Pages

Showing posts with label Curvature Parameters. Show all posts
Showing posts with label Curvature Parameters. Show all posts

Saturday, April 20, 2013

Geometrical Underpinnings

On the Hypotheses which lie at the Bases of Geometry.
Bernhard Riemann
Translated by William Kingdon Clifford

[Nature, Vol. VIII. Nos. 183, 184, pp. 14--17, 36, 37.]


It is known that geometry assumes, as things given, both the notion of space and the first principles of constructions in space. She gives definitions of them which are merely nominal, while the true determinations appear in the form of axioms. The relation of these assumptions remains consequently in darkness; we neither perceive whether and how far their connection is necessary, nor a priori, whether it is possible.

From Euclid to Legendre (to name the most famous of modern reforming geometers) this darkness was cleared up neither by mathematicians nor by such philosophers as concerned themselves with it. The reason of this is doubtless that the general notion of multiply extended magnitudes (in which space-magnitudes are included) remained entirely unworked. I have in the first place, therefore, set myself the task of constructing the notion of a multiply extended magnitude out of general notions of magnitude. It will follow from this that a multiply extended magnitude is capable of different measure-relations, and consequently that space is only a particular case of a triply extended magnitude. But hence flows as a necessary consequence that the propositions of geometry cannot be derived from general notions of magnitude, but that the properties which distinguish space from other conceivable triply extended magnitudes are only to be deduced from experience. Thus arises the problem, to discover the simplest matters of fact from which the measure-relations of space may be determined; a problem which from the nature of the case is not completely determinate, since there may be several systems of matters of fact which suffice to determine the measure-relations of space - the most important system for our present purpose being that which Euclid has laid down as a foundation. These matters of fact are - like all matters of fact - not necessary, but only of empirical certainty; they are hypotheses. We may therefore investigate their probability, which within the limits of observation is of course very great, and inquire about the justice of their extension beyond the limits of observation, on the side both of the infinitely great and of the infinitely small.



Click the image to open in full size.
"We all are of the citizens of the Sky" Camille Flammarion


Seminar on the History of Hyperbolic Geometry, by Greg Schreiber
We began with an exposition of Euclidean geometry, first from Euclid's perspective (as given in his Elements) and then from a modern perspective due to Hilbert (in his Foundations of Geometry). Almost all criticisms of Euclid up to the 19th century were centered on his fifth postulate, the so-called Parallel Postulate.The first half of the course dealt with various attempts by ancient, medieval, and (relatively) modern mathematicians to prove this postulate from Euclid's others. Some of the most noteworthy efforts were by the Roman mathematician Proclus, the Islamic mathematicians Omar Khayyam and Nasir al-Din al-Tusi, the Jesuit priest Girolamo Sacchieri, the Englishman John Wallis, and the Frenchmen Lambert and Legendre. Each one gave a flawed proof of the parallel postulate, containing some hidden assumption equivalent to that postulate. In this way properties of hyperbolic geometry were discovered, even though no one believed such a geometry to be possible.


There is some question here as to what signifies a liberation of a kind and how this may have affected your perceptions. How is it so easy for what you may have read of one page to come back to it later and see and read something different? So how had you changed?

Wigner's friend is a thought experiment proposed by the physicist Eugene Wigner; it is an extension of the Schrödinger's cat experiment designed as a point of departure for discussing the Quantum mind/body problem. See: WIGNER'S FRIEND
Conclusion: *The state of mind of the observer plays a crucial role in the perception of time.* On the Effects of External Sensory Input on Time Dilation." A. Einstein, Institute for Advanced Study, Princeton, N.J.
Einstein:Since there exist 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.

The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean. Bernhard Riemann

Riemannian Geometry, also known as elliptical geometry, is the geometry of the surface of a sphere. It replaces Euclid's Parallel Postulate with, "Through any point in the plane, there exists no line parallel to a given line." A line in this geometry is a great circle. The sum of the angles of a triangle in Riemannian Geometry is > 180°.

While this may seem abstract in term of it's mathematical underpinnings, it allows us to see in ways that we might ever have been privileged to see before. So you turn your head to everything you have observed before and a whole new light has been thrown on the world. By consensus, this new view allows you to see deeper into the universe in ways that we had only taken from a standpoint of a man looking into outer space.

The Binary Pulsar PSR 1913+16:

So while being lead through the circumstance of historical individual pursuers to solving the Parallel postulate, liberation was found in order to move a geometrical proposition forward in time. Some may say that time is a illusion then?

So as a new paradigmatic change that has been initiated it's application and is pushed into the world so as to ascertain it's functionality. Does it then become real?




 "...underwriting the form languages of ever more domains of mathematics is a set of deep patterns which not only offer access to a kind of ideality that Plato claimed to see the universe as created with in the Timaeus; more than this, the realm of Platonic forms is itself subsumed in this new set of design elements-- and their most general instances are not the regular solids, but crystallographic reflection groups. You know, those things the non-professionals call . . . kaleidoscopes! * (In the next exciting episode, we'll see how Derrida claims mathematics is the key to freeing us from 'logocentrism'-- then ask him why, then, he jettisoned the deepest structures of mathematical patterning just to make his name...)* H. S. M. Coxeter, Regular Polytopes (New York: Dover, 1973) is the great classic text by a great creative force in this beautiful area of geometry (A polytope is an n-dimensional analog of a polygon or polyhedron. Chapter V of this book is entitled 'The Kaleidoscope'....)"

Sunday, March 18, 2007

AP May Still be Useful?

Full-sky Temperature Maps-Polarized Light-K-Band Map (23 GHz)-Credit:NASA/WMAP Science Team

The color represents the strength of the polarized signal seen by WMAP - red strong/blue weak. The signal seen in these maps comes mostly from our Galaxy. It is strongest at 23 GHz, weakest at 61 and 94 GHz.

This multi-frequency data is used to subtract the Galactic signal and produce the CMB map shown (top of this page). These images show a temperature range of 50 microKelvin.


It is essential that while we are looking at this universe we understand the makeup and how it is being expressed. We also understand that while we knew the uiverse had to have it's motivation for that expression, it had to have other states of existance as well. This is related to the curvatures parameters and how differing times in the universe's expression this curvature had to be considered. These curvatures at one time in the whole context, as some cosmological constant varied, not seem relevant to the state of the universe?

So you have to explain it. Some may think I am less then desired in my understanding of General relativity, but you can be certain that understand Einstein's work in finding the "geometry of expression" was critical in understanding the "nature of gravity."


The idea behind the Coleman-De Luccia instanton, discovered in 1987, is that the matter in the early universe is initially in a state known as a false vacuum. A false vacuum is a classically stable excited state which is quantum mechanically unstable. In the quantum theory, matter which is in a false vacuum may `tunnel' to its true vacuum state. The quantum tunnelling of the matter in the early universe was described by Coleman and De Luccia. They showed that false vacuum decay proceeds via the nucleation of bubbles in the false vacuum. Inside each bubble the matter has tunnelled. Surprisingly, the interior of such a bubble is an infinite open universe in which inflation may occur. The cosmological instanton describing the creation of an open universe via this bubble nucleation is known as a Coleman-De Luccia instanton.


See more on this here

So by seeing this dynamical nature expressed did not mean you discounted how this universe was acting at various times to become what it is today. You had to find processes that would speak to this,and by defining the continuity of geometrical expression it was important to define this false vacuum in relation towhat the universe was doing as it unfolded itself and from strong curvature parameters settled itself to where it is today.

Did the universe have a negative density value relation that one could interpret? So you have to explain this as well in relation to what contributed ot the universe speeding up or slowing down. What local events within the cosmos could contribute to the universe in it's total expression?

Gravity in the microseconds

Never mind Steven Weinberg's First Three mintes.

The amount of dark matter and energy in the universe plays a crucial role in determining the geometry of space. If the density of matter and energy in the universe is less than the critical density, then space is open and negatively curved like the surface of a saddle See my post on this here

While we talk about the universe I understand that there are "curvature parameters" that can be expressed, at any given time "within context of the whole universe." We had somehow forgotten these events as local expressions of galaxies "may contribute to the larger picture?"

'An unexpected gift' from string theory

The possibility that enormously large galaxies originated from tiny quantum fluctuations may seem too strange to be true. But many aspects of inflationary theory were confirmed by recent astronomical observations, for which the observers won the Nobel Prize in 2006. This gives some credence to an even more surprising claim made by Linde: During inflation, quantum fluctuations can produce not only galaxies, but also new parts of the universe.

Take an expanding universe with its little pockets of heterogeneous quantum events. At some point one of those random events may actually "escape" from its parent universe, forming a new one, Linde said. To use the ball analogy, if it experiences small perturbations as it rolls, it might at some point roll over into the next valley, initiating a new inflationary process, he said.

"The string theorists predict that there are perhaps 101000 different types of universes that can be formed that way," Linde said. "I had known that there must be many different kinds of universes with different physical properties, but this huge number of different possibilities was an unexpected gift of string theory."

According to string theory, there are 10 dimensions. We live aware of four of them—three of space plus one of time. The rest are so small that we cannot experience them directly. In 2003, Stanford physicists Shamit Kachru, Renata Kallosh and Linde, with their collaborator Sandip Trivedi from India, discovered that these compacted dimensions want to expand, but that the time it would take for them to do so is beyond human comprehension. When a new universe buds off from its parent, the configuration of which dimensions remain small and which grow large determines the physical laws of that universe. In other words, an infinite number of worlds could exist with 101000 different types of physical laws operating among them. Susskind called this picture "the string theory landscape."

For many physicists, it is disturbing to think that the very laws and properties that are the essence of our world might only hold true as long as we remain in that world. "We always wanted to discover the theory of everything that would explain the unique properties of our world, and now we must adjust to the thought that many different worlds are possible," Linde said. But he sees an advantage in what some others could see a problem: "We finally learned that inflationary universe is not just a free lunch: It is an eternal feast where all possible dishes are served."


I have been waiting I guess until the appropriate time that I could bring Q9's link of Linde's here for comparison, to what one may think of the landscape. You had to include all the information before this comment to know that what I am talking about has it's relation in the Anthropic Principle.

The theory of strings predicts that the universe might occupy one random "valley" out of a virtually infinite selection of valleys in a vast landscape of possibilities

See info on String Theory Landscape

The title above is taken from Lee Smolin's paragraph listed below. Why I am using it will be come clear after a time in this post. I am working all night because of the duties of life, so I'll have to come back to it tomorrow. I am barely await has a continue to compile the data necessary for understanding the way I see this universe.

We assume the landscape is covered by fog so we can’t see where the real peak is, we can only feel around and detect slopes and local maxima.Lee Smolin

Lee continues on in another forum and is linked to paragraph below.

I should also emphasize that while the book is not an attack on string theory in general it is very definitely an attack on a point of view about string theory that some, but not all, string theorists have adopted. This includes the arguments that the anthropic principle can yielded falsifiable predictions-which have been shown to be fallacious, and the argument that was made by several string theorists that a theory need not give falsifiable predictions for doable experiments to be believed. My book takes a strong stance against this point of view. I am confident here of my reasons, especially given that already in my first book the possibility of an anthropic solution to the landscape problem was considered and rejected. I am glad to know that my view on this is shared by some string theorists such as Brian Greene but not so happy that a number of very smart string theorists continue to believe that some version of the AP may still be useful.


Increased Curvatures

A circle of radius r has a curvature of size 1/r. Therefore, small circles have large curvature and large circles have small curvature. The curvature of a line is 0. In general, an object with zero curvature is "flat."

See my post here and here.

The value of the circle in relation to gravity is important to recognize, in that this value of the universe can be different based on what "critical density" in relation to Omega

In order for one to be concerned about the current state of the universe, it is essential that one realizes it's condition "before it became the way it is?" It's value in relation to the circle.



The big bang should have created equal amounts of matter and antimatter, with subsequent annihilation leaving neither behind. And yet, the observable universe has about ten billion galaxies that consist entirely of matter (protons, neutrons, and electrons) with no antimatter (antiprotons, antineutrons, and positrons). Very soon after the big bang, some forces must have caused the CP violation that skewed the equality in the number of matter and antimatter particles and left behind excess matter.



So while we get this sense here of the hills and valleys, what said that the current system had not taken into consideration the sombrero? The effects of gravity when it was once strong, and now is weak. We still get this sense of the universe doing things.

Wednesday, February 07, 2007

Angels and Demons on a Pinhead

"Observations always involve theory."Edwin Hubble
Curvature Parameters

Of course I had to point to the cosmological understanding that took us to this "geometrical understanding of things that are large." But this is to be short, while I crunch the thoughts of the process to the pinhead. You can follow the "picture links" and learn more on your own time.


Calabi-Yau manifold (3D projection made with Mathematica)-
In either case, gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. In fact, Kaluza and Klein's early work demonstrated that general relativity with five large dimensions and one small dimension actually predicts the existence of electromagnetism. However, because of the nature of Calabi-Yau manifolds, no new forces appear from the small dimensions, but their shape has a profound effect on how the forces between the strings appear in our four dimensional universe. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions.


How many would have thought that such a micro-perspective could have been ever be taken down to "this level" and found an analogy that is suitable? You needed something more here to consider, yet, I will call it "angel and demons" for those who like the mystery.


Image: courtesy Andrew J. Hanson, Indiana University-A computer-generated rendering of a possible six-dimensional geometry similar to those studied by UW-Madison physicist Gary Shiu.

I will try and spell out what is happening at such a microperspective level. You might wonder, how did such ideas become what is, "the good and evil of the world" is really a part of the dynamics that we see geometrically enhanced, as we delve ever deeper into this mystery of reductionism and such. On how, we may look at cosmology that "is different" with this perspective.

Energy "is" Gravitationally Related

At some point, those considering "all this energy" and the way reduction is assigned to the energy at all levels, what shall any calorimetric pick up as such collision processes seek to define "every contact" as we want to "map the pinhead" accordingly?

Lubos Motl saids that he sees the relation to such dynamical situations as "fruitful research" toward the understanding of the cosmological descriptions implied from such micro states. To have it listed according to a "geometrical perspective" we might be able to assign each universe? Okay! He did not say that exactly, so check into his blog entry for an update.

I'd like to thank Quasar9 for reporting on this as well.

Orbitals



My thoughts have been there toward reductionism's more cosmological counterpart for some time now. So I enjoy, that the views that I have had about the microperspective have indeed been sanctioned at some science level according to the scientist in the know. Yes, I can prove my thoughts here for you, so you know what I mean.


The star Eta Carina is ejecting a pair of huge lobes that form a "propeller" shape. Jet-like structures are emanating from the center (or "waist"), where the star (quite small on this scale) is located.


Now it is indeed a "greater depth of perception" that asks us to delve into the microperspective of string world. How is it the cosmological world can have such similarities, while the story of the Calabi Yau, makes itself a headlight news current in the research of string theory?

The First Few Microseconds, by Michael Riordan and Willaim A. Zajc
During those early moments, matter was an ultrahot, superdense brew of particles called quarks and gluons rushing hither and thither and crashing willy-nilly into one another. A sprinkling of electrons, photons and other light elementary particles seasoned the soup. This mixture had a temperature in the trillions of degrees, more than 100,000 times hotter than the sun's core.


See:
  • Angels and Demons
  • Doppelgänger Favors Oscillate
  • Music of the Spheres
  • A Clear Presence-Friday
  • Saturday, January 06, 2007

    Mersenne Prime: One < the Power of two


    It looks as though primes tend to concentrate in certain curves that swoop away to the northwest and southwest, like the curve marked by the blue arrow. (The numbers on that curve are of the form x(x+1) + 41, the famous prime-generating formula discovered by Euler in 1774.)


    This is part of the education of my learning to understand the implications of the work of Riemann in context of the Riemann Hypothesis. Part of understanding what this application can do in terms helping us to see what has developed "from abstractions of mathematics," to have us now engaged in the "real world" of computation.

    In mathematics, a power of two is any of the nonnegative integer powers of the number two; in other words, two multiplied by itself a certain number of times. Note that one is a power (the zeroth power) of two. Written in binary, a power of two always has the form 10000...0, just like a power of ten in the decimal system.

    Because two is the base of the binary system, powers of two are important to computer science. Specifically, two to the power of n is the number of ways the bits in a binary integer of length n can be arranged, and thus numbers that are one less than a power of two denote the upper bounds of integers in binary computers (one less because 0, not 1, is used as the lower bound). As a consequence, numbers of this form show up frequently in computer software. As an example, a video game running on an 8-bit system, might limit the score or the number of items the player can hold to 255 — the result of a byte, which is 8 bits long, being used to store the number, giving a maximum value of 28−1 = 255.


    I look forward to the help in terms of learning to understand this "ability of the mind" to envision the dynamical nature of the abstract. To help us develop, "the models of physics" in our thinking. To learn, about what is natural in our world, and the "mathematical patterns" that lie underneath them.

    What use the mind's attempt to see mathematics in such models?

    "Brane world thinking" that has a basis in Ramanujan modular forms, as a depiction of those brane surface workings? That such a diversion would "force the mind" into other "abstract realms" to ask, "what curvatures could do" in terms of a "negative expressive" state in that abstract world.

    Are our minds forced to cope with the "quantum dynamical world of cosmology" while we think about what was plain in Einstein's world of GR, while we witness the large scale "curvature parameters" being demonstrated for us, on such gravitational look to the cosmological scale.

    Mersenne Prime


    Marin Mersenne, 1588 - 1648


    In mathematics, a Mersenne number is a number that is one less than a power of two.

    Mn = 2n − 1.
    A Mersenne prime is a Mersenne number that is a prime number. It is necessary for n to be prime for 2n − 1 to be prime, but the converse is not true. Many mathematicians prefer the definition that n has to be a prime number.

    For example, 31 = 25 − 1, and 5 is a prime number, so 31 is a Mersenne number; and 31 is also a Mersenne prime because it is a prime number. But the Mersenne number 2047 = 211 − 1 is not a prime because it is divisible by 89 and 23. And 24 -1 = 15 can be shown to be composite because 4 is not prime.

    Throughout modern times, the largest known prime number has very often been a Mersenne prime. Most sources restrict the term Mersenne number to where n is prime, as all Mersenne primes must be of this form as seen below.

    Mersenne primes have a close connection to perfect numbers, which are numbers equal to the sum of their proper divisors. Historically, the study of Mersenne primes was motivated by this connection; in the 4th century BC Euclid demonstrated that if M is a Mersenne prime then M(M+1)/2 is a perfect number. In the 18th century, Leonhard Euler proved that all even perfect numbers have this form. No odd perfect numbers are known, and it is suspected that none exist (any that do have to belong to a significant number of special forms).

    It is currently unknown whether there is an infinite number of Mersenne primes.

    The binary representation of 2n − 1 is n repetitions of the digit 1, making it a base-2 repunit. For example, 25 − 1 = 11111 in binary


    So while we have learnt from Ulam's Spiral, that the discussion could lead too a greater comprehension. It is by dialogue, that one can move forward, and that lack of direction seems to hold one's world to limits, not seen and known beyond what's it like apart from the safe and security of home.

    Tuesday, December 19, 2006

    Cosmic ray spallation


    As this NASA chart indicates, 70 percent or more of the universe consists of dark energy, about which we know next to nothing
    Other explanations of dark energy, called "quintessence," originate from theoretical high-energy physics. In addition to baryons, photons, neutrinos, and cold dark matter, quintessence posits a fifth kind of matter (hence the name), a sort of universe-filling fluid that acts like it has negative gravitational mass. The new constraints on cosmological parameters imposed by the HST supernova data, however, strongly discourage at least the simplest models of quintessence.


    Of course my mind is thinking about the cosmic triangle of an event in the cosmos. So I am wondering what is causing the "negative pressure" as "dark energy," and why this has caused the universe to speed up.


    SNAP-Supernova / Acceleration Probe-Studying the Dark Energy of the Universe
    The discovery by the Supernova Cosmology Project (SCP) and the High-Z Supernova team that the expansion of the universe is accelerating poses an exciting mystery — for if the universe were governed by gravitational attraction, its rate of expansion would be slowing. Acceleration requires a strange “dark energy’ opposing this gravity. Is this Einstein’s cosmological constant, or more exotic new physics? Whatever the explanation, it will lead to new discoveries in astrophysics, particle physics, and gravitation.


    By defining the context of particle collisions it was evident that such a place where such a fluid could have dominated by such energy in stars, are always interesting as to what is ejected from those same stars. What do those stars provide for the expression of this universe while we are cognoscente of the "arrow of time" explanation.


    This diagram reveals changes in the rate of expansion since the universe's birth 15 billion years ago. The more shallow the curve, the faster the rate of expansion.


    So of course these thoughts are shared by the perspective of educators to help us along. But if one did not understand the nature of the physical attributes of superfluids, how would one know to think of the relativistic conditions that high energy provides for us?


    NASA/WMAP Scientific Team: Expanding Universe



    So recognizing where these conditions are evident would be one way in which we might think about what is causing a negative pressure in the cosmos.

    Given the assumption that the matter in the universe is homogeneous and isotropic (The Cosmological Principle) it can be shown that the corresponding distortion of space-time (due to the gravitational effects of this matter) can only have one of three forms, as shown schematically in the picture at left. It can be "positively" curved like the surface of a ball and finite in extent; it can be "negatively" curved like a saddle and infinite in extent; or it can be "flat" and infinite in extent - our "ordinary" conception of space. A key limitation of the picture shown here is that we can only portray the curvature of a 2-dimensional plane of an actual 3-dimensional space! Note that in a closed universe you could start a journey off in one direction and, if allowed enough time, ultimately return to your starting point; in an infinite universe, you would never return.


    Of course it is difficult for me to understand this process, but I am certainly trying. If one had found that in the relativistic conditions of high energy scenarios a "similarity to a flattening out" associated with an accelerating universe what would this say about information travelling from the "origins of our universe" quite freely. How would this effect dark energy?

    In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame energy density ρ and isotropic pressure p.

    Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are neglected. Specifically, perfect fluids have no shear stresses, viscosity, or heat conduction.

    In tensor notation, the energy-momentum tensor of a perfect fluid can be written in the form

    [tex] T^{\mu\nu}=(\rho+p)\, U^\mu U^\nu + P\, \eta^{\mu\nu}\,[/tex]



    where U is the velocity vector field of the fluid and where ημν is the metric tensor of Minkowski spacetime.

    Perfect fluids admit a Lagrangian formulation, which allows the techniques used in field theory to be applied to fluids. In particular, this enables us to quantize perfect fluid models. This Lagrangian formulation can be generalized, but unfortunately, heat conduction and anisotropic stresses cannot be treated in these generalized formulations.

    Perfect fluids are often used in general relativity to model idealized distributions of matter, such as in the interior of a star.


    So events in the cosmos ejected the particles, what geometrical natures embued such actions, to have these particle out in space interacting with other forms of matter to create conditions that would seem conducive to me, for that negative pressure?

    Cosmic ray spallation is a form of naturally occurring nuclear fission and nucleosynthesis. It refers to the formation of elements from the impact of cosmic rays on an object. Cosmic rays are energetic particles outside of Earth ranging from a stray electron to gamma rays. These cause spallation when a fast moving particle, usually a proton, part of a cosmic ray impacts matter, including other cosmic rays. The result of the collision is the expulsion of large members of nucleons (protons and neutrons) from the object hit. This process goes on not only in deep space, but in our upper atmosphere due to the impact of cosmic rays.

    Cosmic ray spallation produces some light elements such as lithium and boron. This process was discovered somewhat by accident during the 1970s. Models of big bang nucleosynthesis suggested that the amount of deuterium was too large to be consistent with the expansion rate of the universe and there was therefore great interest in processes that could generate deuterium after the big bang.

    Cosmic ray spallation was investigated as a possible process to generate deuterium. As it turned out, spallation could not generate much deuterium, and the excess deuterium in the universe could be explained by assuming the existence of non-baryonic dark matter. However, studies of spallation showed that it could generate lithium and boron. Isotopes of aluminum, beryllium, carbon(carbon-14), chlorine, iodine and neon, are also formed through cosmic ray spallation.



    Talk about getting tongue tied, can you imagine, "these fluctuations can generate their own big bangs in tiny areas of the universe." Read on.


    Photo credit: Lloyd DeGrane/University of Chicago News Office
    Carroll and Chen’s scenario of infinite entropy is inspired by the finding in 1998 that the universe will expand forever because of a mysterious force called “dark energy.” Under these conditions, the natural configuration of the universe is one that is almost empty. “In our current universe, the entropy is growing and the universe is expanding and becoming emptier,” Carroll said.

    But even empty space has faint traces of energy that fluctuate on the subatomic scale. As suggested previously by Jaume Garriga of Universitat Autonoma de Barcelona and Alexander Vilenkin of Tufts University, these fluctuations can generate their own big bangs in tiny areas of the universe, widely separated in time and space. Carroll and Chen extend this idea in dramatic fashion, suggesting that inflation could start “in reverse” in the distant past of our universe, so that time could appear to run backwards (from our perspective) to observers far in our past.

    Wednesday, November 22, 2006

    Tunnelling in Faster then Light

    Underneath this speculation of mine is the geometrical inclination of the universe in expression. If it's "dynamical nature is revealed" what allows us to think of why this universe at this time and junction, should be flat(?) according to the time of this universe in expression?

    Omega=the actual density to the critical density

    If we triangulate Omega, the universe in which we are in, Omegam(mass)+ Omega(a vacuum), what position geometrically, would our universe hold from the coordinates given?


    Positive energy density gives spacetime of the universe a positive curvature. A sphere? Negative curvature a region of spacetime that is negative and curved like a saddle? For time travel, and travel into the past, you need a universe that has a negative energy density.

    Thus the initial idea here to follow is that the process had to have a physics relation. This is based on the understanding of anti-particle/particle, and what becomes evident in the cosmos as a closed loop process. Any variation within this context, is the idea of "blackhole anti-particle expression" based on what can be seen at the horizon?



    A anti-particle can be considered as a particle moving back in time? Only massless particle can travel faster then light. Only faster then light massless particles can travel back in time? So of course, I am again thinking of the elephant process of Susskind and the closed loop process of the virtual particle/anti-particle. What comes out of it?

    That's not all. The fact that space-time itself is accelerating - that is, the expansion of the universe is speeding up - also creates a horizon. Just as we could learn that an elephant lurked inside a black hole by decoding the Hawking radiation, perhaps we might learn what's beyond our cosmic horizon by decoding its emissions. How? According to Susskind, the cosmic microwave background that surrounds us might be even more important than we think. Cosmologists study this radiation because its variations tell us about the infant moments of time, but Susskind speculates that it could be a kind of Hawking radiation coming from our universe's edge. If that's the case, it might tell us something about the elephants on the other side of the universe.


    So the anti-particle falls into the blackhole? How is it that I resolve this?? You can consider the anti-particle as traveling back in time. The micro perspective of the blackhole allows time travel backwards.


    Getty Images
    Although a 1916 paper by Ludwig Flamm from the University of Vienna [4] is sometimes cited as giving the first hint of a wormhole, "you definitely need hindsight to detect it," says Matt Visser of Victoria University in Wellington, New Zealand. Einstein and Rosen were the first to take the idea seriously and to try to accomplish some physics with it, he adds. The original goal may have faded, but the Einstein-Rosen bridge still pops up occasionally as a handy solution to the pesky problem of intergalactic travel.


    There are two cases in which the thoughts about faster then light particles are created and this is the part where one tries to get it right so as not to confuse themselves and others.

    Wormholes?

    Plato:
    So "open doorways" and ideas of "tunneling" are always interesting in terms of how we might look at an area like GR in cosmology? Look for way in which such instances make them self known.

    Are they applicable to the very nature of quantum perceptions that such probabilities could have emerged through them? Held to "time travel scenarios" and grabbed the history of what had already preceded us in past tense, could have been brought again forward for inspection?


    Sure I am quoting myself here, just to show one of the options I am showing by example. The second of course is where I was leading too in previous posts.

    So I was thinking here in context of one example in terms of the containment of the "graviton in a can" is really letting loose of the information in the collision process, as much as we like this "boundary condition" it really is not so.

    Another deep quantum mystery for which physicists have no answer has to do with "tunneling" -- the bizarre ability of particles to sometimes penetrate impenetrable barriers. This effect is not only well demonstrated; it is the basis of tunnel diodes and similar devices vital to modern electronic systems.

    Tunneling is based on the fact that quantum theory is statistical in nature and deals with probabilities rather than specific predictions; there is no way to know in advance when a single radioactive atom will decay, for example.

    The probabilistic nature of quantum events means that if a stream of particles encounters an obstacle, most of the particles will be stopped in their tracks but a few, conveyed by probability alone, will magically appear on the other side of the barrier. The process is called "tunneling," although the word in itself explains nothing.

    Chiao's group at Berkeley, Dr. Aephraim M. Steinberg at the University of Toronto and others are investigating the strange properties of tunneling, which was one of the subjects explored last month by scientists attending the Nobel Symposium on quantum physics in Sweden.

    "We find," Chiao said, "that a barrier placed in the path of a tunneling particle does not slow it down. In fact, we detect particles on the other side of the barrier that have made the trip in less time than it would take the particle to traverse an equal distance without a barrier -- in other words, the tunneling speed apparently greatly exceeds the speed of light. Moreover, if you increase the thickness of the barrier the tunneling speed increases, as high as you please.

    "This is another great mystery of quantum mechanics."


    Of course I am looking for processes in physics that would actually demonstrate this principal of energy calculated at the very beginning of the collision process, now explained in the detector, minus the extra energy that had gone where?



    This is the basis for the "Graviton in a can" example of what happens in the one scenario.

    Plato:
    A Bose-Einstein condensate (such as superfluid liquid helium) forms for reasons that only can be explained by quantum mechanics. Bose condensates form at low temperature


    Plasmas and Bose condensates

    So in essence the physics process that I am identifying is shown by understanding that the "graviton production" allows that energy to be transmitted outside the process of the LHC?

    This is the energy that can be calculated and left over from all the energy assumed in the very beginning of this collision process. Secondly, all energy used in this process would be in association with bulk perspective.

    This now takes me to the second process of "time travel" in the LHC process. The more I tried to figure this out the basis of thought here is that Cerenkov radiation in a vacuum still is slower then speed of light, yet within the medium of ice, this is a different story. So yes there are many corrections and insight here to consider again.

    The muon will travel faster than light in the ice (but of course still slower than the speed of light in vacuum), thereby producing a shock wave of light, called Cerenkov radiation. This light is detected by the photomultipliers, and the trace of the neutrinos can be reconstructed with an accuracy of a couple of degrees. Thus the direction of the incoming neutrino and hence the location of the neutrino source can be pinpointed. A simulation of a muon travelling through AMANDA is shown here (1.5 MB).


    So while sleeping last night the question arose in my mind as to the location of where the "higgs field" will be produced in the LHC experiment? Here also the the thoughts about the "cross over point" that would speak to the idea here of what reveals faster then light capabilities arising from the collision process?

    What are the main goals of the LHC?-
    The LHC will also help us to solve the mystery of antimatter. Matter and antimatter must have been produced in the same amounts at the time of the Big Bang. From what we have observed so far, our Universe is made of only matter. Why? The LHC could provide an answer.

    It was once thought that antimatter was a perfect 'reflection' of matter - that if you replaced matter with antimatter and looked at the result in a mirror, you would not be able to tell the difference. We now know that the reflection is imperfect, and this could have led to the matter-antimatter imbalance in our Universe.

    The strongest limits on the amount of antimatter in our Universe come from the analysis of the diffuse cosmic gamma-rays arriving on Earth and the density fluctuations of the cosmic background radiation. If one asumes that after the Big Bang, the Universe separated somehow into different domains where either matter or antimatter was dominant, then at the boundaries there should be annihilations, producing cosmic gamma rays. In both cases the limit proposed by current theories is practically equivalent to saying that there is no antimatter in our Universe.


    So we get the idea here in the collision process and from it the crossover point leaves a energy dissertation on what transpired from this condition and left the idea in my mind about the circumstances of what may have changed the the speed of the cosmos at varying times in the expansion process within our universe. So, this is where I was headed as I laid out the statement below.

    Of course this information is based on 2003 data but the jest of the idea here is that in order to go to a "fast forward" the conditions had to exist previously that did not included "sterile neutrinos" and were a result of this "cross over."


    So what is the jest of my thought here that I would go to great lengths here to speak about the ideas of what happens within the cosmos to change those varying times of expansion? It has to do with the Suns and the process within those suns that give the dark energy some value, in it's anti- gravity nature to align our selves and our thinking to the cosmological constant of Einstein. If we juggle the three ring circus we find that the curvature parameters can and do hold thoughts govern by the cosmological constant?

    It is thus equally important to identify this "physics process" that would allow such changes in the cosmos. So that we can understand the dynamical nature that the cosmos reveals to us can and does allow aspect of its galaxies within context of the universe to increase this expansive process while we question what drives such conditions.

    Monday, October 02, 2006

    CP Violation

    The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean. Bernhard Riemann




    ON a macroscale the blackhole is a understanding of when we investigate curvature parameters with regards to the nature of our universe in spacetime. We understand this right?

    What are the "entropic valuations" being recognized as we look to a earlier time of when the QGP existed and then such manifestaion in the "matters states" have exemplified such characteristics as?


    Both space and spacetime can either be curved or flat.


    I am going to give you a quick summation of what GR is. It is about "Gravity." Now if you hold that in mind you should not loose any time with what I am telling you.

    Now, how is it that we can see the dynamcial nature of the universe, yet, we would not consider the effect of the presence of microstate blackholes in regards to such gatherings in the space, of what we call "spacetime?" What would "such gatherings" show of itself?


    A circle of radius r has a curvature of size 1/r. Therefore, small circles have large curvature and large circles have small curvature. The curvature of a line is 0. In general, an object with zero curvature is "flat."


    Think about the "circle" and it's 2D view of what the blackhole is doing in 3D +time in context of many blackholes. I always refer to "one" so you can see the comparative view that I am having little success in transferring to you, in what I am seeing.

    The curvature parameters are closely associated to the thermodynamic realizations. This is importnat not only on a cosmological level, but on a microstate as well.

    Lubos explains that here.

    Lubos:
    There are lots of other examples what you can do to increase the number of black holes. Change the couplings so that the stars burn their fuel faster, and they will collapse into black hole faster. Reduce the gap between the Planck scale and the QCD scale, and nuclear collisions will be more likely to end up as black holes.

    It is quite obvious that the change of virtually any parameter of the Standard Model (plus inflation) in the right direction (one of the two directions) will result in an increase of the number of black holes. How can you doubt such a trivial thing?


    So there is something about the nature of our universe and the balance that it seeks to maintain of itself? Here we are, looking at events within the cosmo and "secular views of it's manfiestation" different then other locations within the universe. Yet not apart from it, or not indifferent to it's nature to be part of a larger picture?



    Silicon Vertex Tracker. The SVT is the heart of the BABAR experiment at SLAC—in the photo, physicists are putting the finishing touches on improvements to the detector. (Photo Courtesy of Peter Ginter)
    SLAC's BaBar collaboration has discovered that CP violation—an asymmetry between the behavior of matter and antimatter—exists even in a very rare class of particle decays. This result offers the most sensitive avenue yet for exploring matter-antimatter asymmetries, with implications for the future understanding of physics beyond the Standard Model.

    "BaBar has proven to be a fantastic instrument for exploring the origins of matter-antimatter asymmetries, allowing us to probe with exquisite precision very rare processes related to how the early universe came to be matter dominated," said David MacFarlane, BaBar Spokesperson and Professor at the Stanford Linear Accelerator Center.


    So here we are having been given the example of CP violation above and here?

    How is it that anything could be asymmetrical? :) So you introduce anti-matter and matter?


    (ambigram courtesy John Langdon)
    If we could assemble all the antimatter we've ever made at CERN and annihilate it with matter, we would have enough energy to light a single electric light bulb for a few minutes.


    As a observer Einstein made it clear that the observable universe has ideas attached to it. The "Pretty girl and the hot stove analogy" was compelling to those of us who recognized the values we may attach to life. "The Gravity of the situation?" How narrow our view of the world is when we feel the world is lost?

    But the hope and inspiration is, that the world has a bright future when we undertsand the implications of our views. Our involvement in the "toposense of reality? We are "part and parcel" of it?

    So, should we talk about the components of Heaven and Hell( my philosophical discourse on the nature of consciousness?)? You have to understand the picture and the dynamical nature this universe can say about it's entropic valuation?

    While I may have understood Omega, it didn't come to the nature it is by not including a geomtrical perspective about the nature of that same universe.

    That's my point. It had to arise from a earlier time and the manifestation is the matter states we are defining in correlation to the entropic valuations.

    While you see these as macro-characteristics and the relation to blackhole in 3d+time, the result is, a explanation of matter states in "macrostylistic beauty" we see in the events of the cosmo.

    If such inclinations to drive the energy to a ever smaller defined circle, as it gets smaller "the difference is" not so indiscernable that the events of the "particle showers" created are matter states that arise form the energy that was used.

    You see?:)

    The Ceiling

    The deeper implications of such a thought from perspective is focused upward? Yet such perspective can be made from other positions? So some minds were flexible? Others, were just engineers? ;)

    Understanding other worlds came naturally to him. Perhaps it was an inevitable consequence of being the child of Japanese Americans. His parents, though born in California, spent World War II behind barbed wire, guarded by people with machine guns: incarcerated by their own country as enemy aliens. Afterwards his father worked as a gardener, his mother a maid: two of the few jobs that were available to Japanese Americans. Kaku grew up poor, but one of the family treats was to visit the Japanese Tea Garden in San Francisco's Golden Gate Park. It turned out to be the place of a childhood epiphany. Wondering in the way that only a child does, Kaku looked at the carp swimming in a weedy pond and imagined how they would not be able to conceive of other worlds. "A carp engineer would believe that was all there is; but a carp physicist would see the ripples on the surface and start thinking about unseen dimensions," Kaku told me, laying the first of many lashes on his token engineer.


    The "ceiling" is the perspective of the carp, not the perspective of the "carp physicist."

    See:

  • Liminocentric Structures: Which Circle do you Belong Too?-Sunday, July 10, 2005


  • Ps: Some updates are curvature given for perspective. Think of a string, and any point on that string. What does the energy value of "that point" tell you in regards to the circle? The point on that string. It's just a way of looking at the string and the resonantial value assign along the string's length?

    Tuesday, December 20, 2005

    Has Speed of Light changed Recently?

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

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

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

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


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

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

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


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

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


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

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


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

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

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


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

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



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

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

    The Shape of the UNiverse in Omega Values

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

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

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


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


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


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



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

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

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

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




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

    Monday, December 05, 2005

    Bumblebee Wing Rotations and Dancing



    The Bumble Be, Mentality

    So what is the Gluon that binds?:)

    For introduction sake, I might have deviated from Sean Carroll's ideas about the, "what science doesn't know" and traded it for mechanical systems interpretations, and the way we can write comprehension forms from such patterns inherent?

    It always comes down to the lesson of a Beautiful mind? It's struggle for freedom from the illusions that we might perpetuate. The escape from, those delusions, to concrete analysis of such systemic thought patterns within human nature. The triumph and freedom, to overcome all odds?

    If we thought of Belt rotations and Greg Egan, it wouldn't be to hard to place some perspective on how Sean might have intepreted the "wing rotation of slowed photography," and said, "hey, here is this pattern, and something a string theorist could hang their hat on?"

    Satisfactory conclusion to rotations, that equatively reach across and touch us like E=mc2 does, then what's the point of concluding any thoughts if this consistancy can't be accomplished? So herein lies my inexperience, and the last recursive thought of, "okay, what science doesn't know, I scream?" :) Was it emotive enough to make my point?

    And so in reference to string theory work, I couldn't help but think of the rotations, waiters and table trays and such. But it also made me think of the inroads to observation of nature and flight? Wilbur and Orville Wright as well?

    But looking deeper, and from what one could gain from such observations, did I miss Sean's point?


    Kosmopolis 05


    Marc D. Hauser:
    We know that that kind of information is encoded in the signal because people in Denmark have created a robotic honey bee that you can plop in the middle of a colony, programmed to dance in a certain way, and the hive members will actually follow the information precisely to that location. Researchers have been able to understand the information processing system to this level, and consequently, can actually transmit it through the robot to other members of the hive.


    But it's more then the honey bee mentality. It's about communications systems we use to explain? So am I going to get Sean's goat on this one, and reverberate something he does not like? :)

    But we know relatively little about how the circuitry of the brain represents the consonants and vowels. The chasm between the neurosciences today and understanding representations like language is very wide. It's a delusion that we are going to get close to that any time soon. We've gotten almost nowhere in how the bee's brain represents the simplicity of the dance language. Although any good biologist, after several hours of observation, can predict accurately where the bee is going, we currently have no understanding of how the brain actually performs that computation.


    So I have in essence percieved the "Bee HIve Mentality of string theory" as a underlying causation, that if held too, becomes, "how little we really know." What ha/ormonial( I like to play with words?) factor, drives that body/system?

    I bet that sounds like chalk board screeching to him:) Yes I gave the anti-string/M theorist more ammunition.

    I also opened the door to another thought of mine. About the uses of, "Math and the foundations." But this is just me, trying to break down the reistance to mathematical prowness, that any other mathematician might try and hide, as a model of strng theory/M intepretation.

    You can't just sweep it under the rug kind of thing and say what science doesn't know. Has yet to be proved?:) Oops, I extended the board screeching to include, the extension of, and Modifications to GR. I can't help it. The power of the "force" is really string?

    The Cosmological Constant and the Vacuum Energy



    Jacque Distler:
    The cosmological constant is not “predicted” to be Planck scale, simply because, in a QFT context, it is not predicted at all. It is a renormalized coupling and can have any value whatsoever.

    What is true is that, in order to achieve the observed value at low energies, the bare value (at the cutoff scale, which we might take to be the Planck scale) must be fine-tuned to enormous accuracy.

    But that’s not the same thing at all as saying that the value of the cosmological constant is predicted, and that the prediction comes out wrong.




    Jacques Distler has volunteered(?) for the sake of people like myself by opening the doors to clarity issues around the interrpetation of the cosmological constant.

    So this leads to the second part of Sean's post that gets me to thinking about how perception might have been revealled in the dynamics scenario of Omega (w) and how we see that the background as a "energy density," can ever be seen as zero? That such a valuation would limit one to thinking that such a dynamical universe had to explain the nature of the curvature parameters beyond, what was comsologically understood?


    The Friedmann equation which models the expanding universe has a parameter k called the curvature parameter which is indicative of the rate of expansion and whether or not that expansion rate is increasing or decreasing. If k=0 then the density is equal to a critical value at which the universe will expand forever at a decreasing rate. This is often referred to as the Einstein-de Sitter universe in recognition of their work in modeling it. This k=0 condition can be used to express the critical density in terms of the present value of the Hubble parameter.

    For k>0 the density is high enough that the gravitational attraction will eventually stop the expansion and it will collapse backward to a "big crunch". This kind of universe is described as being a closed universe, or a gravitationally bound universe. For k<0 the universe expands forever, there not being sufficient density for gravitational attraction to stop the expansion.



    Plato:
    So on a csomological level we get this sense of curvature and here to further exploit this understanding the means to such equations supplied for this endeavor.


    Now for the vacuum to be define here in a planck scale valuation, it was not important for me, (okay maybe it is needed) to see the positive and negative effect of what and how the universe was doing at any particular stage. I always saw it as expanding, yet within the confines of the universe, it had the capability of doing galaxy dynamics, that would lead to greater intensities, expansive and contraction features, when we looked at the energy and matter cyclical valutions, in a geometrical sense, wrapped as "global" cosmological constant.

    Bumble Bee Economics

    See what happens when the creative juices are added to imagery and analogy gives insight from another perspectve?



    Ed Hessler added this to the comment section of Cosmic Variance.

    Thursday, November 03, 2005

    Onion Signatures

    Yes indeed, we seen where acoustic physics can be related at a fundamental level and be incorporated with the mathematics that some are very proficient at. That while poor ole me struggles, I look for the most direct route to help me comprehend these complex issues which physicists and theoretcians alike, engage themselves, then why not? Why not say, the "aroma"? Is the smell of the onion hold a certain quality like sound, that as "acoustic hawking radiation," if I direct this analogy and comparsion a bit further, somewhere in there is the Higgs boson, that will give mass all the things our layered onion as a detector seeks to manifest particle wise, as presence.

    Acoustic Hawking Radiation

    With an acoustic horizon (a.k.a. "sonic horizon"), this ordered set of definitions breaks down: events behind an acoustic horizon can modify the effective horizon position and allow information to escape from a horizon-bounded region. This results in acoustic horizons following a different set of rules to gravitational horizons under general relativity:


    So here in lies another idea for Clifford and the drama created by the involuntary presence that can make good sane people cry. These onion people are working in another dimension? Some might call it wizardary, only if they did not understand the science and the geometry behind the curvature parameters. It is a hyperphysics mode to which those who has studied would know that Kaku was very kind in bringing common sense to what our ole Geometers had to say in a long line of historical perpective.

    I will bring perspective to quantum geometry shortly in another blog entry.

    Atlas Experiment

    ATLAS (A Toroidal LHC ApparatuS) is one of the five particle detector experiments (ALICE, ATLAS, CMS, TOTEM, and LHCb) being constructed at the Large Hadron Collider, a new particle accelerator at CERN in Switzerland. It will be 45 meters long, 25 meters in diameter, and will weigh about 7,000 tons. The project involves roughly 2,000 scientists and engineers at 151 institutions in 34 countries. The construction is scheduled to be completed in 2007. The experiment is expected to measure phenomena that involve highly massive particles which were not measurable using earlier lower-energy accelerators and might shed light on new theories of particle physics beyond the Standard Model.



    Well most will not comprehend what I am saying, and nor did I, until I came across and looked for a better understanding of what signatures mean to a physicist. Who is working on the Cern project, and the detectors methods for consideration. What the term onion word might spark, as I look back and seen that a previous comment had been planted for another day like today.

    How vast indeed this project, that out of it such collision processes can be accounted for in the way a onion can be peeled, layer upon layer, just like our Atlas Detector is. In the way it had been design for those particle detection methods. There are enough links here to satisfy the inquring mind, as to what these layers are, and what they are designated for in that detection process.

    Frontiers and Mega Magnets

    Like all the detectors used in today’s collider experiments, the ATLAS apparatus is huge – in order to catch the myriad of particles produced when protons smash into each other. It consists of a series of detecting devices in an onion-ring arrangement around the central tube in which the proton beams collide. Each detector does a different job, measuring the positions and energies of the different particles produced – electrons, photons, muons etc. The momenta of the charged particles are measured from the curvature of their trajectories in a magnetic field provided by superconducting magnets. The volume and strength of magnetic field needed are not achievable with conventional magnets.


    Now I highlighted the statement in bold because it means something to me more then just the way we would look at, but what these curvatures can mean in comparative modes of geometrical expressions.

    Now as a lay person, the curvature parameters that were developed from the understanding of the Friedman equations, help me to see the issue of hyperbolic/ spherical as real cosmological issues, but way down at the quantum level, what is this showing us?

    The Friedmann equation which models the expanding universe has a parameter k called the curvature parameter which is indicative of the rate of expansion and whether or not that expansion rate is increasing or decreasing. If k=0 then the density is equal to a critical value at which the universe will expand forever at a decreasing rate. This is often referred to as the Einstein-de Sitter universe in recognition of their work in modeling it. This k=0 condition can be used to express the critical density in terms of the present value of the Hubble parameter.

    For k>0 the density is high enough that the gravitational attraction will eventually stop the expansion and it will collapse backward to a "big crunch". This kind of universe is described as being a closed universe, or a gravitationally bound universe. For k<0 the universe expands forever, there not being sufficient density for gravitational attraction to stop the expansion.


    So the very idea of the expansion and contraction, holds on to my mind, and this dynamical process is very revealling in our point of view. I can't but help feel this GR sense in momentum, as objects and articles are held to the mass impression of the spacetime fabric.

    The Magnet System

    The ATLAS detector uses two large magnet systems to bend charged particles so that their momenta can be measured. This bending is due to the Lorentz force, which is proportional to velocity. Since all particles produced in the LHC's proton collisions will be traveling at very close to the speed of light, the force on particles of different momenta is equal. (In the theory of relativity, momentum is not proportional to velocity at such speeds.) Thus high-momentum particles will curve very little, while low-momentum particles will curve significantly; the amount of curvature can be quantified and the particle momentum can be determined from this value.


    So by quoting here and representing curvature parameters on a cosmological scale, it was not to hard to figure how signatures would be revealled.