# Travel between dimensions

Posted Aug11-08 at 08:28 PM by jal
Updated Dec20-09 at 01:36 AM by jal

Qgsquared conference
Did the clock tick and cause confinement?
Did the clock tick and change the configuration of the points?
Did we go from 3d to 4d or was it 6d to 4d?
If the Clock ticked after the CMB then the signature would be visible to the astronomers. We would be able to perceive the changes. The “Clock” has not clicked for 14.7 billion years. If the “clock” was to tick, as you read this, you would definitly notice the change.

When you add dimensions you are adding 2 points with their connecting lines and their spheres.
A point has an imaginary sphere of possible imaginary lines of one unit long (Planck Scale) that could be drawn. In one dimension, there are two points. Each point is in the center of a sphere with a radius of one unit. An imaginary line could only be drawn through the diameters of those spheres if the distance between the points was one unit. The spheres would overlap each other until the distance was reduced to one unit.
As a result, in one dimension, the spheres are reduced to a diameter of one unit.

PLANCK SCALE EXPANDED TO INCLUDE TWO DIMENSION
There is one restriction, the four points can never get closer than one unit or have a separation greater than two unit.
What can be achieved are equilateral triangles, and squares. The equilateral triangle and square encloses an imaginary two dimensional surface. (fig. 1 a)

PLANCK SCALE EXPANDED TO INCLUDE THREE DIMENSION
LQG ( I think that they want to be known as Lattice Quantum Gravity) uses 5 points in the plane and one point above the plan to make their arrangements of tetras. (fig. 1 b)

PLANCK SCALE EXPANDED TO INCLUDE FOUR DIMENSION
With 8 points it is possible to construct a cube and different arrangements of Tetras. You can make tetrahedron which is a 3-simplex tetrahedra. A tetrahedron is a triangular pyramid, and the regular tetrahedron is self-dual. (fig. 1 c)

Looking “back”, we can observe the crytaline structures. When we reach 10^-15 m we can see the protons which is the confinement of quarks. Looking”back” farther, (we are just about to see to 10^-18 m at CERN), we are into the perfect liquid and it is deconfined.
Are there only three dimensions in a perfect liquid or six?
Something must have happened between our scale and Planck Scale.
Did the “Clock tick”?

There is no curvature at Planck Scale. There is only a little bit of “jiggle room”.
The structure with the least amount of “jiggling room” is a compound of two tetrahedra.
Do we have confinement because of the fourth dimension?

Until more information comes in from CERN we can speculate that there are four dimensions at the Planck Scale.
There are many approaches which are making the assumption that there are four dimensions at the Planck Scale.
The latest, LQG appoach assumes that our universe started from a minimum of 24 Planck Scale units.
These units must be “connected” in some kind of arangements (Kagome Lattice).

PLANCK SCALE EXPANDED TO INCLUDE FIVE DIMENSION

We use the same proceedure as before. Within a sphere of a diameter of five units can we insert two more points or surfaces that have one unit in diameter.

PLANCK SCALE EXPANDED TO INCLUDE SIX DIMENSION

We can place twelve surfaces within a sphere that has a diameter of six units.
We would have a figure that has six units on the equator, three in the north and three in the south.
This is the figure that has the densest packing. (fig. 1 d)

I did find some interesting papers that lets you go from a 2d configuration of 4 points, to a 3d configuration of 6 points, to a 4d configuration of 8 points, to a 6d configuration of 12 points and possibly, to E8. (Something for Garrett to work on).
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Laurent Freidel said at the QGsquared conference http://echo.maths.nottingham.ac.uk/q...squared-slides that they have found a way to mathematically join different dimensions.

According to Abhay Ashtekar, at the QGsquared conference, the universe was once a mini black hole of with a volume 10^115ℓ^3 Pl!
At the same conference Andrzej Gorlich, Causal Dynamical Triangulations, says that in 4d the Universe built of 362,000 simplices has a radius of about 20 Planck lengths and the angle deficit (curvature) is localised at (d -2)-dimensional sub-simplices.
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Where is the “reality” in dimensions?
I think that working and with 4 and 6 will give use some surprising answers.
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http://www.maths.nottingham.ac.uk/re...aurent1234.pdf
Construction and semi-classical limit of 4d Spin foam model
Laurent Freidel
Nottingham, 2008
In collaboration with K. Krasnov 0708-1595
also with F. Conrady 0806.4640, to appear
QGsquared-slides
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http://echo.maths.nottingham.ac.uk/q...rAbhay1234.pdf
Loop Quantum Cosmology
Abhay Ashtekar:
QGsquared-slides
Slide 36
• Quantum Bounces: The ultra-violet issue
For a universe which attains vmax ≈ 1Mpc^3, vmin ≈ 6 ?10^16cm^3 ≈ 10^115ℓ^3 Pl!
What matters is curvature which enters Planck regime at this volume
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http://echo.maths.nottingham.ac.uk/q...1214824381.pdf
Background Geometry in 4D Causal Dynamical Triangulations
Andrzej Gorlich

We observe a four-dimensional universe with well defined time and space extension.
2 The background geometry exactly corresponds to the classical solution of the minisuperspace model (classical Einstein theory).
3 Quantum fluctuations of the spatial volume are also properly described by this simple model.
4The gravitational constant G controls the fluctuation amplitude.
We may estimate that the Universe built of 362,000 simplices has a radius of about 20 Planck lengths.
The angle deficit (curvature) is localised at (d -2)-dimensional sub-simplices.
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The present challenge is to find the pattern in the densest liquid that we have been able to make; unconfined quark gluon liquid.

The difficulties are also present for a black hole and for a proton.

The only way to achieve “confinement” of a proton, is to use 4d.
Black holes could require several dimensions mixed together (up to 6d). Since it is impossible to achieve equally spaced “dimples” of equal size, then the different sizes of the “dimples” is achieved by having the 2d surfaces containing several dimensions.
It is possible to reach the classical sphere packing density (12) in 6d. There will always be more unoccupied space than occupied spaces.

To get an idea of the packing problem on a sphere look at the engineering which has gone into the making of a golf ball.
Look at the different images at
http://www.titleist.com/golfballs/prov1.asp?bhcp=1

and the designs at
http://www.knetgolf.com/GolfBallDimp.aspx
and
http://usasearch.gov/search?input-fo....gov&x=28&y=11

Some explanations
Golf balls are usually covered with dimples in a spherically symmetrical way, and for many values of N, it is impossible to cover the golf ball uniformly without gaps.
You can get an idea of how to space dimples uniformly around a sphere by thinking about the "platonic solids" -- the tetrahedron, cube, octahedron, dodecahedron and icosahedron, and placing a dimple at the corners of an inscribed platonic solid. Variations on this theme give the corners of Buckminster Fuller's geodesic domes, and also the possible symmetrical locations of dimples on a golf ball.
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I expect that we will soon see stories about traveling to other dimensions by using “wormholes”.
It’s not a trip that I would want to take since it would involve going through a “fireball”.
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~~~ Since I’m learning … I reserve the right to change my mind ~~~
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