Here is a quote that covers the general idea.
Poincare Science and Hypothesis“The straight line is a line such that a figure of which this line is a part can move without the mutual distances of its points varying, and in such a way that all the points in this straight line remain fixed" ...
If a flat and hyperbolic geometry can be constructed to describe the same physical event and it is only convention or convenience as to which to select, then can we use the angles made by distant stars to show that we inhabit a flat (euclidean) geometry? Is it impossible to discover the shape...
Hi,
Is the geometry really Minkowskian? Or is applying a Minkowskian geometry the most simple mathematical model to describe the relation between light, masses, and moving bodies in those special cases?
This is the core of my original question. Is there really a fundamental geometry?
Thank you for your response. Sadly the geometry of space section does not cover the mathematical problem of there being no preferred geometry.
I believe that a curved space geometry has been solved that has all the logical consistencies that Euclidean geometry has. If this is true then...
I heard that some physicists are trying to determine the spacial/geometric curvature of the universe by measuring the angles of distant stars (a very large triangle).
Is this possible? Or is Poincare correct when he said that there is no preferred geometry and that there is no experiment...