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Showing posts with label Tomato Soup. Show all posts
Showing posts with label Tomato Soup. Show all posts

Tuesday, May 15, 2012

Illusions of Grandeur?

Illusions of Gravity

Three spatial dimensions are visible all around us--up/down, left/right, forward/backward. Add time to the mix, and the result is a four-dimensional blending of space and time known as spacetime. Thus, we live in a four-dimensional universe. Or do we?

Amazingly, some new theories of physics predict that one of the three dimensions of space could be a kind of an illusion--that in actuality all the particles and fields that make up reality are moving about in a two-dimensional realm like the Flatland of Edwin A. Abbott. Gravity, too, would be part of the illusion: a force that is not present in the two-dimensional world but that materializes along with the emergence of the illusory third dimension.

UC Berkeley's Raphael Bousso presents a friendly introduction to the ideas behind the holographic principle, which may be very important in the hunt for a theory of quantum gravity. Series: "Lawrence Berkeley National Laboratory Summer Lecture Series" [3/2006] [Science] [Show ID: 11140]


This is just a recoup of what had been transpiring since 2005. We have a pretty good picture of the ways such distinctions are held for perspective so that we may look inside the black hole? The labels of this blog entry help with this refreshing.

See Also:

Monday, September 05, 2011

A Holograpical Universe

Plato likened our view of the world to that of an ancient forebear watching shadows meander across a dimly lit cave wall. He imagined our perceptions to be but a faint inkling of a far richer reality that flickers beyond reach. Two millennia later, Plato’s cave may be more than a metaphor. To turn his suggestion on its head, reality—not its mere shadow—may take place on a distant boundary surface, while everything we witness in the three common spatial dimensions is a projection of that faraway unfolding. Reality, that is, may be akin to a hologram. Or, really, a holographic movie.

The journey to this peculiar possibility combines developments deep and far-flung—insights from general relativity; from research on black holes; from thermodynamics, quantum mechanics, and, most recently, string theory. The thread linking these diverse areas is the nature of information in a quantum universe.
Physicists Jacob Bekenstein and Stephen Hawking established that, for a black hole, the information storage capacity is determined not by the volume of its interior but by the area of its surface. But when the math says that a black hole’s store of information is measured by its surface area, does that merely reflect a numerical accounting, or does it mean that the black hole’s surface is where the information is actually stored? It’s a deep issue and has been pursued for decades by some of the most renowned physicists. The answer depends on whether you view the black hole from the outside or from the inside—and from the outside, there’s good reason to believe that information is indeed stored at the event horizon. This doesn’t merely highlight a peculiar feature of black holes. Black holes don’t just tell us about how black holes store information. 
Black holes inform us about information storage 
in any context. See:Our Universe May Be a Giant Hologram

See Also: Physics and Philosophie Pay attention too, #8. (And Stefan submits: What is the ontological status of AdS/CFT?)[also pay attention to comments relating to #8]

Sunday, January 18, 2009

The Pringles Potato Chip

....a higher dimensional version of the Pringle's potato chip. Brian Greene, The Fabric of the Cosmos, pg 483, Para 2, line 29


Again I try remind good scientists that I have nothing to offer other then trying to keep pace with their thinking, and to find myself in world's of abstraction that I really find interesting. Of course, their metaphors too.

You see for me there are interesting correlations of thought that wake me up to the understanding of such abstract thinking, and what purposes it serves. I quote the Pringle Potato Chip to spell out the earlier realization of Maldacena, as well, the idea I have about, the Birth of Approximation. I was trying to tangle with such thoughts in a cosmological sense and here they speak to it in mathematical illustrations.

***


IN their figure 2. Hyperbolic space, and their comparative relation to the M.C.Escher's Circle Limit woodcut, Klebanov and Maldacena write, " but we have replaced Escher's interlocking fish with cows to remind readers of the physics joke about the spherical cow as an idealization of a real one. In anti-de Sitter/conformal theory correspondence, theorists have really found a hyperbolic cow."

Click on image for larger version. See:Solving quantum field theories via curved spacetimes by Igor R. Klebanov and Juan M. Maldacena

Thank you, too "Just Learning" andDavid Berenstein for the information about the article above.

***


See Also:
  • Spherical Cows and their X-ray Sources and related links in article
  • Sunday, November 12, 2006

    Graviton in a Can?

    After you consume "graviton in a can," you might never be the same? Brane thinking may then dominate your every view of the world. Then, it will all make sense?

    Imagine while we peer deeper into the subject of the "perfect fluid/soup" we find that certain aspects of the reductionist work done, has indeed lead us to speculate on how the "new physics" formed through the research and understanding currently being worked in the LHC?

    Is there some architectural design to the "Degree's of Freedom?" Why anything more then the spacetime we have come to recognize, which placed new parameters on our thinking? Moved it from the recogition of Maxwellian and Gaussian coordinates to Riemann geometries in the theory of General Relativity, to become known, as the Theory of gravity. Why "anything" more then that?


    A picture of flux lines in QED (left) and QCD (right).
    Although it didn't properly describe strong interactions, in studying string theory physicists stumbled upon an amazing mathematical structure. String theory has turned out to be far richer than people originally anticipated. For example, people found that a certain vibrational state of the string has zero mass and spin 2. According to Einstein's theory of gravity, the gravitational force is mediated by a particle with zero mass and spin 2. So string theory is, among many other things, a theory of gravity!


    I mean how are such abstract notions in the mathematics supposed to make sense, if we can not see the logic of these formulations working in some kind of reality frame of reference?


    by Jacob D. Bekenstein
    TWO UNIVERSES of different dimension and obeying disparate physical laws are rendered completely equivalent by the holographic principle. Theorists have demonstrated this principle mathematically for a specific type of five-dimensional spacetime ("anti–de Sitter") and its four-dimensional boundary. In effect, the 5-D universe is recorded like a hologram on the 4-D surface at its periphery. Superstring theory rules in the 5-D spacetime, but a so-called conformal field theory of point particles operates on the 4-D hologram. A black hole in the 5-D spacetime is equivalent to hot radiation on the hologram--for example, the hole and the radiation have the same entropy even though the physical origin of the entropy is completely different for each case. Although these two descriptions of the universe seem utterly unalike, no experiment could distinguish between them, even in principle.


    So we have these diagrams and thought processes developed from individuals like Jacob D. Bekenstein to help us visualize what is taking place. Gives us key indicators of the valuation needed, in order to determine what maths are going to be used? In this case the subject of Conformal Filed Theory makes itself known, for the thought process to hone in on what is going to be spoken too?

    Holography encodes the information in a region of space onto a surface one dimension lower. It sees to be the property of gravity, as is shown by the fact that the area of th event horizon measures the number of internal states of a blackhole, holography would be a one-to-one correspondence between states in our four dimensional world and states in higher dimensions. From a positivist viewpoint, one cannot distinguish which description is more fundamental.Pg 198, The Universe in Nutshell, by Stephen Hawking


    So we are given the label in which to speak about the holographical ntions of what is being talked about in the case of the blackhole's horizon.


    Campbell's Soup Can by Andy Warhol Exhibited in New York (USA), Leo Castelli Gallery


    While it is difficult of such images to be found displayed in the bloggery here to show what Dr. Gary Horowitz is saying you get the jest when you go right to the image of the tomato soup can.

    Spacetime in String Theory-Dr. Gary Horowitz, UCSB-Apr 20, 2005

    This year marks the hundredth anniversary of Einstein's "miraculous year", 1905, when he formulated special relativity, and explained the origin of the black body spectrum and Brownian motion. In honor of this occasion, I will describe the modern view of spacetime. After reviewing the properties of spacetime in general relativity, I will provide an overview of the nature of spacetime emerging from string theory. This is radically different from relativity. At a perturbative level, the spacetime metric appears as ``coupling constants" in a two-dimensional quantum field theory. Nonperturbatively (with certain boundary conditions), spacetime is not fundamental but must be reconstructed from a holographic, dual theory. I will conclude with some recent ideas about the big bang arising from string theory.


    Imagine containing everything we know in this can. Yet,we find that the "soup image" has somehow been translated to other factors and values that seem beyond what we know is real. Is real within the confines and boundaries, and is not evidence of the "infinities" that arise from such non containment?

    So, what of the "dilation field" that accumulates, as we speak to what the photon is in the measure of Glast. High energy photon determinations that may also be the valuation of the graviton in expression, as the photon travels through these fields?

    Such unification is important once we move into the bulk perspective and what we see of the 2d image of the brane, as a value, and discernation of the label of the soup can?


    The ALICE TPC in its clean room, where it is undergoing commissioning of all its sectors.

    One of the first cosmic-ray events recorded and reconstructed in two sectors of the TPC.
    The tests use the ALICE cosmic muon trigger detector ACORDE, as well as a specially designed UV laser system, to produce tracks in the detector. Preliminary analysis of the cosmic-ray events and the laser-induced tracks indicate that the drift velocity and diffusion of electrons liberated by traversing charged particles, as well as the spatial resolution, are very close to the design values.


    So here we are then, having graduated in perspective about what is real, as one may ask the sociological aspect of this whole adventure?



    If such missing energy is, "not accounted for" then what happens to the graviton as it is produced and causes energy to travel with them?

    For example, people found that a certain vibrational state of the string has zero mass and spin 2. According to Einstein's theory of gravity, the gravitational force is mediated by a particle with zero mass and spin 2. So string theory is, among many other things, a theory of gravity!

    Thursday, September 15, 2005

    CFT and the Tomato Soup Can

    As always, the layman trying to develope the mathematical views?:)

    Greg Kuperberg on Sep 15th, 2005 at 12:11 pm
    Conformal maps of the Earth are a great introduction to complex analysis. If you identify the Earth with the Riemann sphere, then the Mercator map is exp(i*z), while the quincuncial projection is a Weierstrass elliptic function. Or you could view it as a 2-to-1 conformal projection from a torus to a sphere with four ramified points. I imagine that it is relevant to one-loop calculations in string theory in that guise.




    At what level has this map then progressed if we held such views to the "horizon and boundary conditions." That is now replaces what we talk about of earth, and now relay the mass consideration to events in the gravitational field? Has the mathematic hypothesized now, gone through a revision, and needed support of mathematical views?


    Campbell's Soup Can A. Warhol


    What mathematics would move our perception to the gravitational views seen there? Gary Horowitz relays the outside label of a can of a soup as the conformal surface, while the soup, the spacetime fabric?

    On planet Earth, we tend to think of the gravitational effect as being the same no matter where we are on the planet. We certainly don't see variations anywhere near as dramatic as those between the Earth and the Moon. But the truth is, the Earth's topography is highly variable with mountains, valleys, plains, and deep ocean trenches. As a consequence of this variable topography, the density of Earth's surface varies. These fluctuations in density cause slight variations in the gravity field, which, remarkably, GRACE can detect from space.

    So one would look at topography as something much different then what is laid out on this globe as "hills and valleys"?

    So now this map, has this extra feature to it.

    Holography encodes the information in a region of space onto a surface one dimension lower. It sees to be the property of gravity, as is shown by the fact that the area of th event horizon measures the number of internal states of a blackhole, holography would be a one-to-one correspondance between states in our four dimensional world and states in higher dimensions. From a positivist viewpoint, one cannot distinquish which discription is more fundamental.

    Pg 198, The Universe in Nutshell, by Stephen Hawking

    While on this topic it behooves me to think of the "horizon" and the mathematical construct that has taken us there. While we see to explain the nature of the effect in a fifth dimensional view, it had been reduced to "temperature" as a relation of this conformal view?

    "D-branes provide the fundamental quantum microstates of a black hole that underlie black hole thermodynamics"


    As much as one would try and ignore this position, you cannot get away from the mathematics or the approach and what this has culminated too.

    I like Peter and his no nonsense views, but he has gone to far in rejecting the basis of "mathematical dialogue" in face of what D brane issue had been taken too?

    Why would he reject mathematics on the one hand demonstrative of a particular point of view to which it has developed, then, ignore what position it had taken both string theory and Lee Smolins attempts at the disciption of the blackhole dynamics, from the views of that horizon?

    With regards to the conformal field theory approach. While I am in my infancy, I recognize the views of Bekenstein Bound, and the hologrpahical approach. One must first learn to crawl, then walk I know, but how indeed does one get to the vision held, when he himself(who ever you like) cannot explain how such a mathematics like string theory, arose to help with our views of reality?

    In 1919, Kaluza sent Albert Einstein a preprint --- later published in 1921 --- that considered the extension of general relativity to five dimensions. He assumed that the 5-dimensional field equations were simply the higher-dimensional version of the vacuum Einstein equation, and that all the metric components were independent of the fifth coordinate. The later assumption came to be known as the cylinder condition. This resulted in something remarkable: the fifteen higher-dimension field equations naturally broke into a set of ten formulae governing a tensor field representing gravity, four describing a vector field representing electromagnetism, and one wave equation for a scalar field. Furthermore, if the scalar field was constant, the vector field equations were just Maxwell's equations in vacuo, and the tensor field equations were the 4-dimensional Einstein field equations sourced by an EM field. In one fell swoop, Kaluza had written down a single covariant field theory in five dimensions that yielded the four dimensional theories of general relativity and electromagnetism. Naturally, Einstein was very interested in this preprint .


    While one may use sites to give indicative values ot the information, can we ignore these assumptions mathematically driven. It paved the way for how we view things that we did not see before. Go ahead reject it then:)

    Are we not looking for the Trigger?:)