Dimensions Definition and 1000 Threads

Right, Hello, I am new to this, and do not have much understanding, but can someone here help explain the Dimension Models and String theory to me?

Will someone please explain to me how a theory, such as a quantum field theory, be expressed in more than three dimensions? Is this referring to the spatial dimensions we live in now, or what? And how does someone even begin to ponder these multiple dimensions?

Hello everyone, I’d like to find the following range equalities: Considering the following: A=B+C \\ A=B.C^T \\ A=[ B^T C^T ]^T I would like to find the function f for each equality above. .\\ dim( R(A) ) = f( R(B) , R(C) )\\ Considere that all matrices have compatible...

Homework Statement Find the work done by a force acting in the direction 2i - 5j + k in moving a particle from (3, 3, 1) to (1, 2, 4). Homework Equations The Attempt at a Solution I just found the displacement vector (2,1,-3) and did the dot product with the force vector...

Hi everyone, I'm having trouble understanding a problem on CNT in 2d. I'm given the equation \Delta G = \frac{4}{3} \pi R^3 \rho_s \Delta \mu + 4\pi R^2 \gamma for nucleation in 3d. Here mu is the difference in chemical potential between the solid and liquid phase, R is the radius...

Apriori, I don't see why there should be 10,11 or 12 dimensions? Can't we have indefinitely number of dimensions? Or such an option isn't viable cause we can't test it empirically (not that the hypothesis of less dimensions is testable either, besides the 3+1 we know already).

Look at this page and the Proof part, Fermat's theorem (stationary points) - Wikipedia, the free encyclopedia 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?

So I just got out of my linear algebra midterm, and this question is confusing the hell out of me. Basically, it's a subspace of R^4, such that the coordinates satisfy the following qualifications: (a, b - a, b, 2(b - a)) So basically, a and b can range over the xz plane, and y and w sort...

Homework Statement Given v1, v2 ... vk and v, let U = span {v1, v2 ... vk} and W = span {v1, v2 ... vk, v}. Show that either dim W = dim U or dim W = 1 + dim U. The Attempt at a Solution I'm not really sure where to start. If I knew that {v1, v2 ... vk} was linearly independent, then it would...

Suppose we have a 2d problem (for instance a 2d box). You look for separable solutions in x and y. But it seems to me that the solutions are in a way determined by how we choose the separation constant. Do we know anything a priori that tells us if the separation constant should be negative or...

What is the nature of sound in each dimension e.d 1D, 2D, etc and how can one be differentiated from the other. I do not seek formulas just a straight forward explanation.

Dear experts, I'm not familiar with crystal structure theory. I'm seek expertise to figure out space groups in 2 dimensions Bravais lattice of the attached structures. In the figure, red and greens dots represent different atoms. I'll greatly appreciate your help. Struture 1...

I would like to know what effect does tire width and tire diameter has on performance or overall efficiency of a vehicle.

Homework Statement Three cables are used to tie the balloon shown in the figure. Determine the vertical component of the force P exerted over the balloon at point A, if the tension on cable AB is 259 N. http://img521.imageshack.us/img521/9687/physicsballoonproblem.png (Sorry for the figure...

Homework Statement An event happens in frame S at x=100m y= 10m z=1m at time t=2*10^-3s. What are the coordinates of this event in rame S' that is moving with velocity v=0.92c (ihat) and the orgins coincide at time t=0. Homework Equations Lorentz transformations The Attempt at a...

Is it possible for an object with 6 dimensions to exist in a three dimensional universe?

Advanced Calculus of Several Variables, 5.6: Two vector spaces V and W are called isomorphic if and only if there exist linear mappings S : V \to W and T : W \to V such that S \circ T and T \circ S are the identity mappings of S and W respectively. Prove that two finite-dimensional vector...

Galileo shows that, if any effects due to air resistance are ignored, the ranges for projectiles on a level field whose angles of projection exceed or fall short of 45 degrees by the same amount are equal. Prove this result. A: So ,I tried these vx = v*cos(q) //q is the shooting angle, vx is...

I have reading about cosmic strings and have some questions about them, are they in any way related to other dimensions even though they are one dimensional? Also do they have anything to do with gravitons and the cause of gravity?

Homework Statement A particle leaves the origin with a velocity of 7.2 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (3.0i - 2.0j) m/s2. At the instant the particle moves back across the x-axis (y=0), what is the value of its x coordinate...

Hi, I'd be grateful if someone could tell me whether these proofs I've done are correct or not. Thanks in advanced. Let V be an n-dimensional vector space over \mathbb{R} Prove that V contains a subspace of dimension r for each r such that 0 \leq r \leq n Since V is n-dimensional...

How hard is that SF? – Pharyngula mentions a survey that someone once did, asking people to rate various science-fiction movies on two dimensions. Hard: a work "takes great care in accurately presenting then-known scientific facts". Soft: a work "often and casually violates our understanding...

I have a few questions so I hope it is okay if I ask them all here in this thread. They are all related somewhat. According to brane cosmology, our 4-D universe is embedded inside a higher dimensional space, a hyperspace if you will, called the bulk. The reason we cannot perceive or interact...

So say I have a n-1 form \sum^{n}_{i=1}x^{2}_{i}dx_{1}...\widehat{dx_{i}}...dx_{n} and I want to find the exterior derivative, how do I know where to put which partial derivative for each term, would it simply be?? \sum^{n}_{i=1}...

On all manifolds dimension 1-3, there is only one differential structure per manifold, yet in higher dimensions it seems to follow no pattern. Is there a physical reason why you can construct a certain number on any given dimension? Also, what is it about dimension 4 that is so strange? Using...

Problem: A hockey puck rebounds from a board as shown in figure 16. The puck is in contact with the board for 2.5 ms. Determine the average acceleration of the puck over the interval. t = 0.0025 s |vi|= 26 m/s |vf| = 21 m/s aav = ? *v and a are vectors* I have made several attempts to...

Hi all, I was deriving the free electron gas for practice in 1, 2, and 3 dimensions, and I started wondering why they have different dependencies on energies and what that means. I got: 1D: ##g(E) = \frac{1}{\pi\hbar} \sqrt{\frac{2m}{E}}## 2D: ##g(E) = \frac{m}{\pi\hbar^2}## 3D: ##g(E) =...

find the dimensions of the largest rectangular box with a square base and no top that can be made from out of $1225 in^2$ of material. well, this might be over simplified but since the volume is max of cube to the a surface area I thot making a cube out of the material would be max volume...

Hi! :) I'm trying to calculate the appropriate lenses to use for a project. I need to magnify a 50mm by 50mm square image that is 40mm from a magnifying lens (with a radius of 12.5mm). Due to size constraints, I also have a thin prism to redirect the light. Assume the viewer (an eye) is...

I read on the 'Ask A Mathematician/Ask A Physicist' blog that sound waves behave differently in an even-number of dimensions than they do in odd-number dimensions - that they 'double-back'. Why is this - and what does 'double-back' mean...

Hi all. I'm trying to solve this PDE but I really can't figure how. The equation is f(x,y) + \partial_x f(x,y) - 4 \partial_x f(x,y) \partial_y f(x,y) = 0 As a first approximation I think it would be possible to consider \partial_y f a function of only y and \partial_x f a function of only...

How do you calculate an object in 4 dimensions? Like the 4 dimensional cube. I understand that a point is the beginning of a line and a line is the beginning of a plane. From there a plane translates into a 3 dimensional object. A 3 dimensional object translates into a 4 dimensional thing... I...

Homework Statement the perimeter of a rectangle is 24 ft. the length is 4 ft longer than the width find the dimensions width x length x+4 however, I should be doing it like this: a first equation should start like: 2x+2y=? and the second should start like x=y+? so what's the...

If we assumed an empty space, but also assumed space dimensions are closed ( repeat after some distance D ), what would the metric tensor look like? Is this just equivalent to a space with a constant curvature R? If so, how does R relate to D? Would the time dimension also necessarily be...

Vector Question: 3 dimensions inside a rectangular soild?? Homework Statement Three forces of 5 N, 8 N, and 10 N act from the corner of a rectangular solid along its three edges. a. Calculate the magnitude of the equilibrant of these three forces. b. Determine the angle that the equilibrant...

Hello all, I am currently doing a design project on gyroscopes. My question concerns the flywheel design, specifically trying to determine the dimensions of a flanged free-spinning flywheel to maximize the moment of inertia while trying to minimize the mass, given certain design constraints...

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...

Homework Statement Let f : ℝ2 -> ℝ be some function that is defined on a neighborhood of a point c in ℝ2. If D1f (the derivative of f in the direction of e1) exists and is continuous on a neighborhood of c, and D2f exists at c, prove that f is differentiable at c. Homework Equations...

Quantum mechanics in 1 + 1 dimensions is equivalent to qft in 0 + 1 dimensions. This is because the position x(t) of a particle can be replaced by a scalar field \phi(t) , and the momentum is replaced by the momentum conjugate of \phi(t) . Also, in the bosonic construction of heterotic...

Given that string theory is built on the idea of one-dimensional entities, which seems much too "nice" given the general fuzziness of interpreting quantum mechanics, would it be possible for a universal theory to be based on a non-integer number of dimensions? I basically know nothing of...

All, I am trying to determine the length of line across 3 dimensions (XYZ). My X&Y are WGS 84 coordinates and my Z value is HAE (Height Above Ellipsoid) in meters. I can determine the XY length on a plane, but how do I account for the additional length added by a change in Height...

I am a little confused about dimensions, if the nullspace of a matrix is spanned by the 0 vector, does that mean the dimension of the nullspace of this matrix is 0? In the problems I attached, both A and B reduced to the identity matrix. Note (2) is supposed to be dim(N(B)) and dim(col(B))...

A worker works in a roof and let's a hammer fall over the roof with the speed 4m/s.The roof forms an angle 30 degree related to the horizon and its lowest point its 10meters from the ground.What is the horizontal displacement of the hammer from the moment he leaves the roof to the moment he...

I'm wondering what the Dirac delta of a function would be in n dimensions. What is {\delta ^n}(f(x))? I understand that in 3 dimensional flat space, the Dirac delta function is {\delta ^3}(x,y,z) = \delta (x)\delta (y)\delta (z) and {\delta ^3}({{\vec x}_1} - {{\vec x}_0}) = \delta ({x_1}...

Isn't it so that for 10 dimensions in M Theory to be an actual infinity each of the 3D spatial aspects in each universe have to also be Infinity Large. Thus if each universe is Infinity large would it not contain all possible universes at all possible states in time of All possible universes...

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...

1. On a table (defining the x,y-plane laying 3 identical coins A,B and C with identical diameter of 18.00mm. The coordinates of their centers are Z(0,0), Y(60.0,0), X(60.0, 45.0) all given in mm. Under what angle relative to the x-axis one has to push Z against Y so that Z performs after the...

Greetings, This is basically just an observation I expect it to be laughed at (already has been laughed at in the mensa forum) but you know what they say - the only stupid questions are the ones left unasked and what better way to put it to rest than to ask some real hard core physicists... I...

hello.i need to add chlorine to an OVERHEAD water tank.for that i need to know the proper quantity of chlorine to be added.and for that i need to know the tank capacity.unfortunately i do not know the dimensions of the tank,neither i have drawing of it..BUT...a vertical inline pump sucks water...

I've attached the problem. For S: I form the matrix: 1 0 0 1 0 0 0 0 Thus the dimension is 2. For T: I form the matrix 0 0 1 0 0 1 0 0 Thus the dimension is also 2. Is that the correct idea? Also what does S ∩ T mean? I couldn't find the symbol in my textbook.