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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Mechanics/Statics: How to decide which statics problem can be modeled/solved in 2D or 3D? What are the steps to identify the dimension?
I am a first year mechanical engineering student. In statics we learn to solve/model different problems (free body diagram, sum of forces in $x/y$ etc...) in 2D and in 3D. But how to think about 2D? ...
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Action formalism of braneworld gravity and effective field equation on the brane
Is it possible to derive the effective gravitational field equation on the brane by simply varying the action?
Context: The popular way to derive that equation is by starting from Einstein's field ...
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How many base measurements are there? [closed]
Base understanding:
Given an n-dimension array a(x1, x2 ... xn), where each given dimension x is an 1-dimensional array in the set R.
The data populating x must be non-redundant measurement of reality....
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How many base dimensions are there? [closed]
Let's imagine we have a 1-dimensional line. (This means a flat, straight line). There are electromagnets lying on it. They are like special rocks that can stick to each other and some metals. How ...
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Tensor densities in 1 dimensional space
When we consider a 1 dimensional manifold, is a scalar density with weight (-1) the same as a covector?
In particular, in a theory of gravity, if we consider $\sqrt{-g}$, with $g=\det(g_{\mu \nu})$, ...
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The Lebesgue covering dimension of the Cosmic String interval topology
Take the spacetime $(M,g)$ that satisfies Einstein's Field Equations exactly where $g$ is locally:
$$g= - c^2 dt^2 + d \rho^2 + (\kappa^2 \rho^2 - a^2) d \phi^2 - 2 ac d\phi dt + dz^2 \ $$
in the ...
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How small can we measure space? [closed]
I got this question after looking into transcendental numbers and I noticed how there are some distinctions that should be made from numbers and reality especially in measurement of length for example ...
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3D manifestation of a higher dimensional object
The starting points of this theorical exploration are the following.
I do believe we exist in a universe where 10 (or 11) dimensions do exist, but the ones beyond 3 spatial + 1 time are compactified.
...
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1
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Scalar spherical harmonics in $S_n$
In the Kaluza klein reduction we can "decompose" the spacetime $M_n$ as $M_n = M_4 \otimes K_d$, in which $K_d$ is a compact spacetime. So, functions like a scalar $\phi(x,y)$ can be ...
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Why is $\epsilon$ at most quadratic in CFT with $d\geq 3$? [duplicate]
I am trying to read through these notes on CFT, and author reaches a point in chapter $2$ saying:
$$\Big(\eta_{\mu\nu}\square + (d-2)\partial_{\mu}\partial_{\nu}\Big)(\partial\cdot\epsilon) = 0\tag{2....
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How many null directions are there?
The metric signature of spacetime is usually given as ($3,1$), but spaces can also be ($3,n,1$). Null surfaces include photons and event horizons, which exist, so is $n$ actually $ > 1$ in the ...
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Understanding 4D Gauge Fields in Compactified String Theory
Question:
I have a conceptual question regarding $4$-dimensional compactifications in string theory. For example, if we consider flat $10$-dimensional space with D$6$-branes, we obtain $7$-dimensional ...
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On dimensions as a concept [duplicate]
really naive question here, i don't know anything about physics, in a professional sense.
Light is a electromagnetic wave, and itself requires 3 dimensions to propagate, then how can a one-dimensional ...
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Dirac equation: Green's function specified for only one dimension
Normally, the Dirac equation for the Green's function reads:
$$(i\gamma^\mu\partial_\mu - m)S_F(x,y) = \delta^{(4)}(x-y)$$
Is it possible to define a Green's function describing the propagation ...
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What is the problem with two time dimensions? [duplicate]
I am reading a book "General relativity: The theoretical minimum" by Leonard Suskind.
In page 168-169, the author explains the reason why we don't consider the case with two time dimensions ...
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Still having trouble understanding gravitational lensing [duplicate]
The normal diagram used to explain gravitational lensing shows a two-dimensional plane that is deflected by a heavy weight. This is a two dimensional description that requires an extra dimension to ...
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How to show causality for a Klein-Gordon field in 1+1 dimensions using field commutators?
For a non-interacting massive scalar field $\phi$
in an $n+1$ dimensional minkowskian spacetime,
the field commutator between two event points is
$$
[\phi(x),\phi(y)] = \int
\frac{\mathrm{d}^n p}{(...
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2
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Rotational states in higher dimensions: multiple magnetic quantum numbers
In 4 dimensions, arbitrary rotations are usually double rotations (rotations which can be understood as happening independently on two different planes with different rotation angles). It certainly ...
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Magnets in 2 Spatial Dimensions?
In 2+1 dimensions of spacetime, the electromagnetic field is made up of a vector electric field and a scalar magnetic field. At each point in space, there is a magnetic field value, which we can ...
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Centre of mass of particles in different dimensions
Can we find the centre of mass of a particle in 4 dimensions?
Can we find it in more than four dimensions?
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What's the Newtonian potential in 2+1 gravity?
I understand that there are no propagating degrees of freedom (i.e. gravitational waves) in 2+1 dimensions. There are a couple of arguments to show this. One is to count degrees of freedom of general ...
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Why consider more than 3 dimensions in the Ising model? [duplicate]
Are there real-world physical systems to which higher dimensional ($d>3$) Ising models correspond?
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Extension of a pattern from electrostatics into more than 3 dimensions [duplicate]
I am taking an introductory physics course, and the chapter we are on is about electrostatics.
One section of our textbook has talked about the electric field generated by a charged object that is ...
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Do we live in a 4-dimensional space, i.e. a 5-dimensional spacetime? [duplicate]
As far as we know:
If two one-dimensional lines are placed parallel, they need to be on a two-dimensional plane.
If two 2-dimensional planes are placed parallel, they need to be in a 3-dimensional ...
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0
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What is special about conformal field theory in 2d? [duplicate]
In the most of textbooks about CFT, the special case of 2d is noticed in which complex coordinates play important role and it reads some results like the conformal transformation of energy-momentum ...
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How many independent equations do Maxwell's equations represent in arbitrary dimensions?
In an arbitrary number of spacetime dimensions $D$, Maxwell's equations are
\begin{align*}
\mathrm{d}F &= 0, \\
\mathrm{d}(\star F) &= -J.
\end{align*}
How many independent equations does this ...
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Is there any explicit theoretical application of Brouwer's Topological Invariance of Dimension theorem?
I'm interested in applications of Brouwer's Topological Invariance of Dimension theorem. I study mathematics but know very little about physics, but I imagined that the Invariance of Dimension theorem ...
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Higher dimension observer
In Quantum Mechanics (double slit electron experiment) a third dimension observer could only see two kinds of patterns in a screen:
-Two lines behind each slit if one chooses know the electron ...
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What exactly are the Differential Forms in Maxwell's Equations? [duplicate]
While trying to understand Maxwell's equations (having learned a bit about manifolds) I encounter the following issue:
Gauss' Law seems to integrate the electric field $E$ over a $2$-manifold, ...
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What's the definition of spin for a particle in $d$-dimensional Minkowski spacetime?
Consider a relativistic quantum theory in d-dimensional flat spacetime. Neglecting possible internal symmetries, a particle is defined as a system whose Hilbert space furnishes the support of an ...
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Is there an "escape velocity" for closed dimensions? [closed]
Assuming a closed universe, the shape of the universe is often considered, or at least presented in pop science, to be a glome (4-sphere), and popularly depicted as behaving analogously to a 3-sphere, ...
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What is the minimal count of dimensions in which our curved 3D space can be embedded into? [duplicate]
As I know, GR does not need to assume anything about a >3D space, where our 3+1 spacetime can be embedded into. However, I think the curved 3D space (more clearly, the spacelike cuts of the 3+1D ...
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Why does a degree of freedom vanish from 3D to 2D in that tensor construction?
Let's assume an arbitrary tensor in 3D coordinates: $g_{ij} $ with $i, j$ in $[1,3]$.
It shall be arbitrary, meaning not symmetric.
It has 9 entries which equals 9 degrees of freedom (dof).
Now, I ...
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What is the angle of gravity? [duplicate]
Let's have two objects touching each other, i.e. me standing on the earth. We propel the smaller object directly away from the larger, i.e. I jump. The objects move apart, slow down and then return ...
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Similar to how there's field lines that make equations in Newtonian Gravity more intuitive, is there something that makes GR equations more intuitive?
One way I know to get intuition for the derivation of the force equation $$F=\frac{GM_1M_2}{r^2}$$ in Newtonian Mechanics is to imagine gravitational field lines, in combination with certain ...
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Why can't the metric have more than one timelike coordinate? [duplicate]
In one of his lectures, L Susskind stated that he cannot make sense of a metric with more than one timelike dimension. I also have trouble imagining it, but is there a good mathematical or physical ...
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Is time the fourth spatial dimension? [closed]
Pretty coincidental that time happens to be like the three spatial dimensions.. or is it?
Time is one dimensional with past and future, similar to left and right, up and down, back and forward of the ...
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Is the Christoffel connection in 2D a total derivative?
Can someone comment on my following calculation? Consider the 2D metric $\sigma^{ab}$ and its associated Christoffel connection
$$\Gamma^{a}_{bc} = \frac{1}{2}\sigma^{ap}(\partial_b\sigma_{pc}+\...
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Schwarzschild AdS Black Hole
Why do we study the five dimensional Schwarzschild AdS Black Hole in AdS/CFT? Does it have to do with the symmetries that these theories have?
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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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