A trivial question about the space of Euclidean

In summary, Classical Mechanics defines our space as E^3 which is assumed to be R^3x R_t. However, there is a question about the possibility of defining space as Q^3x Q_t and whether this would make a significant difference or create any logical paradox. The concern is raised about how particles in one dimension would move between coordinates and if they would "hop" instead of moving continuously. This raises questions about solving Newton's laws in intervals with "holes" such as [a, b] \cap \mathbb{Q}.
  • #1
Shing
144
1
Classical Mechanics define our space is [itex]E^3[/itex]
that's also assumed to be [itex]R^3[/itex]x [itex]R_t[/itex]
I just wondering what if [itex]Q^3[/itex]x [itex]Q_t[/itex]?
will it make any significant difference? will it cause any logical paradox?

thanks for reading!
 
Last edited:
Physics news on Phys.org
  • #2
The first thing I wonder about is how a particle in one dimension will get from coordinate a to coordinate b. In my mind, it should always do so in a continuous fashion. But you suppose it would "hop" from one rational to the "next"? You would solve Newton's laws (like F = m x'') in an interval with "holes" (e.g. [itex][a, b] \cap \mathbb{Q}[/itex])?
 

Related to A trivial question about the space of Euclidean

1. What is Euclidean space?

Euclidean space is a mathematical concept that describes a flat, infinite space with three dimensions: length, width, and height. It is named after the ancient Greek mathematician Euclid, who first described it in his famous book "Elements".

2. How is Euclidean space different from other types of space?

Euclidean space is different from other types of space, such as non-Euclidean space, because it follows the laws of Euclidean geometry. This means that the angles of a triangle always add up to 180 degrees, parallel lines never intersect, and the shortest distance between two points is a straight line.

3. What is the importance of Euclidean space in science?

Euclidean space is important in science because it provides a mathematical framework for describing and understanding the physical world. Many scientific theories, such as Newton's laws of motion, are based on the principles of Euclidean geometry.

4. Can Euclidean space have more than three dimensions?

Yes, Euclidean space can have any number of dimensions. In fact, it is possible to mathematically describe and visualize spaces with up to 10 or even 26 dimensions. However, it is difficult for us to imagine or perceive spaces with more than three dimensions.

5. How is Euclidean space used in practical applications?

Euclidean space is used in many practical applications, including engineering, architecture, and computer graphics. It is also used in physics and astronomy to model the behavior of objects in our three-dimensional world. GPS technology, which relies on Euclidean geometry, is another example of a practical application of Euclidean space.

Similar threads

I Calculations to prove the non-Euclidean nature of 3-D space
    • Classical Physics
Replies
5
Views
680
A An ab initio Hilbert space formulation of Lagrangian mechanics
    • Classical Physics
Replies
10
Views
1K
I Physical reality of nontrivial loops in SO(3)
    • Classical Physics
Replies
6
Views
764
I 3-parameter group of symmetries on the plane
    • Differential Geometry
2
Replies
51
Views
896
I Newton Galilean spacetime as fiber bundle
    • Special and General Relativity
Replies
29
Views
1K
B Topology on flat space when a manifold is locally homeomorphic to it
    • Special and General Relativity
Replies
25
Views
2K
I About quantum interference: space and time
    • Quantum Interpretations and Foundations
Replies
0
Views
273
I Difference (if any) between E^1 x E^3 and E^4
    • Differential Geometry
Replies
14
Views
3K
A How to derive Quantum Mechanics in curved physical space?
    • Quantum Physics
Replies
6
Views
1K
I Five points in space with rational distances that are not co-linear
    • General Math
Replies
13
Views
1K

Hot Threads

Recent Insights

Back
Top