What Are the Extra Dimensions Beyond Our Familiar Three?

[Xyooj]

dimensions of our world...

we know our world is three dimensional, that's length, width, height. Then Einstein came along and said don't forgot time as another dimension.

now we have a four dimensional world = length, width, height, time

those who said there are more dimensions, what are these dimensions then?

i could only think of the supernatural world then, such as ghosts, the dead, etc exist in the same world as we (natural world), except in different dimensions than us.

help?

 

[Kevin_Axion]

No, the application of extra spatial dimensions to Physics usually derives from Theodor Kaluza (http://en.wikipedia.org/wiki/Theodor_Kaluza), he proposed a Unified Field Theory for Electromagnetism and Gravity by adding an extra spatial dimension. The only problem was that the Theory didn't provide accurate predictions about physical constants and obviously didn't include the Strong Nucelar Force and Weak Nuclear Force which was Unknown.

To imagine dimensionality, one would argue in Kaluza's idea, "Where is this extra dimension?" Don't we only visualize a 4-dimensional space-time? This is where Oskar Klein was introduced (http://en.wikipedia.org/wiki/Oskar_Klein) and he proposed a solution. Firstly let me explain what a dimension is.

We begin with a point in a Euclidean Space (a basic 3 dimensional coordinate system (x,y,z)), This point has no dimensions, essentially it doesn't stretch in any x,y, and z coordinate. Then this point we extend in any direction in the Euclidean Space to another point. This produces a line that extends in one dimension, it needs one dimension to describe it, a length.
Then, we have the line and we move it perpendicular to the direction of the line to produce a surface this surface is an area and needs two dimensions or quantities to describe it, length and width, it extends in the x,y plane.
Now, we take the area described by length and width and extend it upwards in the z dimension, a dimension perpendicular to the x,y plane. This produces a volume, a cube, which needs 3 quantities or dimension to describe it, x,y, and z.
The fourth dimension isn't very different from the rest, it's impossible to visualize though because are brains aren't evolved to understand or physically see it, although mathematics does help. What happens here is that the volume extends in a direction perpendicular to the x,y and z dimensions, to produce z,y,z, and t which is a hypervolume. A hypervolume needs 4 numbers to describe it, a length, a width, a depth(height) and a hyper extension into a 4-dimensional spatial dimension. Of course in Physics we take the fourth dimension as time but this is just spatial dimensions I'm discussing.
One will ask? "where are these dimensions?" Oskar Klein said that imagine at every point in space or every point in space was not a point but rather a compactified (very small) circle. These are invisible at macroscopic scales and even at current energies we have reached or will ever reach.
In Superstring Theory (I won't get into the details, just the argument of dimensionality) or M-Theory the Theory requires 6 (for Superstring Theories)- 7 (for M-Theory) extra spatial dimensions that are compactified at extremely high energies and coiled into 6 dimensional to 7 dimensional shapes at each point in space, these are known as Calabi-Yau Manifolds (http://en.wikipedia.org/wiki/Calabi–Yau_manifold). Anything can be there I'd presume but I'm quite certain that the Supernatural argument is false because ideas like Spirits aren't necessarily Scientific. Please don't think of those ideas I'm sure you will find the other ideas in Physics much more fulfilling and fascinating.

Kevin,