4d Definition and 116 Threads

What is the most general method of approximating arbitrary systems of ODEs of 4 variables(x,y,z,t) that fit these conditions? The conditions that are assumed true of the ODEs are: 1) that I require differentials to be explicitly defined (but they can be defined in terms of other...

Hello, This might be a bit of a stupid question, but if there were a universe of 4 spatial dimensions and photons behaved in the same way as in ours, would a 4D "hyper-alien" be able to see 4D perspective with only 2 hypershpherical eyes, or would it require more? In case my question isn't...

in a 4D space time, ¿what is de descomposition of de distribution: \delta^{(4)} (P_x+P_y-P_z-P_t) ? i think that is equal to \delta^{(4)} (P_x+P_y-P_z-P_t)=\delta(P_x) \delta(P_y)\delta(-P_z)\delta(-P_t), but, i don't understand...

Hello, I'm trying to construct an explicit map that takes the 4D torus to the 4-sphere such that the wrapping is non-trivial (i.e. homotopically, i.e. you can't shrink it continuously to zero). More concretely, I'm looking for \phi: T^4 \to S^4: (\alpha,\beta,\gamma,\delta) \mapsto (...

The combination of special relativity and quantum mechanics in a single framework makes our understanding of such systems to be true only in 4D, Minkowski space...I have noticed that recent published work concerning 2D systems and I am not sure about this reduction of 4D to only 2D, does it mean...

"If it works in 3D, then it works in 4D" I've been watching Leonard Susskind's lectures on special relativity here. At time 0:59:40 he says, "If the vectors are Lorentz invariant, then if the first 3 components of a 4vectors are equal to the first 3 components of another vector (equation), then...

I posted this in yahoo questions, but perhaps this is a better place for it. The Tesseract assumes that in order to add another Euclidean dimension another orthogonal plane is added into the mix, right? That is the pattern when going from 1D to 2D to 3D, but it seems like something slightly...

We know that a Clifford torus is parameterized in 4D euclidean space by: (x1,x2,x3,x4) = (Sin(theta1), Cos(theta1), Sin(theta2), Cos(theta2)) {0<=theta1 and theta2<2pi} Consider that a clifford torus is the immediate result of Circle * Circle Now, have you encountered a similar manifold...

Homework Statement How many points (x1,x2,x3,x4) in the 4-dimensional space with nonnegative integer coordinates satisfy the equation x1 + x2 + x3 + x4 = 10? I'm not sure which method to use to start this problem. Any ideas?

I've been having trouble visualizing 4D objects(4 physical dimensions, excluding time), in fact I can't seem to be able to do it at all.Can someone help me on it? I don't simply want to imagine how they might simply appear in 3D space and show their 3D projections as they pass by. I want to be...

Hello I was sitting and thinking one evening and got this question. In our 3 dimensional universe we have our sun, we know all the parts that makes the sun and how it interact with objects and space around it. If we say that we have a 4 dimensional universe and have the same sun there...

What is the definition and implications of 4D space? By implications I mean if it existed how will it redefine what we know about physics and reality up to now. (Applications, possibilities, etc)

I have been reading about http://en.wikipedia.org/wiki/3-sphere" and found it was impossible for me to visualize it. I tried visualizing a 4d structure with 3 space-like and one time-like dimensions by imagining a sphere (with 3 dimensions) growing with time, with successive layers (formed...

I need a free description with illustrations on 4D knots theory, especially the 4D generalization of Reidermeister moves and the movie represantation. Where can I find a freely available paper?

Haelfix pointed out the paper http://arxiv.org/abs/1105.4733" , and Witten 2007 (discussed in that thread) expresses doubt that 4D gravity could be exactly solved, precisely because it has local excitations. And yet here Maloney et al have done it in 3 dimensions. Can something about their...

Homework Statement I am given two lines in vector form in 4-space. I need to write an equation for the plane that is parallel to one line, and contains the other line.Homework Equations well i know that in 3d I would find a normal vector for the plane that would be perpendicular to both lines...

Homework Statement Prove that the element dt\ dx\ dy\ dz is invariant under Lorentz boost with velocity \beta along z axis. Homework Equations Convention c=1 Lorentz boost in z direction: L(z)=\left[ \begin{array}{cccc} \gamma & 0 & 0 & -\gamma\beta \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\...

Hello all, Given two 3D lines described by the general equation \vec{L(t)}=\vec{p}+\vec{d}t I found a way to find their intersection point, but it uses the cross product in the derivation. I am assuming a 4D line is a valid thing? And can be described the same way? (except with 4 element...

I know both the 4D SUSY algebra and conformal algebra. However, I'm struggling to find elementary introductions to the 4D superconformal algebra. Anyone has suggestions? Neither introductory SUSY books (e.g. Wess & Bagger) nor CFT books (like Di Francesco) seem to cover this...

Homework Statement Find sup{\epsilon| N\epsilon(X0 \subset S} for X0 = (1,2,-1,3); S = open 4-ball of radius 7 about (0,3,-2,2).Homework Equations If X1 is in Sr(X0) and |X - X1| < \epsilon = r - |X - X0| then X is in Sr(X0) The Attempt at a Solution This is my first foray into...

Just like we can draw 3D-looking images on paper, has anyone tried to "draw" out a 4D image onto 3D space? It's not really drawing, more like building. Since nobody can visualize 4D, it would have to be done mathematically. I've seen projections of hypercubes onto 3D, but it was still 2D since...

1. prove in the 4-dimensional Riemannian space, the 4-divergence of the 4-curl is not zero that is where is the 2d’Alembertian operator 2.∂νGμν = ∂μ∂νaν(xκ)−2aμ(xκ) = 0

Howdy everyone, I'm on a quest for something that is proving a bit elusive at the moment: a Cartesian to polar transform (along with its inverse) for \mathbb{R}^4. I'm well aware of how to derive the transform for both \mathbb{R}^2 and \mathbb{R}^3, as it is just a matter of looking at the...

What would a 3D ball look like if it were partially in 4D space when none of the 4th dimension is visible to the 3D observer? The equivalent question in flatland is: What would a 2D filled circle look like in flatland if it was partially in 3D? I think that there the answer would be a...

Can the strings of string theory live in only 4D spacetime? Do we get anything interesting or useful? What do we lose? Thanks for any ideas or help!

Peter Woit ("Not Even Wrong" blog) reported today on two recent talks by Edward Witten which are available video online. Here is the link to Woit's blog, which gives an brief overview of what the talks are about. http://www.math.columbia.edu/~woit/wordpress/?p=3107 In case anyone is...

Homework Statement There is points: P=(1,2,3,4) Q=(4,3,2,1) and line L passes through P and is parallel to A A=(1,1,1,1). X(t) is anypoint on line L. 1. Find the distance between X and Q as a function of t. 2. Find the minimum distance between Q and the line.(which is 2(51/2))Homework...

I have a temperature distribution T = T(x,y,z). I want to visualise it in MATLAB ( such that the colour(s) used by MATLAB in plotting should give me an idea of depth of temperature i.e whether its high or low compared to its neighbouring points). Please help

In the following question: http://phstudy.technion.ac.il/~wn114101/hw/wn2010_hw12.pdf How Do I caculate the precession rate in 4C? And also in 4D?

I read on a website (http://math.ucr.edu/home/baez/physics/Relativity/GR/gravity.html): "The world we live in consists of four dimensions, the three space dimensions and one that is not exactly time but is related to time (it is in fact time multiplied by the square root of -1)." In my...

Is there an identity for a product of 2 LC Tensors in 4D if one sums over 3 of the indicies? i.e. \epsilon^{\mu \beta \gamma \delta} \epsilon_{\nu \beta \gamma \delta} = ? What if gamma is constrained to be 0? Does this reduce things? Best Regards

Meissner Nicolai conjecture---opening to a 4D ToE Here are five papers by Kris Meissner and Hermann Nicolai: http://arxiv.org/find/grp_physics/1/AND+au:+Nicolai_H+au:+Meissner/0/1/0/all/0/1 The latest contains a conjecture which they summarize in the concluding paragraph: "The main conjecture...

Case 1 In 2D coordinate system the sum of the angles of all quadrants=360 degree in (x,y) plane Case 2 In 3D coordinate system (x,y,z) I took 3 possible planes i.e. (x,y) (y,z) (x,z) each plane provides angle of 360 degree, so can we say that in 3D coordinate system sum of all...

I'm sorry if what I say is not right, or I haven't understood it right, - In 3+1 D we have the photon with spin 1 => it has two polarizations. Our Gauge field A_\mu has 4 components => We have two extra degrees of freedom. => We need to get rid of the extra 2 fixing the gauge. 1. The...

Spacetime is 3D + 1T = 4D Is spacetime in string theory 4D as a result of compactification, or 12D, 11D+1T?

Hi all- I have a question regarding using the find function as opposed to if statements in finding values in a 4D array. These are climate variables, such as temperature (in Kelvin). Missing values are represented as 10^15, and I want to change them to NaN which plots much nicer. I have...

Hidden dimensions of string theory "hiding" in 4D spacetime? Could the hidden dimensions of string theory be "hiding" in 4D spacetime? Thank you for any thoughts.

Hi, I am struggling to understand Stephen Hawking's view of the universe as a 4D closed manifold. In a recent interview, I believe he had this to say: What I don't understand is how this theory is compatible with the scientific observation that the universe is expanding? I have 2 questions: 1)...

iam sorry if this is crackpottery,but is it true that a 4 dimensional figure*called the tesseract has been constructed,i came across this over the net.*kindly rebuke me if iam not abiding with the rules of pf.

What is the name of the theory (or person who thought it up) that the universe is infinite in the 4th spatial dimension and that our big bang is only a local effect?

I am looking for a 4D angular coordinate system (radius and three angles) and its corresponding "hypervolume element". 2D: polar coordinates - dA = r dr dtheta 3D: spherical coordinates - dV = r^2 sin(phi) dphi dtheta dr 4D: ?

I've seen the statement repeated in many places that a stable knot comprising 1D curves cannot be created in 4D, since it's always possible to untie the knot by moving in the 4th dimension (whereas it is possible to create a stable knot in 4D using 2D surfaces). Can anyone point me to an...

Major paper by Fairbairn--a way to put matter into 4D quantum gravity I expect this paper will "raise the dead" in the sense of evoking a comment from John Baez :-). It develops some lines of research he was working on three years ago. It references work by Derek Wise, a Baez PhD----also...

Can a 4-dimensional manifold with the Schwarzschild metric be embedded into a flat manifold of 5 (or more if necessary) dimensions? In other words, are there functions of t,r,\theta , \phi and M such that if x_1 = f_1 (t,r,\theta ,\phi ,M) x_2 = f_2 (t,r,\theta ,\phi ,M) . . etc...

Lisa Randall said "string theory reproduces GR in 10 dimensions" Does string theory gravitons have 4D GR as its low energy limit? I know that its lowest mode vibrations corresponds to a massless spin-2 particle, the graviton. I know GR in 4D can be extended with susy. Does it reproduce...

this may seem quite stupid to many of you but i was wondering how it is possible to draw 4D objects. I have seen pictures of 4D objects such as the hyper-cube etc, but they are drawn in three dimensions. The picture of a hyper cube that i looked at seemed to me to just look like a cube with a...

http://arxiv.org/abs/hep-th/0611042 Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams Aristide Baratin, Laurent Freidel 28 pages, 7 figures "We show how Feynman amplitudes of standard QFT on flat and homogeneous space can naturally be recast as the evaluation of...

Yo anyone, Could someone enlighten me as to why, if there is a 4th spatial dimension, we can't see 3D shadows of 4D objects? Lots of talented people built an amazing 3D shadow of a 4D object but I'm almost certain I've never seen one pop in and out of existence while on the way to the shops...

Any one can guide me to some good books about 4-dimentional electrodynamics? I don't want books that starts from electromagnetical theorems for maxwell, i want them to start from 4-dimentional systems and operations on them or tensors about them Thanks,,

Baez et al revised the title of their March 2006 paper to say "strings" instead of "loops" and reposted it http://arxiv.org/abs/gr-qc/0603085 Exotic Statistics for Strings in 4d BF Theory John C. Baez, Derek K. Wise, Alissa S. Crans 41 pages, many figures. New version has minor corrections and...