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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What does QCD look like in higher dimensions?

It was pointed out as a comment on my question on atomic physics in higher dimensions that that question implicitly rests on an assumption that QCD, and thus the structure of atomic nuclei, is pretty ...
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Plum-pudding atomic physics in higher dimensions?

It is established that "normal" electron orbitals are not stable in more than 3 spatial dimensions, as the available energy levels become unbounded from below. However, this result only applies given ...
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1answer
48 views

Dark matter's effect in 2+1 GR?

In the appendix to The Planiverse, it is acknowledged that GR in 2 dimensional space implies no gravitational forces between separated masses--only in the interior of extended massive bodies. The ...
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31 views

Why are we in 3 spatial dimensions? [duplicate]

I am very curious to find if there is any reason that why are we in 3 dimensions not in any other like 1D would be hard almost impossible but 2D could have been possible, or what about 4D or in ...
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Conversion of the nonlinear schrodinger equation from $\partial_zE$ to $\partial_tE$

While reading some papers about the nonlinear schrodinger equation (NLS) I noticed that the authors sometimes use (for the linear case) $$\partial_zE=\frac{i}{2k_0}\nabla^2E$$ and sometimes $$\...
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Does the CPT theorem hold for all spacetime dimensions?

I can't find any reference which mentions the dependence of the theorem on spacetime dimension, but it would be very interesting to know what if any it has!
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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? ...
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44 views

Does gravity exist in higher dimensions? [duplicate]

I’m very curious to know whether gravity exists in higher dimensions. Because it follows the inverse square law it seems to me that it should be 3D only (just intuition). Is there any mathematical ...
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36 views

longitudinal and transverse components in higher dimensions

I am familiar with the Helmholz decomposition of a vector field in three dimensions: $$\vec{V}=\vec{\nabla}\wedge\vec{A}+\vec{\nabla}\phi$$ But I am interested to show that something similar can be ...
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Dimensional reduction of higher-dimensional Einstein-Hilbert action

I take a spacetime of the form $\mathcal{M}_{d+1}\times \mathbb{S}^n$, with $\mathcal{M}_{d+1}$ some generic non-compact $(d+1)$-dimensional spacetime and $\mathbb{S}^n$ an $n$-dimensional sphere, so ...
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Do particles go into the 4th dimension in 3d waves?

Let's say you create a pulse on a string. The wave moves in 1d(in a straight line) but the particles of the string itself extend into 2 dimensions. The same goes for ripples in water. The wave ...
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Application of Weyl's method in $D$ dimension

I am reading the paper "Shortcuts to high symmetry solutions in gravitational theories" written by Deser and Tekin, http://cds.cern.ch/record/625743/files/0306114.pdf and I am having troubles to ...
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What would it look like to be inside a small space with positive curvature?

Say you're floating in an empty void with a light source. The space you are in has a positive curvature, so going forwards will bring you back to the place you started after about 20 meters. What do ...
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Einstein-Palatini action in $d$-dimensions

The tetradic Einstein-Palatini action can be written as (see, for instance, arXiv:1804.09685) $$S=\epsilon_{IJKL}\int_{\mathcal{M}}e^I\wedge e^J\wedge\Omega^{KL},$$ where $e^I$ are the frame ...
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Would Color Confinement apply in higher dimensions?

As I understand it color confinement comes from the fact that as the distance between two color charges increases the color potential energy increases, instead of decreasing, and the energy needed to ...
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basic question about irrelevance in statements about absorptive and spectral absorptive power

I have read that spectral absorptive power(a...
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2answers
83 views

Finding the dimensions of a spacetime given the Riemann tensor

The question is: For a spacetime the Riemann tensor is given below: $$R_{\mu \nu \rho \sigma} = \frac{R}{6} (g_{\mu \rho} g_{\nu \sigma} - g_{\mu \sigma} g_{ \nu \rho} )$$ What is the dimension of ...
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Extra Dimensions (in String Theory) - What does it mean?

I have been reading a lot about string theory and the necessity of extra dimensions (particularly as visualized in Calabi-Yau spaces), as "curling-ups" in our apparently 3-dimensional (or 4-...
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Observable higher dimensional geometry?

I recently watched a video where in VR someone was manipulating a 4D geometry in 3D space that was changing into all kinds of different shapes as it was moving through space. What i found strange is ...
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Visualizing higher dimension [duplicate]

Why can't we visualize Higher dimensions greater than 3? Is it just because the dimensions doesn't exist (Certainly I know that space-time is four dimensional) or any other physical reasons.
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Is there a higher dimension analogue of Noether's theorem?

So I have recently read the proof of Noether's theorem from the book variation calculus by Gelfand. Basically, what I have already seen is that for any single integral functional, if we have a ...
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1answer
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Interacting conformal field theories in spacetime dimensions higher 6?

Are there any papers which directly tackle the question of whether or not there exists interacting CFTs in spacetime dimensions higher than 6? It has been proven that there do not exist any ...
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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 ...
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Nonrelativistic Quantum Mechanics Results Implying Analogous QFT Results?

One particularly fascinating example of this I have found is the following. The delta function potential has no effect in nonrelativistic quantum mechanics in spatial dimensions greater than or equal ...
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Triviality of Yang Mills in $d>4$?

It has been proved that the $\phi^4$ theory is trivial in spacetime dimensions $d>4$. By trivial I mean that the field $\phi$ is a generalized free field, or in other words, it's only nonzero ...
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Spatial and temporal dimensions orthogonality

It seems that the spatial dimensions are orthogonal: a particle can move along one axis without changing its position in relation to other two axes. It seems that the temporal dimension is somewhat ...
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Time difference between all particles and waves [closed]

Since all elementary particles and waves were created simultaneously in the big-bang (t0) would there be any time difference between any interacting elementary particles and/or waves after t0? I'm ...
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What is the simplest possible explanation of the String Theory? [duplicate]

I was recently reading through 'The Little Book of String Theory' by Steven S. Gubser, and found it too complicated. Now, some people may say that the string theory is meant to be complicated as even ...
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117 views

Relativity in 2+1 or 4+1 dimensions

Whereas we have experience of relativity working with 3 spacial dimensions and one of time would there be similar rules affecting a two dimensional space and one of time or even with a 4 space and 1 ...
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Respect to What Time is Calculated in Space

This may be the silly and stupid question but I have read that time appears to move slower near massive objects because the object's gravitational force bends space-time and the phenomenon is called ...
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Possible extra term in the Gauss-Bonnet Action

Is it possible to add a term like $\epsilon_{\alpha\beta\gamma\delta}R^{\alpha\beta}_{\enspace\mu\nu}R^{\mu\nu\gamma\delta}$ to the Gauss-Bonnet action in higher dimensional theories of gravity? Or ...
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2answers
129 views

Maxwell's equations in differential form in 2-space+1-time dimensions

How does one write maxwell's equation in 2+1 dimensions? It becomes particularly interesting as the components of 2 forms and 1 form are 3. Are there any sources for this?
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Problems with Twistor theory

Penrose developed a theory called "twistor theory" that tries to describe the universe using twistors. (https://en.wikipedia.org/wiki/Twistor_theory) From what I've read, there are a lot of papers ...
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1answer
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Are the “extra dimensions” in string theory universal?

Are the extra (compactified) dimensions from string theory universal, in that any particle/field with a sufficiently small enough wavelength will be able to propagate through them? The reason I want ...
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What would be the Schwarzschild radius of an $n$-dimensional black hole? [duplicate]

The Schwarzschild radius of a 3 spatial dimensional black hole is 2GM/c^2. What would be the Schwarzschild radius of an n dimensional black hole according to Einstein's field equations having n x n ...
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Are there supersymmetry algebras with higher spinor representations?

The super-Poincare algebra contains supersymmetry generators $Q^I$ which satisfy fermionic anticommutation relations. By the higher-dimensional analogue of the spin-statistics theorem, they must ...
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338 views

What is the spin-statistics theorem in higher dimensions?

In $d = 3+1$ dimensions, the spin-statistics theorem states that fermionic particles have half-integer spin and bosonic particles have integer spin, in a well-behaved relativistic quantum field theory....
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What's the difference between internal spaces and extra dimensions?

From a geometrical perspective, we attach a copy of our gauge groups (e.g. $U(1)$ to each point in spacetime. Since Lie groups are manifolds we can, therefore, imagine that there is a little circle, ...
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2answers
75 views

Could we use experimental evidence of micro black holes to prove the existence of additional spatial dimensions?

They are planning to create a new particle accelerator that can smash particles together at a much higher energy than the LHC. If in the process we observe the decay of a micro black hole, would that ...
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23 views

Group velocity in different dimensions

I am given the following equation for the group velocity in one-dimension: $$v_g = \frac{d\omega}{dk}.$$ In solid state physics one has $-\pi/a \leq k \leq \pi/a$ for a one-dimensional lattice with ...
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49 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 ...
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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 ...
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How could we extend Kuramoto Model to Arbitrary Dimensions?

The generalised version of a theory describing synchronisation in an ensemble shows that coherence arises differently depending on whether the number of dimensions is even or odd. But how could you ...
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1answer
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Gamma matrices in (2+1)

I am sure that is very well-known question and see on this site several similar questions but I would like to specify the answer 1) I know that in $(2+1)$-dimensions one can construct $\gamma$-...
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1answer
50 views

Is there a way to separate 2D from 3D? [closed]

When we see object around us in space, we can always interpret those in 2D, by considering them to pass through a plane, its only when we interact with those objects do we realise that it is 3D, is ...
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Bound on large extra dimensions using gravitational waves

Are there proposed observations using gravitational waves which put a bound on the size of large extra dimensions (say in the context of ADD model)? The claim in the ADD paper is that you cannot ...
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Why $\kappa = 8 \pi G$ in $D$ dimensional spacetimes?

Probably another question without an answer! ;-) In most books/papers I saw on General Relativity, everybody writes $\kappa = 8 \pi G_D$ in the right part of Einstein's equation, even for spacetimes ...
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Debye screening in $\mathbb{R^d}$

Consider the Poisson-Boltzmann equation $$ \nabla^2 V(r) = -\frac{1}{\epsilon_0}en\left(1 - e^{e V(r)/k_BT}\right) $$ which models the electrostatic potential in a spherically symmetric ideal gas of ...
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Natural classification of fundamental constants of Nature

I was wondering about the fundamental constants of Nature since several years, and still pondering on them. Of course, I have read a lot of papers on them, but never found any satisfying ...
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What would the periodic table look like in 2 spatial dimensions? [closed]

I looked at this question https://worldbuilding.stackexchange.com/q/13094/, and I think it answers part of my question about how atomic physics would work, but I'm not sure. How many orbitals would ...