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

In summary, the conversation discusses the implications of non-Euclidean modern physics on the existence and properties of straight lines in our universe. It is mentioned that in these geometries, straight lines may not have the same properties as in Euclidean geometry. The concept of geodesics, or straight lines, is also brought up as a generalization of Euclidean geometry.
  • #1
thinkandmull
51
0
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.
 
Physics news on Phys.org
  • #2
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?
 
  • #3
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.
 
  • #4
Oh, so non-Euclidean ideas build of Euclidean ones?
 
  • #5
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.
 

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

1. What is Non-Euclidean Physics?

Non-Euclidean physics is a branch of physics that does not adhere to the traditional rules of Euclidean geometry, which is based on the three-dimensional space described by Euclid. Non-Euclidean physics explores the concept of curved space and how it affects the laws of physics.

2. How does Non-Euclidean Physics differ from traditional physics?

Traditional physics is based on Euclidean geometry, which assumes that space is flat and straight lines are the shortest distance between two points. Non-Euclidean physics, on the other hand, considers the possibility of curved space and altered rules of geometry, which can affect the behavior of particles and the laws of physics.

3. Can Non-Euclidean Physics and traditional physics coexist?

Yes, Non-Euclidean physics and traditional physics can coexist in the sense that both theories can be used to explain different phenomena. However, they may contradict each other in certain scenarios, such as when dealing with extreme gravitational forces or in the study of the universe on a large scale.

4. How are straight lines defined in Non-Euclidean Physics?

In Non-Euclidean physics, straight lines are defined as geodesics, which are the shortest paths between two points on a curved surface. These lines may appear curved in traditional Euclidean geometry, but they are considered straight in Non-Euclidean geometry.

5. What real-world applications does Non-Euclidean Physics have?

Non-Euclidean physics has many applications in modern physics, such as in Einstein's theory of general relativity, which describes the behavior of gravitation and the structure of the universe. It is also used in navigation systems, where curved space must be taken into account for accurate calculations.

Similar threads

Replies
3
Views
210
  • Electromagnetism
Replies
3
Views
1K
Replies
3
Views
1K
Replies
18
Views
2K
  • Other Physics Topics
Replies
3
Views
3K
  • Introductory Physics Homework Help
3
Replies
98
Views
4K
Replies
27
Views
3K
  • Other Physics Topics
Replies
8
Views
1K
Replies
1
Views
831
  • Special and General Relativity
2
Replies
63
Views
3K
Back
Top