# 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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### Link between anomalous dimensions and fractal dimensions

I just realized that anomalous dimensions in quantum/statistical field theory is not that different from fractal dimensions of objects. They both describe how quantitaive objects transform under a ...
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### Double slit - higher dimensions

The double slit experiment is a real-life manifestation of the Huygens principle. As is well-known, this principle depends on whether the number of dimensions is ever or odd; as Evans1 puts it, ...
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### Reference recommendation： QFT in arbitary dimensions $D=1+d$

When I self-study the QFT, I found that many results in textbook heavily rely on the dimension $1+3$. For example, I heard "In 3+1 dim, Majorana fermion cannot have well-defined handedness. But in ...
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### If microscopic dimensions were found in particle experiments, how do we determine whether it is spatial or temporal?

This is not a question asking why our universe is 1T+3D dimensional, and hence not about how the various models such as Itzhak Bars and F theory can incoporate multiple time into a model to describe ...
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### Center of mass/centroid changes between 2D and 3D?

Unless I completely botched the calculation, I noticed something strange: if you find the centroid of a 2d curve, and then revolve the curve around its axis then find the center of mass, the CM is ...
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### Two dimensional spacetime and the Gauss Bonnet theorem

Generally two dimensional spacetimes are deemed to be static, as the Gauss Bonnet theorem implies that the Einstein Hilbert action would be a constant independent of $g$. But as far as I can tell, ...
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### Higher dimensions

1) How we determine whether the higher dimensions are Unstable or Unpredictable? Or on the basis of what assumption we make this prediction? (Source of Image: Max Tegmark. See also this Wikipedia ...
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### 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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### 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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### 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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### 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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### 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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### 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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### How to best describe wave behavior on even dimensions?

Main source: http://www.mathpages.com/home/kmath242/kmath242.htm On this article, as far as I understand, the author claims that wave behavior on even dimensions would give rise to many waves with ...
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### Can a 2D universe be closed?

Consider a universe as a curved 1D line looped onto itself. The second dimension is time. On one hand, this line is easy to visualize as a circle embedded in a flat 2D plane. However, there is only ...
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### Supersymmetry beyond $D=11$ spacetime dimensions

Taking into account the higher spin theories, from which string theory is an effective field theory, I just wondering if there is something to do to extend supersymmetry to any dimension without any ...
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### Multi-temporal theories: why are they no studied as space-like extra dimensions?

Beyond the initial value problem in multi-temporal wave-like equations, the existence of causality problems (we could give up if extra time directions are not too large, I think), or the instability ...
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### Maximum number of dimensions in string/M-theory

M-theory low energy limit is eleven-dimensional supergravity. However I understand that Itzhak Bars and others have been working in generalizations of string theories of 12, 13 and 14 dimensions with ...
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### Compactification of spacetimes always possible?

Consider a metric in a $n+1$ dimensional spacetime given by $$g=\underbrace{g_{tt}(r,t)dt^2 + g_{rt}(r,t)drdt + g_{rr} dr^2}_{g'} +h(t,r,x^A)dx^Adx^B$$ where $h$ is a $n-1$ ...
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### How to extend the notion of pressure to lower dimensional spaces?

Consider the pressure at each point in three dimensional space being given by the scalar function $P(\vec{x})$. By definition, the total force perpendicular to a given surface $S$ in this space due to ...
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### Are there any flow to different dimension?

So far as I know from gauged supergravity there are studies of RG flows from the same dimension. Are there any flow to different dimension, i.e. flow from $AdS_5$ to $AdS_4$?
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### States of equilibrium in an n-sphere

A mass at the center of two points (or a 0-sphere) that is gravitationally attracted to both would be in a state of unstable equilibrium; any disturbance would increase the attraction to one and ...
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### Instability of higher dimensional universes

According to superstring theory, there are at least 10 dimensions in the universe (M-theory actually suggests that there are 11 dimensions to spacetime; bosonic string theories suggest 26 dimensions). ...
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### Dimension of Representation of Majorana Fermions with Euclidean Metric?

It is possible to represent the Dirac matrices in the Majorana basis using $N= 2^{⌊d/2⌋}$-dimensional matrices, as shown here. This source uses a Minkowski metric. It would then be possible to move to ...
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### Space-time dimensions

I was having a look at Seeing the fifth dimension and I was thinking the following. A dot is 0-dimensional entity. A dot "living" in an 1-dimensional world would be a moving dot along a pipe of some ...
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### Can compactified dimensions enlarge and large dimensions compactify in string theory?

In string theory, can six or more dimensions rolled up into high-dimensional compact manifold become large and our 3+1 large dimensions collapse into compact manifold?
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### What relative effects be for object with near light speed velocity in compactified dimensions?

What relative effects be for an object with near light speed velocity in compactified dimensions? Does gravity increase the same as for an object with near light speed velocity in usual spacial ...
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### Does the expansion of the Universe into a higher dimensional space imply that 4D objects are real?

It is my understanding that objects in the Universe are not just getting farther apart but space itself is expanding and so in some real sense, higher-dimensional geometry is "real" -- if so, on a ...
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### QFT decay rates in lower dimensions

My starting point is the decay of a Higgs particle into two fermions, with decay rate proportional to $$\Gamma \propto g_\psi^2 N m,$$ where $g_\psi$ is the coupling, $N$ ...