English

Does Zeeman's Fine Topology Exist?

Mathematical Physics 2012-01-24 v3 math.MP

Abstract

We work on the family of topologies for the Minkowski manifold M. We partially order this family by inclusion to form the lattice \Sigma(M), and focus on the sublattice Z of topologies that induce the Euclidean metric space on every time axis and every space axis. We analyze the bounds of Z in the lattice \Sigma(M), in search for its supremum. Our conclusion --that such a supremum does not belong in Z-- is compared with constructive proofs of existence of the fine topology, defined as the maximum of Z and conceived to play an essential role in contemporary physical theories. Essential mathematical and physical questions arise.

Cite

@article{arxiv.1003.3703,
  title  = {Does Zeeman's Fine Topology Exist?},
  author = {Norberto Sainz},
  journal= {arXiv preprint arXiv:1003.3703},
  year   = {2012}
}

Comments

This paper has been withdrawn by the author due to a substancial error in equation 25, which does not hold true

R2 v1 2026-06-21T14:59:41.969Z