Wave Function and Summing over Histories

Dealing with a 5D World

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".

Paul Valletta:

Being that photons are the energy needed for observation by ‘observers’, what happens to a system when the limit of observation is at a minimum ie single photons?

Of course, I could be wrong?:)

"Which Way"? :)

Bohr's principle of complementarity predicts that in a welcher weg ("which-way") experiment, obtaining fully visible interference pattern should lead to the destruction of the path knowledge. Here I report a failure for this prediction in an optical interferometry experiment. Coherent laser light is passed through a dual pinhole and allowed to go through a converging lens, which forms well-resolved images of the respective pinholes, providing complete path knowledge.

Maybe comparative views can be held in context of the graviton as a force carrier as well, when thinking about your question above? There is a "certain influence" over top of your question?

Will this help us to move beyond the standard model?

Sometimes such a change in perception is necessary, to look to what is "contained" in the "wave function," yet there is something left over, that we had not analyzed yet?

How shall we describe this in context of the fifth force? Such a solution recognizes the advances made in GR with the encapsulation of Maxwell's equations and as well the leading indicators to such geometries, that we had witness in working to the Riemann sphere. BUt beyond this in compactive states of existance(quantum mechanics), how shall such views be encapsulated?

An Introduction to String Theory A Talk by Steuard Jensen, 11 Feb 2004

So how does all this come together into a physical theory? It turns out that the proper procedure is to construct every possible diagram allowed by the theory (for a given state of input and output particles and how they're moving) and add up the corresponding complex numbers. The result is essentially the "wave function" for that specific input-output state combination, and by squaring that number you can determine the probability that the given input will result in the given output. Doing that is how theorists at particle accelerators earn their keep.

Under these principals how shall a photon react to the enviroment in which it is moving? Moving, to encapsulate such views by moving to a fifth force is necessary.



While it is not always easy to see what is taking place, by perserverance I hope to one day understand the fullscope :)


Oskar Klein Collegiate Professorship Inaugural Lecture: "The World in Eleven Dimensions"by Michael Duff




Why?

Such a view of the photon held in context of the fifth force is the joining of gravity and light?

The least-action principle is an assertion about the nature of motion that provides an alternative approach to mechanics completely independent of Newton's laws. Not only does the least-action principle offer a means of formulating classical mechanics that is more flexible and powerful than Newtonian mechanics, [but also] variations on the least-action principle have proved useful in general relativity theory, quantum field theory, and particle physics. As a result, this principle lies at the core of much of contemporary theoretical physics.

Thomas A. Moore "Least-Action Principle" in Macmillan Encyclopedia of Physics, John Rigden, editor, Simon & Schuster Macmillan, 1996, Volume 2, page 840.

It is far better to understand the workings then just have wave a hand at it and said what a "crock of this or that"? What is worth while, that has been put into thinking here?

You just can't sweep it under the rug, and all is fine. Models, help in this regard, and if your comments were deleted becuase you didn't tow the party line, then should you have followed such orders and dismiss this model(your model?) which motivates to comprehension?

Some seem to think so, while they are held in the "same regardas arvix?" to which they themselves have handed out their criticisms and deletions. People who understand this statement, will know exactly what I mean. Those that don't. It wasn't meant for you :)

Laval Nozzle and the Blackhole

Often times model changes help perspective, where previously idealization will be contained. Moving beyond the experimental grasp for new ways in which to interpret, require a mode and offensive into producing new variations of ole thngs held in context? Ths is why such models like string that began in one mode in terms of quark confinement have now bloossomed into modes cocnerned with quantum gravity.



Discovering new dimensions at LHC

More dramatically still, the LHC could produce fundamental string relations of our familiar particles, such as higher-spin relatives of electrons or photons. There is also a possibility that, owing to the now much stronger gravitational interactions, microscopically tiny black holes could be produced with striking signals.

Once idealization and understanding developed in quark Confinement, it is understood the shift to the metric and the idealization of that measure became a property I found in the way we now deal with the perceptions containing dimensional significance? Strng Theory, that had graduade from the model apprehensions early on, here to a more fundamental pursuate of how we see in those extra dimensions, compact as they may be?

Acoustic Metric (29 Dec 2005 Wiki)

In mathematical physics, a metric (mathematics) describes the arrangement of relative distances within a surface or volume, usually measured by signals passing through the region – essentially describing the intrinsic geometry of the region. An acoustic metric will describe the signal-carrying properties characteristic of a given particulate medium in acoustics, or in fluid dynamics. Other descriptive names such as sonic metric are also sometimes used, interchangeably.

Since "acoustic" behaviour is intuitively familiar from everyday experience, many complex "acoustic" effects can be confidently described without recourse to advanced mathematics. The rest of this article contrasts the "everyday" properties of an acoustic metric with the more intensely studied and better-documented "gravitational" behaviour of general relativity

On the Universality of the Hawking Effectby William G. Unruh and Ralf Schutzhold

Addressing the question of whether the Hawking effect depends on degrees of freedom at ultra-high (e.g., Planckian) energies/momenta, we propose three rather general conditions on these degrees of freedom under which the Hawking effect is reproduced to lowest order. As a generalization of Corley’s results, we present a rather general model based on non-linear dispersion relations satisfying these conditions together with a derivation of the Hawking effect for that model. However, we also demonstrate counter-examples, which do not appear to be unphysical or artificial, displaying strong deviations from Hawking’s result. Therefore, whether real black holes emit Hawking radiation remains an open question and could give non-trivial information about Planckian physics.

It is important that when thinking about this universality that the derivations of such thinking is understood by me so I ahve to lay it out in a sequence that suports the end part of this post so that it is brought togher in a nice way. I bold mark thos epoints that help greatly in my understanding.

Acoustic_theory(28 Dec 2005 Wiki)

Acoustic theory is the field relating to mathematical description of sound waves. It is derived from fluid dynamics. See acoustics for the engineering approach.

The propagation of sound waves in air can be modeled by an equation of motion (conservation of momentum) and an equation of continuity (conservation of mass). With some simplifications, in particular constant density, they can be given as follows:


where is the acoustic pressure and is the acoustic fluid velocity vector, is the vector of spatial coordinates x,y,z, t is the time, ρ0 is the static density of air and c is the speed of sound in air.

Fluid Dynamics (28 Dec 2005 Wiki)

Fluid dynamics offers a mathematical structure, which underlies these practical discipines, that embraces empirical and semi-empirical laws, derived from flow measurement, used to solve practical problems. The solution of a fluid dynamics problem typically involves calculating for various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time

So these ideas in terms of analogies help to push forarwd understanding where we might have been limited in our views before. I know, they certainly help me.

"Analogue Gravity"
by Carlos Barceló and Stefano Liberati and Matt Visser

Abstract

Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).

and here......

Parentani showed that the effects of the fluctuations of the metric (due to the in-going flux of energy at the horizon) on the out-going radiation led to a description of Hawking radiation similar to that obtained with analogue models. It would be interesting to develop the equivalent formalism for quantum analogue models and to investigate the different emerging approximate regimes.

I am always interested in how science might take these analogies in concert with how we understand blackhole horizon abilites. To exemplify the understanding of where "this place of virtual reality might issue from such a ground state" might be, in terms of what might flow one way, and what will flow in another, as photon pairs do from around the blackhole.

How far can this be taken as we look to understand Hawking radiation? How would such constrictions pave the way for sound emitted and held in context of Hawking Radiation, flowing through a pipe? We've had our lessons from Cosmic Variance on this, but would it have ever been taken this far?

Well, I still like to think about the gravitational comparisons here, so I would be very happy to have found some geometrical propensities towards how the horizon would have given us a good picture of what "first principle" might be as we look at the nature of hawking radiation, and how the standard model is featured from that horizon. So of course I am thinking deeply about all the things I have been learning.

I hope one day a comprehensive picture forms so that I can finally understand what is going on?

Further "Analogy" sought by me to help my perspective.

Bubble World and Geometrodynamics

Tiny Bubbles

Making Sense of the Nonsensical

From this experiment it is apparent that interference is destroyed by a "which-way" marker and that it can be restored through erasure of the marker, accomplished by making the appropriate measurement on the entangled partner photon p.

In this set up, the "which-way" measurement does not alter the momentum or position of the photons to cause destruction of the interference pattern. We can think of the loss of interference as being due only to the fact that the photons are entangled and that the presence of the quarter wave plates changes this entanglement. The interference pattern can be brought back through the erasure measurement because of the entanglement of the photons, and the way that the presence of the quarter wave plates and polarizer changes the entanglement.

It is very obvious I need some time to digest and listen carefully here. Of course I draw from Wiki quite regularly and I hate to think such efforts to destroy a concerted effort by those whose hearts are pure, for leading others into the correct methods, would not resort ot the efforts and likes of those Lubos has brought to our attention.

ON the note below taken from Lubos update, it is without thinking that I might have lured others into the state of complacency without fully understanding, and hence my part in this effort less than kind? So I'll draw back for a bit here and try and digest what I learnt and see if I can get it together.

Lubos Motl:

Note added later: let me mention that Kastner has submitted another paper criticizing Afshar's conclusions. In my opinion both Unruh as well as Kastner replace Afshar's experiment by a completely different experiment that does not capture the main flaw of Afshar's reasoning. The main flaw is that Afshar does not realize that for a tiny grid, only a very tiny percentage of photons is used to observe the wave-like properties of light; these are essentially the photons for which the which-way information is completely lost. Because most photons go through the lens without any interactions and interference, Afshar is not allowed to say that he observes the wave-like phenomena with visibility close to one. In fact, it is close to zero if a consistent set of photons is used to define both V and K.

Here is the paper >Kastner talks too in regards to the content of Afshar experiment.

Why the Afshar Experiment Does Not Refute ComplementarityR. E. Kastner

ABSTRACT. A modified version of Young’s experiment by Shahriar Afshar demonstrates that, prior to what appears to be a “which-way” measurement, an interference pattern exists. Afshar has claimed that this result constitutes a violation of the Principle of Complementarity. This paper discusses the implications of this experiment and considers how Cramer’s Transactional Interpretation easily accomodates the result. It is also shown that the Afshar experiment is analogous in key respects to a spin one-half particle prepared as “spin up along x”, subjected to a nondestructive confirmation of that preparation, and post-selected in a specific state of spin along z. The terminology “which-way” or “which-slit” is critiqued; it is argued that this usage by both Afshar and his critics is misleading and has contributed to confusion surrounding the interpretation of the experiment. Nevertheless, it is concluded that Bohr would have had no more problem accounting for the Afshar result than he would in accounting for the aforementioned pre- and
post-selection spin experiment, in which the particle’s preparation state is
confirmed by a nondestructive measurement prior to post-selection. In addition,
some new inferences about the interpretation of delayed choice experiments are
drawn from the analysis.

1. Introduction.The Young two-slit experiment is a famous illustration of wave-particle duality: a quantum particle emitted toward a screen with two small slits will produce an interference pattern on a detecting screen downstream from the slits. On the other hand, as has been repeatedly demonstrated, if one tries to obtain “which-way” or “which slit” information, the downstream interference

Presence and Entanglement

The equivalence principle(29 DEcember 2005 Wiki)

The accuracy of the gamma-ray measurements was typically 1%. The blueshift of a falling photon can be found by assuming it has an equivalent mass based on its frequency E = hf (where h is Planck's constant) along with E = mc2, a result of special relativity. Such simple derivations ignore the fact that in general relativity the experiment compares clock rates, rather than than energies. In other words, the "higher energy" of the photon after it falls can be equivalently ascribed to the slower running of clocks deeper in the gravitational potential well. To fully validate general relativity, it is important to also show that the rate of arrival of the photons is greater than the rate at which they are emitted

From a layman perspective, I am seeing that the nature of the gravitational field in a circumstance where such "strengths and weaknesses" would have been viable property to our way of seeing?

Lensing by showing us, that such avenues would have found the valution of the photon travelling the quickest route?

So, by changing the face of what we had always agreed upon( encapsulating Gr perspective bulit upon Maxwells creations and the geometries), as the way of energy and matter relation, such presence, would have then said, as a force carrier, that in these two cases, I will always be the way you would interpret my being in gravitational context?? You assume the model

So "always" in the "presence" of a gravitational field?

Fifth force(29 Dec 2005 Wiki)

A few physicists think that Einstein's theory of gravity will have to be modified, not at small scales, but at large distances, or, equivalently, small accelerations. They point out that dark matter, dark energy and even the Pioneer anomaly are unexplained by the Standard Model of particle physics and suggest that some modification of gravity, possibly arising from Modified Newtonian Dynamics or the holographic principle. This is fundamentally different from conventional ideas of a fifth force, as it grows stronger relative to gravity at longer distances. Most physicists, however, think that dark matter and dark energy are not ad hoc, but are supported by a large number of complementary observations and described by a very simple model.

Now, I am having a bit of a problem with the idea of "high energy" being "redshifted" because of the nature of the blackholes gravitational force? IN this case such a presence wouldhave by nature and strength of curvatures would have forced high enegy states to immediately curve backwards. If such blueshigfting is free to penetrate the fastest routes then such signs woudl have gave indication, yet the immediate horizon vicinity, plays havoc on these ideas?

The only way one could ascertain such a state of redshifting, is if "high energy" was evident in proximaty of the blackhole?

Would this be true or false?

Entanglement

Hypercharge (29 Dec 2005 Wiki)

In particle physics, the hypercharge (represented by Y) is the sum of the baryon number B and the flavor charges: strangeness S, charm C, bottomness and topness T, although the last one can be omitted given the extremely short life of the top quark (it decays to other quarks before strong-interacting with other quarks).

Plectics, by Murray Gellman

It is appropriate that plectics refers to entanglement or the lack thereof, since entanglement is a key feature of the way complexity arises out of simplicity, making our subject worth studying.

So by simlifying these ideas of entanglement, we find a model building from the orientation supplied by Murray Gellman, where expeirmentatin and hisortical pursuate have created a legitamate question about what Penrose might ask of a New quantum world view?




Secondly, entanglement issues were progressive, and historically this helps clear up the issues of spooky?


While dissident took us fastidiously to Hooft, I could also interject with Penrose?

But in doing so, such progressions from "simplifed states of plectics" would have taken us through a whole host of idealization in terms's of "dimensional significance," had we adopted Hooft's holographical vision?

If by Hooft's very beginnings, we had thought deeply about the progresions he had taken us too, then how would such developements have looked, if we were the prisoners, and the light behind us, pointed to the shadows on thew wall?

Acoustic Hawking Radiation

What did we learn from studying acoustic black holes? by Renaud Parentani

The study of acoustic black holes has been undertaken to provide new insights about the role of high frequencies in black hole evaporation. Because of the infinite gravitational redshift from the event horizon, Hawking quanta emerge from configurations which possessed ultra high (trans-Planckian) frequencies. Therefore Hawking radiation cannot be derived within the framework of a low energy effective theory; and in all derivations there are some assumptions concerning Planck scale physics. The analogy with condensed matter physics was thus introduced to see if the asymptotic properties of the Hawking phonons emitted by an acoustic black hole, namely stationarity and thermality, are sensitive to the high frequency physics which stems from the granular character of matter and which is governed by a non-linear dispersion relation. In 1995 Unruh showed that they are not sensitive in this respect, in spite of the fact that phonon propagation near the (acoustic) horizon drastically differs from that of photons. In 2000 the same analogy was used to establish the robustness of the spectrum of primordial density fluctuations in inflationary models. This analogy is currently stimulating research for experimenting Hawking radiation. Finally it could also be a useful guide for going beyond the semi-classical description of black hole evaporation.

I am held to a state of profound thinking when I thnk about Einstein in a dream I had. Where his satisfaction was raised, as a surpize, as I listen to the very sound of ice in a glass jug as I slowly turned it? From it, a certain recognition by Einstein held him in amazement as this sound seem to satisfy what he was so long search for in his answers. Yes it is a dream, but this set the stage from what I had been doing previous as I was thinking about the Webber bars and the way research was moving along this avenue to detect grvaiational waves. Movements to the giant Ligo inteferometers, to help us in our pursuate.

I know it is not always easy to understand the thinking here as it is piecemealed, while my minds works to weave a cohesive picture here. So, my apologies.

There is a special class of fluids that are called superfluids. Superfluids have the property that they can flow through narrow channels without viscosity. However, more fundamental than the absence of dissipation is the behavior of superfluids under rotation. In contrast to the example of a glass of water above, the rotation in superfluids is always inhomogeneous (figure). The fluid circulates around quantized vortex lines. The vortex lines are shown as yellow in the figure, and the circulating flow around them is indicated by arrows. There is no vorticity outside of the lines because the velocity near each line is larger than further away. (In mathematical terms curl v = 0, where v(r) is the velocity field.)

Early on the very idea of measuring discrete functions in relation to how we might percieve quark and gluonic natures which arose from the gold ion collisions, raises the very idea of how we may look at the analogies sought to help shape perspective from the horizon, to what is emitted? A Virtual Photon released in pair production at the horizon can become?

While I had come to recognize the differences in thermodynamic principals held in context of the blackhole, the very idea of He⁴raises some interesting scenario's in relation to sound values, while "extreme curvature" had been lead too as a singularity in the blackhole?? This singuarity thought to besimlar to the hawking no bondary proposal would not sit well with how the very nature of the blackhole actually becomes the superfluid that we hav come to recognize in the collider perspectives. This changes things somewhat. How fortunate is it in relation to how we see the supersymmetry that coudl arise inthe action fo symmetry break that signs could be lea dto the nature of the phton release and stretched under the aupsice of theis grvaiutional field?

Overlap of "quantum" and "classical" behaviour

Explanations of Hawking radiation around a black hole often use a description of quantum-mechanical pair production effects occurring on a curved spacetime background. Although this paradigm does not obviously lend itself to a "classical" reinterpretation, research on the black hole membrane paradigm has revealed some overlap between "classical" and "quantum" descriptions.

Plato:

What conditions would have allowed such a scene to be developed in supersymmetrical view, that I had wondered, could such a perfect fluid be the example needed? What blackholes hole would allow such a view to be carried down to this level in gold ion collisions, that we might see the results of string theory, as a useful analogy in the discernation of what can now be brought forward for inspection.

So having recognized the two phases of superfluids that ha dbeen created how woud such analogies move th emind to coisder this other nature of of a helium whose viscosity woud have allowed the sound to travel under the same aupsice held in context of the photon whose naure would havebeen rvealled in redshifting? Would suchj a thing held in context of blue shifting be cancelled out in quark/gluonic phases. that the analogy no longer suits our purpose? While sound i analogy in helium may have revealled the very nature of the superfluid designs we woudl like to see in comparsion to how thephotons are looked at with such short distances? They are cancelled out here?


Thorne: Black holes and time warps…, chapter 11, "What is reality?"

The laws of black-hole physics, written in this membrane paradigm, are completely equivalent to the corresponding laws of the curved-spacetime paradigm – as long as one restricts attention to the hole's exterior. Consequently, the two paradigms give precisely the same predictions for the outcomes of all experiments or observations that anyone might make outside a black hole …"

What is a Phonon/Photon?

Phonon:

A particle of sound. The energy E of a phonon is given by the Einstein relation, E = hf. Here f is the frequency of the sound and h is Planck's constant. The momentum p of a photon is given by the de Broglie relation, p = h/λ. Here λ is the wavelength of the sound

Photon:

A particle of light. The energy E of a photon is given by the Einstein relation, E = hf. Here f is the frequency of the light and h is Planck's constant. The momentum p of a photon is given by the de Broglie relation, p = h/λ. Here λ is the wavelength of the light.

As you look at the picture above, the very depths to which vision might have been imparted in recognition of this supefluid, what value would be assign something held in the context of the wave nature to have seen it described as a granulization and then thought of in terms of the langangrian perspective as cosmic strings which cross this universe? Make sure you click on the picutre.

Granularity of the Fluid?

Taken from the horizon, how would this fluid look if held in context of William Unruh's previously thought "continous nature" or as a discretium release of Hawking like phonons? It may be "by analogy" help physicists with respect to the nature of gravitational blackholes?

The Single Photon Experiment at Rowan University is a Success!

Einstein/Bohr Debate

"Not often in life has a man given me so much happiness by his mere presence as you have done," Einstein wrote to Bohr. "I have learned much from you, mainly from your sensitive approach to scientific problems."

John G. Cramer

This column is about experimental tests of the various interpretations of quantum mechanics. The question at issue is whether we can perform experiments that can show whether there is an "observer-created reality" as suggested by the Copenhagen Interpretation, or a peacock’s tail of rapidly branching alternate universes, as suggested by the Many-Worlds Interpretation, or forward-backward in time handshakes, as suggested by the Transactional Interpretation? Until recently, I would have said that this was an impossible task, but a new experiment has changed my view, and I now believe that the Copenhagen and Many-Worlds Interpretations (at least as they are usually presented) have been falsified by experiment.

The Single Photon Experiment at Rowan University is a Success!

Entanglement applies to two or more particles even if one of them is used as input to the two slit experiment, it is not applicable to single particle experiments.

Afshars experiment is conducted in such a manner that it is the setup of the experiment coupled with the conservation of momentum that allows us to know exactly which slit the photon has gone through.

Whilst knowing which way the photon has gone we also manage to show the absense of interference with both slits open via intererence minima.

Measurement without “measurement”: Experimental violation of Complementarity and its aftermath

Bohr’s Principle of Complementarity of wave and particle aspects of quantum systems has been a cornerstone of quantum mechanics since its inception. Einstein, Schrödinger and deBroglie vehemently disagreed with Bohr for decades, but were unable to point out the error in Bohr’s arguments. I will report three recent experiments in which Complementarity fails, and argue that the results call for an upgrade of the Quantum Measurement theory. Finally, I will introduce the novel concept of Contextual Null Measurement (CNM) and discuss some of its surprising applications. Web-page: users.rowan.edu/~afshar/ Preprint (published in Proc. SPIE 5866, 229-244, 2005): http://www.irims.org/quant-ph/030503/

Violation of the principle of complementarity, and its implications
Shahriar S. Afshar

Bohr's principle of complementarity predicts that in a welcher weg ("which-way") experiment, obtaining fully visible interference pattern should lead to the destruction of the path knowledge. Here I report a failure for this prediction in an optical interferometry experiment. Coherent laser light is passed through a dual pinhole and allowed to go through a converging lens, which forms well-resolved images of the respective pinholes, providing complete path knowledge. A series of thin wires are then placed at previously measured positions corresponding to the dark fringes of the interference pattern upstream of the lens. No reduction in the resolution and total radiant flux of either image is found in direct disagreement with the predictions of the principle of complementarity. In this paper, a critique of the current measurement theory is offered, and a novel nonperturbative technique for ensemble properties is introduced. Also, another version of this experiment without an imaging lens is suggested, and some of the implications of the violation of complementarity for another suggested experiment to investigate the nature of the photon and its "empty wave" is briefly discussed.

Tiny Bubbles

AS a child, Einsten when given the gift of the compass, immediately reocgnized the mystery in nature? If such a impression could have instigated the work that had unfolded over timein regards to Relativity, then what work could have ever instigated the understanding of the Pea as a constant reminder of what the universe became in the mind of a child, as we sleep on it?

Hills and Valley held in context of Wayne Hu's explanations was a feasible product of the landscape to work with?

'The Princess & The Pea' from 'The Washerwoman's Child'

If Strings abhors infinities, then the "Princess's Pea" was really a creation of "three spheres" emmanating from the "fabric of spacetime?" It had to be reduced from spacetime to a three dimensional frame work?

Spheres can be generalized to higher dimensions. For any natural number n, an n-sphere is the set of points in (n+1)-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is, as before, a positive real number. Here, the choice of number reflects the dimension of the sphere as a manifold.

a 0-sphere is a pair of points
a 1-sphere is a circle
a 2-sphere is an ordinary sphere
a 3-sphere is a sphere in 4-dimensional Euclidean space

Spheres for n ¡Ý 3 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. The notation Sn is also often used to denote any set with a given structure (topological space, topological manifold, smooth manifold, etc.) identical (homeomorphic, diffeomorphic, etc.) to the structure of Sn above.

An n-sphere is an example of a compact n-manifold.

Was it really fantasy that Susskind was involved in, or was there some motivated ideas held in mathematical structure? People like to talk about him without really understandng how such geometrical propensities might have motivated his mind to consider conjectures within the physics of our world?

Bernhard Riemann once claimed: "The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean." His prophesy was realized later with Einstein's general theory of relativity. It is futile to expect one "correct geometry" as is evident in the dispute as to whether elliptical, Euclidean or hyperbolic geometry is the "best" model for our universe. Henri Poincaré, in Science and Hypothesis (New York: Dover, 1952, pp. 49-50) expressed it this way.

You had to realize that working in these abstractions, such work was not to be abandon because we might have thought such abstraction to far from the tangible thinking that topologies might see of itself?


Poincaré Conjecture Proved--This Time for Real
By Eric W. Weisstein

In the form originally proposed by Henri Poincaré in 1904 (Poincaré 1953, pp. 486 and 498), Poincaré's conjecture stated that every closed simply connected three-manifold is homeomorphic to the three-sphere. Here, the three-sphere (in a topologist's sense) is simply a generalization of the familiar two-dimensional sphere (i.e., the sphere embedded in usual three-dimensional space and having a two-dimensional surface) to one dimension higher. More colloquially, Poincaré conjectured that the three-sphere is the only possible type of bounded three-dimensional space that contains no holes. This conjecture was subsequently generalized to the conjecture that every compact n-manifold is homotopy-equivalent to the n-sphere if and only if it is homeomorphic to the n-sphere. The generalized statement is now known as the Poincaré conjecture, and it reduces to the original conjecture for n = 3.

While it is very dificult for me "to see" how such movements are characterized in those higher spaces, it is not without some understanding that such topologies and genus figures would point to the continuity of expression, as "energy and matter" related in a most curious way? Let's consider the non-discretium way in which such continuites work, shall we?

From one perspective this circle woud have some valuation to the makings of the universe in expression, would identify itself where such potenials are raised from the singular function of the circular colliders. Those extra dimensions had to have some basis to evolve too in those higher spaces for such thinking to have excelled to more then mathematical conjectures?

We can also consider donuts with more handles attached. The number of handles in a donut is its most important topological information. It is called the genus.

It might be expressed in the tubes of KK tower modes of measure? That such "differences of energies" might have held the thinking to the brane world, yet revealled a three dimensional perspective in the higher diemnsional world of bulk. These had to depart from the physics, and held in context?



Clay Institute

If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

While three spheres has been generalized in my point of view, I am somewhat perplexed by sklar potential when thinking about torus's and a hole with using a rubber band. If the formalization of Greene's statement so far were valid then such a case of the universe emblazoning itself within some structure mathematically inclined, what would have raised all these other thoughts towards quantum geometry?

In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being 'fit' inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above?

(Greene, The Elegant Universe, pages 248-249)


Was our thoughts based in a wonderful world, where such purity of math structure became the basis of our expressions while speaking to the nature of the reality of our world?


Bubble Nucleation

Some people do not like to consider the context of universe and the suppositions that arose from insight drawn, and held to possibile scenario's. I like to consider these things because I am interested in how a geometical cosistancy might be born into the cyclical nature. Where such expression might hold our thinking minds.


Science and it's Geometries?


Have these already been dimissed by the physics assigned, that we now say that this scenario is not so likely? Yet we are held by the awe and spector of superfluids, whose origination might have been signalled by the gravitational collapse?

Would we be so less inclined not to think about Dirac's Sea of virtual particles to think the origination might have issued from the very warms water of mother's creative womb, nestled.

Spheres that rise from the deep waters of our thinking, to have seen the basis of all maths and geometries from the heart designed. Subjective yet in the realization of the philosophy embued, the very voice speaks only from a pure mathematical realm, and is covered by the very cloaks of one's reason?

After doing so, they realized that all inflationary theories produced open universes in the manner Turok described above(below here). In the end, they created the Hawking-Turok Instanton theory.

The process is a bit like the formation of a bubble
in a boiling pan of water...the interior of this tiny
bubble manages to turn itself into an infinite open
universe. Imagine a bubble forming and expanding at the
speed of light, so that it becomes very big, very quickly.
Now look inside the bubble.

The peculiar thing is that in such a bubble, space and time
get tangled in such a way that what we would call today's
universe would actually include the entire future of the
bubble. But because the bubble gets infinitely large in
the future, the size of 'today's universe' is actually infinite.
So an infinite,open universe is formed inside a tiny, initially
microscopic bubble.

Collapse of the Blackhole

String theory grew out of attempts to find a simple and elegant way to account for the diversity of particles and forces observed in our universe. The starting point was to assume that there might be a way to account for that diversity in terms of a single fundamental physical entity (string) that can exist in many "vibrational" states. The various allowed vibrational states of string could theoretically account for all the observed particles and forces. Unfortunately, there are many potential string theories and no simple way of finding the one that accounts for the way things are in our universe.

One way to make progress is to assume that our universe arose through a process involving an initial hyperspace with supersymmetry that, upon cooling, underwent a unique process of symmetry breaking. The symmetry breaking process resulted in conventional 4 dimensional extended space-time AND some combination of additional compact dimensions. What can mathematics tell us about how many additional compact dimensions might exist?

One of the chief features that have caught my mind is the way in which extreme curvature might have been enlisted to take us a to a place where the infinities have been curtatiled to a way of thinking. You need a model in which to do this, if you are to think that the events in the unverse are to be considered out of what the pre big bang era might have entailed had ths action been defined properly?

So immediately one see's the benfit of cyclical unverses being developed as well as understanding that the particle reductionistic views were well within the range to consider superfluids as part of the working of this interior blackhole? How did one get there?


Kaluza-Klein theory

A splitting of five-dimensional spacetime into the Einstein equations and Maxwell equations in four dimensions was first discovered by Gunnar Nordström in 1914, in the context of his theory of gravity, but subsequently forgotten. In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of very small radius, so that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This extra dimension is a compact set, and the phenomenon of having a space-time with compact dimensions is referred to as compactification.

So first and formeost gathering a perpectve that could immediate take us into the understanding of how these circles could ahve gained value in conceptual models. Of course every one wants the truth and mathematics is saying okay where the heck do we find the matematics that is so pure that by the very means enlisted would take us from the states of superfluids and their capabilities?

Strominger:

That was the problem we had to solve. In order to count microstates, you need a microscopic theory. Boltzmann had one–the theory of molecules. We needed a microscopic theory for black holes that had to have three characteristics: One, it had to include quantum mechanics. Two, it obviously had to include gravity, because black holes are the quintessential gravitational objects. And three, it had to be a theory in which we would be able to do the hard computations of strong interactions. I say strong interactions because the forces inside a black hole are large, and whenever you have a system in which forces are large it becomes hard to do a calculation.

So it is very important that if such views are taken down to these extreme levels that some method be adopted to maintain what might have emerged from the basis of the reality where such pure states as superfluids, may have simplified, immmediate symmetry breaking as arisng from some geoemtrical method?

The general theory of relativity is as yet incomplete insofar as it has been able to apply the general principle of relativity satisfactorily only to grvaitational fields, but not to the total field. We do not yet know with certainty by what mathematical mechanism the total field in space is to be described and what the general invariant laws are to which this total field is subject. One thing, however, seems certain: namely, that the general principal of relativity will prove a necessary and effective tool for the solution of the problem for the toal field.

Out of My Later Years, Pg 48, Albert Einstein

Lubos reminds us in the "strominger linked statement" about the understanding that there is no physics, but I would like to work towards gathering perspective as I am to lead us to the theory in the thinking. What concepts made this thinking valuable might have arisen in the previous years might have found itself explained over and over again.

Where does the pure mathematics changes it's form?

If conceived as a series of ever-wider experiential contexts, nested one within the other like a set of Chinese boxes, consciousness can be thought of as wrapping back around on itself in such a way that the outermost 'context' is indistinguishable from the innermost 'content' - a structure for which we coined the term 'liminocentric'.

The drive to tke this down to such levels of perception and wipe away all the faces of our concepts seems a hard struggle yet I think it a very capable thing in any mind that would move to the forms of pure math? What are these?

Such a simple psychological thinking that would have maintained our views, and find that enlightenment is just a few short steps away. Some mathematics might emerge that will unfold into our everyday world that wil bring together so many things?

So from where in all the probabilstic states could such thinking reveal the smoothness of topological fucntions and relayed the working of all the states havng been reached in the blackhole? Travels of the circle measured in te radius of that same cicle gives inherent energy valution to the concept of the blackhole being multiplied to seeing the macroscopic view of the universe having been driven to it's current state?

The familiar extended dimensions, therefore, may very well also be in the shape of circles and hence subject to the R and 1/R physical identification of string theory. To put some rough numbers in, if the familiar dimensions are circular then their radii must be about as large as 15 billion light-years, which is about ten trillion trillion trillion trillion trillion (R= 1061) times the Planck length, and growing as the universe explands. If string theory is right, this is physically identical to the familiar dimensions being circular with incredibly tiny radii of about 1/R=1/1061=10-61 times the Planck length! There are our well-known familiar dimensions in an alternate description provided by string theory. [Greene's emphasis]. In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being 'fit' inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above?

(Greene, The Elegant Universe, pages 248-249)

So what particles will have emerged from such a process and we find ourselves facing the gluonic phases of sight, and what level should we assign these energy values in relation to the supersymmetrical state now recognized, and moved from in the symmetical breaking that is to be accomplished?

It is from these positions as I am making them clear, that even in face of the perspective shared by the Krausss's and Woit, that the continued efforts of LUbos and all the young minds might do as Peter Woit askes and bring the demands of the recognition of things, that emerge from this process, into full regalia.

For those who were skeptical, hopefully this sets up your minds as to what is being accomplished, and what is being said, is quite beautiful. I find this process very beautiful indeed.

Merry Christmas

Pre-Big Bang: Ekpyrotic and Cyclical

Juan Maldacena (Princeton IAS)

Singularities similar to Singularities of some blackholes in Ads₃->suggest no information Transfer

Has Speed of Light changed Recently?

You have to remember I am not as well educated as the rest of the leaque connected at Peter Woit's site. But how could one think anything less, then what perception can contribute, as less then what the educated mind might have thought of? If it did not have the scope enlisted by others in consideration cosmology might have expressed, then we might have reduced the value of reducitonism role in how we perceive the beginning of the cosmos?

So what Does Peter Woit say here? I am glad that the support(choir:) moved to Peter's cause for truth and enlightenment, is clarifying itself, instead of the ole rants that we had been witnessed too, in the past.

Understanding the clear disticnctions make's it much easier now, instead of what opportunities might have been past by? Of course I understood that he is quite happy with the life given, makes it all the more reason that the value of opinion will have direction(not hidden causes). Contributions by the the opinions generated, held to a educative process that we all would like to be part of.

Peter Woit:

In general, what I really care about and am willing to invest time in trying to carefully understand, are new physical ideas that explain something about particle theory, or new mathematical ideas that might somehow be useful in better understanding particle theory.

Strings /M theory moved to cosmological thinking because of where it had been?

Life, the cosmos and everything:

Lee Smolin stressed that it is only justifiable if one has a theory that independently predicts the existence of these universes, and that such a theory, to be scientific, must be falsifiable. He argued that most of the universes should have properties like our own and that this need not be equivalent to requiring the existence of observers.

Smolin's own approach invoked a form of natural selection. He argued that the formation of black holes might generate new universes in which the constants are slightly mutated. In this way, after many generations, the parameter distribution will peak around those values for which black-hole formation is maximized. This proposal involves very speculative physics, since we have no understanding of how the baby universes are born. However, it has the virtue of being testable since one can calculate how many black holes would form if the parameters were different.

So what are Lee Smolin's thoughts today, and one can see where the interactions might have, raised a claerer perception of what falsifiable is meant in context of today's reasonings. Has this changed from 2003?

Lee Smolin:

My impression, if I can say so, is that many cosmologists undervalue the positive successes of CNS. It EXPLAINS otherwise mysterious features of our universe such as the setting of the parameters to make carbon and oxygen abundent-not because of life but because of their role in cooling GMC’s. It also EXPLAINS the hierarchy problem and the scale of the weak interactions-because these can also be understood to be tuned to extremize black hole production. Further, it EXPLAINS two otherwise improbable features of glaxies: why the IMF for star formation is power law and why disk galaxies maintain a steady rate of massive star formation.

So while we are engaged in the thinking of what can be measured from the big bang till now( Sean Carroll has given us a positon to operate from), but having the Poor man's collider introspective, helps us to consider how we may see the developement of particle interaction, as Pierre Auger experiments have reminded us?

Since the COBE discovery, many ground and balloon-based experiments have shown the ripples peak at the degree scale. What CMB experimentalists do is take a power spectrum of the temperature maps, much as you would if you wanted to measure background noise. The angular wavenumber, called a multipole l, of the power spectrum is related to the inverse of the angular scale (l=100 is approximately 1 degree). Recent experiments, noteably the Boomerang and Maxima experiments, have show that the power spectrum exhibits a sharp peak of exactly the right form to be the ringing or acoustic phenomena long awaited by cosmologists:

Then how would we see such changes and views that might of held the mind to variances in the landscape, as hills and valleys, portrayed in our cosmo? Perception between the Earth and the Sun. What shall we say to these values in other places of the cosmo? Will we see the impression of the spacetime fabric much differently then we do with the fabric as we see it now? Some might not like this analogy, but it is useful, as all toys models are useful?

Had we forgotten Wayne Hu so early here, not to have thought before we let this all slip from our fingers, as some superfluid and how we got there, Whose previous existance we had not speculated(what about Dirac), yet we understand the push to the singularity do we not?

"How do you actually make a collapsing universe bounce back? No one ever had a good idea about that,” Albrecht said. “What these guys realized was that if they got their wish for an ekpyrotic universe, then they could have the universe bounce back."

Such gravitational collapse sets the stage for what was initiated from, yet, we would not entertain cyclical models, that would instigate geometrical propensities along side of physics procedures?

So what do we mean when I say that we have pushed the minds eye ever deeper into the world of the Gluonic phases, which we would like so much to validated from such "traversed paths" that such limitations might have then been projected into the cosmo for a better perspective of time? Langangrain valuations alongside of the cosmic string? Which view is better?



When I started to look at the idea of these xtra dimensions, and how these would be manifesting and the experimental attempts at defining such, I recognized Aldeberger with eotvos contributions here, that a few might have understood and seen?

Together now such a perspective might have formed now around perspectve glazes that we might now wonder indeed why such a path taken by Aldeberger might now have been seen in such fine measures?

The Shape of the UNiverse in Omega Values

Having walked through the curvature parameters, in the Friedmann equations while understanding the nature of the universe, I thought would have been very important from the geometrical valuations, that I have been trying to understand. That it might arise in a terminology called quantum geometry, seems a very hard thing to comprehend, yet thinking about CFT measure on the horizon(Bekenstein Bound) is telling us something about the space of the blackhole?

So people have these new ideas about quantum grvaity and some might have choosen monte carlo methods for examination in the regards of quantum gravity perceptive.

Plato:

Now some of you know that early on in this blog John Baez's view about the soccer ball was most appealing one for consideration, but indeed, the sphere as the closet example could all of a sudden become the ideas for triangulations never crossed my mind. Nor that Max Tegmark would tell us, about the nature of these things.

JUst as one might have asked Max Tegmark what the shape of the universe was, he might of quickly discounted John Baez's soccer ball? Yet little did we know, that such a push by Magueijo might have had some influences? How would you measure such inflationary models?


Plato said:

When I looked at Glast, it seemed a fine way in which to incorporate one more end of the "spectrum" to how we see the cosmo? That we had defined it over this range of possibilties? How could we move further from consideration then, and I fall short in how the probabilties of how we might percieve graviton exchange of information in the bulk could reveal more of that spectrum? A resonance curve?

Variable "constants" would also open the door to theories that used to be off limits, such as those which break the laws of conservation of energy. And it would be a boost to versions of string theory in which extra dimensions change the constants of nature at some places in space-time.

One of the ways that has intrigued my inquiring mind, is the way in which I could see how xtra-dimensions might have been allocated to the views of photon interaction? We know the ways in which calorimetric design helps us see how fine the views are encased in the way Onion people work?

I had recognized quite early as I was getting research material together of Smolin's support of Magueijo, had something to do with the way in which he was seeing VSL approaches to indicators of time valuations?

Again, this is quite hard to conclusive drawn understanding, in that such roads lead too, would have instantly said that (speed of light in a vacuum)C never changes? How many good teachers would have chastize their students, to have this held in contrast to todays way we do things when looking at Magueijo?

Magueijo started reading Einstein when he was 11, but he wanted to comprehend the theory using mathematics rather than words. So he read a book by Max Born, which explains relativity in the language of mathematics. He quotes Galileo as having said, "The book of nature is written in the language of mathematics."

Let's look at what is being said from a fifth dimensional perspective, and tell me why this will not change the way we see? Why model comprehension has not sparked this foundational change in the way we look at the cosmos and the spacetrime fabric?