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Showing posts with label Metrics. Show all posts
Showing posts with label Metrics. Show all posts

Wednesday, March 30, 2005

Raychaudhuri Equation



Is it sand running through our fingers, or a taffy like substance, in symbolic form?

The difference, discretium and fluidity of nature, geometrically/topologically driven, are at war with what we might interpret in time? Early on, Salvador Dali understood well this geometrical propensity to the tesserack, that he embued his art with higher religious context(time). But in real life, he was different man?:)

The issues were not far removed from perspective, that this battle would find itself challenged, in how we would portray the nature of reality? That it had burst forth in science and it's manifestations.

But come back to earth, and we have to wonder indeed if this fluid is slipping through our fingers as time reveals a more intrinistic view of the reality in the cosmos?



Sean Carroll said:Friedmann fights back:
For those of you interested in the attempt by Kolb, Matarrese, Notari, and Riotto to do away with dark energy, some enterprising young cosmologists (not me, I'm too old to move that quickly) have cranked through the equations and come out defending the conventional wisdom. Three papers in particular seem interesting:



Lubos Motl:Superhorizon fluctuations and accelerating Universe:
Several physicists and bloggers, e.g. Jacques Distler, Peter Woit and especially Sean Carroll who may be considered a true expert in these questions and who added a very new article after this article of mine was published, recently noticed a paper that claimed that the cosmological constant was not needed. Instead, the accelerating expansion was conjectured to be a consequence of fluctuations of a scalar field (and the associated stress energy tensor) whose wavelength was longer than the Hubble radius i.e. the size of the visible Universe, roughly speaking.



I agree with Lubos here in regards to what has already been establish to date in the positions. Here with Sean Carroll, Jacques Distler, Peter Woit, and Lubos Motl respectively, that they all agree on the standards set here?

This would be a clear statement of position, and one that would signal, accepted practice on the expository view of our cosmos? Is it to ambitious?

Out of this a standard, even if there are divergences of personality; this is wiped away, so that we are introduced to new information as Sean shows us withRaychaudhuri equation? This gives one direction to look at.

This equation has the special characteristic that it is true without reference to the Einstein equations . That is, it is true for any spacetime. It is an intrinsic property of the volume expansion.

Now we come back to the intuitive development from this standard presence. Would it be so wrong to ask that four minds to stand together and paper their perspective? Then open it up to geometry/topological views, in relation to how we might develop the imagery of what might have been gathered from the dynamical realization of early universe idealizations?



In regards to the tactile experience one might want to comprehend is in the way the universe now has unfolded?

Now there is a most definite need to grasp the issue here in terms of what causality might mean in terms of balckhole/3 brane collapse as a perspective to the dynamics that would be revealled, for photon,/graviton production from the blackhole?

Using Calorimeter, we see where such advances help us to distinquish early universe information in Glast cosiderations, but how much more suttle has this experience need to be expanded upon, to understand the exchange that takes place in the gravitational collapse?

John Baez:
Now, the way Hawking likes to calculate things in this sort of problem is using a "Euclidean path integral". This is a rather controversial approach - hence his grin when he said it's the "only sane way" to do these calculations - but let's not worry about that. Suffice it to say that we replace the time variable "t" in all our calculations by "it", do a bunch of calculations, and then replace "it" by "T" again at the end. This trick is called "Wick rotation". In the middle of this process, we hope all our formulas involving the geometry of 4d spacetime have magically become formulas involving the geometry of 4d space. The answers to physical questions are then expressed as integrals over all geometries of 4d space that satisfy some conditions depending on the problem we're studying. This integral over geometries also includes a sum over topologies.
That's what Hawking means by this:

Stephen Hawking:I adopt the Euclidean approach, the only sane way to do quantum gravity non-perturbatively. In this, the time evolution of an initial state is given by a path integral over all positive definite metrics that go between two surfaces that are a distance T apart at infinity. One then Wick rotates the time interval, T, to the Lorentzian. The path integral is taken over metrics of all possible topologies that fit in between the surfaces.


How would missing energy events isolate the realization that such ventures would have been specific in detailing the envelope capturing all that has evolved in our universe to know that there is this consistancy, that spreads itself through all possibiltyies of Feynman's sum over paths of expression, that still needs to be identified?

Now you must know that there are consequences when we see this collapse take place that asks us to consider the nature of the temperatures and diameter in reduction?

That what has been reduced in this energy developing scenarion of the cosmos in action, is a applicable view to geometry/topology that at the same time reveals the idealization of entropic features of supersymmetical views that we learn to see?

How this experience, as tactile as I approach it, is induced, is at very illusatory experience way back in some speculative past.:)Whooh! What? Careful now, I am analogically speaking here, because I like to see this way. It feels right(not saying it is right) as simple statement quickly summing up many mathematical views in a very short and simple way. That's what I hope anyway.

When you look at this fluid geometrically/topolgically driven what view has transpired in blackhole production? You want to be able to understand the symmetrical breaking that is taking place? Crystalization processes, would quickly surmize a Laughlin view from a fast cooling temperature, to realize, it is much more slower then this in the cooling(15 bilion year assumption) in a cosmological process?

So we understand curvature is well aquainted with vast track of cosmological views, but it become much more diffiult at such microscopic thinking. Sort of, all smeared out in a vast supersymmetrical views of previous states of existance, that quickly gather to form maybe, cosmic strings?:)

John Baez said,
But you shouldn't imagine the mood as one of breathless anticipation. At least for the physicists present, a better description would be something like "skeptical curiosity". None of them seemed to believe that Hawking could suddenly shed new light on a problem that has been attacked from many angles for several decades. One reason is that Hawking's best work was done almost 30 years ago. A string theorist I know said that thanks to work relating anti-deSitter space and conformal field theory - the so-called "AdS-CFT" hypothesis - string theorists had become convinced that no information is lost by black holes. Thus, Hawking had been feeling strong pressure to fall in line and renounce his previous position, namely that information is lost. A talk announcing this would come as no big surprise.

Monday, March 07, 2005

Stretching the Brain

Pettit shakes a remarkably sturdy film of water onboard the ISS. See the full-length movie: Reel 1, Reel 2.
"Observations of nature, no matter how seemingly arcane, are like peeling off one more layer from the great onion of knowledge, tickling your imagination with what you have found but always revealing yet another tantalizing layer underneath," says Pettit.
"I hope we never get to the core." See:Saturday Morning Science

What strikes me as strange is how we could have percieved the language of branes, with somekind of toy model even though we can't see them. For me as a sideliner, who views the world of these theoreticists, I had to try and make sense of this language they are talking about.

So I looked for some comparisons and geometrodynamics came into view, but I mean this couldn't have even been fathomable if we say it is hidden ,what the heck does this mean? The dimensional relevance had to be spoken and our visulizations moved beyond the euclidean points to a non euclidean world of metrics realization between these quark to quark measures.

So in the spirit of Feynmen, how about we use these new features to help us orientate the views of the world that is hidden and help many understand the world contained in the vacuum, that many could never have comprehended?

Lubos likes Moose horns as a analogy for Feynman path integrals?:)

Here I would look at Dvali's analogies to move the consideration forward place within context of this post.

It is part and parcel of the view I am developing, in relation to the geometrical/topological understanding that comes out of the view of how this universe came to be. I know this would quickly align some persepctives in that geometrical consideration. But having viewed Daniel Kabats response how would we describe non conformal geometries that arrive in the spaces Daniel speaks about?

So any way, here is the new toy model that one should work with, and correspond developing language in relation too GR's developing views along side of the small world we all are trying to capture.

LQG is successful here in the intersecting bubble technology(simpleces and monte carlo models in representing quantum gravity?), in regards to it's nodes, but how would string theory survive. You had to know that underlying this language is some kind of consistency. String theory represented in the graviton, points to the question for the quantum geometry/topology that will explain this unseen world that has been theorized.

Quivering, in quark to quark measures are a interesting way in which to see the world theory spaces and not the points. The configurations space would have to explain the geometry in a way the Gaussian coordinates would help us view a dynamical world?

Monday, January 10, 2005

The Emergence of Time, What Lies Beneath?

The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated.

Taken in context of how supersymmetrical levels could have ever been reached, is really a wonderful thnng to consider. If singularities were to be devised in methods that would experiementally bring forth blackholes at the microstates. Then what value is derived from learning about high energy and the levels we must go through to speak about these singularities?

From classical discritpion of GR to the understanding that supergravity could have ever been devised as a method to live in supersymmetrical worlds, would have been a challenge indeed, and we might ask where would time would begin, and what was below time?


The conclusion of this lecture is that the universe has not existed forever. Rather, the universe, and time itself, had a beginning in the Big Bang, about 15 billion years ago. The beginning of real time, would have been a singularity, at which the laws of physics would have broken down. Nevertheless, the way the universe began would have been determined by the laws of physics, if the universe satisfied the no boundary condition. This says that in the imaginary time direction, space-time is finite in extent, but doesn't have any boundary or edge. The predictions of the no boundary proposal seem to agree with observation. The no boundary hypothesis also predicts that the universe will eventually collapse again. However, the contracting phase, will not have the opposite arrow of time, to the expanding phase. So we will keep on getting older, and we won't return to our youth. Because time is not going to go backwards, I think I better stop now.
by Stephen Hawking

It becomes very difficult then for anyone to accept that Robert Laughlin might have "wondered" about about condensed matter physics to have wonder what the building blocks shall be at such levels? That he might have wanted to stay to discrete structures for explanations as far as he could tell experimentally?:)


Likewise, if the very fabric of the Universe is in a quantum-critical state, then the stuff that underlies reality is totally irrelevant-it could be anything, says Laughlin. Even if the string theorists show that strings can give rise to the matter and natural laws we know, they won't have proved that strings are the answer-merely one of the infinite number of possible answers. It could as well be pool balls or Lego bricks or drunk sergeant majors
.

You see this is okay. That one can direct their attention to such infrastructures to ask, what the ultimate building block shall be, that we constantly refocus our mind to the finer things(abstract mathematical forays into these fine building blocks), only to find, we have progress well into the cosmological view, of such microstates?

"The path integral is taken over metrics of all possible topologies, that fit in between the surfaces. There is the trivial topology, the initial surface, cross the time interval. Then there are the non trivial topologies, all the other possible topologies. The trivial topology can be foliated by a family of surfaces of constant time. The path integral over all metrics with trivial topology, can be treated canonically by time slicing. In other words, the time evolution
(including gravity) will be generated by a Hamiltonian. This will give a unitary mapping from the initial surface, to the final.
"


But to follow is this what Peter Woit thinks?

Peter Woit said--?His argument is in Euclidean quantum gravity, which he describes as "the only sane way to do quantum gravity non-perturbatively", something which some might disagree with. What he seems to be arguing is that, while it is true you get information loss in the path integral over metrics on a fixed non-trivial black hole topology, you really need to sum over all topologies. When you do this you get unitary evolution from the trivial (no black hole) topology and the non-trivial topologies give contributions that are independent of the initial state and don't contribute to the initial-final state amplitude.

I guess what this means is that he is claiming that, sure, if you knew you really had a black hole, then there would be a problem with unitarity, but in quantum gravity you don't ever really know that you have a black hole, you also have to take into account the amplitude for not actually having one and when you properly do this the unitarity problem goes away.


You must accept my humble apologies, but to have been given these directions(quotes analogies in reference links and statements, from both Lubos Motl and Peter Woit, I wonder about the difference in their interpretations of the mathematics they are using? Are they so fundamntally at odds with each other, that they do not realize that they are working very close in their idealizations?