Exploring Higher Dimensions: Understanding 5, 6, 7, and 11 Dimensional Space

[Dissident Dan]

I'm confused about what people mean by 5,6,7, and 11 dimensions.

Are they referring to spatial dimension? Are they referring to different dimensions like time is a "dimension" in addition to space?

If we're talking about spatial dimensions, how can you have more than 3? Spatial dimensions are defined as all being orthogonal to each other. Once you get past three, you cannot be orthogonal to all dimensions. The axis is made with components of other dimensions.

 

[LURCH]

The extra dimensions often spoken of in String Theory and other QM models can be mathematically deduced. Not by me, you understand, but I'm told that they can.

The whole problem with perceiving them is that they cannot exist in our 3-D world. For me, the best way to understand this is the illustration of a "tesseract". If you start with a zero-dimensional point, and extend it along one dimension, you get a line segment. Broaden the line segment by extending it along another dimension, and you get a square. And at the corner of this square are two lines that come together at 90^o angles. Extend the square along another dimension, and you've made a cube, and at the corner of the cube, three lines come together, all at write angles to each other. Now, if we extend the cube along another dimension, we get a tesseract, a 4-D object at the corner of which a fourth line comes in at 90^o to the other three.

If you attempt to picture this in your mind, you won't be able to. There is no angle with which you are familliar, or which you could imagine, that would be at a write angle to the three directions represented at the corner of a cube. But even though we can't see it, or even picture it, we can logically deduce its existence.

EDIT TO ADD :

Although the extra dimensions of M-Theory, e.g., may all be spatial there is, according to Green and some others, nothing that says they must be. So there could be 8 spatial directions and 3 temporal ones, or any other combination that includes three or more spatial.

Now isn't that spatial?!

 

[selfAdjoint]

In normal string theory, there is one time dimension and the rest are spatial. Multiple time axes raise different problems and there are a few papers on that (see "many fingered time", a phrase that goes back the Misner, Wheeler, and Thorne's Gravitation).

 

[sol]

Fundamentals on the Brane

http://www.superstringtheory.com/forum/bhboard/messages12/113.html

Rotation is a result of moving first through longitudal and transverse dimensional interpetation that is first geometrically define, and having reached the z direction time becomes the undertanding of Gr and gravity?

Sol

 

[radagast]

Originally posted by Dissident Dan
I'm confused about what people mean by 5,6,7, and 11 dimensions.

If we're talking about spatial dimensions, how can you have more than 3? Spatial dimensions are defined as all being orthogonal to each other. Once you get past three, you cannot be orthogonal to all dimensions. The axis is made with components of other dimensions.

Obviously we only sense three spatial and one time dimension. By definition, another dimension would be orthoganol to all others.

A theoretical 2D creature couldn't concieve of a third dimension, either. Even if the plane he existed in was in three dimensions. He could concieve of width and depth, but the concept of height wouldn't make any sense to him. Unless we had somehow experienced another spatial dimension, trying to understand it is useless, except as lower dimensional spaces compared to 3D.

 

[sol]

Dimension is Relative to Time

http://www.superstringtheory.com/forum/extraboard/messages12/722.html

If one undertands gravity, is also equal to time what value would we have found in distances?

If one undertands the analogies of the http://superstringtheory.com/forum/dualboard/messages11/691.html in which I have relayed, the quark to quark measure, still retains some relationship to the energy?

I am open to corrections.

Sol

 

[sol]

From Gravity to Supergravity

http://superstringtheory.com/forum/dualboard/messages14/112.html

I was looking for practical applications, in which I could compare the understanding here, in regards to Heliosphere and seismology in the Sun, seemed a most appropriate place in which to look?

Any corrections or comments?

Sol

 

[sol]

Supergravity and Dimensions

http://www.superstringtheory.com/forum/dualboard/messages13/218.html

Hope the previous links help.

Sol