Non-Euclidean Physics & Straight Lines: Can They Coexist?

[thinkandmull]

Here's something I've been wondering about: does non-Euclidean modern physics imply that there are no straight lines in our universe? If so, how is this possible? With any circular object or space, one can always draw a straight line through it, right? Thanks.

 

[Nugatory]

What exactly do you mean by "non-Euclidean modern physics"? If you're thinking about the non-Euclidean space-time geometries of relativity, these allow straight lines.

It's also worth taking a few moments to crisply define what you mean by "straight line". If I present you with a path between points... What standards will you use to determine whether that path is a straight line?

 

[andrewkirk]

No. It just means that straight lines - which are called 'geodesics' in Non-Euclidean geometries - don't necessarily have all the same properties that they have in Euclidean geometry.

For instance, in Euclidean geometry there is only one straight line through a point that is parallel to a line that doesn't pass through the point. In some non-Euclidean geometries there will be multiple such straight lines and in others there will be none.

 

[thinkandmull]

Oh, so non-Euclidean ideas build of Euclidean ones?

 

[andrewkirk]

In a sense. They are generalisations of them. Riemannian Geometry might be a better word than Non-Euclidean Geometry though, because Riemannian Geometries include both Euclidean and Non-Euclidean Geometries.