Discussion Overview
The discussion revolves around the definition of "continuity" for maps in Minkowski space, focusing on the appropriate metrics and topologies to use. Participants explore the implications of different definitions and the nature of continuity in this context, touching on theoretical aspects and mathematical foundations.
Discussion Character
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant questions the use of the Minkowski product for defining continuity, suggesting it may misrepresent point proximity.
- Another participant asserts that Minkowski space-time can be viewed as ##\mathbb{R}^{4}## with the canonical Euclidean topology, indicating that continuity should be defined with respect to this topology.
- A participant references the Wikipedia definition of Minkowski space and inquires whether a consistent metric can be induced by the quadratic form associated with it, suggesting reliance on the Euclidean norm for continuity if not.
- Another participant notes that while pseudo-Riemannian metric tensors can theoretically induce a topology, the canonical topology on Minkowski space-time is generated by the Euclidean metric's open balls.
- A later reply mentions a mathematical book that discusses topology in Minkowski spacetime, potentially providing further insights.
Areas of Agreement / Disagreement
Participants express differing views on the appropriate metrics and topologies for defining continuity in Minkowski space. There is no consensus on a singular definition or approach, and multiple competing perspectives remain present in the discussion.
Contextual Notes
Participants highlight the limitations of using the Minkowski product for continuity and the potential need for alternative metrics, indicating unresolved questions about the nature of continuity in this mathematical framework.