What First principle was-- was it the geometry

I thought I would contrast this quote of Dirac's with the one of Feynman's.

You see the very idea of a constancy that spread through all Maxwell's equations was a necessary one which allowed Einstein to move into positive and negative valuations within the geometries? So did Dirac know how this was to be approached?

Dirac:

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

Feynman:

‘Maxwell discussed … in terms of a model in which the vacuum was like an elastic … what counts are the equations themselves and not the model used to get them. We may only question whether the equations are true or false … If we take away the model he used to build it, Maxwell’s beautiful edifice stands…’ – Richard P. Feynman, Feynman Lectures on Physics, v3, c18, p2.

Paul Dirac Talk: Projective Geometry, Origin of Quantum Equations Audio recording made by John B. Hart, Boston University, October 30, 1972

The quote below is in response to Dirac's comments

[ROGER PENROSE]

"One particular thing that struck me... [LAUGHTER]...is the fact that he found it necessary to translate all the results that he had achieved with such methods into algebraic notation. It struck me particularly, because remember I am told of Newton, when he wrote up his work, it was always exactly the opposite, in that he obtained so much of his results, so many of his results using analytical techniques and because of the general way in which things at that time had to be explained to people, he found it necessary to translate his results into the language of geometry, so his contemporaries could understand him. Well, I guess geometry… [INAUDIBLE] not quite the same topic as to whether one thinks theoretically or analytically, algebraically perhaps. This rule is perhaps touched upon at the beginning of Professor Dirac's talk, and I think it is a very interesting topic."

So the question might have been, how this was viewed and what the result was through such a axiomization? What was the first principe here? Was there one that became the guiding principal?

I mentioned the compass for Einstein, as a modelled perception that grew into the later years, but here, we might have seen the beginnings Feynmans toys model for such geometries?

Paul Dirac and Geometrical Thinking?

Into the Antiworld was originally staged at CERN inside the underground cavern that houses the Delphi experiment, in which collisions between electrons and their antiparticles - positrons - are studied. That setting must have been awe-inspiring, particularly as the show closed. The audience would have been whisked from the wonder and novelty of Dirac's theory over 70 years ago to the sophisticated particle physics experiments of today that the discovery inspired. At CERN, the curtain behind the stage ripped apart to reveal the Delphi detector the performance ended - but the gigantic photograph of the Delphi experiment that concluded the show at the Bloomsbury worked surprisingly well.

Oh what fanfare and dance is given these genius's that we find the story ends with where the future begins.

The Quantum Theory of the Electron



Paul Dirac

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

Can one distinguish something that is of nature as the basis of reality, and see this before it is algebraically written? Jacques mention where the intuitive lines ends and where the math begins.

So from this statement then, it would have been impossible for Dirac to know what the matrices would look before it was algebraically written?

If there is "no physics" and we are defining things from the horizon or boundary, then what geometry wil be revealing of this nature? Can it be concieved as it was by Dirac?

I was thinking of Lenny Susskinds picture of the rubber band in his mind after working hard to mathematically understand. Did comprehension come by way of his mathe equations or by geometriclaly viewing?

THE LANDSCAPE [12.4.03]
A Talk with Leonard Susskind

Einstein said he wanted to know what was on God's mind when he made the world. I don't think he was a religious man, but I know what he means.

Albrecht Dürer and The Magic Square



So the complexity of geometrical form would have been of value if we had seen the way that it might have taken that vision into the geometrical formations of spin orientated understandings? Isomorphic relations of the orbitals relations in cosmological events?

Harmonic Oscillation

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

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

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

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

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

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

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

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

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

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



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



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

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

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

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

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

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

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

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

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

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

Lee Smolin saids no to this?

Hidden Symmetries

I think this is one of my greatest struggles to comprehend how such a beginning could have been discerned as a supersymmetrical state, and then have symmetry breaking actions form from from it.

So how do you reconcile the "vacuum state" with the idea of this "elasticity" spread throughout all space, and then have these kinds of actions conceptually form from it?



While we may look at events within this space, "as individual" as some orbital might be seen, it does not pass some my attention that such cosmological events look vaguely familiar?



While I am being quite vague in my discriptions, it is not without some comparisons that one would ask how this universe came into to being. That we would not wonder abut some overall consensus realization from birth to death, and a recyclical nature, as necessay in the forming of these universes?

While I may see these same similarities, I am not sayng this is the way of it, just that there are two perspectives here in relation to the cosmological pallete and the quantum one, that sees some relation? Is there any, I do not know, but I know that this issue needs some more clarification.

Dirac hypothesized that what we think of as the "vacuum" is actually the state in which all the negative-energy states are filled, and none of the positive-energy states. Therefore, if we want to introduce a single electron we would have to put it in a positive-energy state, as all the negative-energy states are occupied. Furthermore, even if the electron loses energy by emitting photons it would be forbidden from dropping below zero energy.

Thus it comes from my mind that a supersymmetrical state of existance, would have found the possibilites and probabilites as a place from which all could express itself. Would we not consider such abilties of vacuum states to have produced a beginning in the form of bubble states, and from the understanding of "Dirac's sea" what possibiltes exists that such virtual particle would show itself and then quickly dissappear? All of this had to come from some where.

So quickly again, the "condense matter physics" comes to mind on how the building blocks of matter, have found some "predesigned abstract schematics"{this is a math reference} speaking to how such symmetry breaking shall make itself known in the forming constituent particles. That as we look deeper, we wonder indeed about this professor crossing the room. The marble drop or dalton board is a wonderful way in which Pascals triangles serves to initiate this idea of a pre-condition for such math expression in the world of abstract math. So what math shall lead this way?

So it held in my mind that zero pont exemplified the condition in the universe that space is really never "empty." That it needed "some thing" in which to arise from.

What geoemtrical and all incluisve could take hold of this action and reveal the wonderful events in our cosmos? So I looked at blackholes in relation to what could dissipate quite quickly(mircrostate balckholes) to what what was happening on a comsological scale in regards to to those same blackholes.

Projective Geometries

Action at a Distance

Now ths statement might seem counterproductive to the ideas of projective geometry but please bear with me.

In physics, action at a distance is the interaction of two objects which are separated in space with no known mediator of the interaction. This term was used most often with early theories of gravity and electromagnetism to describe how an object could "know" the mass (in the case of gravity) or charge (in electromagnetism) of another distant object.

According to Albert Einstein's theory of special relativity, instantaneous action-at-a-distance was seen to violate the relativistic upper limit on speed of propagation of information. If one of the interacting objects were suddenly displaced from its position, the other object would feel its influence instantaneously, meaning information had been transmitted faster than the speed of light.

Test of the Quantenteleportation over long distances in the duct system of Vienna Working group Quantity of experiment and the Foundations OF Physics Professor Anton Zeilinger

Quantum physics questions the classical physical conception of the world and also the everyday life understanding, which is based on our experiences, in principle. In addition, the experimental results lead to new future technologies, which a revolutionizing of communication and computer technologies, how we know them, promise.

In order to exhaust this technical innovation potential, the project "Quantenteleportation was brought over long distances" in a co-operation between WKA and the working group by Professor Anton Zeilinger into being. In this experiment photons in the duct system "are teleportiert" of Vienna, i.e. transferred, the characteristics of a photon to another, removed far. First results are to be expected in the late summer 2002.

One of the first indications to me came as I looked at the history in regards to Klein's Ordering of Geometries. Now I must admit as a layman I am very green at this understanding but having jumped ahead in terms of the physics involved, its seems things have been formulating in my head, all the while, this underatnding in terms of this "order" has been lacking.

In Euclidean geometry, the basic notions are distances and angles. The transformations that preserve distances and angles are precisely the rigid motions. Effectively, Klein's idea is to reverse this argument, take the group of rigid motions as the basic object, and deduce the geometry. So a legitimate geometric concept, in Euclidean geometry, is anything that remains unchanged after a rigid motion. Right-angled triangle, for example, is such a concept; but horizontal is not, because lines can be tilted by rigid motions. Euclid's obsession with congruent triangles as a method of proof now becomes transparent, for triangles are congruent precisely when one can be placed on top of the other by a rigid motion. Euclid used them to play the same role as the transformations favored by Klein.

In projective geometry, the permitted transformations are projections. Projections don't preserve distances, so distances are not a valid conception projective geometry. Elliptical is, however, because any projection of an ellipse is another ellipse.

So spelt out here is one way in which this progression becomes embedded within this hisotry of geometry, while advancing in relation to this association I was somewhat lifted to question about Spooky action at a distance. WEll if such projective phase was ever considered then how would distance be irrelevant(this sets up the idea then of probabilistic pathways and Yong's expeirment)? There had to be some mechanism already there tht had not been considered? Well indeed GHZ entanglement issues are really alive now and such communication networks already in the making. this connection raised somewhat of a issue with me until I saw the the phrase of Penrose, about a "New Quantum View"? Okay we know these things work very well why would we need such a statement, so I had better give the frame that help orientate my perspective and lead to the undertanding of spin.



Now anywhere along the line anyone can stop such erudication, so that these ideas that I am espousing do not mislead. It's basis is a geometry and why this is important is the "hidden part of dirac's mathematics" that visionization was excelled too. It is strange that he would not reveal these things, all the while building our understanding of the quantum mechanical nature of reality. Along side of and leading indications of GR, why would not similar methods be invoked as they were by Einstein? A reistance to methodology and insightfulness to hold to a way of doing things that challenegd Dirac and cuased sleepless nights?



Have a look at previous panel to this one.

While indeed this blog entry open with advancements in the Test in Vienna, one had to understadn this developing view from inception and by looking at Penrose this sparked quite a advancement in where we are headed and how we are looking at current days issues. Smolin and others hod to the understnding f valuation thta is expeirmentally driven and it is not to far off to se ehosuch measure sare asked fro in how we ascertain early universe, happening with Glast determinations.

Quantum Cryptography

Again if I fast forward here, to idealization in regards to quantum computational ideas, what value could have been assigned to photon A and B, that if such entanglement states recognize the position of one, that it would immediately adjust in B?

Spooky At any Speed

If a pair of fundamental particles is entangled, measuring an attribute of one particle, such as spin, can affect the second particle, no matter how far away. Entanglement can even exist between two separate properties of a single particle, such as spin and momentum. In principle, single particles or pairs can be entangled via any combination of their quantum properties. And the strength of the quantum link can vary from partial to complete. Researchers are just beginning to understand how entanglement meshes with the theory of relativity. They have learned that the degree of entanglement between spin and momentum in a single particle can be affected by changing its speed ("boosting" it into a new reference frame) but weren't sure what would happen with two particles.

So there is this "distance measure" here that has raised a quandry in my mind about how such a projective geometry could have superceded the idea of "spooky things" and the issues Einstein held too.

So without understanding completely I made a quantum leap into the idealization in regards to "logic gates" as issues relevant to John Venn and introduced the idea around a "relative issues" held in my mind to psychological methods initiated by such entanglement states.

As far a one sees here this issue has burnt a hole in what could have transpired within any of us that what is held in mind, ideas about geomtires floated willy Nilly about. How would such "interactive states" have been revealled in outer coverings.

The Perfect Fluid

Again I am fstforwding here to help portray question insights that had been most troubling to me. If suych supersymmetrical idealizations arose as to the source and beginning of existance how shall such views implement this beginning point?

So it was not to unlikely, that my mind engaged further problems with such a view that symmetry breaking wouldhad tohave signalled divergence from sucha state of fluid that my mind encapsulated and developed the bubble views and further idealizations, about how such things arose from Mother.

What would signal such a thing as "phase transitions" that once gauged to the early universe, and the Planck epoch, would have revealled the developing perspective alongside of photon developement(degrees of freedom) and released information about these early cosmological events.

So I have advance quite proportinately from the title of this Blog entry, and had not even engaged the topological variations that such a leading idea could have advanced in our theoretcical views of Gluonic perceptions using such photonic ideas about what the tragectories might have revealled.

So indeed, I have to be careful here that all the while my concepts are developing and advanced in such leaps, the roads leading to the understanding of the measure here, was true to form and revalled issues about things unseen to our eyes.

It held visionistic qualities to geometric phases that those who had not ventured in to such entanglement states would have never made sense of a "measure in the making." It has it's limitation, though and why such departures need to be considered were also part of my question about what had to come next.

Trademarks of the Geometer II

John g,



Lubos had some claim about Martian ancestry, but we know that he jests?:)

So I do not want to use up to much more of Lubos's blog for this conversation even though he pushes the envelope. Perhaps, you will start your own blog?

Genuis at Work
(Picture credit: AIP Emilio Sergè Visual Archives)

Lastly, I have know certain "trademarks of people" like Dirac as "the geometer" is inherent at the foundations of such psychologies(even I like to dabble in model developement ex: John Venn), with current information Peter Woit brought forward, are key indicators to me of visualization capabilties that are every advanced for this abstract world. Clifford demonstrates like a Rorshach Ink blot as an experiment, with the picture on that "blackboard"?

Wassily Kadinsky

His art and in composition? As a reference made in the comment section of another artist in realtion to Clifford's article, Wassily came to mind.

The term "Composition" can imply a metaphor with music. Kandinsky was fascinated by music's emotional power. Because music expresses itself through sound and time, it allows the listener a freedom of imagination, interpretation, and emotional response that is not based on the literal or the descriptive, but rather on the abstract quality that painting, still dependent on representing the visible world, could not provide.

How would it be possible to extend let's say the idealization to a history of geometries without establishing this basis in thought? There had to be expanded frontiers that would let people develope towards objective goals in science, based on science and herein lies the difficulites with the INKBLOt. As by subjective interpretaion based on current knowledge bases, these views would be very much different then what someone "well trained might see"? Let alone, classify it to any geometric formulation.



Surely inkblot below is a mask? I have one in relation, drawn from the antiquities of evolution. If you ever visit the Drumheller museum, in Alberta Canada, you'll identify it for sure?:) So what is this "projection" based on?



Keep it simple

I like to keep it simple, and fragmentary indications of my blog entries can be accumulative of something deeper and very revealing about such a nature of these geometers I like to talk about. I had to learn this history in order to understand where we had been taken with Einstein's General Relativity. Another one, who understood after Grossman that such geoemters were needed to bring consistancy to the undertanding of theoretical developement.

I would not have gotten this far without bloggists, like Lubos, Peter, Sean, Clifford, Mark and the rest of the Cosmic Variance group, who are most kind in helping us lay people to recognize issues in ways and helping to develope info according to the academic world. This has been truly a grace.

Entries of my own, would have past as incoherent states of unfamiliar words, on a very simple level dealing with the societal world we live in. I now find comfort, that I am not so strange, in this geometer sense.

Have I excelled myself? On the contrary, its about learning about ourselves and who we are, is all. If it past the stage of pure mathematics( towards that center), then why would we not see that this outward development had some psychological model in which to adorn oneself in this mandalic sense.

Sean, makes brief link entree in that blog of Cliffords on Cosmic Variance.

Indeed, this is where such models helped me understand from a Jungian sense, that such a map had to exist, and models built. This can only come from experience, and from the direction of coming from that center. Why I ask Lubos, or anyone for that matter, about where ideas come from. Here you would see such a flavour and distinction in Plato's ideology, about what could manifest in any mind, and not just any one select part of this society.

No doubt, that like any fisherman's hook, you would need to have some valuation and inclination to manifest. As you develope through any model apprehension, where you could add more ideas to the pot. For a further invitation for probilities to manifest in our everyday conversations. Are some of these "inductions and deductions" always right? Of course not, and this is where our education comes in, and the saving grace of bloggists in general.

Who would of thought by using "internet world" the bloggists could have ever reached the "periphery" of this society? I'll intoduce you to another foreigner whose concept defintiely challenges the mind in this bubble sense. In a way I helped him to develope further, and him, I.

The Succession of thinking

How far indeed the the imagination can be taken to see such processes enveloped in how we percieve these changes all around us. Why is gravity so weak, here and now. I have jumped ahead but will lead into it from the other end of this article.

Never before had I encountered the reasoning of imaging behind the work of "conceptual frameworks" now in evidence. In how a mathmatician, or a scientist, like Einstein or Dirac, had some basis at which the design, of all that we endure, would have its's counterpart in this reality as substantial recognition of what must be done.

I don't think anyone now in the scientific arena needs to be reminded about what it takes to bring theory into the framework of cultural and societal developement, to see how it all actually is working. On and on now, I see this reverberating from Lisa Randall to all scientists that we encounter from one blog to the next, a recognition and developement of this visualization ability.

That Famous Equation and You , By BRIAN GREENE Op-Ed Contributor in New York Times, Published: September 30, 2005


Brian Greene:

After E = mc², scientists realized that this reasoning, however sensible it once seemed, was deeply flawed. Mass and energy are not distinct. They are the same basic stuff packaged in forms that make them appear different. Just as solid ice can melt into liquid water, Einstein showed, mass is a frozen form of energy that can be converted into the more familiar energy of motion. The amount of energy (E) produced by the conversion is given by his formula: multiply the amount of mass converted (m) by the speed of light squared (c²). Since the speed of light is a few hundred million meters per second (fast enough to travel around the earth seven times in a single second), c² , in these familiar units, is a huge number, about 100,000,000,000,000,000.

There are two links here.One by Peter Woit with reference to article and one toSean Carroll who further illucidates the article by Brian Greene.

So here I am at the other end of this referenced article, that other thoughts make their way into my mind. Previous discussison ongoing and halted. To todays references continued from all that we had encountered in what General Relativity surmizes.

That this issue about gravity is very real. So that's our journey then, is to understand how we would percieve the strength and weakness through out the spacetime and unification of a 3 dimension space and one of time, to some tangible reality within this coordinated frame Euclidean defined.

The Succession of Thinking

Mark helps us see in a way we might not of considered before.

Dark Matter and Extra-dimensional Modifications of Gravity

But the issue is much more complicated then first realized if we take this succension of thinking beyond the carefuly plotted course Einstein gave us all to consider.

Plato on Sep 27th, 2005 at 10:23 pm We were given some indications on this site about the state of affairs with Adelberger. Do you think this time span of proposed validation processes, were constructively and experimentally handled appropriately through it’s inception? As scientists would like to have seen all such processes handled in this respect?

So indeed I began to see this space as very much alive with energy that had be extended from it's original design to events that pass through all of creation, then how indeed could two views be established in our thiniking, to have Greene explain to us, that the world holds a much more percpetable view about what is not so understood in reality.

An Energy of Empty Space?

Einstein was the first person to realize that empty space is not nothingness. Space has amazing properties, many of which are just beginning to be understood. The first property of space that Einstein discovered is that more space can actually come into existence. Einstein's gravity theory makes a second prediction: "empty space" can have its own energy. This energy would not be diluted as space expands, because it is a property of space itself; as more space came into existence, more of this energy-of-space would come into existence as well. As a result, this form of energy would cause the universe to expand faster and faster as time passes. Unfortunately, no one understands why space should contain the observed amount of energy and not, say, much more or much less.

All the while the ideas that would leave gravity without explanation in a flat euclidean space, gravity would have been left to that solid response without further expalnatin in a weak field manifestation. But it was always much more then this I think.

While being caution once on what the quantum harmonic oscillator is not, Smolin did not remove my thinking of what was all pervasive from what this "empty space" might have implied, that heretofor "it's strength" was a measure then of a bulk, and what better way in which to see this measure?

Taken in context of this succession, this place where such conceptual framework had been taken too, it was very difficult not to encounter new ways in which to understand how gravity could changed our perceptions.

Thalean views were much more then just issues about water and all her dynamical explanations. It presented a new world in which to percieve dynamical issues about which, straight line thinking could no longer endure. A new image of earth in all it's wander, no less then Greene's analysis to how this famous equation becomes evident in our everyday world. It presented a case for new geometries to emerge. Viable and strengthened resolve to work in abstract spaces that before were never the vsion of men and women who left earth. Yet it all had it's place to endure in this succession that we now have adbvanced our culture in ways that one would not have thought possible from just scientific leanings.

So now I return myself to Einstein's allegorical talk on what concept had taken, when a scientist had wondered on the valuation of time.

Dirac's Hidden Geometries

I find this interesting because I like to visualizze as much as possible, and I sometimes think the basis of the leading ideas in science would had to follow a progression. Klein's Ordering of Geometries was one such road that seem to make sense. The basis of relativity lead through in geometrical principals?

Such an issue with string theory had to have such a basis with it as well, although how do you assign any views to the very begininngs of the universe below planck length? Well there are images to contend with what are these and how are they derived? Rotations held in context of te progression of this universe and all thoughts held to the very nature of particle creation and degrees fo freedom?

[PAUL DIRAC]

When one is doing mathematical work, there are essentially two different ways of
thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

While I am very far from being the mathematician, I understand that this basis is very important. Such summations in mathmatical design, leave a flavour, for conceptiual ideas to form in images, so I understand this as well. It is a progression of sorts I think, as I read, and learn. Geometry lies at the very basis of all such progressions in science?

So Feynmans toy models arose from the ideas of Dirac?

Albrecht Durer and His Magic Square

Albrecht Dürer(self portrait at 28)

It was important to me that I post the correct painting and one that had undergone revision to exemplify the greater context of geometrical forms. In the Topo-sense? Artistic renditions help and adjust views, where information in mathematical minds, now explains something greater. Melencolia II
[frontispiece of thesis, after Dürer 1514]by Prof.dr R.H. Dijkgraaf

"Two images when one clicked on," shows what I mean.

Melancholia in 1514(the original)

The Magic Square

Like Pascal, one finds Albrecht has a unique trick, used by mathematicians to hide information and help, to exemplify greater contextual meaning. Now you have to remember I am a junior here in pre-established halls of learning, so later life does not allow me to venture into, and only allows intuitive trials poining to this solid understanding. I hope I am doing justice to learning.

A new perspective hidden in the Prof.dr R.H. Dijkgraaf
second rendition, and thesis image, reveals a question mark of some significance?:) So how would we see the standard model in some "new context" once gravity is joined with some fifth dimensional view?

Matrix developement?

Like "matrix developement," we see where historical significance leads into the present day solutions? How did such ideas manifest, and we look for this in avenues of today's science.

In 1931 Dirac gave a solution of this problem in an application of quantum mechanics so original that it still astounds us to read it today. He combined electricity with magnetism, in a return to the 18th-century notion of a magnet being a combination of north and south magnetic poles (magnetic charges), in the same way that a charged body contains positive and negative electric charges.

How relevant is this? How important this history? How relevant is it, that we see how vision has been extended from plates(flat surfaces to drawings) to have been exemplified in sylvester surfaces and object understanding. This goes much further, and is only limited by the views of those who do not wish to deal with higher dimensional ventures?



See:

Topo-sense

The Abstract World

CERN and Future Experiments

I needed to come back down to earth for a minute to see where the trend is going with those who shall lead us poor earthlings into the future of experimental research and profound understandings.

It would be nice to see perspectives by Lubos, PeterWoit the group here(meaning their blogs), as we look in this direction for a moment? Peter might be able to set his Dirac Moduli space views here?:)

Peter Woit for emphasizing the importance of the Dirac operator on the moduli space of Calabi-Yau four-folds and the importance of string theory to him.

The next step will again be taken in Japan, with the new J-PARC accelerator starting in 2009 to send neutrinos almost 300 km, again to the Super-Kamiokande experiment, to probe the third neutrino mixing angle that has not yet been detected in either atmospheric or solar neutrino experiments. This may also be probed in a new experiment being proposed for the Fermilab NuMI beam. One of the ideas proposed at CERN is to probe this angle with an underwater experiment moored in the Gulf of Taranto off the coast of Italy, viewing neutrinos in a modified version of CERN's current Gran Sasso beam.

So having quickly gone today I went to look at John Ellis site, and was formally introduced to some of the things that have been happening with him and avenues of experimentation that seem very interesting to me.

High Energy Physics Group

The Theory of Cosmic Rays

Cosmic rays, which have historically provided the first tool to study high-energy phenomena, are playing a new role in modern physics. The origin of high-energy cosmic rays, gamma rays and neutrinos is still an open question in astrophysics. On-going and future experiments will give us new information on astrophysical sources and on high-energy processes.

It still retains high energy considerations even in face of LHC questions about particle reductionism and the effects of dynamical interrelations as we see this travel in neutrino functions. I wanted to point to further information here in terms of micro-state black-hole detection. I get this soon.

2004 promises to be an exceptionally exciting year in General Relativity and Gravitation: the LIGO/VIRGO/GEO/TAMA network of detectors has begun generating scientific results, ushering in the era of gravitational wave astronomy. These detectors will search for gravitational wave signals of the collision of black holes, neutron star mergers and other astronomical events previously undetectable. The fundamentally new science of gravitational wave astronomy opens up a new window on the universe. Up until now, astronomy has relied on observations of electromagnetic wave signals (e.g. visible light, radio waves). The detection of gravitational waves offers a completely new perspective on the universe: they will enable us to "hear" the cosmic orchestra as well as to see it! GR17 will provide the scientific community with one of the earliest opportunities to discuss the first scientific results of this era.

I wanted to add a little more information here to further bolster this idealization that I have found in Brian Greene's statement about turning our views skyward in the hope of seeing strings and cosmological thinking in a new way.

Flight of the Phenix

If mini black holes can be produced in high-energy particle interactions, they may first be observed in high-energy cosmic-ray neutrino interactions in the atmosphere. Jonathan Feng of the University of California at Irvine and MIT, and Alfred Shapere of the University of Kentucky have calculated that the Auger cosmic-ray observatory, which will combine a 6000 km2 extended air-shower array backed up by fluorescence detectors trained on the sky, could record tens to hundreds of showers from black holes before the LHC turns on in 2007.

Brane New World

If some thought is beyond comprehensible to engage string theory and come away with some simple statement about it, imagine if we are taken to the new heights that Brane New World might implicate.

But first, having understood something about the matrix involved I tried to educate myself and look for the thread that would bring feynman to dirac for his toy model production.

P.A.M. Dirac was a gifted mathematical inventor who saw how quantum mechanics rises from classical mechanics, yet transcends it. Dirac did not know of the Bohr atom when he arrived at Cambridge in 1923; yet he quickly began contributing to the mathematical structure demanded by quantum phenomena, discovering the connection between the Poisson bracket and the commutator of Heisenberg”s matrix representation of observables. Then, with careful attention to its classical antecedent, Dirac found the equation governing the evolution of the matrix elements which had eluded Heisenberg in the operator ihdA/dt = [A,H]. He then went on to discover spinors in describing the relativistic electron and antimatter implied by the quantum in relativistic space-time. Dirac conceived the many-time formulation of relativistic quantum mechanics and laid the foundations of the Feynman path integral thereby opening the way to quantum electrodynamics. Newton synthesized the foundations of classical mechanics. In fitting kinship, Dirac, who did the equivalent for quantum mechanics, filled the chair at Cambridge held by Newton.

Well when I moved to the higher dimensions it became extremely difficult to understand that if in Brane New World antics as revealled by Dvali, these concepts are simply discussed, but have far reaching implications.

Dvali uses the analogy of a metallic sheet submerged in water to illustrate the principle. If one hits the sheet with a hammer, shock waves will carry away the energy in all directions. "Most of the energy will travel along the two-dimensional surface. Only at a substantial distance away from the source will the energy loss to water be appreciable," he said. "According to our picture, we are in a very similar situation. We think gravity is 'normal' because we only measure it directly at relatively short distances, but cosmic acceleration indicates leakage.

"

This simple visualization does more to ask, how we could look at what is being held to this brane, to understand that the way that vibration moves across his example, would have some correpsondance somewhwere else for consideration.

It is always easy to visualize the three coordinated universe as a box, and if using loop amplitudes within context of Greg" Egan's example, you are going to meet the faces that these loops reflect. This pointed to something beyond the faces of these coordinates for me, to realize, that beyond the four dimensinal views there was a world that we were missing in consideration. Those missing energy events speak to this, for me.

So the following picture I hope clarifies what I have been saying for sometime from a M Theory perspective.

Unfortunately the image I had on file is no longer connected to it's source so the site gone takes the image with it. This logic was part of the developement I see in the interenet that would reveal the source and not compromize it's auhtor's rights?

So of course I had to go look at how I would see Dvali's statements about the hammer heating the metal sheet.

Quantum Harmonic Oscillator

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

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

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

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

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

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


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

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

?