Quantum Mechanical Discription of the Spacetime Fabric

Richard Feynman developed the path integral formulation of quantum mechanics in 1948 (some preliminaries were worked out earlier, in the course of his doctoral thesis work with John Archibald Wheeler) as a description of quantum theory corresponding to the action principle of classical mechanics. It replaces the classical notion of a single, unique history for a system with a sum, or functional integral, over an infinity of possible histories to compute a quantum amplitude.

I do not know if I have fallen astray from the interesting perspective strings has alloted to us, in the way in which we have always percieve the quantum mechanical discription based on some," sum over history" of all interactions.

Under the heading of "Time and the Quantum," Pg 189 Fabric of the Cosmo, by Brian Greene a interesting statement of historical proportions that askes questions about the nature of the way in which we percieve same. A better indication of the Full Monty, is demonstrated as well?:)

The beam splitter is not a labratory variety, either, but is a intervening galaxy whose gravitatinal pull can act like a lens that focuses passing photons and directs them to earth,as in Figure 7.3. Although no one has yet carried out this experiment, in principle, if enough photons from the quasar are collected, they should fill out an interference pattern on a long-exposure photographic plate, just as in the labratory beam-splitter experiment. But if we put another photon detector near te end of one route or the other, it which provide which path information for the phtons, thereby destroying the interference pattern.

I have shown, where this extra dimension was added by Kaluza in 1919, and unless I am quoting the references to Kaku wrong, then such considerations would to me, have changed the way in which we would percieve all these interactions? Something then has happened to the spacetime fabric and how all these interactions would be conceptually addressed? Hence the reference to what String Theorists have done, by changing the disciption to one of strings?

Similarily, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimensions of space and time, then equations governing light and gravity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained inthe fifth dimension. In this way, we see the laws of light and gravity become simpler in five dimensions.

It has been relatively quiet here in the GP-B Mission Operations Center, since the strong solar flares and geomagnetic storm three weeks ago. Our team continues to adjust the flow rate of the excess helium from the Dewar during the present a 6-week “hot” season, where the spacecraft is continually in sunlight throughout each orbit. (See last week’s highlights for a discussion of the spacecraft’s seasons.)


Immediately to me, the instantaneous feature of photon expression would have detailed a topological value, where such gravitation/photon would demonstrated of itself a continuity of expression? If such geometrical tendencies would have considered the dynamical relationship of the orbital on cosmological correlations then such energy perceptions would have immediately painted a portrait for us, of what has existed in the past, what continues to exist, and what will exist in the future?

Strings Change Quantum Mechanical Discription of the World?

Often times harmonical oscillators can disguise themselves in dialogue, and opposition, and bring about a "signatured state" of recognition? Have they become entangled? Have they defined themselves in terms of new elemental features of existance?

Has strings presented itself as a new issue in entanglement and the "new physics," it would represent?

Physicists have succeeded in entangling five photons for the first time. Although four photons have been entangled before, five is the minimum number needed for universal error correction in quantum computation. Moreover, the same team has demonstrated a process called "open-destination teleportation" for the first time (Z Zhao et al. 2004 Nature 430 54). The results represent a major breakthrough in efforts to exploit the laws of quantum mechanics in quantum information processing.

By taking advantage of quantum phenomena such as entanglement, teleportation and superposition, a quantum computer could, in principle, outperform a classical computer in certain computational tasks. Entanglement allows particles to have a much closer relationship than is possible in classical physics. For example, two photons can be entangled such that if one is horizontally polarized, the other is always vertically polarized, and vice versa, no matter how far apart they are. In quantum teleportation, complete information about the quantum state of a particle is instantaneously transferred by the sender, who is usually called Alice, to a receiver called Bob. Quantum superposition, meanwhile, allows a particle to be in two or more quantum states at the same time

What Do We Mean When We Say "Continuum"?

Here's a description Albert Einstein gave on p. 83 of his Relativity: The Special and the General Theory:

The surface of a marble table is spread out in front of me. I can get from any one point on this table to any other point by passing continuously from one point to a "neighboring" one, and repeating this process a (large) number of times, or, in other words, by going from point to point without executing "jumps." I am sure the reader will appreciate with sufficient clearness what I mean here by "neighbouring" and by "jumps" (if he is not too pedantic). We express this property of the surface by describing the latter as a continuum

There has been some what of a issue here when I have spoken of two points, and I would like to say that I am using this to reference the space in between, like Q<->Q measure, to signify the energy and curvature implied in this space.

“Distances” Determine Geometry

Describe an object with a table of distances between points.

Describe spacetime with a table of intervals between events

.It is not my purpose in this discussion to represent the general theory of relativity as a system that is as simple and as logical as possible, and with the minimum number of axioms; but my main object here is to develop this theory in such a way that the reader will feel that the path we have entered upon is psychologically the natural one, and that the underlying assumptions will seem to have the highest possible degree of security.

—Albert Einstein

Quantum Harmonic Oscillators

If the basis of this thinking has not emerged out of GR then what value could we have assigned zero point vibration? If the scalable features of GR could not have followed some geometrical thinking, then the world that we move too, in non-euclidean views, could have never revealled hyperdimensional thinking. Which needs a quantum mechanical thinking to emerge as well?


In the late 1950s, Weber became intrigued by the relationship between gravitational theory and laboratory experiments. His book, General Relativity and Gravitational Radiation, was published in 1961, and his paper describing how to build a gravitational wave detector first appeared in 1969. Weber's first detector consisted of a freely suspended aluminium cylinder weighing a few tonnes. In the late 1960s and early 1970s, Weber announced that he had recorded simultaneous oscillations in detectors 1000 km apart, waves he believed originated from an astrophysical event. Many physicists were sceptical about the results, but these early experiments initiated research into gravitational waves that is still ongoing. Current gravitational wave experiments, such as the Laser Interferometer Gravitational Wave Observatory (LIGO) and Laser Interferometer Space Antenna (LISA), are descendants of Weber's original work.

Geons, Blackholes & Quantum Foam, by John Archibald Wheeler, with Kenneth Ford, page 236, para 2.
"

This hypothetical entity, a gravitating body made up entirely of electromagnetic fields. I call geon(g for the gravity, e for electromagnetism," and on as the word root for"particle"). There is no evidence for geons in nature and later was able to show that they are unstable-they would quickly self-destruct if they were ever to form. Nevertheless it is tempting to think that nature has a way of exercising all the possibilties open to it. Perhaps geons had a transitory exitance early in history of the universe. Perhaps(as some students and I speculate much more recently), they provide an intermediate stage in the creation of the balckholes

."



Drawing by Glen Edwards, Utah State University, Logan, UT

If such thinking of the spacetime would have been moved from macroscopic thinking, how would we have ascertained the continued developement of GR from this as an microscopic view?



Without some way in which to look at the developing nature of GR, how would we not have not of considered the nature of these gravitational events in the cosmo? If we coud not scale the nature of the measure, between two points, what value would there ever be in considering the strength of the gravitational fields?

Gravitational waves can be viewed as ripples of the space-time. They occur in two fundamental states of polarization, usually known as 'cross' and 'plus'. The effect on matter of the passage of gravitational radiation is a squeezing and stretching, depending on the phase of the wave. For instance the effect on a ring of test masses is shown in fig. 1, in the reference frame that is in free fall with the center of mass. The upper raw refers to the plus polarization while the second to the cross polarization; the ring is deformed by the wave and the effect is shown at different phases

As we look back in time, here it is easy to see having understood this developement of gravitational wave detection that the principals underlying the developing thoughts came from Webber's expansive contractive, features of all things? It would manifest through all things and Kip Thorne deducing this understanding, was lead to consider LIGO as a important fucntion of discerningthese grviaational waves. INstead of Webber's way of thinking he developed another way in which to percieve this energy being deciminated in the bulk of our imaginations.

The Elastic Nature?

As I have explained in a earlier link I am fascinated by the images of bubbles that were demonstrated through a way of thinking of the early universe to arise as Bubble Nucleation.

These images all show the 2-, 3-, 4-, and 5-fold eversions in the upper left, lower left, upper right, and lower right cornerse, respectively. First we see an early stage, with p fingers growing in the p-fold everion. Next we see an intermediate stage when the fingers have mostly overlapped. Finally we see the four halfway models. For p odd, these are doubly covered projective planes.

If we had understood the early universe to have this continous nature and not have any tearing in it, how would such rotations have moved according to some method, that we might have considered the klein bottle or some other concept, that would lend itself to explain some of the ways and means, such dynamics could have unfold, enfolded and everted in the actions of that same cosmo?

It would be very difficult to speak to probability statistics, if you did not envelope the possibilites in some kind of configuration, or compared it to a Dalton Board. The Bell curve, or the pascal's triangle to consider how something could arise in certain situations? Might we have called the basis for a "new math" to emerge? If we had come to accept the departue point for Euclid's fifth postulate then what has we encouter inthe dynamcial world of Gauss? Einstein includethese calculation in the evolving feature of GR, so how could we not see this developing of a geometry that would lead to smooth and topological considerations?

The statistical sense of Maxwell distribution can be demonstrated with the aid of Galton board which consists of the wood board with many nails as shown in animation. Above the board the funnel is situated in which the particles of the sand or corns can be poured. If we drop one particle into this funnel, then it will fall colliding many nails and will deviate from the center of the board by chaotic way. If we pour the particles continuously, then the most of them will agglomerate in the center of the board and some amount will appear apart the center.

UNderstanding then that such cosmological event could be unfolding in the universe, visually to me, these configurations had to follow some pattern of consideration, or it just didn't make sense that such abstract math in topologies could ever work. So in looking at a previous comparison here the dynamical nature of the orbital seemed a valid comparison not only on a cosmological scale, but on a very small one as well?

A Holographical way of thinking?

Quantum Microstates: Gas Molecules in the Presence of a Gravitational Field

Andy Strominger:

This was a field theory that lived on a circle, which means it has one spatial dimension and one time dimension. We derived the fact that the quantum states of the black hole could be represented as the quantum states of this one-plus-one dimensional quantum field theory, and then we counted the states of this theory and found they exactly agreed with the Bekenstein-Hawking entropy.

I do not know of many who could not have concluded that microstates would have been something of an issue, as one recognizes this focus towards cosmological considerations. One aspect of Einstein’s general relativity, helped us recognize the value of gravitation that is extremely strong in situations where energy values are climbing. We had to look for these conditions and work them out?



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.

The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did.

If we did not have some way in which to move our considerations to the energy states that existed in the beginning of this universe what other measures would you use? How would you explain a cyclical model that Neil Turok and Steinhardt talked about and created for us?

Is this a predictive feature of our universe that had to have some probablity of expression and mathematically, if one wanted some framework, why not throw all things to the wind and say, Pascal's triangle will do?:)

The animation shows schematically the behavior of the gas molecules in the presence of a gravitational field. We can see in this figure that the concentration of molecules at the bottom of the vessel is higher than the one at the top of the vessel, and that the molecules being pushed upwards fall again under the action of the gravitational field.

One had to have some beginning with which to understand what could have emerged from such energy configurations. If such energies are concentrated and found to bring us to the supersymmetrical values assigned on that brane, then how would cooling functions of the CMB have figured a direct result would be expressive of those same events? Was there no way to measure chaoticness. Maybe it was all Fool’s Gold?:)

Inverse Fourth Power Law

By moving our perceptions to fifth dimenisonal views of Kaluza and KLein, I looked at methods that would help me explain that strange mathematical world that I had been lead too geometrically. If such a bulk existed, then how would we percieve scalable features of the energy distributed within the cosmo?

The angular movements needed to signal the presence of additional dimensions are incredibly small — just a millionth of a degree. In February, Adelberger and Heckel reported that they could find no evidence for extra dimensions over length scales down to 0.2 millimetres (ref. 11). But the quest goes on. The researchers are now designing an improved instrument to probe the existence of extra dimensions below 0.1 mm. Other physicists, such as John Price of the University of Colorado and Aharon Kapitulnik of Stanford University in California, are attempting to measure the gravitational influence on small test masses of tiny oscillating levers.

In previous posts I have outline the emergence and understanding of hyperdimensional realities that we were lead too. Our early forbearers(scientifically and artistic embued with vision) as they moved through the geometrical tendencies, that if followed , made me wonder about that this strange mathematical world. How would we describe it, and how would it make sense?

Our new picture is that the 3-D world is embedded in extra dimensions," says Savas Dimopoulos of Stanford University. "This gives us a totally new perspective for addressing theoretical and experimental problems.

Quantitative studies of future experiments to be carried out by LHC show that any signatures of missing energy can be used to probe the nature of gravity at small distances. The predicted effects could be accessible to the Tevatron Collider at Fermilab, but the higher energy LHC has the better chance.
These colliders are still under construction, but results also have consequences for "table-top" experiments, being carried out here at Stanford, as well as the University of Washington and the University of Colorado. Here’s the basic idea: imagine there are two extra dimensions on a scale of a millimeter. Next, take two massive particles separated by a meter, at which distance they obviously behave according to the well-known rules of 3-D space. But if you bring them very close, say closer than one millimeter, they become sensitive to the amount of extra space around. At close encounter the particles can exchange gravitons via the two extra dimensions, which changes the force law at very short distances. Instead of the Newtonian inverse square law you’ll have an inverse fourth power law. This signature is being looked for in the ongoing experiments.

As you look at the issue of two points(introduction to hyperdimensional realites of quark confinement as a example), it is well understood, by this point that such emergence had to be geometriclaly consistent on many levels. That such royal roads leading too, culminate in some realistic measure? In that mathematical realm, we had left off, and in recognition of the fifth postulate of euclid. By acceptance and creation of this extra dimension, it was well apparent, that such tendencies were developing along side with the physics as well.

But we had to determine where this mathematical realm had taken us, in terms of measure? We are quckly reminded of the place in which such measures become the constant rallying point around important questions of these views.



Physics at this high energy scale describes the universe as it existed during the first moments of the Big Bang. These high energy scales are completely beyond the range which can be created in the particle accelerators we currently have (or will have in the foreseeable future.) Most of the physical theories that we use to understand the universe that we live in also break down at the Planck scale. However, string theory shows unique promise in being able to describe the physics of the Planck scale and the Big Bang.

It wasn't a game anymore, that we did not suspect that reductionism might have taken us as far as the energy we could produce could take us? So we had to realize there was limitations to what we could percieve at such microscopic levels.

High energy particles have extremely small wavelengths and can probe subatomic distances: high energy particle accelerators serve as supermicroscopes:

To see What?

The structure of matter

(atoms/nuclei/nucleons/quarks)

Faced by these limitations and newly founded conceptual views based on the quantum mechanical discription of spacetime as strings, how would we be able to look at the cosmos with such expectancy? To know, that the views energetically described, would allow further developement of the theoretcial positons now faced with in those same reductionistic views?

What has happened as a result of considering the GR perspective of blackholes, that we had now assigned it relevance of views in cosmological considerations? Such joining of quantum mechanical views and GR, lead us to consider the sigificance of these same events on a cosmological scale. This view, had to be consistent, geometrically lead too?

If we discover the Planck scale near the TeV scale, this will represent the most profound discovery in physics in a century, and black hole production will be the most spectacular evidence of that new discovery

=> A Symmetry Breaking Phase Transition

If we understand what that point suggests, we understand well what the planck length has told us to consider, that even for the briefest of moment, the gamma ray burst would have revealled the CMB in its glory, and slowly we see how such consolidations would have materialize in the current temperatures values of that CMB today?

Below is a quote from Green that help me to recognize the energy values assigned in the KK Tower, to have understood the Radius of this circle, has to reveal symmetrical phases in the developement of that same cosmo. I needed a way in which to see how it was possible geommetrically to absorb the variations in the symmetries of events, in that same cosmo such points could have existed at any time? We needed to look for these locations. These blackholes?

How can a speck of a universe be physically identical to the great expanse we view in the heavens above?

The Elegant Universe, Brian Greene, pages 248-249





G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1)

Here, each arrow represents a symmetry breaking phase transition where matter changes form and the groups - G, H, SU(3), etc. - represent the different types of matter, specifically the symmetries that the matter exhibits and they are associated with the different fundamental forces of nature

Figure 8 [replaced by our Figure 2] is to be conceived three-dimensionally, the circles being cross-sections of spherical shells in the plane of the drawing. A man is climbing about on the huge spherical surface 1; by measurements with rigid rods he recognizes it as a spherical shell, i.e. he finds the geometry of the surface of a sphere. Since the third dimension is at his disposal, he goes to spherical shell 2. Does the second shell lie inside the first one, or does it enclose the first shell? He can answer this question by measuring 2. Assume that he finds 2 to be the smaller surface; he will say that 2 is situated inside of 1. He goes now to 3 and finds that 3 is as large as 1.

How is this possible? Should 3 not be smaller than 2? ...

He goes on to the next shell and finds that 4 is larger than 3, and thus larger than 1. ... 5 he finds to be as large as 3 and 1.

But here he makes a strange observation. He finds that in 5 everything is familiar to him; he even recognizes his own room which was built into shell 1 at a certain point. This correspondence manifests itself in every detail; ... He is quite dumbfounded since he is certain that he is separated from surface 1 by the intervening shells. He must assume that two identical worlds exist, and that every event on surface 1 happens in an identical manner on surface 5. (Reichenbach 1958, 63-64)

As you can see Brain Greene's quote at the top of the page was taken from the context of the paragraph below. One of the difficulties in a commoner like me, was trying to piece together how the develpement of the mind of string theorists, could have geometrically defined the relationships on a more abstract level. As strange as it may seem, I found other correpsondances that would have probably shaken the very foundation of our human thinking, that I could not resist looking and following these developements.

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?

The Elegant Universe, Brian Greene, pages 248-249



I was attracted very early to what I seen in the Klien bottle, that such modelling of these concepts was very striking to me. How could one not have seen some correspondance to the way in which the torus could have been revealled? That one might have considered, such modelling in the shape of our universe, as the point emerged from the brane? This inside/out feature was very troubling to me and still is, that I have endeveaor to follow this line of thinking, alongside of other avenues that were less then appreciated by the scientist/theorist that I have refrained from mentioning it here now.

Figure 15-18b Conformal Changes

Mapping Quark Confinement and The Energy

As I moved through the thinking of those extra dimensions it became apparent to me that the conceptualization of that distance scale was a strange world indeed. How, if we had accept the move to non-euclidean views could we not of accepted the consequences of this move?




Dazzled with the amazing properties of this new mathematical realm, everything seemed a bit magical, as if, experiencing for the first time a taste that is strange indeed? How would I recognize this strange dynamical world, if I had not understood this move to include the geometry that Kaluza and Klien adopted, to gather together another reality of photon engagement with that of gravity?



Fig. 1. In quantum chromodynamics, a confining flux tube forms between distant static charges. This leads to quark confinement - the potential energy between (in this case) a quark and an antiquark increases linearly with the distance between them.

So at the same time you had this distant measure, how could we resolve what was happening between those two points?

Without some supersymmetrical reality(supergravity) how could any point emerge from the brane if it did not recognize the evolution of those dimensions?



So how does this point expand? This is a simple enough question?

A theorem which is valid for a geometry in this sequence is automatically valid for the ones that follow. The theorems of projective geometry are automatically valid theorems of Euclidean geometry. We say that topological geometry is more abstract than projective geometry which is turn is more abstract than Euclidean geometry.

In the above picture Michael Duff draws our attention too, I was drawn to the same principals that Klein demonstrated in his ideas of projective geometry, as the dimensions are revealed?

IN this effort and recognition of appropriate geometry, I had wondered, that if the same consistancy with which these two had demonstrated the principals, euclidean
postulates fell in line, as a basis of this method of applicabilty? Does one now see this thread that runs through the geometry?

Having accepted the road travelled to GR we have come to recognize the royal road has lead us to a strange world indeed. First it was Reimann with Gauss looking over his shoulder, and Maxwell joining Faraday in this celebration, with Einstein bringing all the happy go lucky, into a fine example of what has been implied by the harmonious nature, structure of strings in concert?



But I am not happy yet. If one could not see what was happening between those two points, what's the use of talking any math, without the co-existance of the physics?


The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This, in fact, also gives rise to quantization of charge, as waves directed along a finite axis can only occupy discrete frequencies. (This occurs because electromagnetism is a U(1) symmetry theory and U(1) is simply the group of rotations around a circle).

Gravity and Light in the Fifth Dimension

Theodor Franz Eduard Kaluza November 9, 1885 - January 19, 1954


In Kaku's preface of Hyperspace, page ix, we find a innocent enough statement that helps us orientate a view that previous to all understanding, is counched in the work of Kaluza.

In para 3, he writes,

Similarily, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimensions of space and time, then equations governing light and grvaity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained inthe fifth dimension. In this way, we see the laws of light and gravity become simpler in five dimensions.

Oskar Klein September 15, 1894 - February 5, 1977

Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of very small radius, i.e. 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, in fact, also gives rise to quantization of charge, as waves directed along a finite axis can only occupy discrete frequencies. (This occurs because electromagnetism is a U(1) symmetry theory and U(1) is simply the group of rotations around a circle).