Another Constraint on Quantum Gravity

[Rybo]

Causal Dynamic Triangulations

Yes Rybo, quantum gravity is what we are talking about in this thread. CDT is a newer approach to quantum gravity.
CDT means causal dynamical triangulations
it is a way of implementing a quantum version of Einstein 1915 classical theory of General Relativity. Other approaches tend to do this using a differentiable manifold to represent spacetime but CDT does not. It uses approximation by PL manifolds (also called simplicial manifolds)
the einstein action is implemented without using coordinates.
here is a short CDT paper that could serve as an introduction
http://arxiv.org/hep-th/0404156 [Broken]
t

Thanks Marcus, I have not been following this thread close enough
Quantum Graivity is the topic indeed ( Rybo-duhhh :).
I did go to the link you gave and read and saved the PDF document and now have good intro into Causal Dynamical Triangulations. (1) Why are triangulations more significant than squares or other polygons ergo the title CDT?

Most of the mathematics disscussed here are way above my head, HOWEVER, I do like to skim, pick and choose what goes well with my Synergetic interpretations and extrapolations thereof.

(2) Does CDT interpret( may be ) or require( is ) the physcial universe as being macro-finite? Here below is quote from PDF introduction to CDT.

..."This leads us to conclude that we have observed the emergence of a four-dimensional macroscopic world with three-dimensional spatial geometries. Judging from the computer simulations, this dynamically generated quantum geometry acts as a background geometry around which small quantum fluctuations take place. Further numerical studies will be needed to make this into a quantitative statement. The situation is really rather remarkable: we started out from an explicitly background-independent formalism and have rederived a particular stable background geometry.".......

Rybo

 

[marcus]

... saved the PDF document and now have good intro into Causal Dynamical Triangulations. (1) Why are triangulations more significant than squares or other polygons ergo the title CDT?
...

(2) Does CDT interpret( may be ) or require( is ) the physcial universe as being macro-finite? Here below is quote from PDF introduction to CDT.

..."This leads us to conclude that we have observed the emergence of a four-dimensional macroscopic world with three-dimensional spatial geometries. Judging from the computer simulations, this dynamically generated quantum geometry acts as a background geometry around which small quantum fluctuations take place. Further numerical studies will be needed to make this into a quantitative statement. The situation is really rather remarkable: we started out from an explicitly background-independent formalism and have rederived a particular stable background geometry.".......

Rybo, I'm glad you found the article interesting. You quoted a key paragraph right at the end, in the conclusions section.
Ooops, have to attend to something. be right back.

Now I am back. I will try to respond. first I think Buckminster Fuller probably found simplicial manifolds interesting if he studied them at all. Or else would have, if he had encountered them

Some CDT work involves cubes and pyramids as well as simplexes. I see them in Renate Loll papers. Personally I tend to stick to what is simplest and easiest. the straight simplex-based manifold is the easiest to construct and think about.

one reason for sticking to the mainstream PL-manifold or simplicial manifold is because there is tons of previous mathematics work done on it going back for decades. Its always nice when mathematicians for their own abstract reasons have gone in and explored and mapped out a subject and proven a bunch theorems which the Applied person can then use!

Ambjorn has an excellent 1996 online tutorial covering PL (piecewise linear) manifolds, of course, as he points out, it is a category, what isnt?
but the original sources go back to 1960s, 1970s. they just are not online whereas Ambjorn tutorial is online.

Intuitively, triangle is such a simple shape that if you have a bunch points you can always draw triangles with those points as vertices, and it is clear what the analogs are in higher dimension, less to worry about. the points of a simplex form a complete graph with the edges as links, dont have to stop and think about which points to connect and which not. Fraid Im being incoherent, but you get the message: simplex is simple.

Here is your other question

(2) Does CDT interpret( may be ) or require( is ) the physcial universe as being macro-finite?

I think it does not. Only the SIMULATION in a finite computer requires that the model be finite.

have fun.

 

[Rybo]

2D-3D-4D and 11D

thanks Marcus, Nightcleaner and Rybo
That's more than enough information to keep me amused, confused and enlightened for quite some time
I like how you say Marcus, it's not whats the same it's whats different that makes it interesting, so yes I can understand your excitement
CDT sounds like modelling the wire frame of an object before you skin it up in a 3d computer program ?

Spice, keep in mind that Jacob Bekenstien stated in his Scientific American article Feb 2002 or 03 that we humans are 2D beings only having an illusion of the 3Dness. I know it is one of teh hardest things for any human toever believe but that is what his black hole mathematics has led him to deduce.

This is also explained by Lee Smolin in his 3 roads to Quatum Gravity book in the holgraphic chapter. Holgraphy being the 3rd possibility along with String and LQG.

SO, we have
1) Holgraphy( 2D superfically appearing as 3D ). This is based in and around the event horizon being equal to the the entropy inside the black hole. See my home page for how I see the geomtrical versin of this scencario palying out.
http://home.usit.net/~rybo6/rybo/index.html [Broken]

2) CDT's 3D superfically based on 4D manifolds?

3) Strings 4D( includes time ) superfically based on 11D.

Here is another graphic rendition( my interpetation ), that I espesically like, of what I see as the outer perimter/circumference of the gravitatinal Universe. Disreagard the stars in the background for more accurate represntation IMHO.
http://gregegan.customer.netspace.net.au/SCHILD/SCHILD.html

Rybo

 

[Spin_Network]

I like this:http://home.usit.net/~rybo6/rybo/id6.html [Broken]

What are the current advances you have via the "25" turnaround?

It reminds me of this:http://homepage.ntlworld.com/paul.valletta/PRIME GRIDS.htm

I also found Ian Stewart a very interesting Mathematician, being that I was working on something I came across in his Royal Christmas Lecture, great Man.

The 'Einstein Wave' is what I called it:http://www.freewebs.com/moorglade/riemannshypothesesthetru.htm [Broken]

will be found to be the 'eternal' running constant, but that is for another day!

 

[Rybo]

Primes and physics

I like this:http://home.usit.net/~rybo6/rybo/id6.html [Broken]
What are the current advances you have via the "25" turnaround?
It reminds me of this:http://homepage.ntlworld.com/paul.valletta/PRIME GRIDS.htm
I also found Ian Stewart a very interesting Mathematician, being that I was working on something I came across in his Royal Christmas Lecture, great Man.
The 'Einstein Wave' is what I called it:http://www.freewebs.com/moorglade/riemannshypothesesthetru.htm [Broken]
will be found to be the 'eternal' running constant, but that is for another day!

SpinN, Glad you like that page. Ive nt gone much further in that specfic research but the #25 as a turnaround number I found in Synergtics. Here is link that chapter.
http://www.rwgrayprojects.com/synergetics/s12/p2200.html
Specifically you wil want to get to the 3 sets of graphs at 1223.12

I looked at Valletta's pattern of primes and entropic speculations. Interesting indeed and I want to study it more. Do we have better place to discuss primes than this thread?

Here is link to my yahoo geophysic web site. You can join and receive no mail or if you do it wont be much becasue it rare it recives any posts excetp from me.

http://groups.yahoo.com/group/Geophysiclink
I also have most of my graphic ideas listed in files there. Check it out.
I had MSN site with same but it expired. :--(

Rybo

 

[Rybo]

CDT Graviton

Rybo, I'm glad you found the article interesting. You quoted a key paragraph right at the end, in the conclusions section.
Ooops, have to attend to something. be right back.
I think it does not. Only the SIMULATION in a finite computer requires that the model be finite.
have fun.

Marcus, does CDT have a geometric hypothisis, or other, for a graviton?
Strings have a closed loop and string bits of many possible ones?
Holopgraphy( Bekenstien ) has spin-networks of which one, or more, trianlge is a graviton?
LQG has several traingles and squares equaling one graviton?( Jan Ambojorn )

Thanks if you have any leads. Fun right back at you.

Rybo

 

[spicerack]

Spice, keep in mind that Jacob Bekenstien stated in his Scientific American article Feb 2002 or 03 that we humans are 2D beings only having an illusion of the 3Dness. I know it is one of the hardest things for any human to ever believe but that is what his black hole mathematics has led him to deduce.

This is also explained by Lee Smolin in his 3 roads to Quatum Gravity book in the holgraphic chapter. Holgraphy being the 3rd possibility along with String and LQG.

SO, we have
1) Holgraphy( 2D superfically appearing as 3D ). This is based in and around the event horizon being equal to the the entropy inside the black hole. See my home page for how I see the geomtrical versin of this scencario palying out.
http://home.usit.net/~rybo6/rybo/index.html [Broken]

2) CDT's 3D superfically based on 4D manifolds?

3) Strings 4D( includes time ) superfically based on 11D.

Here is another graphic rendition( my interpetation ), that I espesically like, of what I see as the outer perimter/circumference of the gravitatinal Universe. Disreagard the stars in the background for more accurate represntation IMHO.
http://gregegan.customer.netspace.net.au/SCHILD/SCHILD.html

Rybo

nifty grafix Rybo :!!)

so by projecting 2 spatial dimensions onto <enter arbitrary dimensional number here> and add 1 for time we get perceptions of 3d including movement ?

meaning we exist in a 2d brane plane of bubble like foam

forgive me for even trying to get my head around this stuff but it interests the hell out of me and i would like to think that somewhere along the line it may have implications for the average person in the home like me :tongue:

 

[Spin_Network]

SpinN, Glad you like that page. Ive nt gone much further in that specfic research but the #25 as a turnaround number I found in Synergtics. Here is link that chapter.
http://www.rwgrayprojects.com/synergetics/s12/p2200.html
Specifically you wil want to get to the 3 sets of graphs at 1223.12

I looked at Valletta's pattern of primes and entropic speculations. Interesting indeed and I want to study it more. Do we have better place to discuss primes than this thread?

Here is link to my yahoo geophysic web site. You can join and receive no mail or if you do it wont be much becasue it rare it recives any posts excetp from me.

http://groups.yahoo.com/group/Geophysiclink
I also have most of my graphic ideas listed in files there. Check it out.
I had MSN site with same but it expired. :--(

Rybo

Thats quite amazing!..I mean I had no knowledge of Fuller's work, except for the 'Buckyball' of the mid eighties, I presume its the same man.

I am going to start a new thread later, but first I will explore the pages further, thanks again.

 

[nightcleaner]

Hi Rybo and Spin Network

I too, have been interested in the cubeoctahedron. IIRC Fuller called the dense packed sphere structure the 'isomatrix.' Johannes Kepler, the famous astronomer, studied the dense pack relations of spheres also. I noticed yesterday that Mathworld now has a graphic header showing this same arrangement. It seems to me that interest in this form is spreading.

It is a highly symmetrical form. Thirteen spheres, twelve dense packed around one, makes fourteen faces, has twelve vertices, twentyfour edges. Eight of the faces are triangular simplexes, six are squares. The faces are parallel to each other on opposite sides of the figure, so that the faces define parallel sets of planes of spheres. There are four sets of parallel planes which are made of triangular simplexes, and three sets of parallel planes made up of square simplexes. The figure can be subdivided in various ways into collections of tetrahedra.

It is interesting to me how the platonic solids are generated by this isomatrix structure by the simple matter of increasing scale. Kepler thought for a while that there was a relationship between the platonic solids and the orbits of the planets, but later abandoned that idea when it was discovered that the orbits were eliptical, not circular.

My thought has been that progress might be made by thinking of the isomatrix as a structure resulting from the expansion of the individual spheres. One might begin by imagining empty space, then adding the small perturbation of a single expanding sphere. This sphere would expand indefinitely in empty space. If there were other similar spheres in the space, they would eventually come into contact.

If we assume that the spheres are Planckian, then they would be impenetrable to each other. Therefore the meeting of two expanding spheres would result in the centers of the spheres undergoing gravitic acceleration. In gravitation we like to think of the spheres as attracting each other, but in this model the attraction is seen to be dual to the expansion of the sphere.

Further expansion (or infall) and contact would result in the cubeoctahedral shape being formed preferentially to any other shape. However there would be irregular features on the surface of the expanding isomatrix. These irregularities would be energy states, since the cubeoctahedral form is the lowest state, or alternately the state of highest symmetry, and any variation from it would tend eventually to be "forced" into the cubeoctahedral form.

In this model the irregularities actually are the physical manifestation of energy, and hence, of mass. The "perfect" or most highly symmetric form of any collection of Planck spheres would be in the shape of a faceted crystal, possessing vertices and edges as in the Platonic solids. But the tendency induced by infall or by the dual process of expansion would be like a force pushing outward on the faces and inward on the vertices and therefore possessing a form of curvature along the edges, in general promoting a spherical shape to the agglomeration rather than the faceted shape.

I would be interested to know if you are thinking along similar lines.

Thanks,

Richard

 

[Rybo]

2D, 3D, etc....

nifty grafix Rybo :!!)
so by projecting 2 spatial dimensions onto <enter arbitrary dimensional number here> and add 1 for time we get perceptions of 3d including movement ?
meaning we exist in a 2d brane plane of bubble like foam
forgive me for even trying to get my head around this stuff but it interests the hell out of me and i would like to think that somewhere along the line it may have implications for the average person in the home like me :tongue:

Glad you like them Spice. Your are probably refering to the ones icosahedral buble-like foams on my home page.

I found those on the net somewhere. In my scenarios there would be a 3D ness type relationships hapening inside them also, th to what extent is something im still not clear on.

Keep in mind that im no implying any reality in only 2D. It is Jacob Bekenstien and his resultant holographic theories proposing those truly unbelieveable 2D ideas i.e. the 2D bubble-like foam scenarios taht may indeed be liken to the icosahedral bubble on my home page.

Jacob did use a icosahedron in his Sciencitic American article to explain the event horizons equanimity to the internal entropy of a black hole but I do believe his choice of the icosahedron for that demostration was insignificant.

Her again is my yahoo egroup with all my older files leading me to my current web site and thoughts.
http://groups.yahoo.com/group/Geophysiclink

You dont have to recieve any mail to just look at graphic files.

Rybo