All Questions
23
questions
0
votes
0
answers
32
views
Still having trouble understanding gravitational lensing [duplicate]
The normal diagram used to explain gravitational lensing shows a two-dimensional plane that is deflected by a heavy weight. This is a two dimensional description that requires an extra dimension to ...
- 319
11
votes
2
answers
1k
views
Features of General Relativity applicable only to 3+1 dimensions?
While studying general relativity, I noticed that much of the theory could easily be generalized from a $(3,1)$-dimensional spacetime to an $(n,1)$-dimensional spacetime without any changes. So, is ...
- 1,588
1
vote
0
answers
40
views
What is the lower bound on the dimension of the LOCAL imbedding of a General relativistic Lorentzian manifold in a pseudo-Euclidean spacetime?
What is the lower bound on the dimension of the LOCAL imbedding of a General relativistic Lorentzian manifold in a pseudo-Euclidean spacetime?
Imbedding is Isometric embedding to me.
What about these ...
- 1,268
0
votes
1
answer
76
views
Does intrinsic curvature in a higher dimension mean that the lower dimensions also exhibit curvature?
If our universe has intrinsic curvature in a higher dimension, would that mean the 3 dimensions that we live in would be curved? and if so would the lower dimensions exhibit intrinsic or extrinsic ...
- 23
2
votes
1
answer
364
views
Why does Misner, Thorne, and Wheeler’s Gravitation visualization technique breakdown in dimension $> 4$?
In this chapter we will introduce and discuss at length one of the ways that physicists sometimes visualize “nice” differential forms. In essence, we will be considering ways of visualizing one-forms, ...
- 1,389
0
votes
2
answers
77
views
Is there any way to prove that contrarly to a flat 3D space, a curved 3D space can only be constructed in a 4D manifold?
This question is a result of me trying to understand how this universe can be possibly infinite if it isn't infinitely old. So to compare with an area that is flat it can be constructed both in 2D and ...
- 2,255
4
votes
3
answers
691
views
Why does GTR not need a higher dimension to describe the bending of spacetime?
I am a bit confused on how GTR uses intrinsic curvature instead of extrinsic curvature. Maybe it is just a misunderstanding, but I will do my best to describe my question:
If we take an object of $n$ ...
- 3,778
4
votes
3
answers
182
views
Given that 1D space $\mathbb{R}$ and 3D space $\mathbb{R}^3$ are in bijection, why do we describe our physical world as 3D?
Mostly the reason given is that that three numbers are required to specify a point uniquely in our world. But this is utter nonsense!
It has long been mathematically proven that $\mathbb{R}$ is in ...
- 1,951
0
votes
2
answers
105
views
Connected and disconnected dimensions
The usual way of determining the dimensionality of space is from the number of values needed to define a unique point.
However, when choosing a ski, my body is defined by two numbers - my mass and ...
4
votes
1
answer
652
views
What is dimension? What is the size of dimension?
Recently I heard a TED talk by Brian Greene where he was speaking about String Theory working on $(10+1)$ dimensions. Plus he said that we live in only in $(3 +1)$ dimensions. So where are others?
...
- 625
3
votes
2
answers
262
views
Meaning of $n+1$ dimensions
Is there anything mathematically significant about studying a theory in $n$ dimensions or $m+1$ dimensions if $n=m+1$? For instance in the context of general relativity I hear people talk about the ...
1
vote
0
answers
80
views
Kaluza-Klein approach and Gauss-Cadazzi approach
Can you tell me the difference or physical application of Kaluza Klein approach and Gauss Codazzi approach?
In Kaluza Klein theory, 5 dimensional theory can be dimensional reduced to 4 dimensional ...
- 3,622
7
votes
1
answer
384
views
Spacetime has an infinite number of choices for differentiability. Coincidence?
Spacetime can be modelled using a four-dimensional topological manifold. Say we denote the manifold using $(M, \mathcal{O})$ where $\dim M =d$. The structure $(M,\mathcal{O})$ is not sufficient for ...
user199113
1
vote
0
answers
59
views
Compactification of spacetimes always possible?
Consider a metric in a $n+1$ dimensional spacetime given by
\begin{equation}
g=\underbrace{g_{tt}(r,t)dt^2 + g_{rt}(r,t)drdt + g_{rr} dr^2}_{g'} +h(t,r,x^A)dx^Adx^B
\end{equation}
where $h$ is a $n-1$ ...
- 31
11
votes
2
answers
841
views
Any "connection" between uncountably infinitely many differentiable manifolds of dimension 4 and the spacetime having dimension four?
Self-studying general relativity, I came across a rather mind-blowing statement (for a beginner like me). Maybe this question is a naive one because of my lack of knowledge in differential geometry.
...
- 3,905