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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2
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1answer
141 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
votes
3answers
250 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
votes
3answers
220 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 ...
8
votes
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
votes
2answers
118 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
votes
1answer
153 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
votes
1answer
134 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
votes
1answer
89 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
votes
1answer
91 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 ...
1
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0answers
85 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 ...
1
vote
1answer
263 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 ...
0
votes
2answers
97 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, ...
1
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2answers
138 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?
1
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2answers
626 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 ...
1
vote
1answer
83 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.
-1
votes
1answer
158 views

Why we can only perceive 3 dimensions [closed]

What is the reason that we cannot perceive more than 3 dimensions with our senses?
1
vote
1answer
317 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
245 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 ...
0
votes
1answer
163 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 ...
4
votes
1answer
94 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
votes
1answer
618 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 ...
3
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0answers
81 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
votes
1answer
84 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} ...
7
votes
2answers
334 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|} ...
7
votes
2answers
514 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
votes
2answers
266 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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votes
1answer
225 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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vote
3answers
990 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
votes
1answer
88 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?
1
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2answers
263 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 ...
13
votes
5answers
787 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
votes
2answers
516 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
vote
2answers
138 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
votes
2answers
223 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
votes
3answers
144 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
votes
2answers
190 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" ...
6
votes
3answers
1k 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 ...
0
votes
0answers
53 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 ...
1
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1answer
84 views

Mass of particle w.r.t. dimension

I heard in a lecture recently - just as a comment - that a particle which is massive in say $D=4$ can be seen as a massless particle in higher dimensions and vice versa. Our prof didn't give any ...
1
vote
1answer
115 views

Doubts regarding dimension of a system:Definitions and algorithms

I need to do phase reconstruction from time series data. In doing so, I encountered Takens' embedding theorem and Cao's minimum embedding dimension $d$ by nearest neighbor method. In paper "Optimal ...
0
votes
1answer
83 views

How does the warping of time behave as a fourth dimension?

My problem is that I have a hard time grasping something if I can't conceptualize it, though maybe this can not be conceptualized, just accepted, in which case I thank you for your patience. The ...
2
votes
1answer
109 views

Key difference between 3D and 4D solutions

In many papers in theoretical physics especially in the more advanced theories, I notice that physicists solve problems in 3 dimensions (2 spatial+ 1 temporal). In some specific papers (I can't seem ...
5
votes
4answers
486 views

Why is space-time four dimensional?

Wikipedia says, "In special relativity, four-momentum is the generalization of the classical three-dimensional momentum to four-dimensional space-time. Momentum is a vector in three dimensions; ...
4
votes
1answer
125 views

Is it possible to project a problem of mechanics in a lower dimensionality?

I had the intuition that, in classical mechanics, when the trajectory of a body is known, then analysis of its motion can be done in the linear space of that trajectory, if all forces are projected on ...
1
vote
1answer
169 views

Could we see a lower dimension within our universe? [closed]

My question refers to the fact, that, say if our universe were to be sitting on a 4 (spatial) dimensional plane, that we cannot see, then within our universe could there be a point mass in which 1 or ...
0
votes
2answers
340 views

3 Questions about modern Physics [closed]

First i'd like to apologize for both my writting skills (i'm not english) and for my physics knowledge (being them very basic and/or naive). With general relativity from Einstein, gravity is no ...
5
votes
1answer
275 views

Why does one of the extra dimensions of F-Theory have to be a temporal dimension?

F-Theory, as I understand it, is a realisation of Type IIB String Theory as a 12-dimensional theory in such a way that the $SL(2,\mathbb Z)$ symmetry becomes natural because Type IIB String Theory is ...
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2answers
185 views

How can time be a dimension?

In physical terms, dimension refers to the constituent structure of all space and its position in time. Time is same throughout the universe. So, how can time be a dimension?
4
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1answer
182 views

Behavior of black holes in higher- and lower-dimensional space-times

The behavior of black holes in 3+1 dimensional space-time as our own is rather well known: formation, event-horizon size, mass, spin, radiation etc. However, my question is what would black holes ...
2
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7answers
3k views

As 3-dimensional beings, do we really have 3-dimensional vision?

I was watching this video on YouTube of a high school student explaining perception in different dimensions, basically stuff he learned from reading the book Flatand. At one point in the video, he ...