Curled Up Internal Spatial Dimensions Viewed Through Systemic Functional Linguistics

Penrose (2004: 325-6):

The spaces that we need for the gauge theories of particle interactions (other than gravity), are different from these (and so they are something new), and it is best to think of them as referring to a kind of ‘spatial’ dimension that is additional to those of ordinary space and time. These extra ‘spatial’ dimensions are frequently referred to as internal dimensions, so that moving along in such an ‘internal direction’ does not actually carry us away from the spacetime point at which we are situated. …

Indeed, in many (or most?) of the current attempts at finding a deeper framework for fundamental physics (e.g. supergravity or string theory), the very notion of ‘spacetime’ is extended to higher dimensionality. The ‘internal dimensions’ then come about through the agency of these extra spatial dimensions, where these extra spatial dimensions are put on an essentially equal footing with those of ordinary space and time. The resulting ‘spacetime’ thus acquires more dimensions than the standard four. Ideas of this nature go back to about 1919, when Theodor Kaluza and Oskar Klein provided an extension of Einstein’s general relativity in which the number of spacetime dimensions is increased from 4 to 5. The extra dimension, enables Maxwell’s superb theory of electromagnetism to be incorporated, in a certain sense, into a ‘spacetime geometrical description’. However, this ‘5th dimension’ has to be thought of as being ‘curled up into a tiny loop’ so that we are not directly aware of it as an ordinary spatial dimension.

The analogy is often presented of a hosepipe, which is to represent a Kaluza–Klein-type modification of a 1-dimensional universe. When looked at on a large scale, the hosepipe indeed looks 1-dimensional: the dimension of its length. But when examined more closely, we find that the hosepipe surface is actually 2-dimensional, with the extra dimension looping tightly around on a much smaller scale than the length of the hosepipe. This is to be taken as the direct analogy of how we would perceive only a 4-dimensional physical spacetime in a 5-dimensional Kaluza–Klein total ‘spacetime’. The Kaluza–Klein 5-space is to be the direct analogue of the hosepipe 2-surface, where the 4-spacetime that we actually perceive is the direct analogue of the basically 1-dimensional appearance of the hosepipe.

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the notion of the internal dimensions of spacetime being curved ('curled up in a tiny loop') confuses circumstance (spacetime) with thing (surface). This confusion invalidates theories that depend on this notion, including all versions of string theory.