New level of relativity
- 64 Downloads
In their origins Einstein’s studies of relativity principles called into question the validity of important assumptions that had previously been made in formulating physical theories, assumptions made without investigation into alternatives. Examples of this include notions of absolute time and space, flat Euclidean geometry, and trivial topology. In this paper, we review an intermediate niche, differentiable (smooth) structure, which must be defined between topology and geometry. We now know that this choice need not be trivial. Just as it seemed for centuries to be obvious that space should be flat, so it would seem until recently that standard, trivial, smoothness for spacetime is the only choice. We now know that this is not true. In this paper we review these topics in the light of very surprising and often counter-intuitive mathematical discoveries of the last 20 years or so. Since our regions of observability are necessarily constrained we do not have any a priori justification for extending standard smoothness globally. This opens up the possibility of non-standard extension of solutions to field equations to exotically smooth regions, leading to examples such as exotic black holes and exotic cosmological models.
KeywordsRelativity Differential topology
Unable to display preview. Download preview PDF.
- 2.Kretschmann E. (1917). Über den physikalischen Sinn der Relativitätspostulate, A. Einstein neue und seine ursprüngliche Relativitätstheorie. Ann. Phys. 53: 575–614 Google Scholar
- 3.Jammer M. (1960). Concepts of Space. Harper, New York Google Scholar
- 6.Milnor, J.: The discovery of exotic spheres. In: Cappel, J., et al. (eds.) Surveys on Surgery Theory. Princeton University Press, New Jersey (2000) Google Scholar
- 10.Harvey, F., Lawson, H.: A theory of characteristic currents associated to a singular connection, Astérique 213 ed., Société Mathématique de France (1993)Google Scholar