big ones," said Dr Sykes

http://news.bbc.co.uk/1/hi/sci/tech/1573450.stm

Sort of reminds of a show that I went looking for, that had Keenu Reeves and Morgan Freeman who had created this new energy device? It had to have just the right note to initiate.





So indeed, we walk a fine line

 

[selfAdjoint]

There are two ways of testing new theories, one of course is experiment. The other is connection to present day science. This connection would be expressed mathematically, just as the calculations to predict experiments have to be mathematical. Strings, twistors, and LQG all are missing the experimental test so far, but they all pass the connection test; read Rovelli's book, or Zwiebach's first course in string theory or from what I've heard Penrose's new book, and you will see the author's pet theory DERIVED FROM KNOWN PHYSICS. From quantum mechanics and relativity and electromagnetism, in fact.

Now when I said that physicists hunger for the new breakthrough, I didn't mean a breakthrough that simply ignores present day physics. If we have to break the quantization paradigm (I don't at all imply that we do!) then we have to explain why and how we do that. This is bound to be an argument like the one over Thiemann's LQG approach to string theory, all about technicalities that the general population can't follow. Even if somebody came up with an easily understood principle that gave a valid way out of quantization, it would have to be explained on the basis of existing mathematical models of the universe.

Kuhn's two examples of paradigm shift that he produced professional histories of are Copernicus' revolution and Planck's introduction of quantized emission and absorption of radiation. In both cases they justified their new ways with traditional math. Copernicus showed that the diameters of the planetary deferents always passed through the sun, in terms of the epicycle theory. And Planck showed that the quantum followed form 19th century mathematical idealizations of the black body.

 

[sol2]

There are two ways of testing new theories, one of course is experiment. The other is connection to present day science. This connection would be expressed mathematically, just as the calculations to predict experiments have to be mathematical.

I am often reminded of the road to validation, and it has not past my attention that such devlopements have there roads to follow.

I am reminded of those like Peter Woit who hold firmly to the validation process, even though the mathematical routes are being established. My discussions with you over the years have reiterated this stance you yourself have held to in terms of, listen we'll wait and see what comes, yet nothng conclusive had been reached.

We talked about the creation of math, whether it was natural or invented? Yet the roads too,are always a interesting assesssment? I speak of Smolin here again and his mode of operandi. A new math emerges? What the heck does this mean?

Strings, twistors, and LQG all are missing the experimental test so far, but they all pass the connection test; read Rovelli's book, or Zwiebach's first course in string theory or from what I've heard Penrose's new book, and you will see the author's pet theory DERIVED FROM KNOWN PHYSICS. From quantum mechanics and relativity and electromagnetism, in fact.

You run for the books, yes I heard you the first time.

Now when I said that physicists hunger for the new breakthrough, I didn't mean a breakthrough that simply ignores present day physics. If we have to break the quantization paradigm (I don't at all imply that we do!) then we have to explain why and how we do that.

Well I am going to give you a example, and you can tell me if they did not find something weird. Anomalistic you might say. One sec.

Einsteins position on EPR, and what did John Bell do for us? Now we have these crazy people who talk about quantum entanglement? And now imagine...teleportation

Theoretical positions change the way we percieve things, although indeed, must be grounded in some reality? In order to delve into those theoretcial positions it mght be a philosophy that begins the creation of this math or that math? There had to be some logical reasoning applied to the pursuate of any of these directions.

https://www.physicsforums.com/showpost.php?p=277080&postcount=18

But that's not what I wanted to show you, so I'll get right to it.

Peter or Jeff can answer with "credibitly" as to what is being done in the colliders. String theory developed out of the need to comprehend where this energy was going, and pushing for great energy requirments, found limitations

https://www.physicsforums.com/showpost.php?p=277026&postcount=13

.

Now why would I ask such stupid questions? And finally we are back to the point.

Kuhn's two examples of paradigm shift that he produced professional histories of are Copernicus' revolution and Planck's introduction of quantized emission and absorption of radiation. In both cases they justified their new ways with traditional math. Copernicus showed that the diameters of the planetary deferents always passed through the sun, in terms of the epicycle theory. And Planck showed that the quantum followed form 19th century mathematical idealizations of the black body.

Well let's not forget the ideas that have developed the roads to general relativity. Leading perspective changes, in regards to Mecuries orbits or Taylor and Hulse, is "not" the point of Quantization? It is to explain what is happening with the energy produced from one, the orbit and two, the rotational binary stars. Each one of these processes is leaving us with "information" in the bulk.

Now what does that "information" consist of?

You see where http://www.sciam.com/singletopicissue/ has a really interesting angle here?

The past, present and future are only illusions, even if stubborn ones

Now imagine being in a sea of gravitons where every graviton is describing one part of the GR wave. Would gravitons of one part of the wave, be similar to another grvaiton describing the same wave in another location? Are these two location actually connected in terms of dimensions?

What is the organizing principle amidst the matters? So I say a String is Energy, and then I say, a String Curves,

How the heck did they get to branes?

 

[selfAdjoint]

Now imagine being in a sea of gravitons where every graviton is describing one part of the GR wave. Would gravitons of one part of the wave, be similar to another grvaiton describing the same wave in another location? Are these two location actually connected in terms of dimensions?

Not if those are stringy gravitons and the two locations are spacelike related. String theory respects relativity, as I said.

Originally Posted by sol2
What is the organizing principle amidst the matters? So I say a String is Energy, and then I say, a String Curves

Exactly the problem. A string is not "energy", they are two different things. And as for curving, the point of strings is that they vibrate, and we are in a sea of that, vibrating strings so small they can't be seen with our equipment, but the vibrations making the particles that we see.

The point is that what I just said can be developed coherently, mathematically, from QM, EM, and SR, plus the string Lagrangian, and what you said cannot.

 

[sol2]

Exactly the problem. A string is not "energy", they are two different things. And as for curving, the point of strings is that they vibrate, and we are in a sea of that, vibrating strings so small they can't be seen with our equipment, but the vibrations making the particles that we see.

See, I am speaking also of the windings. I just asume that this is understood. Not only are we holding a magnefying glass to the cosmos, we are holding it to the energy consideration we currently use in our colliders. Sometimes we have to hold it to the fine print

I am looking at this situation from two standpoints. One the gravitonic one, and the other, from a energy consideration. Yet I recognize the layering that is going on. I see the electromagnetic field and outside of that .

Of course I reocgnize the history to this developement. Remember that T-shirt those college students like to wear, and Then There Was Light?

So we take it a step further. You know what this means right?

Obvious though this commonsense description may seem, it is seriously at odds with modern physics. Albert Einstein famously expressed this point when he wrote to a friend, "The past, present and future are only illusions, even if stubborn ones." Einstein's startling conclusion stems directly from his special theory of relativity, which denies any absolute, universal significance to the present moment. According to the theory, simultaneity is relative. Two events that occur at the same moment if observed from one reference frame may occur at different moments if viewed from another.




The most straightforward conclusion is that both past and future are fixed. For this reason, physicists prefer to think of time as laid out in its entirety--a timescape, analogous to a landscape--with all past and future events located there together. It is a notion sometimes referred to as block time. Completely absent from this description of nature is anything that singles out a privileged special moment as the present or any process that would systematically turn future events into present, then past, events. In short, the time of the physicist does not pass or flow.

Scratch scratch! Hmmmmmm...I move my hand through the thickness of these gravitons and they just seem to fall in behind

Continuity and topology, have there place in the roads of projective geometry do they not? It has to be consistent.

The point is that what I just said can be developed coherently, mathematically, from QM, EM, and SR, plus the string Lagrangian, and what you said cannot.

What I did say is that there is a distilling going on and the information that I present in response has to be consistent. I am observing, and gathering perspective thoughts.

Although, I might think that the world in which we live has a direct relation to the consciousness we hold, I have never shown this position?

Time

 

[sol2]

MOved from other location

Moving to non euclidean perspectives, are very important features of moving from the fifth postulate of Euclid. I wonder, about those like Saccherri, Gauss and Reimann. It is a new way seeing beyond what we are accustom too, and these gentlemen are very instrumental in this process. Exploring the realm here then one can also point to Kaku and ask how could any mind project itself into the eyes of the carp and then look to the surface of the water?

Many of the theorems found in today's non-Euclidean geoemtry textbooks ultimately are derived from the theorems proven in Jerome Saccheri's 1633 book - and this usually without crediting Saccheri. Here are presented a few of his theorems illustrated by using the Poincaré model.

By use of similar triangles and congruent parts of similar triangles on the Saccheri quadrilateral, ABDC with AC = BD and ‚A = ‚B = p/2, he establishes his first 32 theorems. Most are too complicated to be treated in a short paper, but here some examples are merely stated, some are illustrated and some are proven. For those proofs which are brief enough to show here, the main steps are indicated and the reader is invited to fill in the missing details of the argument. A century after Saccheri, the geometers, Lobachevsky, Bolyai and Gauss would realize that, by substituting the acute case or the obtuse case for Euclid's postulate Number V, they could create two consistent geometries. In doing so they built on the progress made by Saccheri who had already proven so many of the needed theorems. They were able to create what we recognize today as the "elliptical" and "hyperbolic" non-Euclidean geometries. Most of Saccheri's first 32 theorems can be found in today's non-Euclidean textbooks. Saccheri's theorems are prefaced by "Sac."

http://www.faculty.fairfield.edu/jmac/sj/sacflaw/sacther.htm

So we look for other ways in which to interpret the curvature parameters and to get a feel for the dynamics in the realm of non-euclidean perspective. Looking at gaussian fields help as well as the metric fields

Helmholtz was the first to advocate the idea that human beings, living in a non-Euclidean world, would develop an ability of visualization which would make them regard the laws of non-Euclidean geometry as necessary and self-evident, in the same fashion as the laws of Euclidean geometry appear self-evident to us. (308)

http://www.bun.kyoto-u.ac.jp/~suchii/RonHelmholtz.html

Things get more complicated when we graduate from space to spacetime. Remember that the Minkowski metric has a spacetime distance function dS2 that can be negative, positive or zero, whereas the distance functions in space dL2 can only be positive.


The means we have to separate our geodesics on the basis of whether the distance function dS2 is positive, negative or zero. Goedesics with dS2 < 0 are called spacelike geodesics. Goedesics with dS2 = 0 are called null geodesics. Goedesics with dS2 > 0 are called timelike geodesics. The behavior of timelike and null geodesics are the most important for understanding time travel.

Timelike geodesics behave the opposite from geodesics in space. They actually represent the longest spacetime distance between two spacetime events.

http://www.theory.caltech.edu/people/patricia/grelb.html

Non-Euclidean Geometry

Since the bounding circle is "infinitely far away", the motion of the picture does not exactly parallel the mouse drag motion, but instead moves about the same non-Euclidean distance as the Euclidean distance moved by the mouse. So the picture will appear to lag behind the mouse.

http://www.math.umn.edu/~garrett/a02/H2.html

Further to understanding these dynamics the ideas of this flat universe concide nicely from what I see, relevant to the CMB temperature our universe is now holding. If we look back to the temperature values of our perspective looks we soon learn to see what a supermicroscope the colliders are in helping us in undertanding the first moments of the universe and it's compacted shape.

http://physicsweb.org/objects/world/13/11/8/pw1311084.gif

According to Einstein's general theory of relativity, the gravitational potential due to an isolated source is proportional to rho + 3P, where rho is the energy density and P is the pressure. For non-relativistic matter the pressure is negligibly small, whereas for radiation P = rho/3. Therefore, for the same value of the energy density, radiation produces a deeper and more attractive gravitational potential (left) than non-relativistic matter (centre). If rho + 3P is negative, as in the case of quintessence * in this example P = *2rho/3 * the sign of the gravitational field is transformed from attractive to repulsive (right).

http://physicsweb.org/box/world/13/11/8/pw1311084

http://www.faculty.fairfield.edu/jmac/sj/sacflaw/B1.GIF


It came down to the question of using the triangle on different surfaces. By adding up the degrees it was easy then to assume the shape with which these surfaces spoke of themself.

So now we see where this universe having assumed such a large spherical extension of a early expansive form, has reached the flatness of today?


You have to remember the direction the temperatures values are leading us in its cooling function. Look back to the beginning of the universe and what do you see? If particle discriptions, are becoming evident and the energy values climbing, what has been revealed?

Reductionistic views, have paved the way for extraordinary energies and what is happening in the cosmos. You have made a exchange, from a reductionsitic one, to a energy one.

Of course we are assuming that your are developing your geometry along the way much like Einstein did with help from Grossman(Where has projective geometry lead us?). Does this road end?

Of course not and why all of sudden we have this topic about Quantum geometry explaining quantum gravity.

But there is a problem with relativistic views explaining, and integrating with the small word of the colliders. You had in this exchange a realization that geometrically forced you to consider the strength of those gravitational fields?

I am of course open to corrections.