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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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297 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?
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1answer
219 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 ...
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0answers
154 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 ...
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4answers
393 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 ...
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2answers
296 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 \...
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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\...
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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 ...
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4answers
278 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 ...
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4answers
359 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
137 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
168 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
86 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
49 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
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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3answers
367 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 ...
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1answer
404 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
184 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?
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2answers
306 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 ...
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1answer
82 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 ...
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1answer
172 views

Does spinor formalism work just in four dimensions?

Does spinor formalism work just in four dimensions? I am reading the book "Spinors and space-time" written by Penrose. I didn't understand a statement. Penrose says that besides tensor formalism and ...
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1answer
66 views

How to express 3 dimensional motion in Minkowski space?

We can easily visualize Minkowski space diagrams with 2 spatial coordinates but how to express 3 spatial coordinates?
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0answers
115 views

Clifford Algebra in 3D [duplicate]

Why the gamma matrices are taken 2 by 2 (Pauli matrices) in 3 dimensional Clifford Algebra. As in 4D Clifford Algebra the matrices are 4 by 4, in 3D Algebra why are they not 3 by 3 matrices? The ...
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1answer
199 views

How can there be an eleventh dimension if the tenth is the last? [closed]

So in string theory (or to be precise, F theory) we have an eleven dimensional torus over the ten space dimensions and this torus vibrations give us the supergravity theory. But my question is, when I ...
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1answer
274 views

2d CFT versus higher dimensions

I am starting a reading course this quarter in conformal field theory. Is it necessary to do CFT in 2 dimensions first in order to understand it in 3 or greater dimensions, or would I be able to just ...
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2answers
504 views

Higher dimensional relation between angular momentum, moment of intertia and angular velocity

In 3 dimensions we have the well known relation (summation convention is being used) $$ L_i = I_{ij} \omega_j $$ However, as is well known the angular momentum and angular velocity are not vectors ...
8
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1answer
207 views

Why is the trivial analogous expression for Feynman's checkerboard approach to Dirac's equation in 3+1 dimensions (as described below) not correct?

Feynman's checkerboard approach to Dirac's equation in 1+1 space says that a half spin particle can be assumed to be traveling at speed of light and switching directions only after discrete intervals ...
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2answers
121 views

What are the evidence that gravitational force act across all spatial dimensions?

I keep hearing in the folk theory of physics that gravitational force (if a force it indeed is) will act across parallel universes or higher spatial dimensions. Where did this idea come from? Does it ...
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3answers
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Can electrons be non-fundamental in higher dimensions?

I was wondering, is it necessary that all elementary particles remain elementary in higher dimensions too, or can there be a higher curled dimension (like those in string theory) where an electron, ...
0
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2answers
217 views

How can we be certain our world has only three spatial dimensions? [duplicate]

It's common knowledge that the universe has three spatial dimensions, and one temporal. But how can we be so sure? Physics tells us that vector forces act independently along different dimensions, so ...
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5answers
7k views

How many dimensions does electricity have? [closed]

My six year old daughter asked me this morning, 'how many dimensions does electricity have ?' What would be the best answer bearing in mind the age !?
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1answer
85 views

Wouldn't micro black holes in the atmosphere have noticeable effects?

If there are extra dimensions of space,the force of gravity would (in microscopic distances) increase way more than a factor of 4 times when the distance between masses is halved,which is the case in ...
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1answer
54 views

Is there a connection between Newton's law of universal gravitation and the area of a sphere? [duplicate]

According to Newton, the force between two objects of masses $m$ and $M$ is $$ F = \frac{GmM}{r^2}, $$ where $r$ is the distance between the two objects. Basically, if distance between the object ...
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2answers
132 views

Is general relativity a background dependent theory in five dimensions?

I read the article What is a background-free theory? by John Baez and was wondering that if I add a fifth dimension to a background independent theory like general relativity I get a background ...
2
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1answer
82 views

Is it possible for there to be a spacetime which shares one of our dimensions?

Imagine two 2D spacetimes, one with $x,y$ axes and the other with $x,z$ axes. They share a dimension in common with the x axis. Is it possible that a spacetime which shares at least one dimension with ...
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1answer
115 views

Fourth Dimension- I don't understand this

According to this video at $1.20$, we, humans, perceive objects in $2$ dimensional. He also gave an example with a sphere: "Take a perfect sphere for example... If you're looking at a sphere, it ...
2
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1answer
4k views

Why are there specifically 10, 11, or 26 dimensions in string theory? [duplicate]

I know that current string theories state that there are 10, 11, or 26 spacetime dimensions in superstring theory, M-theory, and bosonic string theory, respectively. But when I looked up why those ...
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1answer
818 views

Do you travel in the 5th dimension? [closed]

If you travel freely through the first 3 dimensions, and you travel in a singular direction through time, how do you travel through the other dimensions, like the 5th?
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3answers
224 views

Do new gravitational effects emerge in higher dimensions?

Effects like gravitational waves and the curvature surrounding black holes do not occur in spacetimes with one time-like coordinate and two space-like coordinates. This is because the Einstein Field ...
2
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1answer
78 views

Zero net charge in two space dimensions?

I recently came across the statement (without further explanation) that the net charge in a two dimensional system has to be zero. Obviously in two dimensions, the electric field $\vec{E}$ due to a ...
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2answers
201 views

Is there any thing composed of elementary particles in this world that is not 3 dimensional? [closed]

Is there any thing composed of elementary particles in this world that is not 3 dimensional? I know that there is graphite which is singular atom thick. Is there anything in this world that has no ...
2
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1answer
3k views

Why is Coulomb's law is an inverse square law? [duplicate]

I read about Coulomb's law it says the force of attraction or repulsion between two charges is inversely proportional to the square of the distance between them. So generally if I say then Coulomb'...
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0answers
78 views

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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1answer
77 views

Why spacetime has 3+1 large dimensions and remaining higher dimensions underwent compactification? Why spacetime hasn't got eg. 5+4 or 3+5 dimensions?

Yesterday I wrote very, very big thread which proved to be too broad, so according to your instructions I divided it. Content is unchanged. I read that it might be related to the phenomenon of ...
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2answers
471 views

Any “connection” between uncountably infinitely many differentiable manifolds of dimension 4 and the spacetime having dimension four?

Self-studying general relativity, I came across a rather mind-blowing statement (for a beginner like me). Maybe this question is a naive one because of my lack of knowledge in differential geometry. ...
2
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1answer
66 views

Difference of the length according to dimension of the coordinate system

We know that the length of a vector does not depend on the coordinate system we choose. It's always the same. But is it still true when we add additional dimensions to our coordinate system? As long ...
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0answers
89 views

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 ...
5
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1answer
253 views

Are dimensions a fundamental property of the universe or an emergent result of other physical laws?

Are space-time dimensions a fundamental property of the universe or an emergent result of other physical laws?
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1answer
138 views

How come divergence of $\vec E$ is zero in this case where $\vec E=\xi\frac{\left[x,y\right]}{\sqrt{(x^2+y^2)^3}}\,?$

I hope you could help me clearing some doubts about Gauss' law of the electric field that states $\epsilon_0\nabla\cdot\vec E=\rho$. Take for instance the case of a point charge in the origin in empty ...
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2answers
524 views

Interacting With One-dimensional Objects [closed]

If I had a one dimensional object, lets say a string (the really small kind) that I managed to grow to the size of 1 meter in front of me. Would I be able to see or touch it? How would I be able to ...
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4answers
474 views

How does superstring theory explain the inverse square gravity law, given that it requires 9 spatial dimension?

In superstring theory, the spacetime dimension is either 10, one of them is time, the rest are spatial dimensions. But based on geometrical argument, we can say that $F\propto r^{1-D}$, where $D$ is ...