Quantum Geometry
(17 previous messages)Sol
- Jun 24, 2004 8:29 pm (#18 of 222)
marcus sol you have quoted Yaron Oz in your last post, or an article from march 1999 in CERN courier paraphrasing Oz.
yes of course.
It makes a striking contrast with the mood nowadays!
I appreciate seeing the difference----showing the optimism of 5 years ago.
(I hope I am reading your article correctly)
One of the pictures was taken from John's Baez' article made avaliable through John's links.
Using strings wrapped and dividing in the pant style[ topological considerations ](quoted article), in relation to todays conclusions, I wanted to draw attention to the way in which Quantum gravity is looked at with these two models. This hasn't change from 1999, in terms of continuity and discreteness. This is a foundational principal of how quantum gravity is looked at between these two camps.
Strings 
Topology becomes an important tool in superstring when it is treated as quantum mechanical object. This branch of mathematics is concerned with smooth, gradual, continuous change of geometric shape. For example, a square can be continuously deformed into a circle by pushing in the corners and rounding the sides. The essential rule is that no new hole can be created in the new form by tearing. Some topological equivalent objects are shown in Figure 15-17.
http://universe-review.ca/F15-particle.htm
LQG
One way to simulate a surface is to use a triangulation. Instead of keeping track of every spot on the surface, we can approximate a two dimensional surface with a mesh made of triangles. An example of a triangulation is shown at left. The points at the corners of the triangles are called nodes. The lines that join the nodes and form the sides of the triangles are called links. The triangles themselves are sometimes called simplexes, and this is why the science of studying quantum gravity this way is called simplicial quantum gravity.
In the simplest of all simplicial quantum gravity simulations, the computer must only keep track of how the nodes are connected to form triangles.
http://simscience.org/membranes/advanced/essay/gravity_simulation1.html
Simscience and Quantum Gravity
I am open to corrections here.
Sol
- Jun 24, 2004 9:16 pm (#19 of 222)
Antonio Lao:
sol2,
After reading the link on Klein's ordering of the geometries (and also thanks for this link as well) , I realized that I have been working on a Euclidean geometry without the notion of angles. But then another realization is that projective geometry, which I think I am also using, does not preserve distances. I have to assume that at the local infinitesimal domain of spacetime, the geometry of two linked topologies is elliptic which is the merging of two hyperbolic geometries.
Sometimes it is like asking if there are distinct lines in magnetic fields. Yet we know that the field exists. Some have even allowed us coordinates to consider (higher dimensions), like Gauss. This is a different kind of thinking, yet if I showed you soap bubbles, and then a soccer ball( its surface), how would your thinking change?
Sol
- Jun 25, 2004 2:13 am (#20 of 222)
Antonio Lao:Thanks for all these links to various discussions on topology.
When Dirac proposed the existence of magnetic monopole, his thinking was in term of closed surfaces similar to the supposed structures of charged particles or neutrally charged particles such as neutron and neutrinos. But as verified by experiments, all particles, charged or neutral, are point-particles and they all possess magnetic dipole moments.
My proposal is that closed surfaces do not exist in nature. The genus of the topology that is behind magnetic field is possibly 2. It's like a sphere with two holes, one at the north pole and one at the south pole. And between these holes, some kind of torus topology can be described. And the limiting dynamic makes one topology shrunk to zero while the other approaches an infinitely extended line. The middle ground of these extreme topologies is a Hopf ring.
I am wondering is there a relationship between the genus of a topology and the concept of spin in quantum theory?
This last point in bold is a really interesting question for me because if you take all that we have discussed and geometrically apply some consistancy what would this look like? We don't know if we have a way of measuring it. The visualization you have, how will you verify it?
I make this issue deeper when the ideas of Optiverse is given, because now we have answered something about the nature of this geometry from a whole new perspective 
If we now engage the universe and the dynamics that are going on, how shall we see this brane world when focus on the brane? Remember the topology place in winnipeg?
From this perspective we were given some ideas here on the dynamcial nature and interwoven aspects revealled by a pelastrian notion of elasticity( maybe he will share some of his diagrams and perspective here as it is a really good exercise in looking at the question and nature of this elasticit). How would we ever conceptualize this?
With powerful parallel computers networked to virtual environments, we can explore previously inaccessible problems in geometry, especially where a complex object evolves so as to optimize its shape. For instance, an unknotted loop of string, no matter how tangled, can be persuaded to move (automatically and without breaking) into a round circle. In 4-dimensions, a surface (like a topological sphere) may be knotted. When it is merely tangled we evolve it to its familiar round shape to show it was unknotted. We guide surfaces towards optimality by minimizing mathematical abstractions of physical energies like the Coulomb potential or the bending energy of bilipid membranes. Mathematical surfaces in 3-dimensions (like shadows from 4-dimensions) generally self-intersect, but the Willmore bending energy can still be used to optimize their shape. A sphere can be turned inside out, keeping the surface smooth, but allowing complex self-intersections; we demonstrate this by presenting for the first time a geometrically optimal and computationally automatic eversion of the sphere.
http://new.math.uiuc.edu/laterna/
The question in bold is directly answered by Glast and imagine the Gamma ray feature of this universe? But there is more to it that has been spoken to before on your very point in bold. Gravity Probe B?
So now all of a sudden we have this view of the cosmos and the dynamcis that are going on. Olias new thread today, is speaking to this. It is a exercise in what we have been talking about After you read his post go look for the Bose Nova and tell me what you see? To join electromagnetism with Gravity there is a direct resulting view that must be adopted? Should we now speak again to your bold statement?
Sol
- Jun 28, 2004 12:11 pm (#21 of 222)
OliasTruth is, knowone actually knows whether or not Space is expanding!
I am afraid this statement is quite incorrect.
Sometimes I look at the whole cosmos and see the ideas in GLAST, from a early measure of Supernovas for consideration now, and this vast distance is foretelling, as I have realized thoughout our conversations.
From a galaxy perspective these events also become foretelling as the bose nova sequence of events reveal. Our talk on Heisenberg's collapsing sphere was a early sign to me of the dyamics you were seeing and talking about.
So we had to encapsulate this perspective of the whole cosmos in perspective views and how shall we do this with forces in relation to dimension?
So classical realizations have to move to quantum theory models for consideration and must formulate geometrical discriptions for us.
Antonio is developing these math discriptions from the undertanding of topological movements. We have detailled the differences from discrete natures to continuity as ways in which speak to the ideas of quantum gravity.
So how can we further the persepctive that has been adopted from the forces and relations of dimensin and I have detail one aspect for consideration, but I would also like to detail a image for consideration to support your position and encapsulate the views from a M perspective.
Look at the image changes on this page and we have to warm to the statement of, Window on the Universe As those images change they are very discriptive to me of what you are saying. I thought I would add ths for your conisderation and also point Antonio to how we might have amalgamated these math structures to serious discriptions as these images portray.
Would this be a most suitable conclusion to the relations of "force to dimension"?
Sol
- Jun 28, 2004 12:42 pm (#22 of 222)
Antonio LaoThe origin of dark energy is still a mystery. It is used to explain the forces of antigravity in an inflationary universe. An inflationary universe is a step more advanced timewise than the big bang singularity. There still no theory that can explain the singularity of the standard model of the big bang.
In terms of theoretical developement, what views would have supported cyclical universes? If Singuarities are a not a end feature anymore from the possibiltiy of the action of Fission/fusion being detailled in blackhole creation?
The collapse fo the balckhole signals other considerations, and needed to be geometrically consistent in the model explanatiosn topological considered?
How would you do that? We develope theorectical models in place of actual physics, in the hopes of being pointed in complete visualized summations, one might have understood how the geometry of bubble inversion might comeout of expansitory modes, while entrophy understanding of those balckholes become geometrical defined.
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Quantum Geometry