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Showing posts with label Summing over Histories. Show all posts
Showing posts with label Summing over Histories. Show all posts

Thursday, September 01, 2011

Setting Time Aright



Time has no independent existence apart from the order of events by which we measure it.Albert Einstein

While Event has since past, I hope the lecture itself will remain in public domain. It helps so as to see the context of the discussion provided by this conference with regard to that subject of time.




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See:Setting Time Aright

In 1952, in his book Relativity, Einstein writes:

Since there exists in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence
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Setting Time Aright
View more presentations from Sean Carroll

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  If man thinks of the totality as constituted of independent fragments, then that is how his mind will tend to operate, but if he can include everything coherently and harmoniously in an overall whole that is undivided, unbroken, and without a border then his mind will tend to move in a similar way, and from this will flow an orderly action within the whole. (David Bohm, Wholeness and the Implicate Order, 1980)


Lee Smolin:
I suspect this reflects the expectation many people have that time is not fundamental, but rather emerges only at a semiclassical approximation in quantum cosmology. If you believe this then you believe that the fundamental quantities a quantum cosmology should compute are timeless. This in turn reflects a very old and ultimately religious prejudice that deeper truths are timeless. This has been traced by scholars to the theology of Newton and contemporaries who saw space as “the sensorium” of an eternal and all seeing god. Perhaps the BB paradox is telling us it is time to give up the search for timeless probability distributions, and recognize that since Darwin the deep truths about nature cannot be divorced from time.

The alternative is to disbelieve the arguments that time is emergent-which were never very convincing- and instead formulate quantum cosmology in such a way that time is always real. I would suggest that the Boltzman Brain’s paradox is the reducto ad absurdum of the notion that time is emergent and that rather than play with little fixes to it we should try to take seriously the opposite idea: that time is real.

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Bar of Lead Tungstate Source: A Quantum Diaries Survivor-Calorimeters for High Energy Physics experiments - part 1 April 6, 2008
Calorimeters measure the collective behavior of particles traveling along approximately the same path, and are thus naturally suited for the measurement of jets-Dorigo Tommaso


See

Wednesday, March 14, 2007

IN Search of Mandelstam's Holy Grail



There are two posts that reflect the purpose of this post today. One is Clifford's linked through Lee Smolin's comment and the other, at Backreaction. Good Physics is Conflict

A lot of you may never understand the significance of the mystery that follows the thinking of the Holy Grail. Yet is it more the knowledge that can be gained from all soul's day, that on this occasion we may have called it Halloween.

We celebrated the past, in the living of today? You philosophize, while you become the thoughts of models created by science leaders shared? I do not think any have a "personality disorder" like I do:)

Lee Smolin:
Here is an example of the kind of question I found I needed a book to explore: what to think of the problems that arise from the need for higher dimensions in string theory, such as the problem of moduli stabilization and the vast number of static solutions. To approach this I read books on the early history of GR and unified field theories and learned that higher dimensional compactifications were explored many times between 1914 and 1984 and that close to the beginning these problems were appreciated and discussed by Einstein and others. I weave this story into my book because I find it useful when trying to judge how serious the present issues in string theory are to know how Einstein and many others struggled with the same issues over decades.


So of course when we think of the persons of science who walked before us (shoulders of giants), what are their whole stories, but what is evidenced to us as we read those words? So you compile your data accordingly, and from it, we say at certain spots, how are we to react to the challenge now facing us?



Stanley Mandelstam, Professor Emeritus, Particle Theory

My present research concerns the problem of topology changing in string theory. It is currently believed that one has to sum over all string backgrounds and all topologies in doing the functional integral. I suspect that certain singular string backgrounds may be equivalent to topology changes, and that it is consequently only necessary to sum over string backgrounds. As a start I am investigating topology changes in two-dimensional target spaces. I am also interested in Seiberg-Witten invariants. Although much has been learned, some basic questions remain, and I hope to be able at least to understand the simpler of these questionsStanley Mandelstam-Professor Emeritus Particle Theory


As a lay person watching the debate it is difficult for me to discern the basis of these arguments. But I strive to go past what you think is surface in conduct in science's response, as some may show of themself in a reactionary pose. Should we all be so perfect, that the human condition is not also the example by which we shall progress in science?

Dealing in the Abstract



A sphere with three handles (and three holes), i.e., a genus-3 torus.

Of course the thinking may seem so detached from reality that one asks for some reason with which to believe anything. It required, that the history of this approached dust off models in glass cabinets, that were our early descendants of the museum today.

Sylvester's models lay hidden away for a long time, but recently the Mathematical Institute received a donation to rescue some of them. Four of these were carefully restored by Catherine Kimber of the Ashmolean Museum and now sit in an illuminated glass cabinet in the Institute Common Room.




How many of you know how to work in such abstract spaces, and know that what you are talking about has it's relationships in the physics of today? Or that, what satellites we use in measure of, have some correlation to how one may have seen "UV coordinates supplied by Gauss?"

Thursday, December 29, 2005

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 :)

Friday, October 21, 2005

Resonance: Brownian Motion

Now before I go into this I am thinking also if how "weathered effects and chaos" would have allowed quantum probability valuations (let's say spintronic idealization to channel) to have been curtailed to a Professor crossing the room. Brane orientation and fermionic considerations held, while helping to orientate views further out in the bulk?

This encompasses the generalization in terms of bubble dynamics, or how could any singularity too "inside/out" be of value to that same gravitational collapse, regardless of macro or micro considerations?

So one would have to seen how, Langrangian "points" help to view dynamcial situations in relation to the Sun Earth Moon. I would like to have thought of a chaldni plate analogy here, pointing, to a place for consideration of movement of our satelittes with less efffort. It is a vision of geometrical correlations that such idea could have been artistically embued.

Resonance
This is a magazine that Clifford drew our attention too, and while looking in the archive I found reference here below that sort of caught my attention.



Brownian Motion Problem: Random Walk and
Beyond
,

I really find this quite interesting from a "artistic point of view".

While indeed the issue is quite complex in terms of environmental flows and such, this kind of dynamcial valution might seem interesting from the point of view of early plasmatic conditions, would it not?

Now if such supefluid conditions would arise in the collider developements then, this expression would defintiely need to answer the way in which we look at what superpsymmeterical valuation would have ever resulted in symetry breaking valuation sought from these bubble dynamics, fromthe fluid of that early universe.



What constraints would limit you from making such a comparison and the idea of bubbles that form from this bath? To viewing dynamic situations in terms of thermodynamic realization offered from other perspectves. I give some examples shortly. Just know, that gravitational collapse would have signalled a better determination then one how ever discerned, to point to efforts to understand this supersymmetrical valuation. If all grviaational states of collpase are revealled as leaidng indicators to this supersymmetreicla valuation, then the idea to me is that this points to a underlying reality that exists in our moments around us.

While Microstate blackhole would be quick to dissipate, it is equally sufficient to my thinking to see that infomration realease from this "supersymmetrical breaking" would give indictaions as information in UV indications?

Of course it's all speculation from the point of the fluid, because we have evidence of this already. So all I am doing is saying that having the stage set, then how would such relations signal new universes?

So from a geometrical standpoint, having been told that there are no physics and geometry below a certain length (is this a quantum grvaity ascertion since there is no consensus?), this makes it extremely difficult to theoretically deal with how such a issue I am relaying in terms of Brownian motion could have ever spawned those same bubble universes out of such a fluid state.


This gallery was inspired by a lecture of Dr. Julien Sprott and his work.To learn how these are created, check out my Strange Attractor Tutorial. Click on the images to enlarge them.


So my mind is set in this chaotic enviroment, but indeed, the continuity of all these movements and flows seem disjointed from one perspective, that one point over here, might be different in the way a guassian map might reveal of point "p" over there. So we know on the surface, seeing valuation in terms of gaussion coordiantes that we can spell out on the face value of this surface, would have given a uv of P a very much different look.


Gaussian Coordinates
We can sum this up as follows: Gauss invented a method for the mathematical treatment of continua in general, in which ?size-relations? (?distances? between neighbouring points) are defined. To every point of a continuum are assigned as many numbers (Gaussian co-ordinates) as the continuum has dimensions. This is done in such a way, that only one meaning can be attached to the assignment, and that numbers (Gaussian co-ordinates) which differ by an indefinitely small amount are assigned to adjacent points. The Gaussian co-ordinate system is a logical generalisation of the Cartesian co-ordinate system. It is also applicable to non-Euclidean continua, but only when, with respect to the defined ?size? or ?distance,? small parts of the continuum under consideration behave more nearly like a Euclidean system, the smaller the part of the continuum under our notice.



Now if such bubble dynamics were to be self revealling, such surface measures would give evidentary features of the shape of this bubble, defining geometrical propensities as a surface valuation. I am thinking here of the "rainbow colors as refractory relevance" that would seem to define heavier color variations over this surface, if using soap bubble as an example.

Plato:
So just to carry on a bit with this point "P" in gaussian coordinated of frame of UV, what realization exists that we could not find some relevance here in the geometry to have further exploited the mind's capabilties by venturing into the Wunderkammern of thinking. By association, of Nigel Hitchin's "B Field manifestations geometries" to realize that althought these might be limited to what Jacque is saying , then what value this geometry if we can not see the landscape as something real in time variable measures?



Now you know you could have never come to this "shape" without the birthing process of expansitory values of a new universe right? So of course there is something troubling about chaotc environments, but also the nice fluidic forms of expression that would seem to reveal the dynamics of nature in overlaid valuation, of motion.

Having come to a surface valution of expansitory features such as a measdure of the earth in a "time variable mode", makes much more sense to me having accumulative histories and use of Grace, that we would now say hey, ourviews of spherical and round earth we live on has a certain new feature about it, that does not seem so pretty. Well, we defined the valuation gravitationally over this whole planet and it is encased. So I see it as a bubble defined to it's mass context and density variations etc.

Wednesday, December 08, 2004

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?

Friday, November 26, 2004

No Royal Road to Geometry?




All those who have written histories bring to this point their account of the development of this science. Not long after these men came Euclid, who brought together the Elements, systematizing many of the theorems of Eudoxus, perfecting many of those of Theatetus, and putting in irrefutable demonstrable form propositions that had been rather loosely established by his predecessors. He lived in the time of Ptolemy the First, for Archimedes, who lived after the time of the first Ptolemy, mentions Euclid. It is also reported that Ptolemy once asked Euclid if there was not a shorter road to geometry that through the Elements, and Euclid replied that there was no royal road to geometry. He was therefore later than Plato's group but earlier than Eratosthenes and Archimedes, for these two men were contemporaries, as Eratosthenes somewhere says. Euclid belonged to the persuasion of Plato and was at home in this philosophy; and this is why he thought the goal of the Elements as a whole to be the construction of the so-called Platonic figures. (Proclus, ed. Friedlein, p. 68, tr. Morrow)


It was interesting to me that I find some thread that has survived through the many centuries , that moves through the hands of individuals, to bring us to a interesting abstract world that few would recognize.



While Euclid is not known to have made any original discoveries, and the Elements is based on the work of his predecessors, it is assumed that some of the proofs are his own and that he is responsible for the excellent arrangement. Over a thousand editions of the work have been published since the first printed version of 1482. Euclid's other works include Data, On Divisions of Figures, Phaenomena, Optics, Surface Loci, Porisms, Conics, Book of Fallacies, and Elements of Music. Only the first four of these survive.

Of interest, is that some line of departure from the classical defintions, would have followed some road of developement, that I needed to understand how this progression became apparent. For now such links helped to stabilize this process and the essence of the departure form this classical defintion needed a culmination reached in Einstein's General Relativity. But long before this road was capture in it's essence, the predecessors in this projective road, develope conceptual realizations and moved from some point. To me, this is the fifth postulate. But before I draw attention there I wanted to show the index of this same projective geometry.

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.

The move from the fifth postulate had Girolamo Saccheri, S.J. (1667 - 1733) ask the question?

What if the sum of the angles of a triangle were not equal to 180 degrees (or p radians)?" Suppose the sum of these angles was greater than or less than p. What would happen to the geometry we have come to depend on for so many things? What would happen to our buildings? to our technology? to our countries' boundaries?




The progression through these geometries leads to global perspectives that are not limited to the thread that moves through these cultures and civilizations. The evolution dictates that having reached Einstein GR that we understand that the world we meet is a dynamical one and with Reason, we come t recognize the Self Evident Truths.

At this point, having moved through the geometrical phases and recognitions, the physics of understanding have intertwined mathematical realms associated with Strings and loop and other means, in which to interpret that dynamical world called the Planck Length(Quantum Gravity).

Reichenbach on Helmholtz