Is 1D Space a Subspace of 2D Space in Physics?

In summary, the conversation discusses the concept of subspaces in physics, particularly in relation to different dimensions and how they can be represented mathematically. The question of whether a 1D space is a subspace of 2D space is explored, and it is determined that there is an "isomorphism" between the two but they are not strictly the same. The concept of subspaces in physics and their applications in special relativity is also mentioned.
  • #1
gianeshwar
226
14
Please excuse me for my less knowledge. I always tried to physically visualise mathematics facts.
My first question is " Is 1D space of physics a subspace of 2D space of physics and so on...
So in this way our 3D space is a subspace of 4 D space(spacetime).
Can I imagine applying all properties of vector space applicable in physical world?
My study of Advanced Algebra is still in infancy.
Please let me know if my question is irrelevant.
Thank you all in advance.
Please reply so that I start further discussion related to Advanced Algebra. I want to master it.

In classical mechanics some process can be defined in terms of generalised coordinates like density , temperature , location , time and so on...
Now a space is defined with independent dimensions density,temperature,location, time and suppose colour.
Is space generated by density, temperature and location a subspace of above space.
Is it embedded in the above space?
Can I have two different subspaces of five dimensions of the above space?
 
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  • #2
If n < m, then n dimensional space can be considered a subspace of m dimensional space.
Example: Let{(x,y,z)|x,y,z real} be a 3 dimensional space. Then {(x,y,a)|x,y real, a fixed} is a 2 dimensional subspace for each value of a.

I think this should help you with the second question. You can have as many subspaces as you want.
 
  • #3
Notice the difference between your question "Is 1D space of physics a subspace of 2D space of physics and so on... So in this way our 3D space is a subspace of 4 D space(spacetime)."

and mathman's response "If n < m, then n dimensional space can be considered a subspace of m dimensional space."

Strictly speaking, no, 1D space is NOT a subspace of 2D space and 3D space is not a subspace of 4Dspace. Points in 1D space can be designated by a single number, a, while points in 2D space are designated by pairs of numbers, (x, y). But we can associate the point, a, with the pair (a, 0) so there is an "isomorphism" between 1D and a subspace of 2D. This is NOT the same as saying 1D is a subspace itself because there are many different such "isomorphisms" or assignments: a with (0, a) or with (a, a) or (a, ma) for fixed m, etc.
 
  • #4
Thank you dear friends!
 
  • #5
To a large extent physics in the plane can be considered a super position of physics on two lines. However, be careful. Special relativity with physics in 4 D (Space-time) is like physics in conventional four dimensions except the metric is different. The interval in special relativity is (often): sqr root(x squared + y squared + z squared - time squared).
 

Related to Is 1D Space a Subspace of 2D Space in Physics?

1. What is a subspace in 2D space of physics?

A subspace in 2D space of physics is a subset of the two-dimensional space that satisfies certain properties. In physics, this often refers to a subset of the space that is relevant to a particular physical phenomenon or theory.

2. How is a subspace different from the entire 2D space?

A subspace is a smaller subset of the 2D space that satisfies specific conditions or constraints, while the entire 2D space includes all possible points and dimensions. Think of a subspace as a smaller, more focused version of the entire space.

3. What are some examples of subspaces in 2D space of physics?

Some examples of subspaces in 2D space of physics include the phase space in classical mechanics, the wave function space in quantum mechanics, and the vector space of forces in Newtonian mechanics.

4. How do subspaces relate to the laws of physics?

Subspaces are essential in understanding and applying the laws of physics. The properties and constraints of a subspace can help determine the behavior and interactions of physical systems within that space.

5. Can a subspace of 2D space of physics be visualized?

Yes, a subspace in 2D space of physics can be visualized using various techniques such as graphs, diagrams, and mathematical models. These visualizations can aid in understanding and analyzing the properties and behaviors of physical systems within the subspace.

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