Use this tag for dimensions of a manifold, typically the space-time. DO NOT USE THIS TAG for dimension of a physical quantity.

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11 views

How does LHC explores extra dimensions?

The large hadron collider is been smashing particles for a long time and sometimes people say that they have found new dimensions. But,how's that even possible for a particle accelerator to find new ...
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1answer
8 views

Purpose of the multidimensional NLSE/GNLSE

I know the purpose of the NLSE (Evolution of a complex field envelope in a nonlinear dispersive medium). Usually I am solving the 1d-GNLSE when simulating the propagation of a light pulse through a ...
2
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2answers
97 views

What does it mean for an integral's differential to be raised to a power, like e.g. $d^3r$ or $d^3u$?

I was reading Zwelfel's book on reactor physics and saw the following notation: Notice that the differential of the integral is raised to the third power. What is the meaning of this notation? ...
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1answer
57 views

String Theory Vs. Holographic Theory of the Universe. Compatibility [on hold]

String Theory claims strings to be one dimensional objects vs. dimensionless point particles of the Standard Model. String Theory also needs 10 or possibly more spatial dimensions to operate in. ...
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0answers
37 views

Force and dimension is the same? [on hold]

I read somewhere that maybe we have 10 dimensions. We know that we have four dimensions (3 dimensions of space plus one of time). There are also four forces: gravity, electromagnetism, the strong ...
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0answers
27 views

What is the fifth dimension? [on hold]

What is known as the fifth dimension, and if the fifth dimension is not defined (yet), are there theories? Which? I have heard about the fifth dimension being gravity but that doesn't seem to make ...
10
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0answers
297 views

Are there topological non-trivial states in zero dimension?

The periodic table of topological insulators and superconductors suggests that there can be topological non-trivial phases in zero dimension in non-interacting system with certain symmetries. A 0D ...
6
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2answers
57 views

Significance of electrical fields of infinite objects

I've noticed a pattern with the electric fields of charged objects of infinite dimensions. A point charge, which can be considered a charge of 0 dimensions, has an electric field that goes as $r^{-2}$...
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3answers
57 views

What is the measure of distance in higher dimensions?

In our world we are using kilometers to measure distance. What measurement is used to measure distance in higher dimensions?
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0answers
79 views

Clarification on the 11 dimension in the M-theory [closed]

In the book the Grand Design by Stephen Hawking, he wrote about the M-theory, and how in that theory it has 11 dimensions. I do not quite get that, so can someone explain it to me a little bit. I ...
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5answers
9k views

Why does string theory require 9 dimensions of space and one dimension of time?

String theorists say that there are many more dimensions out there, but they are too small to be detected. However, I do not understand why there are ten dimensions and not just any other number? ...
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0answers
46 views

Why do strings need 9+1=10 spacetime dimensions to exist? [duplicate]

Why do strings need 9+1=10 spacetime dimensions according to previous theory, or equivalently, 11 dimensions as per M-theory? Why cannot they exist in the 4-dimensional world?
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4answers
134 views

Is it reasonable to visualise an additional dimension of time as a part of 4th dimensional spacetime

[EDIT] In the spirit of asking a "good question", this question is considerably more refined that the one I decided to blurt out earlier thanks to a little additional research and nudges from comments....
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3answers
75 views

Is there any experimental evidence that Universe has more than 3 spatial dimensions?

Someone asked about proof of higher dimensions. But discounting time as a dimension, along with the hyper-dimensional GUTs/Supersymmetry theories, has this possibility been tested and what did the ...
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1answer
17 views

Ising simulation-dimensionless

My question is about dimensions in Ising model.When we want to simulate Ising we use dimensionless parameter as you know.We choose J to be 1 and also K equal 1 and when temperature is 2.26 then it's ...
5
votes
2answers
135 views

Gravitational waves in other dimensions

I know this question is purely speculative, as we don't know if more dimensions do exist and also we do not know if gravity is indeed stronger in other dimensions (if they were to exist). But, one of ...
6
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1answer
156 views

Theories that predict the number of space-time dimensions

My impression in that most theories assume three spatial dimensions and one temporal dimension, though could in principle be formulated in others numbers of dimensions without inconsistencies. I know, ...
0
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0answers
79 views

What would a universe with 2 time dimensions be like? [duplicate]

In a universe with 2 dimensions of time, and 3 spatial dimensions, the equation for finding the change in time is: $\Delta T= \sqrt{(\Delta \alpha_1)^2+(\Delta \alpha_2)^2} \geq 0$ Where $T$ is the ...
7
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2answers
795 views

Deriving Gauss-Bonnet Gravity (Or just higher order corrections)

I have been working for some time now on deriving the equations of motion (EOM) for the Gauss-Bonnet Gravity, which is given by the action: $$\int d^D x \sqrt{|g|} (R^2-4R_{ab}R^{ab}+R_{abcd}R^{abcd})...
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0answers
42 views

Multidimensional Area and Volume

In 3D the volume is $xyz$, the product of three coordinates. But in $N$ dimension ,how to define area and volume?
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3answers
93 views

How can time be a dimension when it is relative? [closed]

I understand that by definition dimension is defined by just another coordinate to pin-point something in space-time. Therefore we need to know not only where but when. At the same time, this somehow ...
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3answers
87 views

Is “time” a singular dimension or multiple dimensions? [closed]

We know of x, y, and z dimensions. We also know of "time"... Another dimension we are aware of, which is a "non-physical dimension" called a "temporal dimension". Now, we all look at "time" as a "...
2
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0answers
103 views

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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1answer
40 views

Why are dimensions regarded as square/perpendicular?

Starting from the second dimension, the dimensions are basically represented by a square, cube, tesseract, and so on. I don't know if this is a stupid question or not, but is there an obvious or less-...
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1answer
44 views

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 ...
10
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1answer
162 views

What is known about the hydrogen atom in $d$ spatial dimensions?

In a first (or second) course on quantum mechanics, everyone learns how to solve the time-independent Schrödinger equation for the energy eigenstates of the hydrogen atom: $$ \left(-\frac{\hbar^2}{2\...
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1answer
69 views

Could it be theorically posible “cut off” a piece of space-time? [closed]

I know I may not have an accurate idea of what are the properties of space-time, but here is the idea: By doing an analogy with moving from 2 to 3 dimensions, I have been wondering if in theory it ...
22
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2answers
331 views

How can dimensional regularization “analytically continue” from a discrete set?

The procedure of dimensional regularization for UV-divergent integrals is generally described as first evaluating the integral in dimensions low enough for it to converge, then "analytically ...
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1answer
77 views

Is most of what everything is made from in another dimension?

If there are eleven dimensions as M-Theory asserts would that mean that the majority of what we are made from exists in the seven other dimensions?
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0answers
32 views

What is the relationship between potential energy and electrical potential?

I actually always thought this was trivial, now I am not so sure. For a potential $\phi$ the potential energy is $V=q\phi$ where q is a test charge. Now I am thinking this may work differently in two ...
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2answers
46 views

2 space and 1 time dimensions [closed]

I know it is impossible to visualise a 3 space and 1 time dimensions. But what about 2 space and 1 time dimensions? Will it be like similar to 3 space dimensions or different? If different will it be ...
0
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0answers
22 views

Compare a normal spring and a torsion spring

Consider a torsion spring with a known spring constant $K_c$. I would like to calculate the required $K_l$ for an equivalent linear spring, which would store the same amount of energy when compressed. ...
1
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2answers
759 views

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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1answer
45 views

Number of supercharges in $N\ge 1$ SUSY in $d\ge4$ dimensions

I have a couple of questions concerning supercharges and superalgebras: 1, In four-dimensions, the minimal spinor representations are Weyl spinors. These have 4 real degrees of freedom (dof). This ...
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1answer
846 views

Can quantum entanglement be a proof of a 4th spatial dimension?

What I know about quantum entanglement is almost nothing. What I know can be resumed to: "two particles created together have a correlated behaviour no matter the distance between them". This is ...
2
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1answer
1k views

Nanotech - zero dimensional fullerene

Not really a physics junkie, and I think this is a chemistry question, but since there's no chemistry.stackexchange.com (yet) I think here is the best place. I was just reading up on nanotech and ...
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3answers
568 views

Why time is considered a dimension?

Why is time considered to be a dimension? And the other 7 (except the 3 dimensions of space, and the dimension of time) dimensions that string theory suggests, why can't they be realized?
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1answer
37 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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0answers
37 views

Time. Is it really a dimension? [duplicate]

I have trouble accepting that time is a dimension, in the same way that space has three dimensions. Wherever there is space and matter, it has spatial properties. You can move back and forwards in ...
0
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0answers
46 views

Magnetic monopole in arbitrary dimension

Assume we have D-dimensional space-time in spherical coordinates $(t, r, \theta_1, ..., \theta_k)$. We have Maxwell equations for $k$-form $F^{\alpha_1, ..., \alpha_k}$ $$\partial_{\mu} F^{\mu \...
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0answers
41 views

Could a 3+1 space be embedded in a 4+1 space and retain its 3+1 characteristics? [closed]

I'm confused because I can conceptualize this embedding scenario in two seemingly incompatible ways. Which of the following scenarios are possible?: 1) 4+1 space automatically enforces 4 dimensions ...
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0answers
38 views

Is there a limit in dimension?

According to wikipedia Dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any ...
1
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1answer
54 views

Is there an underlying reason why some forces are inversely proportional to the square of the distance? [duplicate]

This is the first time I'm studying those subjects (I'm still in high school) and my teacher couldn't give me an answer. I'm referring specially to Newton's law of gravitation and Coulomb's law of ...
0
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1answer
73 views

Black hole's singularity: Does it has to be multi-dimensional?

We assume that there is an infinite density at the center of a black hole. But we also know that if it was really infinite, it would apply an infinite gravitational force to masses even if they were ...
6
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1answer
112 views

Are path integrals integrals with countable or uncountable infinite dimensions?

Path integrals are integrals with infinite dimensions. But I recently became confused about if the number of dimensions are discrete/countable or continuous/uncountable. I always thought it should be ...
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1answer
39 views

In what ways is four dimension relevant to modern physics?

In what fields can the consideration of four perpendicular vectors be useful to making theories and models in physics? Is the concept of four dimension restricted to spatial dimensions?
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0answers
21 views

Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?

Say the diffusion coefficient of the concentration of a particle in a fluid in 3-dimensions is $D_{3\textrm{d}}$. Can we estimate the diffusion coefficient of the same particle in the same fluid, in a ...
3
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1answer
98 views

On the c-theorem

I have been reading a few papers on CFT and AdS/CFT regarding the c-theorem and I have a few questions regarding c-theorems: a) Why is it that the c-theorem is usually considered for only unitary ...
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1answer
73 views

General Relativity, Curvature, and extra dimensions

Setup of idea I had somewhat of a thought question regarding general relativity. Consider a simple situation of a sphere and arrow. You hold the arrow and walk from the equator to the north pole. ...
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3answers
1k views

How to imagine higher dimensions?

In the link below Carl Sagan described about higher dimension: http://www.youtube.com/watch?v=UnURElCzGc0 and here's a description of Brian Greene: http://www.youtube.com/watch?v=v95WjxpMIQg Carl ...