Dimensions Definition and 1000 Threads

Hello, I want to understand if the 'extra space dimensions' is a realizable physical concept. They are just an assumption made by some theories (string theory for example) but i can't understand it at all. Ofcourse, my 'baby' argument is: -How can they exist since i can move my hand only in 3...

Is there any properties with the curvature tensors in 3 dimensions? (Maybe between the Ricci tensor and the Ricci scalar, they are proportional to each other? ) I heard about it in a lecture, but I can not remember the details. The 3 dimensional case is not discussed in many reference books...

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...

Homework Statement Consider integer sequence n_{1},...,n_{r} and matrices A_{1},...,A_{n-1}. Assume im\left(A_{i}\right) = ker\left(A_{i+1}\right) Using the rank-nullity theorem, show that \sum^{n}_{i=1}\left(-1\right)^{i}d_{i} = 0 Homework Equations The rank-nullity theorem...

Are there any exact solutions for two-dimensional projections of 3-body problems?

Homework Statement An m = 6.20-kg clay ball is thrown directly against a perpendicular brick wall at a velocity of 22.0 m/s and shatters into three pieces, which all fly backward, as shown in the figure. The wall exerts a force on the ball of 2660 N for 0.110 s. One piece of mass m1 = 2.20 kg...

I am designing an eddy current brake system for use in roller coaster design. I have the flux density required to reduce the speed to what i want it to be. what i need to do from that is work out the dimensions needed to obtain his flux density. the configuration is for identical magnets...

Detecting Vanishing Dimensions via Primordial Gravitational Wave Astronomy http://prl.aps.org/abstract/PRL/v106/i10/e101101

Is a three dimensional universe not a requirement for electrons to be configured as we know them? Wouldn't atoms at the least have to exist on a three dimensional brane for the electron clouds to exist as they do?

Hi all! I am having great trouble in the last days trying to make MATLAB plot for me a function of a matrix exponential of a variable t. Here's my attempt: first, I define the z-Pauli matrix s_3 and the identity matrix I by: %define the pauli matrices and the identity I% I = [1 0; 0...

I recently answered several questions in the biology forum regarding integrating over the change of voltage with respect to time. Although it wasn't part of the posters' question, I'm not sure about the physical dimensions of this integral. Electrical potential can be expressed as energy per...

Hello, we have been asked: i) State the dimensions of voltage. The work W done to move an amount of charge Q (coulombs) through a potential difference of V volts is given by W = VQ. ii) state it's SI units. Would I be correct to say i) the dimensions are V=J/C or could I word it V=W/Q ? ii)...

I've heard that there can be said to exist 11 dimensions of space and time, only 4 of which are perceptible to us directly. My question is this, is it possible that these extra dimensions are just collapsed gravitationally, and if so could this account for the apparently weak force of...

Hi, Here's a http://blogs.discovermagazine.com/cosmicvariance/2011/03/04/fractal-black-holes-on-strings/" ). Basically, they showed that if http://en.wikipedia.org/wiki/Black_string" is to be expected. However naked singularities would be such a strange thing that it seems safe to...

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...

Homework Statement proof at 0,0 g(x,y) is differentiable Homework Equations notes says i have to write in the form fx(0,0)\Deltax + fy(0,0)\Deltay + E1\Deltax + E2\DeltayThe Attempt at a Solution i compute fx(0,0) = 0 and fy(0,0) = 0 but what's the E talking about? what am i trying to do...

Hello! This is my first post but definitely not my last. I am programming a space simulator and my first problem to solve is to make gravitation work properly. If I have two objects at arbitrary positions in three dimensional space I can calculate the net force between them in a straight...

From what I have gathered, M-theory states that there are 11 dimensions. We live in 4 of these dimensions, and I believe the common understanding is that the 7 other dimensions are incredibly small. At the time of the Big Bang, these 3 dimensions expanded along with the universe while the...

Homework Statement A rectangular poster is to be made out of cardboard. The margins on the top and the bottom will be 2 inches. The margins on the sides will be 1 inch. the are of the poster devoted to the printed material must be 300 square inches. (a) To the nearest .001 inches, find...

Hello, first post, probably a beginner question, but I am stumped. I modeled a set of data in MATLAB using the finite difference method. I then solved the system of linear equations and the solutions are in an N x 1 matrix. The problem is, I need to use the pcolorcommand to plot it and need...

From what I have gathered, M-theory states that there are 11 dimensions. We live in 3 of these dimensions(unless time is considered its own dimension), and I believe the common understanding is that these other 8 dimensions are incredibly small. At the time of the Big Bang, these 3 dimensions...

What are all the 26 dimensions in the M theory, named?

Homework Statement Find the work done by a force of 3 Newtons acting in the direction 2i + j + 2k in moving an object 2 meters from (0, 0, 0) to (0, 2, 0). Homework Equations Commonly known vector operations. The Attempt at a Solution I found the displacement vector to be 2j...

Hello fellow physicists! Last meeting with my supervisor I had just recovered from disease so all I have left are some equations for the math behind path integrals that don't make to much sense.. I was wondering if, maybe someone can help and clarify what he was trying to get at. It would be...

Hi All, In Ken Onos lecture he mentions Hausdorff dimensions appertaining to prime numbers: 5,7,11 relate to 0 dimension and primes from 13 to 31 as 1 dimension. Are there more dimensions and if so do they also easily appertain to a set of prime numbers? Thanks Chris

I often read claims that string theory cannot possibly break Lorentz invariance. Whether people have feedback right now, or for future reference, I would like to open a thread on the following paper. A Slant on Warped Extra Dimensions

I am currently reading Dirac Equation from Peskin-Schroeder. In a particular para it says, "Now let us find Dirac Matrices \gamma^\mu for four-dimensional Minkowski Space. It turns out that these matrices must be at least 4X4." What is the proof of the above statement? I think (not sure)...

Homework Statement Let W1 and W2 be subspaces of a finite-dimensional vector space V. Determine necessary and sufficient conditions on W1 and W2 so that dim(W_1 \cap W_2)=dim(W_1)Homework Equations Replacement Theorem The Attempt at a Solution To clarify on the question: is the problem asking...

Homework Statement [PLAIN]http://img406.imageshack.us/img406/3756/fmp1.jpg How do I calculate the magnitude of the sum of these 3 vectors? Also, how do I find the angles the sum of the vectors make with each axis? F1 = 260N F2 = 75N F3 = 60N Homework Equations F = F1 + F2 + F3The Attempt at a...

Homework Statement The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 cm2, find the dimensions of the poster with the smallest area. Homework Equations Area of a rectangle is length...

Is it just me, or are dimensions supposed to simply add another coordinate, i.e., I can move 1m in x, y or z direction and be 1m away from where I started, are the dimensions in string theory based on this concept or do I not understand what a dimension is? The most confusing part is how these...

Homework Statement Two important quantities associated with air are the pressure and density. How can the pressure and density be combined to produce dimensions of speed? Look up the pressure and density of air at sea level and use your equation to estimate the speed of sound. Is your answer...

Would I be right in supposing that the function of coordinates is to allow one to find an object that one knows to exist in relation to another which one also knows exists? And if said coordinates do an acurate job then these coordinates are said to be correct until such time as...

I've read that string theory requires 11 dimensions, our 3 spatial dimensions, time, and then 7 more dimensions that only exist at sub-nuclear distances. They are described as tightly wound up dimensions, much smaller than a proton. I don't understand this picture. Mathematically, we can...

I am trying to solve something of an inverse problem for inertia, and having a real tough time with it. Any suggestions would be helpful. For a rectangular prism the mass and moments of inertia are: m = rho*A*B*C Ixx = m/12*(B^2 + C^2) Iyy = m/12*(A^2 + C^2) Izz = m/12*(A^2 + B^2)...

Brilliant forum, wish i'd spent time browsing it years ago. In my layman's "understanding" of string theory six dimensions are compactified and usually presumed to be of very small size. My questions are: 1. Is there any mathematical or (better still) physical reason why this space does...

hi, I have a very simple question: why is there really a need for more than 4 spacetime dimensions? are there any concepts for which 4 dimensions are not sufficient? thank you!

I have a few questions on non-critical string theory... terminology: 1: Are "Gepner models" a subset of non-critical string theory? technical: 2: Given a set of spectrum, are there ways to construct a non-critical string theory with enough symmetries so that the CFT becomes minimal and...

Homework Statement Hello everyone, i have been stuck on this question on the Physics year 12 Nelsons textbook, and it is pissing me off because I've been working so hard on it and i can not get it. It is in the chapter of Movement in one and two dimensions. The question is: A person...

Search for Microscopic Black Hole Signatures at the Large Hadron Collider Authors: CMS Collaboration http://arxiv.org/abs/1012.3375 (BTW, slashdot is running this as a falsification of string theory, based on a jokey summary on the Not Even Wrong blog. Not Even Wrong has posted an update...

Homework Statement An object moves clockwise with decreasing speed around an oval track. There are velocity vectors at two points (G and H). G has a greater speed than H. Is the angle between the acceleration and velocity vector of G greater than, less than, or equal to 90 degrees...

Can dimensions exist that are not space dimensions nor time dimensions? I was just curious.

Homework Statement This question is from a correspondence course I'm taking: Two spacecraft from different nations have linked in space and are coasting with their engines off, heading directly toward Mars. The spacecraft s are thrust apart by large springs. Spacecraft 1, with a mass of...

Homework Statement Jim moves a 2kg brick along the ceiling by applying a force at an angle of 24.6 degrees. If the brick moves with no acceleration and the coefficient of kinetic friction between the brick and the ceiling is 0.467, what is the magnitude of the applied force? Homework...

I am not sure under which rubric questions about string theory or M-theory should go. Anyway, since this question concerns sizes down to the Planck distance, I suppose it should go here. The question is two fold: in such a case as the 6 extra spatial dimensions of string theory, how does...

I am wondering if anyone here conversant with information theory could tell me what the difference is in potential information content between 3 dimensions and 4 dimensions.

dimensions of the one-dimensional wave function? is it [si]=L-1/2?

Homework Statement [PLAIN]http://img515.imageshack.us/img515/5139/physicsproblem.jpg Homework Equations in the image The Attempt at a Solution I don't know if i placed the angles theta1 and theta2 correctly in the diagram..I feel like this is incorrect, since the value i...

Is there a possibility that there are infinite dimensions in our universe.M theory predicts that there are 11 dimensions,but why not more?

Homework Statement Attached Homework Equations 5.104 mentioned in the problem is Also attached The Attempt at a Solution Suppose the mass is moved to (x,y), the distance from the mass to the left spring is denoted by A, the distance from the mass to the right spring is denoted...