the Instrinsic Structure of Time

and

the Multiplicity of Observed Space Dimensions

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.

2. Saniga, M. (1996) On the transmutation and annihilation of pencil-generated space-time dimensions, in W.G. Tifft and W.J. Cocke (eds.), Mathematical Models of Time and Their Application to Physics and Cosmology, Kluwer Academic Publishers, Dordrecht, pp. 283--290.

3. Saniga, M. (1998)

4. Saniga, M. (1998)

5. Saniga, M. (1998)

6. Saniga, M. (1998)

7. Saniga, M. (2000)

8. Saniga, M. (2001)

9. Saniga, M. (2002)

10. Saniga, M. (2002)

11. Saniga M. (2003)

12. Saniga, M. (2004)

Metod Saniga, Last modified on August 22, 2003

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