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Space is locally euclidian. You can easily define pi as a universal constant in our universe, in terms of local flat regions.
by wyager 5y ago
Space is locally euclidian. You can easily define pi as a universal constant in our universe, in terms of local flat regions.
- blamestross 5y agolocal euclidian-ness is an approximation. Nowhere is flat and it wont be until well after the heat death of the universe when every particle is outside the light cone of every other (making a lot of dubious assumptions about the eventual fate of the universe)
- nimish 5y agoNo, local euclidean-ness is (more or less) the equivalence principle. The locality could be very small though! But it would break GR if local flatness weren't possible.
- blamestross 5y agoEquivalence principal is about the fact we can't differentiate between a flat spacetime+force and a curved spacetime. It doesn't require actual flat spacetime to exist anywhere outside of a model. It only says you can't tell how curved it is based on the forces acting on you. Different argument to same end: as long as the universe is expanding, nowhere can be flat. Any 2 things have an inherent repulsive force due to spatial expansion.