Transformation Definition and 1000 Threads

Dear all, I'm taking a second look at the Newtonian limit of GR and the covariance group. My main interest is to see how the Newton potential transforms under the covariance group of Newtonian gravity. I know that the gradient of the potential is given by the Christoffel symbol \Gamma^i_{00}...

Homework Statement dy/dx = (2x +y -1) / ( 4x -2y +1) , x= X +1 , y = Y-1 ,, how to make it into differential equation ? my ans is not same as the ans given . P/s : in the second photo , it's lnx +c , sorry for the blur photo Homework EquationsThe Attempt at a Solution

I'm reading A. Zee's GR book and I'm in the section in which he is showing how to transform coordinates to be locally flat in a neighborhood of a point. He said that we can always choose our neighborhood to be locally flat for any space of any dimension D. "Look at how the metric transforms...

Homework Statement The given problem is that we have a rocket ship, accelerating at a constant rate of 1g (in its own instantaneous inertial rest frame) for 40 years. We must find the distance it travels in that time, as measured by an observer on earth. Homework Equations dx'=gamma*(dx-vdt)...

Homework Statement Check if L(p)(x)=(1+4x)p(x)+(x-x^2)p'(x)-(x^2+x^3)p''(x) is a linear transformation on \mathbb{R_2}[x]. If L(p)(x) is a linear transformation, find it's matrix in standard basis and check if L(p)(x) is invertible. If L(p)(x) is invertible, find the function rule of it's...

I am trying to make sure that I have a proper understanding of contravariant transformations between coordinate systems. The contravariant transformation formula is: Vj = (∂yj/∂xi) * Vi where Vj is in the y- frame of reference and Vi is in the x-frame of reference. Einstein summation...

Homework Statement Given the line element ##ds^2## in some space, find the transformation relating the coordinates ##x,y ## and ##\bar x, \bar y##. Homework Equations ##ds^2 = (1 - \frac{y^2}{3}) dx^2 + (1 - \frac{x^2}{3}) dy^2 + \frac{2}{3}xy dxdy## ##ds^2 = (1 + (a\bar x + c\bar y)^2) d\bar...

Homework Statement The image of a linear transformation = columnspace of the matrix associated to the linear transformation. More specifically though, given the transformation from Rn to Rm: from subspace X to subspace Y, the image of a linear transformation is equal to the set of vectors in X...

Hi.. I am new to this forum and not sure whether this is the right place to ask for a help. I have to transform angular velocity vector of a satellite from Earth Centered Inertial (ECI) coordinate system to Local Vertical Local Horizontal(LVLH) system. How can I do that..? Any help appreciated..

When a test charge is stationary, it generates an E field with zero curl. When it moves, it generates a circulating magnetic field B...( as well as the E field.) Is there a geometric reason for this? How does motion alone generate a circulating field B? Can we call this change a...

I have a left-handed ##SU(2)## lepton doublet: ## \ell_L = \begin{pmatrix} \psi_{\nu,L} \\ \psi_{e,L} \end{pmatrix}. ## I want to know its transformation properties under conjugation and similar 'basic' transformations: ##\ell^{\dagger}_L, \bar{\ell}_L, \ell^c_L, \bar{\ell}^c_L## and the general...

Homework Statement We now specify the velocity v to be along the positive x1-direction in S and of magnitude v. We also consider a frame \overline{S} which moves at speed u with respect to S in the positive x1-direction. question 1 : Write down the transformation law for p^\mu . question 2...

Homework Statement Being ##f : \mathbb R^4\rightarrow\mathbb R^4## the endomorphism defined by: $$f((x,y,z,t)) = (13x + y - 2z + 3t, 10y, 9z + 6t, 6z + 4t)$$ 1) Determine the basis and dimension of ##Ker(f)## and ##Im(f)##. Complete the base chosen in ##Ker(f)## into a base of ##\mathbb R^4##...

Homework Statement 1.) Prove that the infinitesimal volume element d3x is a scalar 2.) Let Aijk be a totally antisymmetric tensor. Prove that it transforms as a scalar. Homework EquationsThe Attempt at a Solution [/B] 1.) Rkh = ∂x'h/∂xk By coordinate transformation, x'h = Rkh xk dx'h =...

The thought experiment used to prove Lorentz transform uses a light signal as an assumption. What if there was something other than the light signal then Lorentz transformation would have totally different term in place of 'c'(speed of light).

Homework Statement Question: What is the defect of a linear transformation? 2. The attempt at a solution A defective matrix (of a linear transformation) is a matrix that doesn't have a complete basis of eigenvectors. Does this mean that linearly dependent vectors of a matrix are called defects?

Homework Statement What can be special cases, in the study of electrical circuits, in which one can not apply wye delta transformation? Can someone graph them in some way? Homework EquationsThe Attempt at a Solution

Is there an alternative set of equations similar to Lorentz Transformations that transforms vectors from one dimension to a higher or lower dimension?

Iam having trouble understanding how one arrives at the transformation matrix for spherical to rectangular coordinates. I understand till getting the (x,y,z) from (r,th ie., z = rcos@ y = rsin@sin# x = rsin@cos# Note: @ - theta (vertical angle) # - phi (horizontal angle) Please show me how...

Homework Statement Evening all, I'm trying to solve the 2-D diffusion equation in a region bounded by y = m x + b, and y = -m x -b. The boundary condition makes it complicated to work with numerically, and I recall a trick that involves a coordinate transformation so that y = m x + b, and y =...

Evening all, I'm trying to solve the 2-D diffusion equation in a region bounded by y = m x + b, and y = -m x -b. The boundary condition makes it complicated to work with numerically, and I recall a trick that involves a coordinate transformation so that y = m x + b, and y = -m x -b are mapped...

I have seen this calculation on web Let consider that old man displaced the cart from pole A to Pole B on platform. Observers are on platform S & in train S', moving with velocity –V then (let, X-axis is parallel to train direction) 1) When AB (displacement) parallel to the direction of train...

Homework Statement Let A(l) = [ 1 1 1 ] [ 1 -1 2] be the matrix associated to a linear transformation l:R3 to R2 with respect to the standard basis of R3 and R2. Find the matrix associated to the given transformation with respect to hte bases B,C, where B = {(1,0,0) (0,1,0) , (0,1,1) } C =...

Homework Statement Prove that there exists only one linear transformation l: R3 to R2 such that: l(1,1,0) = (2,1) l(0,1,2) = (1,1) l(2,0,0) = (-1,-3) Find Ker(l), it's basis and dimension. Calculate l(1,2,-2) Homework EquationsThe Attempt at a Solution I still find linear transformations...

Homework Statement Can anybody suggest hints on how to show that x'=xcosΘ-ysinΘ, y'=xsinΘ+ycosΘ by using the infinite string of poisson brackets? Homework Equations ω→ω+a{ω,p}+a^2/2!{{ω,p},p}+... The Attempt at a Solution Sorry, I just can’t think of any way, substituting doesn’t work.

In obtaining (5.362) from (5.359), we first get ##U_{\tau}i\hbar\frac{\partial}{\partial t}\Psi(t) = U_{\tau}H^*\Psi^*(-t)## In order to obtain the LHS of (5.362), ##U_{\tau}## must commute with ##\frac{\partial}{\partial t}##. But how do we know that they commute?

Spinors in $N=2, D=4$ supergravity can be simplified using gauge transformation and thus canonical spinors can be found. In the case of $N=2, D=4$ supergravity the gauge transformation Spin (3,1) is used. My question is how do we know which transformation can be used in a certain theory in order...

Homework Statement Is the transformation ##Y:(t,x,y,z)\rightarrow (t,x,-y,z)## a Lorentz transformation? If so, why is it not considered with P and T as a discrete Lorentz transformation? If not, why not? Homework Equations The Attempt at a Solution A Lorentz transformation ##\Lambda##...

In Newmann-Penrose formalism, a Null rotation with ##l## fixed is $$l^a−>l^a\\ n^a−>n^a+\bar{c}m^a+c\bar{m}^a+c\bar{c}l^a\\ m^a−>m^a+cl^a\\ \bar{m}^a−>\bar{m}^a+\bar{c}l^a$$ Using this transformation, how to prove? $$π−>π+2\bar{c}ϵ+\bar{c}^2κ+D\bar{c}$$ Ref: 2-Spinors by P.O'Donell, p.no, 65

Hi All; I was trying to understand Lorentz Transformation equation and special theory of relativity, but as I compared the derivation with a thought experiment which I imagined I found the whole Lorentz Transformation Equation fails. The details of the problem is given below. I know I m wrong...

Hi All; I was trying to understand Lorentz Transformation equation and special theory of relativity, but as I compared the derivation with a thought experiment I created I found the whole Lorentz Transformation Equation fails. The details of the problem is given in the pdf file attached. I know...

Homework Statement Given the transformation fh : R 3 → R 3 defined by fh(x, y, z) = (x−hz, x+y −hz, −hx+z), where h ∈ R is a parameter. a) Find, for all possible values of h, Ker(fh), Im(fh), their bases and dimensions. b) Is fh an isomorphism for some value of h? Homework Equations Ax=o The...

Alternate title: Is the textbook contradicting itself? imgur link: http://i.imgur.com/3sTVgwr.jpg But imgur link: http://i.imgur.com/33Ufncb.jpg So...it would appear that transposing has the property of linearity, but no matrix can achieve it...is transposing a linear transformation? The...

Mod note: Moved from Precalc section 1. Homework Statement Given l : IR3 → IR3 , l(x1, x2, x3) = (x1 + 2x2 + 3x3, 4x1 + 5x2 + 6x3, x1 + x2 + x3), find Ker(l), Im(l), their bases and dimensions. My language in explaining my steps is a little sloppy, but I'm trying to understand the process and...

Homework Statement Hi this isn't really a question but more so understanding an example that was given to me that I not know how it came to it's conclusion. This is a question pertaining linear transformation for coordinate isomorphism between basis. https://imgur.com/a/UwuACHomework Equations...

Homework Statement Point transformation in a system with 2 degrees of freedom is: $$Q_1=q_1^2\\Q_2=q_q+q_2$$ a) find the most general $P_1$ and $P_2$ such that overall transformation is canonical b) Show that for some $P_1$ and $P_2$ the hamiltonain...

I am having a hard time understanding vector transformations. I know that vectors must transform a certain way and that dual vectors (or covectors) transform the "opposite" way. What is strange to me is that the basis vectors transform like dual vectors and the basis dual vectors transform like...

Homework Statement I've posted a few of these recently. I have one question about this problem -- hopefully my calculations are correct. f: R2 to P1, f(a,b)=b+a2x Is this a linear transformation? Homework Equations f(u+v) = f(u) + f(v) f(cu) = cf(u) where u and v are vectors in R2 and c is...

While 2nd law of thermodynamics emphasizes past->future time direction, CPT theorem says that at least microscopic physics has some symmetry between past and future. For example the Feynman-Stueckelberg interpretation suggests to see anti-particles as traveling back in time. So thermodynamics is...

If I have the following relations: X = sqrt(1-V^2)*cos(U) Y = sqrt(1-V^2)*sin(U) Z = V where (-pi < U < pi) and (-1 < V < 1) are independent random variables, both with uniform distributions. How do I use the CDF method to find X_pdf(x)? X_pdf(x) = X_cdf'(x) = ( P( X < x ) )' = ( P(...

Homework Statement R2 to R1 f(x,y)=xy Determine if the transformation is linear or not Homework Equations T(V1+V2) = T(V1) + T(V2) T(cV1) = Tc(V1) The Attempt at a Solution If the function f(x,y) = xy we can define another function f(a,b)=ab Therefore, f(x,y) = f(a,b), so xy=ab, so all...

Homework Statement A train travels in the +x direction with a speed of β = 0.80 with respect to the ground. At a certain time, two balls are ejected, one traveling in the +x direction with x-velocity of +0.60 with respect to the train and the other traveling in the −x direction with x-velocity...

Homework Statement A ball that weights 1kg is thrown in the air, the hand being 1m above the ground. The velocity the ball was thrown at was 14m/s and it's maximum height was 6.5m above the ground. What is the efficiency for this energy transformation? Homework Equations Do I just get the...

Homework Statement There are three observers, all non accelerating. Observer B is moving at velocity vBA with respect to observer A. Observer C is moving at velocity vC B with respect to observer B. All three observers and all their relative velocities are directed along the same straight line...

I asked this question to PhysicsStackExchange too but to no avail so far. I'm trying to understand the way that the Higgs Mechanism is applied in the context of a U(1) symmetry breaking scenario, meaning that I have a Higgs complex field \phi=e^{i\xi}\frac{\left(\rho+v\right)}{\sqrt{2}} and...

Hi, Could you please explain me why, under the transformation of a complex valued field Φ→eiαΦ, for an infinitesimal transformation we have the following relation? δΦ=iαΦ Thanks a lot

Homework Statement I'm trying to find the direction and magnitude of Earth's gravity on some projectile. The question states that I can ignore z, and that the origins of the x and y axes should be on the surface of the planet. I should then use Newton's law of Gravity to find the direction and...

Hi, the following is taken from Peskin and Schroeder page 36: ##\partial_{\mu}\phi(x) \rightarrow \partial_{\mu}(\phi(\Lambda^{-1}x)) = (\Lambda^{-1})^{\nu}_{\mu}(\partial_{\nu}\phi)(\Lambda^{-1}x)## It describes the transformation law for a scalar field ##\phi(x)## for an active...

Homework Statement I have a particle moving with uniform velocity in a frame ##S##, with coordinates $$ x^\mu , \mu=0,1,2,3. $$ I need to show that the particle also has uniform velocity in a frame ## S' ##, given by $$x'^\mu=\dfrac{A_\nu^\mu x^\nu + b^\mu}{c_\nu x^\nu + d}, $$ with ##...

Ok, so as far as I understand it, it is impossible to turn linear momentum (p) into rotational momentum (L), but I don't quite understand why. The main thought experiment I have in my head is this: A ball in space is traveling with a momentum mbVb, and gravity and friction are assumed to be...