Dimensions Definition and 1000 Threads

Homework Statement Fast Eddie McSpeedy is a receiver for the Kennesaw Kilowatts in the Metro Metric Football League and Big Bobby Clobber plays defense in the rival Marietta Megatons. Eddie has a mass of 85 kg and Bobby has a mass of 140 kg. Eddie catches the ball and runs eastward at 2.4 m/s...

Homework Statement A 100kg mass is supended by 3 ropes. one rope is attached at a point 1mxˆ + 1myˆ, one is attached at 1mxˆ - 1myˆ and one is attached at -4mxˆ. The three ropes all connect at -1mzˆ, at which point the mass is attached. What is the tension T in the rope attached at -4mxˆ...

Suppose we have a mxn matrix, where each row is an observation and each column is a variable. The (i,j)-element of its covariance matrix is \mathrm{E}\begin{bmatrix}(\vec{X_i} - \vec{\mu_i})^t*(\vec{X_j} - \vec{\mu_j})\end{bmatrix}, where \vec{X_i} is the column vector corresponding to a...

In my general relativity course my professor recommended that it would be useful to convince ourselves that in 3 dimensions the vacuum field equations are trivial because the vanishing of the Ricci tensor implies the vanishing of the full Riemann tensor. However, I am unsure of how to show this...

Homework Statement A car initially traveling due north goes around a semicircle having a radius of 500 m at a constant speed of 20 m/s. A) How long does this take? B) What is the magnitiude and direction of the average acceleration? Homework Equations a = Δvx/Δt(xhat)+Δvy/Δt(yhat)...

In this excerpt from the notes of Sean M. Carrol, he says: "Einstein’s equations may be thought of as second-order differential equations for the metric tensor field gμν. There are ten independent equations (since both sides are symmetric two-index tensors), which seems to be exactly right...

I can easily visualize the 3 dimensional way to do so, and already have. I'd like to rotate from the (-1,-1,-1,-1) -- (1,1,1,1) line to the x-axis (-1,0,0,0) -- (1,0,0,0). To do so in 3 dimensions (-1,-1,-1) -- (1,1,1) line to the x-axis (-1,0,0) -- (1,0,0) I rotated around the z...

Homework Statement A tennis player standing 8.0 meters from the net hits a ball 1.5 meters above the ground toward her opponent. The ball leaves her racquet with a speed of 25.0m/s at an angle of 14.0 degrees above the horizontal. The net is 1.0 meters high. The baseline is 12 meters back...

According to M-theory as I understand, the 7 additional spatial dimensions to our familiar 3 are curled up all around us but they are too small for us to see. However I have difficulty in understanding how this constitutes a "dimension" because dimensions allow additional degrees of freedom...

Homework Statement A common dimensionless group used in heat transfer calculations is defined as: Nu=\frac{hD}{k} where h is the heat transfer coefficient, and D is the diameter of the pipe in which heat transfer takes place. Please determine the dimensions of the quantity k in...

Would someone here be able to write down for me an example of a metric on a manifold with both macroscopic dimensions, and microscopic "curled up" dimensions with some radius R ? Number of dimensions and coordinates used don't matter. Not going anywhere with this, I am just curious as to how...

Homework Statement Let P represent a force and x, y, and z represent distances. Determine the dimensions for each of the quantities listed below. I attached the problem I need help with. (it's a small picture) So I'm a bit confused since the it involves both dx and dy. The dimensions for P...

Homework Statement In the equation z = ct + d, z is measured in meters and t is measured in seconds. What are the dimensions (units) of d? answer options are... s/m, m/s, m, s, m*sHomework Equations The Attempt at a Solution plugged in m for z, s for t, and m/s for c. solved for D and got 0.

Homework Statement "A particle moves in the horizontal plane that contains the perpendicular unit vectors i and j. Initially it is at the origin and has velocity 18ims^-1. After accelerating for 10 seconds its velocity is (30i + 8j)ms^-1. Assume that the acceleration of the particle is...

hello all I am so glad to have found this forum. I've always had an interest in astrophysics, cosmology, SR/GR, etc, and no place to ask questions. I'm an engineer and was once a member of Mensa (I only left the organization because I thought other members were crazy. Sorry). So although I'm...

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...

If we have a unit circle within a square s.t. the square touches the circle in 4 places then the biggest gap we can find is just √2 - 1. Doing a similar thing with a sphere in a cube we get √3 - 1 I've heard the n-dimensional analogue is √n - 1. Which is crazy as it means the gap is bigger...

Here's what i know about Dimensions... Infinite stacks of a 1D world makes a 2D world, And Infinite stacks of a 2D world makes a 3D world and Infinite stacks of 3D world makes a 4D world and so on... So if we humans are 3D creatures, then we perceive 4th D as time, Same goes for 4D creatures...

Homework Statement I will get to it. Homework Equations None. The Attempt at a Solution Does the D'Alembertian have the same dimensions 1/length as the Laplacian operator except the D'Alembertian takes into consideration four dimensions?

Homework Statement The edges of a thin plate are held at the temperature described below. Determine the steady-state temperature distribution in the plate. Assume the large flat surfaces to be insulated. If the plate is lying along the x-y plane, then one corner would be at the origin...

Does anyone know how to write the classical solution to the Klein-Gordon equation in NON natural units? Where do all the c's and h's go?

For example, finding the properties of an n dimensional figure. Is this called something in math, or do I just refer to it as 'geometry in multiple dimensions'? What subjects can I find this topic under?

This is really more of a differential geometry question than a GR question. Is it possible to have torsion in two dimensions? I've seen statements implying that torsion is only of interest in 3 or more dimensions, but I don't see why. My understanding is that in two dimensions, you could not...

Hi, I'm trying to measure how far a rod that passes through a tube is offset from the center. Assume that the axis of the tube runs parallel to that of the rod. I can only access the interior of the tube from above (it hangs vertically), and the access hole I have is smaller than the radius...

My understanding was that the product of two groups A and B will yield a group C for which the dimension of C is dim(A)*dim(B). Now however, the author I'm reading defines the group product multiplication as: (a1, b1) * (a2, b2) = (a1*a2, b1*b2), for a1,a2 in A and b1, b2 in B. Does this...

How would you test empirically for the existence of extra curled dimensions of space?

Other dimensions have been proven... Since other dimensions have been proven both mathmatically and at cern, I do not consider the topic of warping out of our current space/time dimension out of the realm of possibility especially if it is done on an atomic or quantum level initially. A carrier...

Homework Statement Homework Equations The Attempt at a Solution Just a question on dimensional analysis here. I believe that when an integral is taken with respect to time for instance, dt appears as a dummy variable yes? Imagine we had \int E\ dt Does this have dimensions of energy times...

Homework Statement Hi! I need some help to describe a Wess Zumino model in two dimensions: spinors are real (because of the Majorana condition \theta=\theta^{\ast}) and have two components; the superfield is: \phi \left( x,\theta\right)=A\left( x\right) +...

In the distant past at bigbang the universe was very hot and dense. Can i say it was dimensionless then? If so did it come to this 3 dimension through 1 and 2?a little more speculation... is/will it go to higher dimensions?

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

Which is the mass dimension of a scalar filed in 2 dimensions? In 4 dim I know that a scalar field has mass dimension 1, by imposing that the action has dim 0: S=\int d^4 x \partial_{\mu} A \partial^{\mu} A where \left[S\right]=0 \left[d^4 x \right] =-4 \left[ \partial_{\mu} \right]=1...

I noticed that in quantum physics, an elementary particle has no dimensions, and is point like, but in string theory has one dimension. Why is this?

Hello. Okay, so there are some theories like string theory that say that there are extra dimensions of space that we cannot see. Extra dimensions if they exist would allow more degrees of freedom in movement. This website demonstrate how barriers insurmountable in a lower dimension would be...

A room 7m x 6m x 3m high is to be electically heated to maintain the inside temperature at 20 C, when it is 0 C outside. The room has 2 windows each 1.2m x 1.8m and a sliding glass door 2.4m x 2.1m. The transmission coefficients u in Wm^2/C are given below. Floor: concrete slab (100mm thick)...

Dimensions -- Disc Brake Surface Area During frequent braking under race conditions the disk brake rotors on the car described above reach a temperature of 500C. These disk brakes rely on forced convection to cool them. The dimensions of each disk rotor are: outer radius 130mm; inner radius...

A long time ago, physicists thought that only a small class of quantum field theories (QFT's) makes physical sense - those which are renormalizable. But then gradually it became accepted (Weinberg was the most influential figure in that regard) that QFT does not really need to be renormalizable...

I read about this expression for the Coriolis force \frac{\omega c}{\sqrt{G}} Would I be right in saying this has dimensions of force? Thank you!

Homework Statement Given a symmetric tensor T_{\mu\nu} on the flat Euclidean plane (g_{\mu\nu}=\delta_{\mu\nu}), we want to change to complex coordinates z=x+iy, \,\overline{z}=x-iy. Show, that the components of the tensor in this basis are given by...

Hey people, 1. The problem statement, I'm doing a Uni Art assignment, and I'm going to be projecting a video onto a canvas (which I don't know the exact dimensions of yet). Video file dimensions are stated as 1080 x 980 and so forth, whereas the real life canvas will be something like 50...

I had three questions that had to do with spacetime, digital physics, and the holographic principle: 1. Why are there dimensions in space? 2. Why isn't there just some sort of information matrix as suggested in digital physics? 3. How do these two ideas work with the holographic principle?

suppose that i have a wire with a known thickness ... and i want to wind it around a solid cylinder with known dimensions, and in the end make a coil with the same length as the solid cylinder how do i relate between the length of wire required and the diameter of this coil?

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...

I've been considering this problem for about a year now (whenever I remember about it, that is), and I've come to the conclusion that I can't figure out a way to do what I want to see is possible, and so I've decided to ask it here to see if anyone else can. The original question I...

Homework Statement Given the current: J^{\epsilon}_{0} (t,x) = \overline{\psi_{L}}(t,x + \epsilon) \gamma^{0} \psi_{L}(t,x - \epsilon) = \psi_{L}^{\dagger} (x + \epsilon) \psi_{L}(x - \epsilon) with \psi_{L} = \frac{1}{2} (1 - \gamma^{5}) \psi_{D}. Use the canonical equal time...

Howdy folks I've gotten a number of answers to this in various fora, some contradictory. I need to do 3 things to a set of datapoints in 3space (X,y, and z real values). 1)Test for linearity (pearson's R?). 2)If passed, find line of best fit (SSE?) 3)See if line of best fir is...

Homework Statement Prove that the shortest path between two points in three dimensions is a straight line. Write the path in the parametric form: x=x(u) y=y(u) z=z(u) and then use the 3 Euler-Lagrange equations corresponding to ∂f/∂x=(d/du)∂f/∂y'. Homework Equations Stated them...

Homework Statement Assuming that Pressure (P) of a particle is given by P = b - t^2 / ax where t = time, x = position Find the dimension of b/a. Homework Equations The Attempt at a Solution Using dimensional homogenity, I know that b represents time interval.

If Eisenstein taught us the space time is one and the same thing, then how did he mathematicaly prove that. How did he put dimentions into his E=mc2 formula. The first 3 dimensions are strictly positions, positions in 3D require 3 numbers, and time is linear movement in one direction, the...

Hi I am trying to solve Newtons equation for a particle in (x, y, z) using NDsolve. Here I what I have so far: sol = NDSolve[{ x''[t] == acceleration[x'[t], y[t], z[t]], y''[t] == acceleration[y'[t], x[t], z[t]], z''[t] == 0, x[0] == 2, x'[0] == 0, y[0] == 0, y'[0] ==...