The Word "Dimension"

Islam Hassan

I have some difficulty understanding the exact connotation of the word "dimension" as used in string theories re "extra dimentions".

Are these extra dimensions really meant to be dimensions of space or are they simply extra parameters that need to be integrated mathematically into the description of reality proposed by these string theories? It sometimes seems to my lay mind that the word "dimension" is not used in a specific, rigourous way...


IH

phinds

the extra dimensions in string theory are dimensions exactly as you think of the 3 dimension we observe, it's just that they are somehow tiny or "curled up" or something that makes them not observable to human senses. Yes, it's weird.

Islam Hassan

Thanx...I guess the notion of "curled up" also does not lend itself to clarity. Unobservable/unperceivable is much better. To my mind, anything labelled as spatial "dimension" also has a connotation of infinite extent. It's difficult to conceive of a dimension as being spatially nestled within three others.

Perhaps it's more a semantic problem that we face here than a physical one? Would there be a more accurate term to attach to string theories' "extra dimensions"?


IH

cosmik debris

The word dimension has a number of meanings in Physics and Mathematics. In this context the number of dimensions is the number of independent basis vectors that span the vector space.

LouisB

If you want to describe the position of a point on a carpet, you can use a coordinate
(x,y, d) where (x,y) describes the position of a curled carpet hair and d is the distance on that hair.

String Theory contains 10 dimensions, the regular 4 dimensions (x,y,z,t) plus 6 more, curled in a geometry of Spacetime called the Calibi-Yau manifold. String Theory posits that the smallest bits of matter are not point-like particles but vibrating bits of string forming either loops or open strands. Vibrating in different ways corresponds to different particles of nature.

Even our more powerful microscope which is the Large Hadron Collider probe reality at too high spatial scale to empirically prove that there are more than the four regular dimensions. The other 6 are like the hairs of the carpet seen from afar. I do not believe this theory but this is roughly how I understand it.

phinds

Yep, I'm with you on both of those statements

Chronos

In mathematics, a 'dimension' is merely a degree of freedom.

Nabeshin

This isn't necessarily true (or at least, doesn't necessarily have to be true). The so-called Large Extra-Dimension Theories developed in the late 1990s allowed for theories in which the extra dimensions were on the order of millimeters in size (as compared to the standard assumed planck length). Now, it's true that these models have been severely constrained by LHC data, but nevertheless they're a theoretical possibility.

tom.stoer

In mathematics (differential geometry) dimension does not require infinite extent. A manifold with dimension N looks locally like N-dim. Euclidean space; globally it may be different, e.g. curved, compactified etc.

Note that compactification in this sense des not require embedding in a higher-dim. flat space; therefore the compactified dimensions of String theory are not embedded in a larger space.

Look at the garden hose example: it's a two dim. manifold with one large and one small (circular) dimension. In differential geometry it's possible to describe this manifold w/o referring to the three dim. embedding space! We use it for visualisation, but mathematically it is absent.

Naty1

not a good way to think about 'dimension' as already noted...we do not even know if the three space dimensions we can observe are infinite or not...nor if the fourth, time, is.

LouisB

I think that Islam was not about the validity of sting's theory. I thought he was simply interested to know what the word "dimension" means in the context of this string theory.