Dimension Definition and 881 Threads

The Bohr magneton is (see e.g. Wikipedia) in SI units: $$\mu_B=\frac{e\hbar}{2m_e}$$ and in CGS units: $$\mu_B=\frac{e\hbar}{2m_ec}$$ So the dimension of the electric charge in SI, ##[q_{SI}]##, is related to the dimension of the electric charge in CGS, ##[q_{CGS}]##, by...

Homework Statement Suppose a particle moves along the x-axis beginning at 0. It moves one integer step to the left or right with equal probability. What is the pdf of its position after four steps? 2. Homework Equations Binomial distribution ##P(k) = {{n}\choose{k}} p^k (1-p)^{n-k}## The...

How can I choose the characteristic linear dimension? For example in pipe it is its diameter, but on a surface is the length, on a flat plane it can be measured as 4A/P. I was having problems determining the characteristic linear dimension for a diffusion problem in a "rectangular" pipe. I don't...

- Does anyone know , why for instance a muon or a tau , can't be considered as Kaluza-Klein tower(s) ? M.

In learning QFT, I've found that the renormalization group is often introduced with the MS scheme. I noticed that if one uses the on-shell scheme instead and calculates the anomalous field dimension using \gamma_{\phi} = \mu \frac{\partial \ln Z_{\phi}}{\partial \mu} one finds that...

Hello all, i read several threads concerning the a.m. topic, but are still not sure if i got it right. Is "passing time" or moving in the 4th dimension in relativistic means a real changing of position in grade 4 spacetime or is it just a mathematical effect ? Why asking: If i understood...

[mentor note: thread moved from Linear Algebra to here hence no homework template] So, i was doing a Linear Algebra exercise on my book, and thought about this. We have a linear map A:E→E, where E=C°(ℝ), the vector space of all continuous functions. Let's suppose that Aƒ= x∫0 ƒ(t)dt. By the...

In Galilean transformation,it is said that time is a physical quantity while space is dimension. What do we mean by this i.e. time is a physical quantity while space is dimension ? Isn't space a physical quantity in Galilean transformation? Here, too, we plot graph of position(on y-axis) as a...

How do we decide dimension of motion? Consider a particle moving along ##\hat x ## direction. This motion is known as one dimensional motion as only one coordinate i.e. x is changing with respect to time. Consider a particle having circular motion in X-Y plane. In Cartesian Coordinate system...

So I am reading a calculus book, and went online to find explanations for why a circle is 1D. Theres the explanations that say something about zooming in very close and seeing that it's indistinguishable from a Real line. Or you can specify any point on it with only one variable Or if there was...

Hi, I am trying to work out how much each dimension of a solid (for instance an annular disc) made out of steel changes assuming that the solid is heated uniformly and is not constrained at any of its boundaries. Am I right in saying that, the linear expansion equation L = L_0 (1+ α ΔT) can be...

Homework Statement What is the dimension of ##M_{24}##? Homework Equations attached The Attempt at a Solution [/B] I am confused what the (mod 12) is referring to- is it referring to the ##[k/12]## where the square brackets denote an equivalent class and the ## k \equiv 2## / ##k \notequiv...

On an exam we just took, we were asked to find the dimension of a set using the box counting technique. So choose an epsilon, and cover your object in boxes of side length epsilon, and count the minimum number of boxes required to cover the object. Then use a smaller epsilon and and count the...

Homework Statement You approach an enemy ship at a speed of 0.5c measured by you, and the ship fires a missile toward your ship at a speed of 0.7c relative to the enemy ship. What speed of the missile do you measure, and how much time do you have measured by you and the enemy ship before the...

Instead of the 10,11, and 26 dimensions proposed by various theories, could there be, let's say 10 positive dimensions, existing of 9 of space and one of time, but also 1 negative dimension? This is just a random theory. I have no idea what a negative dimension would hold, but I think it would...

I often here claims that higher dimensions such as the 5th and 6th dimensions deal with different possible realities, be it branching off or from different start conditions. I find this confusing and would like to have it cleared up how it is possible for different so called realities to occur...

Hi, I'm trying to understand the bound states of a periodic potential well in one dimension, as the title suggests. Suppose I have the following potential, V(x) = -A*(cos(w*x)-1). I'm trying to figure out what sort of bound energy eigenstates you'd expect for a potential like this. Specifically...

Homework Statement I'm a pharmacologist and I have a modern physics course to do. This is not my field and I'm completely lost... We were given this problem to do. Thanks a lot in advance. Consider a potential where U(x) = 0 for x ≤ 0 U(x) = -3E for x > 0 Consider a particle of energy E...

Hi, I am computing the anomalous dimension of a mass operator in the MSbar scheme, but i have a doubt. The following is the solution of an exercise given by a professor but i don't understand a passage. I have computed the counterterm ##\delta## and i have the formula $$\gamma=-\mu...

Homework Statement hi I have read a lot on homogenous coordinates and I feel like I now have a solid foundation. However none of the videos or books I have read give an explicit reason as to why translation with the extra dimension works(i.e. it does not result in scaling). Here 's what I...

Homework Statement Show the (real) dimension of su(n) is ##n^2-1##. Homework EquationsThe Attempt at a Solution ##su(n) = \{ A \in M_n(\mathbb{C}) | A+A^T = 0, tr(A) =0 \}## Maybe the solution is obvious, because I can't find a thing online about how to do this. But I can't see how to do it! I...

Homework Statement Let ##n>1\in\, \mathbb{N}##. A map ##A:\mathbb{R}_{n}[x]\to\mathbb{R}_{n}[x]## is given with the rule ##(Ap)(x)=(x^n+1)p(1)+p^{'''}(x)## a)Proof that this map is linear b)Find some basis of the kernel b)Find the dimension of the image Homework Equations ##\mathbb{R}_{n}[x]##...

If time is a dimension, what would be the dimension of a photograph in such a space?

Homework Statement Draw the third view and the points on each view. In the first picture you have what the exercise has given us and in the second what I have drawn. I have turned the page so that the first view is the one on the left, the horizontal one is the one on the right. Is that OK...

Hey! :o Let $U_1,U_2$ be vector subspaces of $\mathbb{R}^4$ that are defined as $$U_1=\begin{bmatrix} \begin{pmatrix} 3\\ 2\\ 2\\ 1 \end{pmatrix}, \begin{pmatrix} 3\\ 3\\ 2\\ 1 \end{pmatrix}, \begin{pmatrix} 2\\ 1\\ 2\\ 1 \end{pmatrix} \end{bmatrix}, \ \ U_2=\begin{bmatrix}...

Hi, Excuse me this is probably a really stupid question but I ask because I thought that the definition of the dimension of a space is the number of elements in the basis. Now I have a theorem that tells me that ## dim M_{k} = [k/12] + 1 if k\neq 2 (mod 12) =[k/12] if k=2 (mod 12) ## for ## k...

I was doing some reading on String Theory...I'm not a scientist, but i enjoy it (so forgive me if my question is stupid) and i was wondering: Being time a dimension, could it be the dimension the strings exist in? And interaction between all particles and all forces determine how they vibrate...

How is it possible that a point like particle is 0 dimensional? Could it only exist within pure mathematics? or actually exist physically in our universe?

Is the 4th dimension right under our noses? In the book "Hyperspace" written by Machio Kaku (fantastic book, check it out), Kaku uses what he calls "flatlanders" to depict how, us, 3 dimensional people, could actually be involved in the 4th SPACIAL dimension (4th dimension is not used in the...

haruspex submitted a new PF Insights post Can Angles be Assigned a Dimension? Continue reading the Original PF Insights Post.

Homework Statement For c not equal to ±1, what is the dimension of the eigenspaces of A The characteristic polynomial of A is (x-1)(x+1)(x-c) The Attempt at a Solution each term in the characteristic polynomial has a multiplicity of 1 so does this mean that the dimension of the eigenspaces...

Homework Statement ##\mathbb{H} = \{(a,b,c) : a - 3b + c = 0,~b - 2c = 0,~2b - c = 0 \}## Homework EquationsThe Attempt at a Solution This definition of a subspace gives us the vector ##(3b - c,~2c,~2b) = b(3,0,2) + c(-1,2,0)##. This seems to suggest that a basis is {(3, 0, 2), (-1, 2 0)}, and...

I searched for a proof of the statement in the title and found this document. But it just proves that for two norms ## \rho(x) ## and ## ||x|| ##, we have ## m\rho(x)\leq ||x|| \leq M \rho(x) ## for some m and M. But how does it imply that the two norms are equivalent? Thanks

In a lecture from a course in QM, it was mentioned that Shroedinger's equation is deterministic in one and two dimensions. But in third dimension it gives unstable solutions, loosing it's determinism. It was mentioned that "in space of D dimensions Gauss theorem leads to the conclusion that...

For a research problem, I'd like a way to find the distance of each of 4 lines perpendicular to one of 4 walls connected to a point that is within a box of known dimension. I know the distance from the center of each wall to the point of interest (C1 to C4), but I do not know the angle this...

Because it takes time to get from one point to another?

Can one shed light on the velocity of the photon through the fourth dimension x4 using limits? To begin with, please study the mathematics from Brian Greene’s book An Elegant Universe. The upshot is that the faster an object moves through space, the slower it moves through the fourth...

What is the velocity of the photon through the fourth dimension x4? Photons are real, physical entities. The fourth dimension is a real, physical entity. Therefore, photons must have a relationship with the fourth dimension. They must have some velocity relative to it. What is the velocity...

Can there be a bounded space without a boundary without embedding in a higher spatial dimension? This seems to be the kind of question I get stuck on when the big bang comes up. Thanks

Hi, I want to find the number of parameters needed to define an orthogonal transformation in Rn. As I suppose, this equals the dimension of the orthogonal group O(n,R) - but, correct me if I'm wrong. I haven't been able to figure out how to do this yet. If it helps, I know that an orthogonal...

Homework Statement Let S denote (x,y,z) in R3 which satisfies the following inequalities: -2x+y+z <= 4 x-2y+z <= 1 2x+2y-z <= 5 x >=1 y >=2 z >= 3 Homework Equations How to find the dimension of the set S ? The Attempt at a Solution I have tried to transform the inequalities into matrix form...

Homework Statement Two points P and Q move in a straight line AB.The point P starts from A in the direction AB with velocity and acceleration http://latex.artofproblemsolving.com/b/b/2/bb2c93730dbb48558bb3c4738c956c4e8f816437.png.At the same instant of time Q starts from B in the direction of...

Hello there, I'm working on a design project where I have come upon a mechanical problem that I'm having trouble with. Basically I'm making a kind of specialized stapler (at least I think that's a good translation...), and I want it to clamp the staplers using a mass accelerated by a spring...

I need to know if the Symplectic Majorana spinors in 5 dimension have any advantage with respect to the Dirac spinors in 5 dimension, since they have the same number of components. For example if the Symplectic Majorana spinors have a manifested symmetry that the Dirac spinors don't have, or if...

From the de Broglie wave formula we know, Rhamda=h/p [SIZE=16px]In actual examples of course the answer would be 'something [meters]' I am having hardtime to understand how unit of h/mv [J*s]/[kg]*[m/s] turn into wavelength unit [m] I studied the Mass-Energy relation part earlier, But still...

I want to understand why and where exactly we use dirac delta function? what is its exact use?

Homework Statement Identify the motion that the different sections of the graph describe Homework EquationsThe Attempt at a Solution t=0-2 is accelerating t=2-4 is stationary t=4-5 accelerating t=5-9 decelerating/slowing down Options which are given: Constant speed, moving back to the...

I'm confused about this. I know that if the dimension of the vector space is say, 2, then there will be 2 elements, right? eg. ## \left( \begin{array}{cc} 1 & 0\\ 0 & -1 \end{array} \right)## What I want to know is if the dimension of vector space is still two if the matrix is like this...

What's the dimension of the space of $2 \times 2$ matrices? What's the dimension of the space of $m \times n$ matrices? I know that matrices of size $m \times n$ with components in field $K$ form a vector space over $K$. To find the dimension, I would have to find basis. This I'm not quite sure...

Homework Statement 5) A free particle moving in one dimension is in the state Ψ(x) = ∫ isin(ak)e(−(ak)2/2)e(ikx) dk a) What values of momentum will not be found? b) If the momentum of the particle in this state is measured, in which momentum state is the particle most likely to be found? c)...