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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75 views

Can “state” be considered a 5th dimension?

I searched for an answer to this question on Google but just found articles that mention either string theory or a 5th dimension in passing (such as Maxwell equations as they relate to Riemann ...
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1answer
52 views

Our universe the surface of a 4-dimensional sphere?

The cosmic microwave background that we observe uniformly around us is usually explained by assuming that our universe is the surface of a four dimensional sphere. That way the uniformity makes sense ...
3
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1answer
39 views

Number of supersymmetric charge and the meaning of $\cal N$

I have been thinking about the definition of the notation $\cal N$ and its relation to the number of supercharges in SUSY, but still feel a little confused. In dimension 2, we usually denote, for ...
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0answers
50 views

Dimension in string theory [duplicate]

Why are strings in string theory only one dimensional? Does that imply that if we try to detect width of strings (I know that it is not possible now) then we can not detect anything because in that ...
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0answers
117 views

Why dimensionality of the Electric Charge varies with the spacetime dimensions?

The point is: We can find via dimensional analysis that the electric charge dimensionality varies with the dimension of space-time. $$[\text{charge}] = eV^{(3-D)/2}$$(You can see below the way I did ...
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1answer
72 views

Where do our 4 macroscopic spacetime dimensions reside in multidimensional models of the universe?

In models such as M-theory with 7 'higher dimensions' plus the 4 macroscopic spacetime dimensions, where do our 4 macroscopic spacetime dimensions reside ordinally? My reason for asking is TV shows ...
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3answers
91 views

Quantum entanglement: does it necessarily imply superluminal information transfer? [duplicate]

From what I understand, information is communicated instantly between two quantum-entangled particles regardless of the spatial distance between them. However, does this necessarily imply superluminal ...
1
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1answer
51 views

Maxwell's equations of Electromagnetism in 2+1 spacetime dimensions

What would be different in the theory of electromagnetism if instead of considering the equations of Maxwell in 3+1 spacetime dimensions, one would consider 2+1 spacetime dimensions?
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1answer
64 views

Are subatomic partices n-dimensional hyperspheres or another n-dimensional shape?

This guy derives the formula for the volume of an n-dimensional hypersphere, which can also be found here on the Wikipedia page, and he shows that it is equal to this equation: $V_n = ...
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0answers
29 views

antimatter moving back in time [duplicate]

This just blew my mind away! I was watching a video about imagining the fourth dimension and the narrator said that little line. Can some people elaborate on this. Also please keep it simple not ...
4
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1answer
72 views

Kaluza Klein theories, dilation field, and dimensional reduction

I am reading something about Kaluza Klein theories and compactification. I have some conceptual question: (1) Why do we call the fifth scalar field $\Phi$ the dilation field? Is there any scaling ...
2
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1answer
100 views

Pseudo-Riemannian Manifolds with multiple temporal dimensions

Consider a Pseudo-Riemannian Manifold with signature $$ (\underbrace{+,\cdots,+}_p,\underbrace{-,\cdots,-}_q) $$ For any positive integers $p$ and $q$. Can this kind of manifold contain closed ...
3
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3answers
141 views

What Does it Mean for an Extra Dimension to Have Size?

Recently I watched this presentation by Brian Greene on string theory. In it he describes how the reason we don't observe the extra dimensions required by string theory could be because they are very ...
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3answers
145 views

Number of Parameters of Lorentz Group

We embed the rotation group, $SO(3)$ into the Lorentz group, $O(1,3)$ : $SO(3) \hookrightarrow O(1,3)$ and then determine the six generators of Lorentz group: $J_x, J_y, J_z, K_x, K_y, K_z$ from the ...
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2answers
912 views

Does space curvature automatically imply extra dimensions?

Total newbie with basically no physics knowledge here :) I would welcome any correction to the steps of my reasoning that lead to my question, which could easily turn out to be invalid :) My current ...
2
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2answers
104 views

What might be a satisfying criterion to qualify something as having physical existence?

I'm a philosophy undergraduate student who has an interest in, and respect for (as most people do) what physicists know about the world. In philosophy, the traditional criterion of physical ...
3
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1answer
131 views

How can one learn to visualize 4 dimensional spacetime?

I was watching Professor Leonard Susskind's lecture on Quantum Entanglements and he said that there are physicists and people who study physics, who 'rewire' themselves so they can visualize 4 ...
3
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1answer
114 views

Group analysis forbids band-crossing in 1D?

Group analysis forbids band-crossing in 1D in terms of conventional band theory. I read this in a good solid state physics book. But there's no explanation at all. Can anyone help on this?
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1answer
83 views

Alternative Critical Dimensions in String Theory

Is it possible to write down a Lagrangian for a string theory with a critical dimension different than the familiar 10 or 26? How could one find a string theory Lagrangian for a given dimension? Could ...
4
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1answer
79 views

Could quarks be free in higher-dimensional space than 3D?

Reading this answer, I now wonder: if quarks are confined by $r^2$ potential, could their potential allow infinite motion in higher-dimensional space? To understand why I thought this might be ...
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0answers
58 views

Ricci scalar higher dimensions

I was wondering if there is a straightforward way to compute the Ricci curvature of a metric that has the form (à la Kaluza-Klein): $g_{MM}\equiv\begin{pmatrix}g_{\mu\nu}&g_{\mu ...
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1answer
69 views

2 Time Dimensions

Our universe has 4 dimensions, 3 spacial and 1 temporal. We can add another spacial dimension and use math to explore it. I cannot think of any reason why we cannot add add another temporal ...
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2answers
90 views

Length of a dimension?

I am really confused about what is the minimum length for a dimension to exist (I don't know the exact word). Like I mean, we call the paper to be a 2 dimensional object but if we magnify its edges, ...
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2answers
95 views

Potential Energy of a Particle in One Dimension?

Since a particle in one dimension can only move in a straight line. Is it possible to have potential energy? And how would the kinetic energy and potential energy differ in higher dimensions?
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2answers
208 views

Can we actually prove with 100% accuracy that there is more than 3 dimensions plus time (t,x,y,z)? [duplicate]

Can we actually prove with 100% accuracy that there is more than 3 dimensions plus time? In the news there are always articles like "there are probably 7, 11 or more dimensions", "time is actually ...
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1answer
79 views

How can a string be unidimensional if they can be open ended or close ended?

I just don't understand how a object with 2 ends can be unidimensional.
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1answer
104 views

Why we can only perceive 3 dimensions [closed]

What is the reason that we cannot perceive more than 3 dimensions with our senses?
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1answer
198 views

Isotropic harmonic oscillator in polar versus cartesian

I read another Phys.SE post here: 3D Quantum harmonic oscillator that I believe says the wave function in Cartesian coordinates for a 3D harmonic oscillator is the product of the 3 one dimensional ...
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2answers
204 views

Dimensions of strings in string theory

In the above image taken from wikipedia, at the string level the strings have been shown as some loops, the article in wikipedia says that in string theory the particles at lower level are broken ...
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1answer
88 views

Do electric fields generated by plane charges lose intensity over distance? If not, why?

Sparknotes' studyguide for the SAT II: Physics test says that for a point charge (1-dimensional, e.g. an electron), the formula for intensity of the generated electric field is given by ...
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0answers
36 views

Problem in applying Takens correlation dimension

I am trying to implement Takens' correlation dimension for noisy time series formula given in Eq (8) in (Estimation of the dimension of a noisy attractor. Schouten JC, Takens F, van den Bleek CM ...
4
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1answer
83 views

Content of the N=2 Graviton Multiplet in 6D

I've been looking into extended Supersymmetry in higher dimensions recently. What I keep wondering about are some components of the gravity multiplet, that seem to appear from the construction of ...
8
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1answer
324 views

Gravitational constant in higher dimensions?

From Newton's law of gravitation we know that $$F=G\frac{m_1m_2}{r^2}$$ where $G$ is gravitational constant. We can also see that it has dimensions $$[G]=\frac{[L]^3}{[M][T]^2}$$ and we have a ...
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0answers
68 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 ...
0
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1answer
79 views

Representation of the velocity field

Im trying to understand this line given by our prof. : "Representing fluid parameters as a function of the spatial coordinates($x$, $y$, $z$) and time $t$. For example: $$\vec{V} = u(x,y,z,t) \vec{i} ...
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2answers
241 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|} ...
5
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2answers
465 views

Is there an intuitive way of thinking about the extra dimensions in M-Theory?

Why are 11 dimensions needed in M-Theory? The four I know (three spatial ones plus time) have an intuitive meaning in everyday life. How can I think of the other seven? What is their nature (spatial, ...
3
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2answers
172 views

Universe being flat and why we can't see or access the space “behind” our universe plane?

I'm a layman, but i watched some intereting videos about big bang on youtube[michio kaku, hawking this kind of things, not some crackpots :)] I described everything on my picture: So is there ...
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1answer
102 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 ...
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3answers
582 views

2 dimensional Coulomb's law equation

We can notice that in the Coulomb's law equation, $$\begin{equation}\tag{1}F=\frac{1}{4\pi\epsilon}\cdot\frac{q_1q_2}{r^2}\end{equation} $$ $4\pi r^2$ factor in the denominator expresses directly ...
2
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1answer
83 views

Can all theories of theoretical physics be generalized to any (arbitrary) number of dimensions?

Please explain from: mathematical point of view "laws of mathematics", and, physical point of view "laws of physics"? Or is there any bound on number of dimensions?
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2answers
179 views

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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5answers
743 views

Proof that Our Planet is 1D

I have took a discrete mathematics course this summer and there we talked about power of groups and functions,and yesterday I though and realize that if we can map all the 3D coordinates with a one on ...
2
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2answers
221 views

Mass dimension of coupling constants in various dimensions

Just a quick question: Suppose I want to consider QED or YM in 4 dimensions we always say that the coupling constants are dimensionless and that the field then has a specific mass dimension. What ...
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2answers
108 views

How can we detect the topological order in 1+1D topological superconductor numerically?

I read some material in this forum and realize that entanglement entropy does not correspond to long range entanglement. Then what quantity can be used to characterize the topological order in 1+1D ...
2
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2answers
155 views

Newtonian gravity equation in a 2 dimensional world [duplicate]

I am wondering if my line of thought is correct - and thus the resulting answer to the problem above would be correct. As we know the gravitational force (of two point masses) is given by $$F = ...
2
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3answers
137 views

Non-normalizable QM bound state in 4 spatial dimensions?

Edit 26/Sept/13: Fixed Typo in potential I'm solving the following (seemingly simple) quantum-mechanical problem in four spatial dimensions. In natural units ($\hbar^2/2m=1$), the Schrödinger ...
2
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2answers
101 views

Dimensionality of Hilbert space

Simple question, but I can't seem to find the answer searching very easily. Does the dimensionality of a Hilbert space correspond to the number of possible states a system can take on? ("The system" ...
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3answers
325 views

What are the fundamental problems of being in a 2 dimensional world?

I was reading through Stephen Hawking's explanation of two - dimensional space. In that he mentioned that it will be very difficult to design a living being that could exist only in 2 dimension. What ...
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0answers
52 views

Extra dimensions and the big bang [duplicate]

If there were extra compact dimensions,and at the big bang all dimensions were compact,my question is why the big bang failed to expand those presumed extra dimensions like it did with the 3 spatial ...