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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44
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7answers
3k views

Is 3+1 spacetime as privileged as is claimed?

I've often heard the argument that having 3 spatial dimensions is very special. Such arguments are invariably based on certain assumptions that do not appear to be justifiable at all, at least to me. ...
19
votes
1answer
1k views

Intuition for multiple temporal dimensions

It’s easy, relatively speaking, to develop an intuition for higher spatial dimensions, usually by induction on familiar lower-dimensional spaces. But I’m having difficulty envisioning a universe with ...
17
votes
7answers
5k 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 ...
7
votes
3answers
641 views

Why (in relatively non-technical terms) are Calabi-Yau manifolds favored for compactified dimensions in string theory?

I was hoping for an answer in general terms avoiding things like holonomy, Chern classes, Kahler manifolds, fibre bundles and terms of similar ilk. Simply, what are the compelling reasons for ...
13
votes
8answers
5k 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 ...
47
votes
5answers
4k views

Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions?

Coulomb's Law states that the fall-off of the strength of the electrostatic force is inversely proportional to the distance squared of the charges. Gauss's law implies that a the total flux through a ...
20
votes
1answer
5k views

How to define angular momentum in other than three dimensions?

In classical mechanics with 3 space dimension the angular momentum is defined as $\mathbf{L} = \mathbf{r} \times \mathbf{p}$ In relativistic mechanics we have the 4-vectors $x^{\mu}$ and $p^{\mu}$, ...
20
votes
4answers
3k views

Why are so many forces explainable using inverse squares when space is three dimensional?

It seems paradoxical that the strength of so many phenomena (Newtonian gravity, Coulomb force) are calculable by the inverse square of distance. However, since volume is determined by three ...
9
votes
2answers
1k 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 ...
15
votes
2answers
974 views

Why one-dimensional strings, but not higher-dimensional shells/membranes?

One way that I've seen to sort-of motivate string theory is to 'generalize' the relativistic point particle action, resulting in the Nambu-Goto action. However, once you see how to make this '...
13
votes
6answers
762 views

More than one time dimension

We know that space-time dimensions are 3+1 macroscopically, but what if 2+2? Obviously it is tough to imagine two time dimensions, but mathematically we can always imagine as either having two ...
6
votes
4answers
694 views

Measuring extra-dimensions

I have read and heard in a number of places that extra dimension might be as big as $x$ mm. What I'm wondering is the following: How is length assigned to these extra dimensions? I mean you can ...
3
votes
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 ...
-1
votes
1answer
129 views

Are all galaxies we see really our Milky Way? Any possibility?

There is a possibility for our universe to be the surface volume of a (higher-dimensional) hyperspace. So if this possibility is true,then is there also a possibility that the other galaxies we see ...
8
votes
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, ...
19
votes
3answers
936 views

Has the concept of non-integer $(n+m)$-dimensional spacetime ever been investigated by theoretical physicists?

The following image serves to aid the reader in understanding the "privileged character" of $3+1$-spacetime. The wikipedia article on spacetime, and the sub-article "The priveleged character of $3+...
6
votes
4answers
9k 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? ...
5
votes
2answers
2k views

How can one imagine curled up dimensions?

Actually I'm learning String Theory, and one of its proposals is that there are actually 25+1 dimensions of which only 3+1 are visible to us-- and the remaining are curled up. However, superstring ...
19
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3answers
3k 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. ...
21
votes
3answers
6k views

If I squeeze something really hard, will it ever become two-dimensional?

A mosquito just wanted to bite me! Päng - and it stuck to my hand, hardly recognisable anymore. I said to my girlfriend: "Just reduced the dimension of the mosquito by one!" Therefore the question: ...
3
votes
2answers
408 views

String theory: why not use $n$-dimensional blocks/objects/branes?

I have a basic question: if we use 1d string to replace 0d particle to gain insight of nature in string theory, and advanced to use 2d membranes, can we imagine that using $3$- or $n$-dimensional ...
2
votes
1answer
89 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 ...
1
vote
1answer
204 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 ...
1
vote
1answer
516 views

Difficulty in visualizing more than three spatial dimension [closed]

Is there is any other way than abstract mathematics to visualize higher dimensions. Physicists working in high energy physics live in higher dimensions (pun intended), with their sophisticated ...
1
vote
4answers
1k views

Vectors with more than 3 components

I have some confusion over Vectors, Its components and dimensions. Does the number of vector components mean that a vector is in that many dimensions? For e.g. $A$ vector with 4 components has 4 ...
17
votes
5answers
5k 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 ...
5
votes
2answers
7k views

Do we live in a world with 4 or more dimension?

A NOVA show have told the audience that we are live in 3 dimensional world, the world we lived in is compose by 3 element: the energy, matter, space. By the time Einstein have invented the 4-...
5
votes
2answers
1k views

Does the Hilbert space of the universe have to be infinite dimensional to make sense of quantum mechanics?

Does the Hilbert space of the universe have to be infinite dimensional to make sense of quantum mechanics? Otherwise, decoherence can never become exact. Does interpreting quantum mechanics require ...
4
votes
6answers
709 views

what are dimensions?

First, discrete examples. In a computer screen I can specify any "2D" point with just one single number (pixel order starting count from first at upper left, and going on, left2right and up2down ...
1
vote
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
votes
1answer
306 views

Could the 6 extra dimensions in superstring theory be a product of two manifolds?

Could the 6 extra dimensions in superstring theory be a product of two manifolds?
3
votes
1answer
2k views

Why does the universe exhibit three large-scale spatial dimensions? [duplicate]

Possible Duplicate: Is 3+1 spacetime as privileged as is claimed? Regardless of your favorite theory of how many dimensions the universe has in total, the universe seems to have a deep ...
1
vote
2answers
746 views

How exactly do superstrings reduce the number of dimensions in bosonic string theory from 26 to 10 and remove the tachyons?

In bosonic string theory, to obtain the photon as the first excited state, the ground state must have a negative mass (tachyon). By applying $1 + 2 + 3 + \cdots = -1/12$, it can be shown (in a ...
8
votes
1answer
738 views

Mathematically rather than physically speaking, is there something “special” about 10 (or 11) dimensions?

As I understand it, string theory (incorporating bosons and fermions) "works" in $9+1=10$ spacetime dimensions. In the context of dual resonance theory, I've read descriptions of why that is "...
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 ...
2
votes
2answers
2k views

Electric potential due to a point charge in Gaussian/CGS units

I learned electrostatics in SI units. In SI, the electrostatic potential due to a point charge $q$ located at $\textbf{r}$ is given by $\Phi(\textbf{r}) = \frac{q}{4 \pi \epsilon_0 |\textbf{r}|}$. ...
1
vote
1answer
189 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?
-1
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2answers
3k views

Regarding possibility of infinitely many spatial dimensions

Recently I was taking a look at a video explaining the existence of fourth spatial dimension and thereupon that infinitely many spatial dimensions are possible. Also it showed that what Einstein told ...
20
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3answers
5k views

Gravity in other dimensions than 3 and stable orbits

I have heard from here that stable orbits (ones that require a large amount of force to push it significantly out of it's elliptical path) can only exist in a three spatial dimensions because gravity ...
21
votes
3answers
2k views

Can light exist in $2+1$ or $1+1$ spacetime dimensions?

Spacetime of special relativity is frequently illustrated with its spatial part reduced to one or two spatial dimension (with light sector or cone, respectively). Taken literally, is it possible for $...
13
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2answers
924 views

How is graphene a 2D substance?

How is graphene a 2D substance? It has length, width and some thickness to it, else it would be invisible. Why is it considered a 2D substance?
8
votes
1answer
265 views

Plausible explanations for 3 local space dimensions

Every now and then I see accounts of models that claim to explain why we experience only 3 space dimensions (locally, i.e. within cosmic horizons and outside black hole horizons). One such of course ...
9
votes
2answers
466 views

Some questions regarding $n+m$-dimensional spacetime [duplicate]

Possible Duplicate: Has the concept of non-integer $(n+m)$-dimensional spacetime ever been investigated by theoretical physicists? The following image: serves to aid the reader in ...
5
votes
1answer
443 views

Why do Calabi-Yau manifolds crop up in string theory, and what their most useful and suggestive form? [duplicate]

Why do Calabi-Yau manifolds crop up in String Theory? From reading "The Shape of Inner Space", I gather one reason is of course that Calabi-Yaus are vacuum solutions of the GR equations. But are there ...
5
votes
1answer
428 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 ...
4
votes
1answer
131 views

Are atoms unstable in 4+1 dimensions when quantum mechanics is taken into account?

I understand that in 3+1 dimensions according to classical physics atoms should be unstable however atoms are stable in 3+1 dimensions because the behavior of atoms is governed by quantum physics ...
3
votes
2answers
434 views

Why M-theory has only M2 and M5 branes?

Why M-theory has only M2 and M5 branes? In string theory, depending on the type one considers, you get all kind of D-branes. What is so special in M-theory that only allows 2 and 5 branes?
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?
3
votes
3answers
518 views

Is it time or duration? [closed]

Taking this post: "Is there a proof of existence of time?", as a starting point. Therein was mentioned that there is confusion between: "time" and "flow of time". There was a comment (of mine) that ...
1
vote
1answer
114 views

Theoretical implications of multidimensional Time [duplicate]

While the idea of extra spatial dimensions has been around for quite a while now, is there a possibility or any theory which proposes extra time dimensions? If so, what could be theoretical ...