4 ms·
"Locally flat" means flat only very close to the point of consideration. That is the mathematical definition, the "practical" definition is "flat only as long a
by krastanov 5y ago
"Locally flat" means flat only very close to the point of consideration. That is the mathematical definition, the "practical" definition is "flat only as long as you do not stray further away than some characteristic measure of distance defining your problem and accuracy requirements". So as long as your circle is very small then the " experimentally measured" pi and the math pi are the same. The moment your circle becomes big enough to pass through interesting (measurable) gravitational effects, the experimental value will be different. If anything, experimentally measuring that difference is one way to experimentally measure spacetime curvature.
- ithinkso 5y agoThat's why I asked about GR specifically, to have a common framework to work with. Without it you can say words like experimentally, practical and talking about differences between different pis whatever that means but this will only lead to misunderstandings at best and nonsense at worst