Dimensions Definition and 1000 Threads

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] ==...

Hello, I am an amateur physics enthusiast and would like to pose a question to you. It is my understanding that for string theory to make sense there should be 11 dimensions. Three extended spatial dimensions and one time dimension that we perceive, as well as seven hidden dimensions which...

Homework Statement Homework Equations From my notes I'm aware of the following equation: dim(A + B) = dimA + dimB − dim(A ∩ B).The Attempt at a Solution I'm assuming part of the solution involves the equation above and rearranging it but I'm not sure how I would determine dim(A + B). I also...

My Professor frequently uses the term higher dimensions. Could someone tell me exactly what is a dimension. I think of it as some parameter which can vary. Also, I only know of 4 dimensions: time, length, width and height. Could someone give me more examples of dimensions? And lastly could...

I am seeking to understand reflection groups and am reading Grove and Benson: Finite Reflection Groups On page 6 (see attachment - pages 5 -6 Grove and Benson) we find the following statement: "It is easy to verify (Exercise 2.1) that the vector x_1 = (cos \ \theta /2, sin \ \theta /2 )...

I don't know how to frame my question but i will try - Is it a rule / property / characteristic of (our) universe that we have three dimensions and all are independant of each other? I am not sure about my doubt but i think what confuses me is the independance of the three dimensions

I seem to have read something once that suggested that gravity may be leaking into other dimensions/branes, this could explain why this force is so weak. I've been left thinking that it makes sense as a possibility. If it turns out to be the case, could Dark Energy then be leaked gravitational...

Homework Statement A light passenger vehicle weighing 1470 N collides with a train engine weighing 1.23 x 10^5 N, which was being moved from one rail siding to another. The train engine and the vehicle were entangled after the accident and from your measurements you have been able to...

Homework Statement A neutron (mass 1.7x10-27 kg) traveling at 2.7 km/s hits a stationary lithium nucleus (mass 1.2x10-26 kg). Afterwards, the velocity of the lithium nucleus is 0.40 km/s at 54° to the original direction of the motion of the neutron. If the speed of the neutron after the...

"Find the most economical dimensions of a closed rectangular box [. . .]" Homework Statement Find the most economical dimensions of a closed rectangular box of volume 8 cubic units if the cost of the material per square unit for (i) the top and bottom is 5, (ii) the front and back is 2 and...

Homework Statement a wire carrying a current of 3.2A has a radius of 1.2mm. the material of the wire has 2.5x10^25 free electrons per cubic metre. the elementary charge is 1.6x10^-19 Homework Equations I=Anev cross section = pi*r^2 The Attempt at a Solution pi*0.0012^2 =...

There might be 11 dimensions like some physicists say, but why can't we see them? Is it because we are too small or too big to see them? what if dimensions were something relative? the bigger/smaller you become in comparison with something else, the less/more dimensions you can experience from it?

Maria designed a rectangular storage unit with dimensions 1m by 2m by 4m. By what should he increase each dimension to produce an actual storage that is 9 times the volume of his scale model? v= (1) (2) (4) v= 8 v has to be 9 times larger v= (x+1) (x+2) (x+4) How do i find the value of x?

If you search electric charge on the German Wikipedia (search electric charge on Wikipedia and click on the "Deutsch" blue link on the left side) its dimension is defined as "M^(1/2)*L^(3/2)*T^(-1)". I always thought of electric charge as fundamental property that by definition has its own...

Hi, I was wondering whether it's possible to define a rotation in 3 dimensions about the origin. Is it necessary to define an axis of rotation or would it be legal to say that you rotate abput the origin (like a phasor in 3 dimensions.) Thanks!

Hi Everyone, I have not understood or even studied string theory. However I was wondering whether the extra dimensions demanded by M-theory (10 spatial dimensions in that case), other string theories or even any other field theories necessarily demand the dimensions higher than four...

[SOLVED] Elastic collision in 2 dimensions Homework Statement A ball with mass m and initial velocity v1i collides elastically with a second ball of the same mass that is initially at rest. After the collision, the first ball moves away at an angle of θ1 with respect to the initial...

I am participating in science project on behalf of my school. I am a 12th grade student and very much interested in Maths,Physics and Computer Science. My teacher has assigned me to do project on Multi Dimension i.e Fourth Dimension. I need some good stuff of resource and information on Fourth...

Supposed reality was described by String Theory and there were 6 compactified dimensions. Could it describe quantum non-locality or does it still take light speed to travel in the compactified dimension? For example. You live in New York, I live in California. If we can send signal in one of the...