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 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
94 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
123 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
379 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
80 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
123 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
239 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
238 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
138 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
40 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 ...
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1answer
92 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
469 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
76 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 ...
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1answer
82 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
273 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|} ...
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2answers
489 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
215 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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2answers
177 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
805 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 ...
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1answer
86 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
217 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
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5answers
768 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
405 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
129 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
185 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
141 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 ...
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2answers
132 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
628 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 ...
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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 ...
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1answer
99 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 ...
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1answer
79 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
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1answer
104 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 ...
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4answers
431 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; ...
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1answer
122 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 ...
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1answer
153 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 ...
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2answers
305 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 ...
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1answer
240 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
172 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?
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1answer
169 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 ...
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7answers
2k 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 ...
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1answer
148 views

Dimension & non - locality problem in string theory

I have some questions with string theory: Why is it that there is exactly 4 large spacetime dimensions while the rest remain small? It is a nonlocal QFT. How could that fit in GR?
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1answer
214 views

Does string/M-theory address higher-dimensional membrane vibration modes?

A loop is a 1-sphere that can vibrate in increasingly complex ways as it is embedded in higher dimensional spaces. Does string theory assume that 1-spheres are the only possible vibrating ...
2
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0answers
120 views

Bose-Einstein condensation in 3D

I have read in many books that BEC takes place in momentum space and in only 3-dimensions. What is meant by this statement?
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2answers
232 views

Should we necessarily express the dimensions of a physical quantity within square brackets? [duplicate]

For example, should we write the dimension of mass, e.g. $\mathrm{kg}$ as $[M]$ or is it enough to write it as $M$?
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5answers
492 views

How to prove that we are living in a 3D world?

Is there any scientific experiment that can lead us to conclude we live in 3 dimensions without the premise of the conception of limited dimensions? Thank you all who helped in the improvement of ...
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2answers
93 views

What is an $n$ dimensional space? [closed]

How an $n$ dimensional space looks like? Is it possible that we are really in a space of dimension greater than 3?
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0answers
46 views

how must i understand this 2-loop integral?

let be the 2-loop integral... $$ \int d^{d}l\int d^{d}k \frac{1}{k^{4}(k+p)^{2}(k+l)^{2}}=I(p)$$ dimensional regularization over the variable 'l0 to evaluate $$ \int ...
5
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1answer
270 views

${f=ma}$: a duality between F-theory and M-theory?

$$F = M \Big|_{A(T^2) \to 0}$$ The above equation is the duality equation between F-theory and M-Theory on a vanishing 2-torus. What's the explanation for this equation? Is there anything similar ...
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1answer
113 views

Relationship between lightlike and spatial compactification

The compactification of a spatial dimension, say $x^1$ given by the identification $x \sim x^1 + 2\pi R$ is said to be related to the lightlike compactification by a Lorentz boost : $$ \left( ...