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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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58 views

Can motion be considered a dimension?

Okay, go easy on me, I’m in no way any kind of physicist, or even a scientist, I graduated High School and that’s it, but I do have a very mechanically based mind, (probably why I wound up a Diesel ...
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Magnetic field “lines” in $D \ne 4$ spacetimes

The electromagnetic field is represented by an antisymetric tensor $F_{ab} = -\, F_{ba}$ (the faraday). In $D = 4$ spacetimes, it has 6 independent componenents: 3 describing the electric field: $F_{...
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4answers
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Can light exist in $2+1$ or $1+1$ spacetime dimensions?

Spacetime of special relativity is frequently illustrated with its spatial part reduced to one or two spatial dimension (with light sector or cone, respectively). Taken literally, is it possible for $...
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Does string theory really associate 6 dimensions to electromagnetism & the nuclear forces?

1) I understand string (superstring) theory often ends up with 10 dimensions, 9 space-like and 1 timelike. Typically I read that these are all associated to space-time. 2) So, I was interested when I ...
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Could dark matter actually be matter which resides in a different spatial dimension? [closed]

I have at best a rudimentary understanding of the math in this side of physics, so bear with me. I am also aware of this question, but it was asked and answered 4 years ago and I don't want to ...
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1answer
87 views

Can a “time dimension” be part of a spherical topology?

I've heard it speculated that the spatial dimensions of the universe is a 3-sphere. Or a 3-torus. But usually, I guess, it's assumed that the "time" dimension just has its own geometry, like a line, ...
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1answer
333 views

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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1answer
81 views

Bending light by warping space? [closed]

If I ask what is space, space is purely a mathematical abstraction, an area described by a set of dimensions defined with numbers, space is devoid and has no physical properties what so ever, ...
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48 views

Critical dimension from the symmetries of the string action

(Related: This post and this post.) In this thesis it is said (on page 13) that just by assuming that we have some general action with the same symmetries as the Polyakov action (Poincare invariance, ...
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2answers
385 views

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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1answer
42 views

Counting independent components of the Riemann curvature tensor

In 4D spacetime, we may choose a locally inertial frame at point P, that is we always have a transformation such that $g_{{\mu'}{\nu'}}(P) = \eta_{{\mu'}{\nu'}}$ and its first derivatives vanish. ...
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2answers
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Vanishing of the Ricci tensor in higher spacetime dimensions

I understand how, if the Riemann tensor is 0 in all its components, since we construct the Ricci tensor by contracting the Riemann, Ricci tensor would be 0 in all components as well. I've read that ...
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10answers
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Is the “spacetime” the same thing as the mathematical 4th dimension?

Is the "spacetime" the same thing as the mathematical 4th dimension? We often say that time is the fourth dimension, but I am wondering if it's means that time is like the fourth geometrical axis, or ...
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How to explain (pedagogically) why there is 4 spacetime dimensions while we see only the 3 spatial dimesions?

I have been asked this question by a student, but I was able and in the same time incapable to give a good answer for this without equations, so do you have ideas how one can explain this in a simple ...
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Count degrees of freedom of gauge tensors

For degrees of freedom (dof) it is said that spin-1 massless boson like photon has 2 dof in 4d, like U(1) gauge theory. it is said that spin-2 massless boson like photon has 2 dof in 4d, like ...
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4answers
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Is a shadow 2D?

I had always thought anything below third dimensions couldn't exist in our 3rd-dimensional world. Correct me if I'm wrong but anything 0d 1d or 2d is massless and also can't have energy so it just can'...
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Gravity in a spacetime with 2 indistinguishable dimensions, with all spacetime directions equivalent

A spacetime with 2 indistinguishable dimensions and all spacetime directions equivalent would have the signature (++) meaning that there would be no difference between spacelike and timelike ...
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1answer
160 views

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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1answer
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How do we know the laws of physics remain the same in different dimensions?

Section on Wikipedia dealing with the possibility of different dimensions. When reading this section it feels like there's a giant elephant in the room that is not addressed. For example, here's a ...
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3answers
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When exactly is a dimension spatial?

I every so often hear claims like: M-Theory predicts that there are 10 spatial dimensions! Now I'm not really sure what these claims mean. There are three spatial dimensions that I normally ...
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2answers
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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 ...
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1answer
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Should the 4D normalization constant $8\pi$ in Einstein field equations (EFE) be changed to $(n-2)S_{n-2}$ in other spacetime dimensions?

Should the 4D normalization constant $8\pi$ in Einstein field equations (EFE) be changed to $(n-2)S_{n-2}$, where $S_{n-2}$ denotes the area of a $n-2$-sphere, in higher dimensions? The reason is that ...
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1answer
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If there exists a universe with other than 3+1 dimensions, could we quantum tunnel to it?

Section of Wikipedia article on the possibility of universes with space & time dimensions other than 3 and 1 respectively. If one of these other universes exist, could we in principle quantum ...
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1answer
67 views

What exactly is dimension?

In class 11th, I studied in first chapter of physics (that is unit and measurement) that dimension is an expression of a physical quantity in terms of fundamental quantity. But immediately in second ...
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How exactly do superstrings reduce the number of dimensions in bosonic string theory from 26 to 10 and remove the tachyons?

In bosonic string theory, to obtain the photon as the first excited state, the ground state must have a negative mass (tachyon). By applying $1 + 2 + 3 + \cdots = -1/12$, it can be shown (in a ...
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Intuitive way to get 10 dimensions in string theory?

To get the 26 dimensions is sort of intuitive (in a handwavey sort of way). Basically we solve: $$(D-2)\frac{1}{2}(1+2+3+4+...)=-1$$ Where $1+2+3+..$ times $\frac{1}{2}\hbar$ are the ground energy ...
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1answer
76 views

Is there a cosmological constant $\Lambda$ in 2D?

It is well known that the Einstein tensor is trivially 0 in any two dimensions spacetime: \begin{equation}\tag{1} G_{\mu \nu}^{(2)} \equiv 0. \end{equation} Thus, it is not possible to formulate the ...
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Standard References for 5d or 6d SUSY theories?

I'd like to learn more about them, but I need a text that I know is worth reading to start!
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2answers
108 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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2answers
107 views

Why time is 4th dimension not 1st? [closed]

Yeah we can not define a line without a point but why time is not 1st. Also time exist in 1st dimension as well doesn't it?
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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
87 views

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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1answer
55 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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1answer
137 views

Is there a negative dimensional object similar to a black hole / singularity?

My view of negative dimensional objects is one where different objects are all stacked up one on top of the other within the same co-ordinates. Multiple objects may occupy the same space in negative ...
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1answer
144 views

Is the center of the universe in another dimension?

If we live in a four dimensional world and when we try to find the center of the universe (where the big bang occured) we found that there is no apparent center, could that means that the big bang ...
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1answer
122 views

Locally accessible dimensions of configuration space

I am reading a book called "Structure and Interpretation of Classical Mechanics" by MIT Press.While discussing configuration space and degrees of freedom,the authors remark the following: Strictly ...
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1answer
128 views

Could an holographic universe consist of 3d embedded in 4d instead of 3d embedded in 2d?

In the holographic model, information about a given dimension can be embedded in a lower dimension, so our 3d universe could be considered as a 2d one. Could it happen the other way? I mean, could the ...
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1answer
154 views

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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1answer
161 views

How to define *dynamical* dimensions?

I'm considering a simple toy model. The spacetime is flat with $d$ space dimensions. Using cartesian coordinates, the spacetime metric is Minkowskian : $$\tag{1} ds^2 = dt^2 - dx_1^2 - dx_2^2 - dx_3^...
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Has the concept of non-integer $(n+m)$-dimensional spacetime ever been investigated by theoretical physicists?

The following image serves to aid the reader in understanding the "privileged character" of $3+1$-spacetime. The wikipedia article on spacetime, and the sub-article "The priveleged character of $3+1$-...
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0answers
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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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1answer
140 views

Spacetime Of Flatland

I'm trying to really get the intuition of spacetime. This video explains how Minkoswki was the first to think that maybe our universe does not consist of a 3d space which evolves in time, but ...
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1answer
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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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1answer
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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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1answer
123 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? ...
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Does the derivation of the Lorentz transformation depend on space having at least two spatial dimensions?

Eisberg's 'Fundamentals of Modern Physics' derives the space contraction formula from a mirror experiment in which A reflects a light beam in a direction perpendicular to the motion of B, both ...
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1answer
270 views

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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46 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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0answers
45 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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1answer
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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 ...