Dimensions in string theory

[Guille]

Correct me if I'm wrong, but I thingk it's correct:

M-theory has 11 dimensional universe.

3 of the 5 different string theories (I can't remember their' names) have 10 dimensional universe.

The other 2 string theories have 11 dimensional universe.

String are 1 dimensional.

All types of string theories have 1 time dimension, not more.

The d-branes can be 0, 1 or 2 dimensional.

If there is something I haven't mentioned, please state it.

[AntonioLao]

each spacetime point is associated with exactly 6 directions (shortest line segment connecting 2 spacetime points). If direction is dimension then a point of spacetime is six-dimensional. But each point can be connected to the infinite other points and these connections are multiple of the 6 shortest ones. if one connection is one dimension then n-point spacetime is n(n-1)/2 dimensions. If there are 100 points of spacetime then this spacetime of 100 points is 4950-dimensional. But organizing into groups of 3's

0-dimension (number of string) = 1 spacetime point.
1-dimension (number of string) = 2 spacetime points (2 ends of a string)
3-dimension (number of string) = 3 spacetime points.
6-dimension (number of string) = 4 spacetime points (tetrahedron)
10-dimension (number of string) = 5 spacetime points.
15-dimension (number of string) = 6 spacetime points.
21-dimension (number of string) = 7 spacetime points.
... ad infinitum

[Guille]

each spacetime point is associated with exactly 6 directions (shortest line segment connecting 2 spacetime points). If direction is dimension then a point of spacetime is six-dimensional.

Actually, isn't a point in spacetime associated with 8 directions?

there are 6 directions in space. and two in time.
6+2=8 directions in spacetime

[AntonioLao]

Actually, isn't a point in spacetime associated with 8 directions?

a point can have infinite directions to choose from but only 6 are the shortest. These are the unit vectors along the Cartesian axes (+/-). Instead of a lattice Cartesian system, a spherical surface of unit radius separate the point from the outside points. There are still infinite point on the surface of the sphere but there are a lot more points outside. Einstein defined this closed surface as a hole in spacetime. In order for his field equations to be generally covariance, he made the assumption that the metric radius of the hole must be zero, the same as the spacetime interval of special relativity. Another name for this unit vector is the quantum of length, a concept which is still not fully defined in physics. In special relativity, the unit vector or spacetime interval must be zero in order for the speed to reach a maximum of ~186,000 miles (~300,000 km) per second. In quantum field theory both c (light speed) and h (Planck's constant) are normalized to unity.

time is considered as one of the 6 shortest directions, which leaves 5 shortest directions for space. So that a six components spacetime vector can be represented by (1, -1, -1, -1, -1, -1). Negative sign means motion toward the point. Positive sign means motion away from the point. So, if all 6 directions are directed away from the point the vectors are represented by (1,1,1,1,1,1) and if moving toward the point by (-1,-1,-1,-1,-1,-1), these represent a point in true vacuum and a mass point respectively. If all points in spacetime are (1,1,1,1,1,1)'s then they indicate a global expansion of spacetime. Similarly, if all points are (-1,-1,-1,-1,-1,-1)'s then they represent the big bang singularity.

[Guille]

I want to add that d-branes are only a type of a all the branes called p-branes.

p-branes can have from 0 to 9 dimensions.

d-branes, are the type of p-branes were the ends of the open string are joint to.

and d-branes can have from 0 to 2 dimensions.

[AntonioLao]

there is another way of looking at dimensions. This is the level of existence (LOE). Each LOE contains 3 spatial dimensions and 1 time dimension. the next higher level 2 LOE has 6D space and 1D time, level 3 LOE has 9D space and 1D time, level 4 LOE has 12D space and 1D time, 5 level LOE has 15D space and 1D time, 6 level LOE has 18D space and 1D time, 7 level LOE has 21D space and 1D time, 8 level LOE has 24D space and 1D time, 9 level LOE has 27D space and 1D time,..., N level LOE has 3N space and 1D time. Each LOE can be the same as a brane.

[Guille]

I didn't know about the level of existence before, but it is very interesting concept, and helps a lot to understand it, thak you for it.

But how can you make it valid for string theory? becuase string theories have 10 or 11 dimensions.

[Guille]

CUld there be a, decimal place for dimensions?

do you think that we could give to the sqaushed dimensions for string theory, a decimal place for eahc, then, the universe wiuld be:

4.7 dimensional in 3 string theories and

4.6 in the other 2 string theories.

[Guille]

I wanted to post this in the post before, but I forgot:

The names for the string theories:

There are six string theories, not five like i said so before. What happends is:

that the sixth of those theories is dedicated to the forces (bosons).

The other five thoeries are dedicated to both fermions and bosons.

The sixththeory is called the bosonic theory, and has 26 dimensions.

The other five thoeries are called type: I, IIA, IIB, HO and HE.

The five theories have 10 dimensions. but when analised:

IIA and HE can derive another dimensions, the 11th.

Referring to p-branes:

strings are a type of p-branes, which are 1 dimensional. they might be composed of even more fundamental particles.

Membranes, which for some scientists are the basic particles of the universe, and the basic of the m thoery, are 2 dimensional.

Membranes are supposed to be supergravity particles.

(If anybody knows what supergravity is based on, please explain it, and if you can, the simplest way possible)

The f-theory (father thoery) has 12 dimensions. and the knew dimension it adds is the second time dimension, which is more ligical than the 1d time strings and m thoeries, because the second time dimension clears up all the paradoxes.

To get more information, see these web pages, they are very usefull:

http://superstringtheory.com/basics/basic5.html
http://www.mkaku.org/articles/mtheor...rstrings.shtml

[AntonioLao]

CUld there be a, decimal place for dimensions?

in chaos theory of nonlinear dynamic systems, there is such a thing as fractal dimension.

and in the theory of complexity, i am classifying the pure energy state of existence as a completely chaotic system and the matter state as a complex system and the space state as an orderly system. Human beings are complex systems, which lie between complete disorder of energy and total order of space.