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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13
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7answers
4k views

Could negative dimension ever make sense?

After some quick check I found that negative dimensions are not used. But we have negative probability, negative energy etc. So is it so likely that we won't ever use negative dimension(s) ? Update ...
15
votes
2answers
1k views

Is it possible to generalize the Maxwell equations to higher dimensions?

The usual Maxwell equations are for 3 spatial dimensions, right? Is it possible to generalize them to 2 spatial dimensions or 4 spatial dimensions?
12
votes
3answers
2k views

Maxwell in multiple dimensions: What happens to curl?

I read this answer a while ago, and while thinking about $\nabla$, I realized something. Since the cross product can be written as a determinant, in higher dimensions we require extra vector inputs. ...
3
votes
3answers
920 views

How many dimensions does a singularity have?

my understanding of a singularity is that it is a 'point' in the universe with an infinite energy density. I have also read on the internet that a singularity is one-dimensional. This is a concept ...
-3
votes
0answers
51 views

How is it physically possible for strings to only be one-dimensional? [duplicate]

How can something have length, but no width or height? If something is one-dimensional, does it even exist? By one-dimensional, do they mean that the height and width of the strings are so small ...
7
votes
2answers
323 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 ...
4
votes
0answers
95 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 ...
0
votes
0answers
25 views

Does dimensionality determine the net effects of randomly oriented forces on an object?

My question relates to the orthogonality of random vectors in high dimensional space, and the relationship of random vectors as a function of dimensionality. My question can be formulated as a ...
0
votes
3answers
118 views

Speed as the fifth dimension

In spacetime there are four general dimensions, three of space and one of time. Why is it that other dimensioned qualities seem to be rarely considered as part of spacetime? For example, why isn't ...
-3
votes
0answers
49 views

How does the Universe connect with other Dimensions? [duplicate]

I was wondering that if the Universe was expanding, what was it expanding into. I came up with a theory and I was wondering if there was any information to support my theory, if my theory is wrong ...
2
votes
2answers
310 views

Circle becomes Sphere in 3d? [closed]

I was watching a movie Interstellar when it came out. Its been months but now I cant keep it inside and I must ask this question. So a guy was talking about wormhole in movie and ask the other guy ...
1
vote
1answer
108 views

How can extra (non-curled up) dimensions be hidden from us?

Wikipedia says: If extra dimensions exist, they must be hidden from us by some physical mechanism. One well-studied possibility is that the extra dimensions may be "curled up" at such tiny ...
1
vote
1answer
73 views

How to extract depth of a pixel from an image?

I'll have a few pictures that show the same scene, but only a few things move around a little bit. Now I don't have an information about any size in real life but I'd like to extract a scaling factor ...
7
votes
2answers
881 views

Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$

If $D$ is critical dimension of Bosonic strings, a particular derivation goes like the following, where we arrive finally at $$ \frac{D-2}{2}\sum_{n=1}^\infty n + 1 = 0. $$ Now mathematically this is ...
0
votes
1answer
52 views

How many Dimension do we have? [duplicate]

I know that Einstein described three dimensions for space and one for time. But I also have heard something about a world with so many dimensions or 11 dimensions of space or ... On the whole due to ...
0
votes
1answer
57 views

Why are we not able to visualize Dimensions beyond 3 (or maximum 4 including time)?

We consciously know and feel the first three dimensions and with some thinking time as well. But according to literature like String theory etc., we have many many more dimensions. We can readily ...
20
votes
5answers
4k views

What exactly is a dimension?

How do you exactly define what is and isn't a dimension? I heard somewhere that it is "anything you can move through" but if that is right, why wasn't time and space considered a dimension before ...
0
votes
1answer
52 views

How will gravity behave in a fourth spatial dimension? [closed]

If we were somehow able to see or experience the fourth spatial dimension, how would gravity act on us in there? Does the direction of the pull change? Will it have any effect on light or anything ...
1
vote
2answers
234 views

Is the universe 5 dimensional space-time or 4?

we've been told that in General Relativity (GR), matter tells space how to curve and space tells matter how to move. But my question is, if 3 dimensional space was curved by matter then it should be ...
6
votes
3answers
2k 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 ...
2
votes
2answers
115 views

What's the degree of freedom of this kind of matrix?

We first have a unitary matrix $$\{a_{ij}\}\quad(n\times n)$$ I know how to calculate its degree of freedom, which is $n^2$ if we consider a real variable as one degree of freedom. Now we have a ...
0
votes
3answers
81 views

Why is the ratio dark matter / normal matter bigger today than in the past? Is it the dark matter that increased or the normal matter that decreased?

These two pie charts clearly show that the ratio dark matter / normal matter is bigger today than it was in the past. But why? How is it possible? And does it mean that the amount of dark matter ...
3
votes
2answers
69 views

Creating a 3-D object from 2-D objects

I'm reading a book, 'Warped Passges' by Lisa Randall. In it she mentions how we can envision higher dimensions by explaning how higher dimension ojects can be created from lower dimension objects. So ...
1
vote
1answer
11 views

Is the index of time in the unit equivalent to force dependent on the number of dimensions

When the unit of force is represented as $\text{distance per time}^n$ in 3 dimensions $n$ is equal to 2. Is n also equal to 2 for higher or lower dimensions (2D, 4D, 5D, ...) or is it dependent on the ...
2
votes
1answer
83 views

4 dimensional interpretation

Has it ever been hypothetized that, in a 4 dimensional space, being time the 4th D, one body could travel through the dimensions at the combined speed of $c$? If a body is at rest in the classical 3 ...
0
votes
1answer
72 views

Why is the ground state energy of a 2DEG higher compared to the 3DEG?

I am reading something about a 2DEG (2-dimensional electrongas model) and can not understand it. My book says the ground state of the 2DEG is higher compared to a 3DEG because the confinement to 2D ...
3
votes
4answers
5k 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? ...
-1
votes
2answers
167 views

Why do we (3 dimensional creatures) see in 2 spatial dimensions? [closed]

Why do us humans, as 3-dimensional (in terms of space) creatures, see everything in 2 dimensions? Is it because the surface of every 3-dimensional object is 2 dimensional? Or because light enters our ...
0
votes
1answer
130 views

How do we know there are dimensions above the third?

Excluding the interpretation of time being the forth dimension, what mathematical evidence is there that suggests it exists? When talking about string theory they say how there is 12 dimensions and I ...
4
votes
2answers
201 views

Why doesn't the number of space dimensions equal the number of time dimensions?

It seems as though symmetry is a driving force behind theoretical physics. With symmetry in mind, should we expect that the number of time dimensions should be the same as the number of spatial ...
3
votes
1answer
283 views
1
vote
0answers
37 views

Need explanation for $CY_3$ folds comes first rather than algebraic curves comes first [duplicate]

The example I am aware of so far is quintic 3-fold equipped with $SU(3)$ holonomy. Why it is more natural to talk about $CY_3$ folds or Calibi-Yau 3 folds without talking about algebraic curves in ...
10
votes
4answers
709 views

Can dimension analysis be used in developing more advanced physics equations?

It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known. My question is whether this ...
15
votes
7answers
4k views

Experimental evidence of a fourth spatial dimension?

As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist. Is there any direct or indirect evidence ...
8
votes
2answers
565 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
votes
0answers
24 views

How can a string “shield” a tear in a flop transition? Can our expanded dimensions tear?

I have read recently that in a process called flop transition in calabi yau dimensions space actually tears and is then somehow "fixed" to create a new shape of Calabi Yau dimension. If a string wraps ...
28
votes
4answers
5k views

Why does moving through time not require energy?

Moving through the other three dimensions necessitates energy. But why doesn't moving through time necessitate energy?
0
votes
1answer
44 views

Infinite Energies of a particle in a rectangular box

For a particle trapped inside a rectangular box of side lengths $l_x$ $l_y$ and $l_z$, the energies are ...
3
votes
2answers
99 views

Can a hypothetical universe have more than 2 types of dimensions: spatial and temporal?

Our universe is often described as having 3 space-like dimensions and 1 time-like dimension. Can hypothetical universe exist with more than space- and time-like dimensions? If so how would these ...
3
votes
2answers
380 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?
1
vote
1answer
81 views

Inverse Square Law and extra space dimensions

Newton's famous Inverse Square Law says that in $n=3$ dimension of space, force is inversely proportional to the square of the distance between a source and a target. I understand that for higher ...
12
votes
8answers
4k views

Why are extra dimensions necessary?

Some theories have more than 4 dimensions of spacetime. But we only observe 4 spacetime dimensions in the real world, cf. e.g. this Phys.SE post. Why are the theories (e.g. string theory) that ...
0
votes
1answer
173 views

What is dimension and how many types of dimensions are there in the universe?

What is dimension and how many types of dimensions are there in the universe? I mean how many total dimensions are there? I have only heard about 2d and 3d. Other than these two, are there any other ...
3
votes
3answers
605 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 ...
3
votes
0answers
68 views

How one can write $\bar{\psi}$ in odd dimension?

I know that the Dirac equation in general dimensions has a form of $$ (i\gamma_{\mu} \nabla_\mu - m ) \psi =0 $$ and the action for that is written as $$ S = \int d^d x \bar{\psi} (i\gamma_{\mu} ...
0
votes
1answer
65 views

Is the center of the universe in another dimension?

If we live in a four dimensional world and when we try to find the center of the universe (where the big bang occured) we found that there is no apparent center, could that means that the big bang ...
3
votes
0answers
62 views

Questions about the existence of 5d & 6d version of 4d ${\cal N}=2$ SCFTs

Given a 4d N=2 Superconfomal field theory (SCFT) with a global flavor symmetry ( $\mathfrak{f}$ as the corresponding lie algebra), can we clam that this theory can always flow from a 5d ${\cal N}=1$ ...
2
votes
2answers
169 views

Chern Simons action in 4 dimensions

I can not understand why we do not have a Chern-Cimons action for 4 or even forms? And why it not good theory for (3+1) dim?
4
votes
1answer
118 views

In 2-dimensional and 3-dimensional universes, stellar systems and galaxies are flat and disky. But what about in 4-dimensional universes?

I just watched that interesting video: https://www.youtube.com/watch?v=tmNXKqeUtJM In 2 dimensions a cloud of particles rotating in a plane is flat by definition since it's in 2 dimensions. ...
1
vote
1answer
155 views

Gravity in $d$ spacetime dimensions

Given the following action $$S=\frac{1}{16\pi G}\int d^4x \sqrt {-g}(R+aR^2+bR_{\mu\nu}R^{\mu\nu}+cR_{\mu\nu\lambda\sigma}R^{\mu\nu\lambda\sigma}),$$ which is in 4D. How to we generalise this ...