Current Research
On a Possible Intimate Link Between
the Instrinsic Structure of Time
and
the Multiplicity of Observed Space Dimensions
There are very few things
that fascinate equally a theoretical physicist studying black
holes and a patient undergoing serious psychosis. Time,
undoubtedly, can well be ranked among them. For the measure of
time inside a black hole is no more/less bizarre than the
perception of time by a schizophrenic, who may perceive it as
completely ``suspended," ``standing still," or even ``reversing"
its direction. The nature of time is surely one of the most
profound mysteries that science has ever faced. This, perhaps,
since the concept entails multifarious, and even incongruous,
facets.
My interest in the topic goes back as far as some ten years ago
when I first became familiar with a puzzling discrepancy between
the way we, humans, perceive time and what modern physical
theories tell us about the concept, i.e. between psychological and
physical aspects of time. Motivated by this contrariety, I started
a search for a theory that could not only grasp, at least
qualitatively, our experience of time, but also attempted at
bridging the gap between the two concepts. My first, although
quite rudimentary, model of the ``subjective" time dimension
employed the concept of so-called pencil-generated spacetime(s) in
a projective plane over a (commutative) field of arbitrary
characteristic [1-7]. Although, as already mentioned, this theory
was originally aimed at a deeper insight into the puzzling
discrepancy between perceptional and physical aspects of time, I
soon realized that it also had an important bearing on the problem
of the dimensionality of space. Namely, I found out that there
seems to exist an intricate relation between our sense of time and
the observed number of spatial dimensions [2-5]. Mathematically,
this property is substantiated by the fact that I treat time and
space from the very beginning as standing on topologically
different footings. As for their ``outer" appearance, both the
types of dimension are identical, being regarded as pencils, i.e.
linear, single-infinite aggregates of constituting elements. It is
their ``inner" structure where the difference comes in: the
constituting element (``point") of a spatial dimension is a line,
whereas that of the time dimension is a (proper) conic.
The theory acquired a qualitatively new standing when I raised the
dimensionality of the projective setting by one, i.e. moved into a
projective space, and identified the pencils in question with
those of the fundamental configurations of certain Cremona
transformations [8-12]. The 3+1 macroscopic dimensionality of
space-time was demonstrated to uniquely follow from the structure
of the so-called quadro-cubic Cremona transformations -- the
simplest non-trivial, non-symmetrical Cremona transformations in a
projective space of three dimensions [8,9]. In addition, these
transformations were also found to fix the type of the pencil of
fundamental conics, i.e. the extrinsic geometry of the time
dimension, and to provide us with a totally unexpected, yet
extremely promising, conceptual basis for the sought-for
reconciliation between the two above-mentioned extreme views of
time. However, a most intriguing feature of these Cremonian
spacetimes is undoubtedly the fact that they provide us
with a sound framework for getting a further insight into the surmised
connection between the
structure of time and the multiplicity of space
dimensions [11]; and I am currently pursuing this fascinating line of
scientific enquiry.
It goes without saying that both
the true nature of time and the total dimensionality of space are
conceptual issues of utmost importance in physics in general, and
quantum gravity and stringy cosmology in particular. The
above-oulined line of research may well prove very profitable for
both of these fields.
Metod Saniga,
Last modified on August 22, 2003
Back to Top