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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225 views

Is there no fourth dimension (time) in the universe? [closed]

In this article (and numerous others) http://phys.org/news/2011-04-scientists-spacetime-dimension.html and http://www.rebelscience.org/Crackpots/notorious.htm they suggest that there is no time ...
2
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0answers
50 views

Hierachies of AdS/CFT holographies

One of the most disturbing aspects of General Relativity is the 'Marble versus Wood' duality of the theory: Matter creates curvature, and curvature doesn't create curvature (at least not directly) ...
3
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1answer
148 views

Quantum Field Theory with (2,2) metric

Does someone know some reference which treats QFT in a space with the following non-Lorentzian signature: $g_{\mu\nu}=\text{diag}(-1,-1,1,1)$. I'm interested in basic stuff like the shape of the ...
10
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2answers
726 views

A sketch of various combinations of numbers of space and time dimensions

I came across this picture/sketch on the internet, however there is no any explanation about it: What is "UNPREDICTIBLE"? "UNSTABLE"? "TOO SIMPLE"? "elliptic", "ultrahyperbolic"?? Some related ...
0
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1answer
141 views

Dimension of gamma matrices in higher dimensional Dirac equations

Reading about Dirac's equation in higher dimensional space-times I have read that the gamma matrices are $2^{[D/2]}\times{}2^{[D/2]}$. So, if we have $D=11$, for example, how is this formula supposed ...
2
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1answer
219 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 ...
0
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1answer
869 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 ...
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2answers
224 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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2answers
565 views

Why does the dimension of the electric charge depend on the number of spacetime dimensions?

We can find via dimensional analysis that the dimension of the electric charge varies with the dimension of space-time $(D+1)$: $$[\text{charge}] = (\text{eV})^{(3-D)/2}.$$ It is dimensionless if ...
2
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1answer
141 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
370 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 ...
3
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1answer
1k 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
245 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 = \frac{\pi^\frac{...
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0answers
39 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 ...
5
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1answer
618 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 ...
3
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1answer
163 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 ...
4
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2answers
405 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 ...
2
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3answers
440 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
1k 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
133 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
221 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
176 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?
5
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1answer
103 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 ...
5
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1answer
118 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
119 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 i}\\g_{i\nu}&...
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1answer
651 views

2 Time Dimensions [duplicate]

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
109 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
234 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
3k views

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

Can we actually prove with 100% accuracy that there are 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 ...
1
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1answer
96 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
355 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
649 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 ...
4
votes
2answers
325 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 down ...
0
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1answer
286 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 $E=\frac{kq}{r^...
4
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1answer
124 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 ...
10
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1answer
2k 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 ...
4
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0answers
137 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
92 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
776 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})...
8
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2answers
642 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
493 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
812 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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5answers
2k 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
127 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
655 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 ...
14
votes
5answers
840 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 ...
3
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2answers
1k 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 ...
1
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2answers
218 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
831 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 = G\...
2
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3answers
166 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 ...