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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1answer
2k views

Why is quantum mechanics called 0+1 dimensional QFT?

I know that quantum mechanics is sometimes called 0+1 dimensional quantum field theory. What is the meaning? How should we understand it?
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3answers
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If I say time is the fourth dimension am I wrong?

As far as I know the prevailing view is that time is the fourth dimension, but I've read there is also a spatial fourth dimension and even higher spatial dimensions after that so I hesitate to say ...
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1answer
54 views

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 ...
2
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0answers
234 views

The Lorentz group in three dimensions; Parity operator?

In three dimensions the Lorentz group is defined as \begin{align} \text{O}(2,1)=\{\Lambda\in\text{GL}(3,\mathbb{R}),~~~ \eta=\Lambda^T\eta\Lambda,~~~ \text{det}(\Lambda)=\pm 1\},~~~\eta=\begin{...
6
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1answer
219 views

Is Yang-Mills theory confining in any dimensions?

What is the current understanding of Yang-Mills theory (pure non-Abelian gauge theory without matter field) in the infrared limit? (To avoid the subtlety of renormalizability, we may restrict our ...
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2answers
158 views

Radial direction is one dimensional or two?

When students were asked a question, give example for one dimensional physical quantity, a student writes radial acceleration. He argues that in polar coordinates, just with $r$ one can give the ...
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2answers
100 views

How to visualize multi-dimensions in topological periodic table?

This is a question for those who are familiar with topological periodic table. The first row and right side columns represents dimensions of topological materials in periodic table. I know that for ...
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1answer
194 views

1D or 2D crystal?

If I have a 2D ladder of atoms, can I desribe it with two primitive vectors $a_1=a(1,0)$ , $a_2=a(0,1)$, or do I need to desribe it using only one primitve vector $a_1=a(1,0)$ and basis: $b_1=(0,0)$, $...
0
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1answer
57 views

Field equation of electromagnetics for (1+1)-dimensional spacetime

I am a computational mathematician currently working on space-time finite element approximations to PDEs. I am reducing our model equations from (3+1)D to (1+1)D to test our algorithms. Can we use ...
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2answers
207 views

Is curl of a vector a scalar quantity in 2 spatial dimensions? If it is so, then somebody help me understanding Maxwell's equations in 2+1 D

I have seen on wikipedia that in 2 spatial dimensions, Green's theorem, Gauss's divergence and Stokes theorems are equivalent and it makes sense. When I tried to write Maxwell's equations in 2+1 ...
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3answers
504 views

How many dimensions are there in the electric field?

I am not a physicist. I am buying some polariser for my camera. Circular polariser intrigues me. Basically you pass light through a linear polariser, then through a waveplate, you get circular ...
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1answer
41 views

Is there a sensible way to model a long-range, lower-dimensional force?

For example, in our universe, gravity and electromagnetism obey an inverse-square law due to the dimensionality of space; in higher dimensions, they would drop off faster (with the consequence that ...
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1answer
60 views

Can laws of physics work in a realm without space and time? [closed]

I think this question is a lot philosophical. However, i am asking it out of curiosity. Every physics equation that i have come across has the component representing space or time in it. Don't bash me ...
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2answers
147 views

Is there an analogue of Maxwell's equations in $2+2$ dimensions?

I'm quite familiar with Maxwell's equations in the context of real Lorentzian manifolds in $1+2$ and $1+3$ dimensions. But then is there an analogue of Maxwell's equations in $2+2$ dimensions? How ...
0
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2answers
583 views

Should black holes be considered two-dimensional or three-dimensional?

Should a black hole be considered two-dimensional or three-dimensional? It means that a black hole doesn't occupy space, but interacts with it. Or it actually occupies space, and still interacts with ...
1
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1answer
57 views

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 $AdS_4$?
2
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1answer
122 views

Why did Kaluza need to invent a new theory to unify general relativity and electromagnetism?

Wikipedia (and many other sources) say that by extending the number of spacetime dimensions from four to five, Kaluza–Klein theory unifies general relativity and electromagnetism into a single theory. ...
8
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0answers
376 views

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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0answers
265 views

Levi-Civita in 4 dimensions to 3 dimensions

i was calculating Pauli ljubanski vector in the case of massive particles . considering the rest frame(m,0,0,0) $W_i =-(m/2)\epsilon_{0ijk} M^{jk}$. I got $\epsilon_{0ijk}=\epsilon_{ijk}$. so, $W_i=-...
4
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2answers
395 views

Why are extra timelike dimensions seldom considered? [duplicate]

There are a number of models (String theory, Cascading Gravity, Emergent Dimensions) that contain extra space like dimensions. Why do people tend to avoid considering extra timelike dimensions? The ...
5
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1answer
177 views

Does string theory give any values for the predicted “leakage” of gravity into extra spatial dimensions?

Sorry if this is a duplicate. I have read that string theory has a good explanation for the "hierarchy" problem of the force strength disparity between the fundamental forces because as gravity ...
12
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2answers
435 views

$2+1$-dimensional Einstein gravity is topological and only non-trivial globally

$2+1$-dimensional Einstein gravity has no local degrees of freedom. This can be proved in two different ways: In $D$-dimensional spacetime, a symmetric metric tensor appears to have $\frac{D(D+1)}{2}$...
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Metre Definition from speed of light [duplicate]

Why is 1 metre defined as the distance travelled by light in 1/299792458 seconds rather than 1/300000000 seconds?
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2answers
196 views

Can someone explain the basics of Kaluza-Klein Theory (with as minimal math as possible) and why it was discredited?

Most of what I know about Kaluza-Klein Theory comes from a book I read a while back by Brian Greene called "The Elegant Universe". What he said was that Kaluza had figured out a way to incorporate a ...
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2answers
110 views

Things in 2D world, i.e. a world with 2 spatial dimensions [closed]

There are many question about life and physics in higher dimensions. but is there any physical thing (i mean things like force, momentum, speed,...) that cannot exist in 2D world? could 2D world have ...
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0answers
35 views

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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3answers
168 views

Large $D$ limit of (Anti) de Sitter Space is Minkowskian Space?

As is well known, the solution of the vacuum Einstein equations with a non-zero cosmological constant, $G_{\mu\nu}+\Lambda g_{\mu\nu}=0$, is an asymptotically (anti) de Sitter space based on the sign ...
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1answer
55 views

Why was there a need of defining spatial dimensions more than 3? [duplicate]

3 dimensional universe looks like the limit for me. I can't even imagine a fourth dimension, and there are physicists talking of 11 dimensional spacetime. There are even mathematical generalisations ...
9
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1answer
358 views

Any nice interpretation of differentiating $j(j+1)$ to get $2j+1$?

If $j$ is a continuous variable, then differentiating the function $f(j)=j(j+1)$ with respect to $j$ gives $f'(j)=2j+1$. Of course I've chosen the letter to evoke quantum mechanical angular momentum, ...
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0answers
132 views

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). ...
28
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2answers
2k views

Basis for the Generalization of Physics to a Different Number of Dimensions

I am reading this really interesting book by Zwiebach called "A First Course in String Theory". Therein, he generalizes the laws of electrodynamics to the cases where dimensions are not 3+1. It's an ...
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4answers
289 views

In Einstein's General Relativity, do the space-time dimensions curve?

In Einstein's General Relativity, do the space-time dimensions curve according to the positions of stars, planets, and masses?
3
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1answer
195 views

Are there superconformal field theories in 10D?

I've heard that there is a belief that interacting conformal field theories do not exist in dimensions greater than 6, and in 6D the only known nontrivial CFTs are superconformal field theories. What ...
2
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0answers
147 views

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 ...
6
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4answers
336 views

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 ...
0
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2answers
266 views

How to think of acceleration vectors

I understand: How average/instantaneous acceleration works for 1D-motion Velocity vectors But I don't understand the concept of acceleration for 2D-motion. What does the vector subtraction $\Delta \...
8
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1answer
195 views

Only vacuum is possible in the large $D$ limit of General Relativity?

The Einstein equations with a cosmological constant $\Lambda$ read as: $R_{{\mu}{\nu}}-\dfrac{1}{2}Rg_{{\mu}{\nu}} + \Lambda g_{{\mu}{\nu}} =8\pi T_{{\mu}{\nu}}$ Therefore, $R-\dfrac{D}{2}R+D\...
0
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3answers
80 views

Query regarding bent space-time in General Relativity [duplicate]

I am just a beginner in this topic and I accept I haven't gone through whole of the content of GR. However after going through some of the basic ideas, I encountered a problem. If I did my homework ...
7
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4answers
262 views

How could we know that the relativistic curvature of universe is intrinsic?

General relativity tells us that the universe is bent by gravity, but this curvature is intrinsic to the universe (the universe bends, but not in a fourth spatial dimension, the universe having only ...
3
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4answers
344 views

In string theory why are the “extra” dimensions super-compact?

Is the only reason the "extra" dimensions of string theory are considered to be super-compact, so we can avoid dealing with the question "why can't we experience them?"?
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2answers
129 views

Dimension of an equipotential surface

How many dimensions has an equipotential surface? My book says it has $3$ dimensions but I think it has $2$ dimensions because a plane is an object of dimension $2$ as well. From linear algebra, I ...
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0answers
164 views

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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1answer
84 views

Does nature have more than four dimensions? [duplicate]

Does nature have more than four spacetime dimensions? If so, what is their size? Are dimensions a fundamental property of the universe or an emergent result of other physical laws? Can we ...
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0answers
47 views

Inverse square laws & dimensionality [duplicate]

I have been thinking about the famous Inverse square-laws and how they came out to be that way. Gauss's law elegantly describes the square law for electricity to spherical distribution. Now I am ...
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1answer
130 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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3answers
334 views

How would Newtonian gravity work in a 1-dimensional universe?

I have come across the idea of gravity in different dimensional space. From the standard formula for gravity $F=\frac{GMm}{r^2}$ I have found that the $1/r^2$ term is a result of a three dimensional ...
0
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1answer
362 views

Dimensions of a tensor product space

Susskind, in his 'Theoretical Minimum' book about QM says that given two 2-dimensional spaces, the product state of two vectors, one from each space, is determined by four real parameters. But, he ...
2
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1answer
178 views

Why a 3D Universe?

The universe as it stands is perceived by us to be 3 dimensional. Why is it that the universe formed into 3D space and not 4D or 5D space for example?
2
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2answers
293 views

The inverse square law [duplicate]

Why the nature has chosen the inverse square law. For instance, the gravitational force as well as the Coulomb force is inversely proportional to the square of distances. Why not these forces are ...
1
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1answer
81 views

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 ...