Questions tagged [spacetime-dimensions]

Use this tag for dimensions of a manifold, typically the space-time. DO NOT USE THIS TAG for dimension of a physical quantity nor for the size of an object.

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64
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9answers
5k 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. ...
36
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5answers
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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 ...
28
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2answers
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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 ...
71
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6answers
6k 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 ...
18
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6answers
2k 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 ...
27
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1answer
7k 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 $p^{\mu}$, ...
24
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9answers
10k 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 ...
22
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7answers
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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 ...
12
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2answers
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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
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5answers
18k 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? ...
9
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3answers
953 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 ...
3
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2answers
960 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 any ...
21
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4answers
1k 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 $3+1$-...
25
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3answers
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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. ...
18
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2answers
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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 '...
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1answer
1k 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 ...
6
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4answers
936 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 ...
-1
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1answer
171 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 ...
28
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3answers
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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 $...
14
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2answers
562 views

In a universe with four spatial dimensions would there be elementary particles with intrinsic isoclinic spin?

Elementary particles have an intrinsic property called spin which is different from classical spin as it does not involve actual rotation and the magnitude of spin cannot be changed but particles with ...
9
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2answers
779 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, ...
5
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3answers
2k views

Why are there 4 Dimensions and 4 Fundamental Forces?

Is it a coincidence that there are four fundamental forces and four spacetime dimensions ? Does a universe with three spacetime dimension contain four fundamental forces? Can magnetism be realized in ...
15
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1answer
612 views

What is known about the hydrogen atom in $d$ spatial dimensions?

In a first (or second) course on quantum mechanics, everyone learns how to solve the time-independent Schrödinger equation for the energy eigenstates of the hydrogen atom: $$ \left(-\frac{\hbar^2}{2\...
20
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3answers
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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: ...
12
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2answers
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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 ...
5
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4answers
11k views

Electric field and electric potential of a point charge in 2D and 1D

in 3D, electric field of a piont charge is inversely proportional to the square of distance while the potential is inversely proportional to distance. We can derive it from Coulomb's law. however, I ...
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5answers
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How to prove that we are living in a 3+1D world?

Is there any scientific experiment that can lead us to conclude we live in 3 spatial dimensions without the premise of the conception of limited dimensions? Thank you all who helped in the ...
7
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2answers
4k 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 ...
2
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1answer
123 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 ...
25
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5answers
11k 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 ...
9
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1answer
399 views

Are atoms unstable in $d\geq 4$ spatial 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 ...
8
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1answer
317 views

Plausible explanations for 3 large space dimensions

Every now and then I see accounts of models that claim to explain why we experience only 3 large space dimensions (locally, i.e. within cosmic horizons and outside black hole horizons). One such of ...
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2answers
2k 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 ...
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3answers
548 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 ...
9
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1answer
936 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 "...
2
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2answers
662 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 ...
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2answers
198 views

Is there any thing composed of elementary particles in this world that is not 3 dimensional? [closed]

Is there any thing composed of elementary particles in this world that is not 3 dimensional? I know that there is graphite which is singular atom thick. Is there anything in this world that has no ...
14
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4answers
3k 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 ...
16
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1answer
344 views

What is the spin-statistics theorem in higher dimensions?

In $d = 3+1$ dimensions, the spin-statistics theorem states that fermionic particles have half-integer spin and bosonic particles have integer spin, in a well-behaved relativistic quantum field theory....
13
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3answers
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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?
9
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2answers
943 views

Why are the generators of rotation in the 4-dimensional Euclidean space correspond to rotations in a plane?

In three-dimensions, the rotation generators are represented by $J_1$, $J_2$ and $J_3$ where $1,2,3$ respectively stands for the generator of rotation about $x,y,z$ axes respectively. In general, in ...
7
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5answers
880 views

Perception of Depths and Stereovision [closed]

I watched a video on Youtube and read a few articles which say that human beings see 3D because we have two eyes. But does that mean when I close one of my eyes, I should see 2D? It doesn't happen so. ...
5
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2answers
34k 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-...
4
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6answers
887 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 ...
12
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1answer
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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 ...
7
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4answers
267 views

How could we know that the relativistic curvature of universe is intrinsic?

General relativity tells us that the universe is bent by gravity, but this curvature is intrinsic to the universe (the universe bends, but not in a fourth spatial dimension, the universe having only ...
5
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3answers
223 views

Do new gravitational effects emerge in higher dimensions?

Effects like gravitational waves and the curvature surrounding black holes do not occur in spacetimes with one time-like coordinate and two space-like coordinates. This is because the Einstein Field ...
3
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2answers
504 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
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2answers
1k 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
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2answers
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Gravity in 2d space and inverse linear law

In our three-dimensional universe, gravity obeys the inverse square law. In a four-dimensional universe, gravity would be expected to obey the inverse cube law et cetera. In a two-dimensional ...