Questions tagged [spacetime-dimensions]
Use this tag for dimensions of a manifold, typically the space-time. DO NOT USE THIS TAG for dimension of a physical quantity nor for the size of an object.
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Multidimensional space and Newton's inverse square law deviation [duplicate]
Many times I have heard the physicist Michio Kaku saying that the deviation on Newton's inverse law could demonstrate the existence of multidimensional space, which could support one of the aspect of ...
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Another dimensions [closed]
Just a science ponderer, and pretty much interested in physics. Please guide me if I am wrong.
There have been many statements made by the physicists about the existence of other dimensions (...
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Could black holes be a three dimensional object breaking through space time and falling 4th dimensionaly [closed]
I was thinking about general relativity and I was thinking about it in two dimensions where a heavy metal ball would be placed on a mesh fabric (this is just how I’m imagining it) and if the ball was ...
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Thought experiment of 0 times infinity and dimensions [closed]
Take a cube at 1x1x1 and cut it in half. Take the 0.5x1x1 and cut it in half again. Eventually, you get an object that is 0x1x1. The object does not disappear. It instead now exists in the 2D world. ...
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If the radius of a sphere is reduced by half due to relativistic length contraction, will the volume also be half?
We know that volume is cubicly proportional to radius of a sphere. But if the radius is become half due to relativistic Length contraction, it's being reduced from only one dimension, not three. And ...
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Are branes topological defects? How else could they be physical?
As far as I understand, the branes of brane cosmology are lower-dimensional "sub-manifolds" of some space. It was hard to imagine for me how such structure could exist and be physical. But ...
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How many independent degrees of freedom does the metric tensor have in vacuum (at every point)?
A field of metric tensors fully characterises the curvature of a vacuum space-time. (For example, the spacetime between some single point masses which are themself not part of the manifold)
The metric ...
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Writing a gravity equation
I need a maple cod to variation this action with respect to tensor metric $g_{\mu\nu}$.
This called the Einstein equation. To obtain the Einstein equation, we vary the action with respect to the ...
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Could the universe be a topological defect in a higher space?
I am a mathematician with an undergrad understanding of physics. I recently learned of topological defects in quantum fields. It is an intriguing idea that there could be regions in our universe that, ...
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Why is Spacetime described as flat even though we live in 3 dimensions of space?
I’ve always heard and seen diagrams that show spacetime as being “flat” or in 2 dimensions with curvature. How does this correspond to the 3 spacial dimensions that we perceive to exist in?
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Can someone explain intuitively why "black rings" are possible in 4+1 dimensional gravity? [duplicate]
In 3+1 dimensional general relativity, all black holes must be topologically equivalent to a sphere.
However in 4+1 dimensional gravity, this isn't the case, there Torus shaped black holes are ...
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Does gravity exist in two spatial dimensions? [duplicate]
I've been studying anyons and was wondering if gravity exists in two spatial dimensions and how it affects these particles?
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How does the lifetime and temperature of a black hole scale with mass in higher dimenstions?
I've tried to find out how the lifetime and temperature of a black hole scale with mass in a universe with more then 3 spatial dimensions. I've spent a while trying to look up an answer to this ...
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$N$-body problem in 2 dimensions
I have been trying to implement a 2D $N$-body physics simulator and am currently using newton's law of gravitation to calculate the magnitude of the force a pair of particles experiences.
$$F=\frac{...
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GR metric tensor from extra dimensions
In a flat Euclidean 2d plane, the metric tensor is given by:
$g_{\mu\nu} = \begin{pmatrix}
1 & 0 \\
0 & 1
\end{pmatrix}$
If we imagine this plane as curving into an external 3rd dimension ...
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Lack of independence between the spatial dimensions and time within space-time
I am having a conceptual difficulty understanding the following issue regarding space-time: it is clear to me why a full description of coordinates requires three spatial dimensions plus time. However,...
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In relativity, is the fourth spacetime dimension spatial or nonspatial?
In "An Introduction to Modern Astrophysics" Carroll and Ostlie describe the curvature of space by mass as:
curving in a fourth spatial dimension perpendicular to the usual three of "...
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How do fields exist in higher dimensions appear in the $D=4$ universe?
I'm studying a five-dimensional model with a spacetime background metric:
$
ds^2= e^{2\sigma} g_{\mu\nu} dx^\mu dx^\nu + dy^2,
$
Where $\sigma$ is called a dilaton field , $\mu,\nu=0, 1, 2,3$, and $y$ ...
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$n$-dimensional Gauss Law and Dirac Delta [duplicate]
I was searching for a fundamental proof of Gauss Law using the divergence of the electric field. In three dimensions the divergence of $\hat{r}/r^2$ evaluates to 0. So a book I was reading said that ...
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How to "naively" calculate the vacuum energy density in a $4 + d$ spacetime?
The "naive" calculation of the vacuum energy density in flat 4D spacetime is resumed by the following divergent integral (I'm considering only free massless fields):
$$\tag{1}
\rho_{\text{...
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The relationship between dimensionality and space [duplicate]
The number dimensions defined by new theories keep going up. Is there a limit as to how many dimensions the universe can have?
Weird question. The curse of dimensionality in computer science ...
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Trying to get a metric like $ds^2 = -e^{2H_0t} dt^2 + dx^2$ from a higher dimensional Minkowski spacetime
Since the 4D de Sitter spacetime can be found by slicing up a 5D Minkowski spacetime:
de Sitter space from generalized Minkowski spacetime
resulting in a metric like:
$ds^2 = - dt^2 + e^{2H_0t} dx^2$
...
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Dimensionality of system vs dimensionality of space time
Suppose we work in GR, then space time is four dimensions, but, if we have a mechanical system with a high number of degree of freedoms, say five then how would we fit it into a four dimensional space ...
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$\gamma_5$ in non-integer dimension $D$
I need to calculate a trace containing a single $\gamma_5$ in $D$ dimensions.
The trace is given by
$$\displaylines{
\text{Tr}\bigg[ \gamma^{\alpha\tau\eta} (p_1-p_2)_\tau (p_1)_\eta \left(\gamma\cdot ...
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Which dimensions do self-dual even Lorentzian lattice exists?
I am reading page 499 of Peter West's Introduction to Strings and Branes where he stated 'Self-dual even Lorentzian lattices only exist in dimensions $8n+2$, $n=1,2,...$, the simplest such lattice is ...
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What is the dimension of an Instanton?
My thought process about this question was this:
A point particle couples to a $p=1$-Form field and is itself $p-1=0$-dimensional.
A string couples to a $p=2$-Form field an is $p-1=1$ dimensional.
An ...
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Rigorously, what is the permutation operation in Quantum Mechanics?
I am an undergraduate wanting to understand anyons (in order to understand topological quantum computing). The foundational observation upon which the existence of anyons rests seems to be that the ...
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Dimensionality problem in special relativity
Suppose $A$ is a null $4$-vector in Minkowski space-time, $M$. Then the vector space spanned by $A$: $\operatorname{span}(A)$ is unidimensional. The orthogonal complement of this vector space $\...
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Asymptotic freedom of the $\phi^4$ theory depending on spacetime dimensions?
I heard that $\phi^4$ theory in $4-$dimensions is NOT asymptotically free.
But in lower dimensions like $2$ and $3$, it is said to be asymptotically free.
However, what confuses me is that in $3-$...
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Is this statement accurate: We are 4D beings (l,w,d,t) with the ability to visualize in 3D (using our brain) and see in 2D (using our retinas)? [closed]
I've read conflicting information on us being 4D beings (length, width, depth, time) and in what dimension we are able to see. Interested to hear your thoughts, especially if you provide sources.
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Why is non-abelian gauge theory unique in 4 dimensional spacetime?
On my QFT lecture note there is a comment that says 'Non-abelian gauge theory is extremely unique in 4-dimensional spacetime'. However, I didn't really catch what that means. Why is it extremely ...
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Why does the inhomogenous wave equation solution change form with a different number of spatial dimensions?
Assume $c = 1$ for what follows.
For the general inhomogenous wave equation in one spatial dimension $$\left(\frac{\partial^2}{\partial t^2} - \frac{\partial^2}{\partial x^2}\right)\phi = v(x, t),$$ ...
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1+1D simple vacuum EFE solution
Can there be any solutions for simple vacuum Einstein Field Equations in 1+1D (1 space and 1 time dimension) i.e $R_{\mu\nu} = 0$ except for flat space?
I tried different combinations of random ...
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Newton's approximation of 2+1D gravity
I learnt that the curvature tensor in 2+1D spacetime is zero in vacuum. How is it possible to come from there to the Newton's theory in 2D + time, where I guess, the gravitational force law is still ...
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Do the "extra dimensions" in string theory have equivalent physical value to regular dimensions?
I've seen hyperspace dimensions being discussed in models for superstring theory, where there are 6-7 hyperspace dimensions iirc. But the explanation as to why we don't perceive these extra dimensions ...
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Dimension of a vector space of all tensors of rank $(k,l)$ in 4D
Dual vector space is the set of all linear functionals defined on a given vector space. The vector space and dual vector space is isomorphic and hence have the same dimension. A rank $(k,l)$ tensor is ...
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In the fibre bundle description of gauge theories, what is actually the difference between dimension of spacetime and dimensionality of the bundle? [closed]
Please pardon me if my words are not rigorous mathematically, but I hope you understand what i mean.
In the fibre bundle description of gauge theories, what is actually the difference between ...
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Where do I fail, trying to adapt Gauss law in 2D? [duplicate]
So I went through the Khan Academy tutorial on divergence and flux calculations for an area C encircled by a parametric function $s(t)$.
Here $C$ will be a circle with a radius $r$, centered by a ...
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Mermin-Wagner theorem for curved spaces?
i'm searching for the Mermin-Wagner theorem formulation for negative curvature surfaces. Something like that exist?
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What does it mean to have a zero-dimensional induced metric?
I have an integral on the form
\begin{equation}
S=\int d^dx g_{\mu \nu} h^{ab}.
\end{equation}
In this example, $g_{ab}$ is a $d$-dimensional metric, $h_{ab}$ is an co-dim 2 induced metric. I wanted ...
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Normalization of zero point energy in string theory
Following Joe Polchinski’s Little Book of String, page 12, he use the sum $$1+2+3+...=-1/12$$ to find the zero point energy of the bosonic string (and later used the result to argue that we must have ...
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What is the definition of a dimension? [duplicate]
We live in a 3-dimensional world with time, but what even is a dimension? I've often heard that anything can be a dimension because the math works either way. If this was true then why is finding the ...
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Small and large extra dimension(s) of the physical space
Trying to make sense of small and large extra dimension(s) of phyiscal space in a simple intuitive example.
Consider a two dimensional manifold like $\mathbb{R}^2$ and we are trying to add a small and ...
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What is the nonrelativistic limit of the Einstein field equations in arbitrary dimensions?
A standard exercise in essentially any introductory textbook on general relativity is to work out the non-relativistic limit of the 3+1D Einstein field equations. This is most commonly done in order ...
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Why must the stress-energy tensor be traceless in 2D classical general relativity?
It's easy to show that the Einstein tensor is always traceless in 1+1 spacetime dimensions; this is just a simple algebraic identity that follows directly from the definitions. The Einstein field ...
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How are poles and equators geometrically defined in a 3D matrix (curved space) that is a part of a 4D matrix (hyperspace)?
Our planet's surface is a curved 2D that has an infinite number of equators although we chose just one for vital geom. orientation purposes. Every of those equators has its 2 conjugate poles that can ...
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Why don't the extra compact dimensions collapse on themselves?
Why are the extra compact dimensions stable and do not collapse?
I know the anomaly cancellation is the reason why the extra dimensions are necessary.
But I can not visulize how the anomaly ...
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Would quantum gravity be renormalized if the number of spacetime dimensions decreased at small distances?
In the discussion below (bottom of page on link) if the number of dimensions of spacetime d was lower than 3 at small distances would a theory of quantum gravity be renormalizable? Is is possible that ...
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Would 2d or 1d spacetime allow a renormalized theory of quantum gravity? [duplicate]
In the discussion below (bottom of page on link) if the number of dimensions of spacetime d was lower than 3 at small distances would a theory of quantum gravity be renormalizable? Is is possible that ...
user353451
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Where can I find a real representation for 8 dimensional gamma matrices?
I understand that gamma matrices can be real in $d = 8$ and with Euclidean signature, with minimal dimension $16\times16$. Does anybody know where I can find such a representation explicitly written?