Why can't each point in space be pan dimensional?

[Not Sure]

What if the smallest unit of space is a granular point, measuring one Plank's length in every possible dimension? This would cause a string to be pan dimensional as well, measuring one Plank's length in every possible dimension, and capable of vibrating in the direction of any dimension.

 

It makes no sense to assume that space is capable of behaving like the mathematical concept of dimension. It makes no sense to assume that space can be purely one or two or three dimensional.

 

If the smallest unit of space is redefined as being composed of pan-dimensional granular points it allows for a fascinating series of extrapolations that might better explain the observed data.

 

I could go on, unless it can be shown why this is not possible.

 

[ajb]

This would cause a string to be pan dimensional as well, measuring one Plank's length in every possible dimension, and capable of vibrating in the direction of any dimension.

For consistency strings need 9+1 dimensions.

 

It makes no sense to assume that space is capable of behaving like the mathematical concept of dimension. It makes no sense to assume that space can be purely one or two or three dimensional.

Well, one has to create mathematical models somehow. It seems that most of what we would expect from space can be mathematically modelled. This is a slightly different questions as to if reality really is mathematical or not.

 

If the smallest unit of space is redefined as being composed of pan-dimensional granular points it allows for a fascinating series of extrapolations that might better explain the observed data.

Granular points is a term to avoid. However, you are right in the fact that people do consider various generalisations of space-time modelled on discrete sets or noncommutative geometry.

[Mordred]

One thing to be clear on is what dimensional analysis really details. Many do not realize it is a geometric math term of influence or measurement. They tend to think of the sci-fi ideas of dimensions.

 

String theory is an excellent example. The dimensions are broken down into interactions including rotational interactions linear interactions etc.

 

Here is a useful article on dimensional analysis.

http://www.physics.gatech.edu/~mj38/Fall_2012/2211AB/main/supplements/dimensional_analysis.pdf

Ajb Is however us far more the expert on geometric dimension analysis than I

My fav textbook though covering this aspect is "Roads to Reality" by Sir Rogers Penrose

http://www.amazon.com/The-Road-Reality-Complete-Universe/dp/0679776311

Edited November 13, 2014 by Mordred