Higher dimensions Definition and 79 Threads

If there are computer simulations of four-dimensional space are there any possibilities to digitally simulate a space -time with time having more than one dimension? Please, leave some related links, if possible.

The ansatz for the 5D metric is \begin{equation} G_{\mu \nu}= g_{\mu \nu}+ \phi A_{\mu} A_{\nu}, \end{equation} \begin{equation} G_{5\nu} = \phi A_{\nu}, \end{equation} \begin{equation} G_{55} = \phi. \end{equation} This information was extremely enlightening for me, but what's the analogous...

Assuming there are higher spatial dimensions are there things that exist in 3D that actually cannot exist in higher dimensions? Maybe even dimensions?

I'm watching Sean Carroll's video on symmetry [relevant section at around 8:05] He talks about 120 degree rotations of triangles that leave them invariant. Then he proceeds to talk about flipping them with an interesting (at least to me) remark - "there's nothing that says I'm confined to...

I am uncertain if this belongs in the differential geometry thread because I don't know what area of mathematics my question belongs into begin with, but of the math threads on physics forums, this one seems like the most likely to be relevant. I recently watched a video by PBS infinite series...

Neural networks have come a long way since I first took a course, 25 years ago. Now that I'm in the Online Masters in Analytics program at Georgia Tech, I see these topics come up often. I found the following article an interesting read...

In 3D the most general motion of a rigid body consists of a displacement and a rotation. In higher dimensions is this still the most general motion? Or are there unexpected ways of moving with more freedom? One subtlety, for example, is that we would have to allow for multiple rotations...

Homework Statement: I do know how to solve the resistance network problem in two dimensions. However, in this problem they want it in 3 dimensions and higher and I don't know how to do that Homework Equations: - In the picture you can see the solution to the two dimensional version

Homework Statement Examine if the function is differentiable in (0,0)##\in \mathbb{R}^2##? If yes, calculate the differential Df(0,0). ##f(x,y) = x + y## if x > 0 and ##f(x,y) =x+e^{-x^2}*y## if ##x \leq 0 ## (it's one function) Homework Equations ##lim_{h \rightarrow 0}...

Looking at Munkres "Analysis on Manifolds", it says for $A\subset R^n, f: A \rightarrow R^m$ suppose that $A$ contains a neighborhood of $a$. Then $f$ is differentiable at $a$ if there exists an $n$ by $m$ matrix $B$ such that, $\frac{f(a+h)-f(a)-Bh}{\left| h \right|}\rightarrow 0$ as...

The second Randall-Sundrum model was based on a large as opposed to compactified dimension. Has the possible existence of large higher dimensions been eliminated and what evidence rules them out?

Hello! Can someone recommend me some good readings about spinors in physics? I know some basics (i.e. how they work in Minkowski space for Dirac field), but I would like to understand more of the mathematical formalism behind them (how can you build them, in a general number of dimensions, how...

Homework Statement Consider gamma matrices ##\gamma^0, \gamma^1, \gamma^2, \gamma^3## in 4-dimension. These gamma matrices satisfy the anti-commutation relation $$ \{ \gamma^\mu , \gamma^\nu \}=2\eta^{\mu \nu}.~~~(\eta^{\mu\nu}=diag(+1,-1,-1,-1)) $$ Define ##\Gamma^{0\pm}, \Gamma^{1\pm}## as...

What's so special about higher dimensions? I did some youtube research and didn't find a lot of information. All I found is that beyond 5 dimensions all dimensions have only 3 platonic solids. I've got this simulation I'm working on. I don't want to go into detail for obvious reasons but so...

will there be any effect on the speed of light ,when it travels from higher dimensions to three dimensions of space ?

Why can't we perceive higher dimensions?

Is there an alternative set of equations similar to Lorentz Transformations that transforms vectors from one dimension to a higher or lower dimension?

I am reading the proof of the Riemannian Penrose Inequality (http://en.wikipedia.org/wiki/Riemannian_Penrose_inequality) by Huisken and Ilmamen in "The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality" and I was wondering why they restrict their proof to the dimension ##n=3##...

It's my understanding that, if we ignore the temporal dimension and just focus on spatial ones, then you get to the third dimension by starting with a point and adding perpendicular lines to them. Once you've done this a couple of times, you get three dimensions. Obviously, to the layman, it...

Halo, I was reading about geometry from Tim Gowers book titled "A very brief introduction to mathematics". I came across fractional dimensions and the 4th dimension. The koch snowflake has dimension 1.2 yet he could comfortably drawn it on a 2d page (or is it complete?). Has not he just...

In the links below Carl Sagan and TED-Ed described about higher dimension: and here's a description of Brian Greene: Carl Sagan and TED-Ed explained, we can not see the higher dimensions because we are limited to perceive only three dimensions. They didn't say a dimension can be small or...

I was wondering if I can expand the FRW metric in d spatial dimensions, like: g_{\mu \nu}^{frw} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & - \frac{a^2(t)}{1-kr^2} & 0 & 0 \\ 0 & 0 & - a^2(t) r^2 & 0 \\ 0 & 0 & 0 & -a^2 (t) r^2 \sin^2 \theta \end{pmatrix} \rightarrow g_{MN} = \begin{pmatrix} g_{\mu...

Caution: I'm new at this stuff. On page 573 of Gravitation (Misner, Thorne, Wheeler), they write down what I think is the electromagnetic wave equation for a discussion on Optics, "Next insert the vector potential (22.25) into the source-free wave equation (22.19d):" I am wondering if the...

Is there an intuitive reason or proof demonstrating that in general dimensions, there is no direct analogue of the binary cross product that yields specifically a vector? I came across Wedge Product as the only alternative, but am just learning linear algebra and don't quite comprehend yet...

It is frequently stated in the literature that the first attempt to unify gravitation and electromagnetism through a theory in higher dimensions was attempted by Kaluza and Klein. Yet, today I have realized that this is not true. The first such attempt was done by Nordstrom in 1914...

Local Electrodynamics in higher dimensions?? So I am an unexperienced undergrad but the other day I had a few thoughts which are most likely crazy. I'm just wondering why they don't work. And whether the questions I'm asking are answered elsewhere. So I've heard: (i) Maxwell's...

Let me try to explain. If I take a reel of movie film, I can unwrap it see different frames simultaneously. How ever if I were "trapped" in the movie I could only experience one frame at a time. Now this example is not a direct proposition I am making. It''s just to imagine a higher...

If the universe follows a 3-torus or finite unbounded shape, or we are situated on the surface of a 4D sphere, then the 'centre' if the universe will exist. If one could locate the position of this origin in 4D space, and remain stationary with respect to it, then would that object be at...

[FONT=Georgia]Look at this page and the Proof part, Fermat's theorem (stationary points) - Wikipedia, the free encyclopedia [FONT=Georgia]How to change the proof 2 into a proof of higher dimensions or can you give a proof of Fermat's theorem of higher dimensions?

Hairy ball theorem - Wikipedia is not as good or as well-referenced as I'd hoped, and it mainly discusses vector fields on the 2-sphere, the ordinary sort of sphere. In particular, it does not mention the minimum number of zero points of a continuous vector field on a sphere. I would guess...

Every picture I've seen to illustrate wormholes is always a shortcut from one point on a 2D surface to another. And it's easy to see that the distance is shorter through the wormhole since we are view it from a 3D perspective. This makes me wonder if higher dimensions are required to construct...

Weinberg wrote that in 3D and higher spaces all particles must be bosons or fermions. The proof used the fact that particles are really indistinguishable i.e. we can't "mark" any particle and the mathematical replacement of two particles of the same type should not change any physical...

I thought it was pretty straightforward until 4:26, until they started making some questionable claims. I'm no expert so I thought I'd ask here. http://www.youtube.com/watch?v=0ca4miMMaCE

A problem in Linear Algebra by Jim Hefferson: Euclid describes a plane as \a surface which lies evenly with the straight lines on itself". Commentators (e.g., Heron) have interpreted this to mean \(A plane surface is) such that, if a straight line pass through two points on it, the line...

My Professor frequently uses the term higher dimensions. Could someone tell me exactly what is a dimension. I think of it as some parameter which can vary. Also, I only know of 4 dimensions: time, length, width and height. Could someone give me more examples of dimensions? And lastly could...

I seem to have read something once that suggested that gravity may be leaking into other dimensions/branes, this could explain why this force is so weak. I've been left thinking that it makes sense as a possibility. If it turns out to be the case, could Dark Energy then be leaked gravitational...

In 3 space dimensions consider a 1D string under tension between two fixed points. Let the string lie at rest on the z axis between z = 0 and z = ∞. We can produce linearly polarized and circularly polarized waves if I move the end of the string properly? Now if we add an extra space dimension...

What Higher Dimensions "Feel" Like nevermind.

What is the study of higher dimensions called? What I'm referring to are hyper cubes and such. I finished basic math this past year (calc123, ode and linear alg) and I really want to learn the calculus of higher dimensions. Does a field like this exist?

Homework Statement Let \textbf{F}: \textbf{R}^m \rightarrow \textbf{R}^n and \textbf{G}: \textbf{R}^p \rightarrow \textbf{R}^m Prove that ({\textbf{F} \circ \textbf{G}})'(x) = {\textbf{F}}'(\textbf{G}(\textbf{x})) {\textbf{G}}'(\textbf{x}) Homework Equations Assume the single...

Consider the following model. Put a lattice of N electrical nodes on a sphere. The lattice doesn't have to be perfectly regular. Each node is connected to others by copper wires that run through the interior of the sphere. The wires do not interfere with each other. In some initial state...

Hi, I've been reading quite a few popular science books (Michio Kaku, Stephen Hawking) where the specific example for us to visualise how a 4D creature would interact with us is portrayed through us interacting with 2D "flatlanders". The specific example is how we would lift a 2D flatlander of...

Homework Statement Do the following limits exist? State any relevant ideas. a) limit as (x,y) -> (0,0) of (xy)/(x2 - y2) b) limit as (x,y) -> (0,0) of (x2)/(3x4 + y2) c) limit as (x,y) -> (0,0) of sin(2x)/y The Attempt at a Solution I don't really know where to start; I can't...

Hi, I was thinking about Knot Theory for a while and started thinking about higher dimensionalities. Could the knots we know so well (knots in 3d space) be undone if allowed to be manipulated through a fourth spatial dimension? Could they be made topologically equivalent to the unknot? And if...

Do you know of any papers about spin in dimensions>4? It seems that there are two independent spins in 4+1 dimensions, since you can replace spatial dimension 1 with 2 and 3 with 4, each pair not messing with the other. I found only one paper on arxiv: <http://arxiv.org/abs/0908.2484> on 5D...

Hi everyone , this is my first time here :) My question is simple , if gravitation is basically a space distortion so it's fair to say that at least a fourth dimension exists , since a distortion must occur in higher dimension than the one of the concerned space . Is it correct putting it...

it seems that the vector product between vectors in three dimensions is peculiar property of the three dimensional space

a derivation of the formula for arc length is simple enough: given a function f[x], find the length of the arc from x0 to x1. lim(x1-x0)/n=dx n->inf x1 S=^{i=n-1}_{i=0}\sum\sqrt{(x+(i+1)dx-(x+idx))^2+f(x+(i+1)dx)-f(x+dx))^2} xo...

Strings live in 9+1 world, M, 10+1 one line of criticism is string theory is unable to account for the number of large and compactified dimensions, i.e 1 (line) large, 9 curled, 2 large (sheet), 7 curled, 3 large 6 curled (our world) all the way to 9 flat or 9 curled. Is there an a priori...

Hey there, I've just started learning quantum mechanics and I'm currently reading about gravity and higher dimensions. That is, I know so very little and would like to see if somebody could lend me some clarification . The uncertainty relation comes from the fact that matter waves in and out...