Transformation Definition and 1000 Threads

Why does it use t' in that equation and not t? Isn't the equation relative to what an observer in the external frame of reference see? So if it is why not using the time he register? (The equation is uploades in the photo)

I am told that the trace function tr(A) is a linear transformation. But this function maps from the space of matrices to the real numbers. How can this be a linear transformation if the set of real numbers isn't a vector space? Or is it? Can a field also be considered a vector space?

Homework Statement Starting from the expression of the Delta-Y resistor transformation work out the conductance transformation equation. Homework Equations 3. The Attempt at a Solution [/B] I will just be using one equation as others are done analogically. My Δ has ##(R_{12},R_{23},R_{13})##...

The D'Alembert equation for the mechanical waves was written in 1750. It is not invariant under a Galilean transformation. Why nobody was shocked about this at the time? Why we had to wait more than a hundred years (Maxwell's equations) to discover that Galilean transformations are wrong...

What was the need for Lorentz transformation in pre-relativity period? Why was it necessary for the velocity of light to be invariant between different inertial frames and hence what was the need for Lorentz transformation when it was believed that velocity of light was constant with respect to...

Homework Statement Students used a speed gun to measure the final speed of slider at the bottom of the slide. They measure the height difference between the top and bottom of the slide to be 3.0 m. If the speed of a slider at the bottom of the slide is 5.0 m/s, what is the efficiency of the...

Homework Statement Use matrix multiplication to find the 2×2 matrix P which represents projection onto the line y =√3x. Can you suggest another way of finding this matrix? Which vectors x∈R2 satisfy the equation Px = x? For which x is Px = 0? Homework Equations Dot product of vectors The...

Hello! I don't know exactly how to state my question so I'll show you what my problem is. Ex. Let T : R[x]_3 →R be the function defined by T(p(x)) = p(−1) + \int_{0}^{1} p(x) \,dx , where R[x]_3 is a vector space of polynomials with degree at most 3. Show that $T$ is a linear map; write down...

Homework Statement For the theta series given by : ##\theta(t) = \sum\limits_{n\in Z} e^{2\pi i n^2 t} ## in 1-d there is the transformation formula: ##\theta(-1/4t)=\sqrt{-2it\theta(t)}## To prove this one uses the fact that this theta function is holomorphic and so by Riemann theorem it is...

Homework Statement From the circuit diagram ( http://postimg.org/image/lldnr7mf7/ ) calculate the net charge flown through the capacitor 2. Homework Equations 3. The Attempt at a Solution [/B] I actually don't need to solve the full problem as i understand how, what i have trouble with is the...

In Mobius geometry it is assumed that a line is a circle of infinite radius.Does this have any physical significance?

Are the assumptions in mobius transformation valid in Newtonian physics?

let df=∂f/∂x dx+∂f/∂y dy and ∂f/∂x=p,∂f/∂y=q So we get df=p dx+q dy d(f−qy)=p dx−y dqand now, define g. g=f−q y dg = p dx - y dq and then I faced problem. ∂g/∂x=p←←←←←←←←←←←←←←← book said like this because we can see g is a function of x and p so that chain rule makes ∂g/∂x=p but I wrote...

We know, $$\delta(x) = \begin{cases} \infty & \text{if } x = 0 \\ 0 & \text{if } x \neq 0 \end{cases}$$ And, also, $$\int_{-\infty}^{\infty}\delta(x)\,dx=1$$ Using Fourier Transformation, it can be shown that, $$\delta(x)=\lim_{\Omega \rightarrow \infty}\frac{\sin{(\Omega x)}}{\pi x}$$ Let's...

Hello everybody. I am currently comparing fourier's transformation of one physical phenomena and a two models which seek to emulate it. One of the models nails the frecuency and the other one even though it's displaced to higher frequencies the power (defined as 2* absolute value of fourier's...

Hello everybody. I am triying to calculate a band-pass filter using the Fourier transform. I have a vector with 660 compomponents; one for each month. I am looking for a phenomenon which has a periodicity between 3 and 7 years (it's el niño, on the souhtern pacific ocean). I want to make zero...

I am reading Chapter 9 of Classical Mech by Goldstein.The symplectic condition for a transformation to be canonical is given as MJM' = J, where M' is transpose of M. I understood the derivation given in the book. But my question is : isn't this condition true for any matrix M? That is it doesn't...

I don't quite get this question, how is it done ?

Homework Statement The occupation of each single-particle state with wave vector k =/= 0 in the ground state is given by nk = <0|bk†bk|0> where b and b† are bogoliubov transformaition. Find an expression for nk. bk = cosh(θ)ak - sinh(θ) a†-k bk† = cosh(θ)a†k - sinh(θ)a-k Homework EquationsThe...

In my simulation of the twin paradox, i used the Lorentz transformation formulas to map events from one inertial reference frame into another IRF. Reading through various threads here, i read that spacetime is curved and that space can be considered flat only for small distances. So my...

Homework Statement Hi all I am having trouble working part b of a question that I am currently doing. I have attached the question below in a pdf file. I am really not sure where to start, I have looked in several book and can only think of relating to the light clock thought experiment. But...

Dear PF members. I am requesting again your help as I keep struggling with the LaPlace transformation. I have this exercise to do(please see below) We know that L[f(t)]= integral from 0 to infinity of f(t)*e^(-st) dt thus in our case, L[f(t)]= integral from 0 to infinity of sin(t)*e^(-st) dt...

Hi guys, I'm reading a book where the author, only form the invariance of the speed c draws conclusions about the transoformation from a system to another in inertial motion. The author shows a spacetime diagram (x,t) and the two dimensional light cone, he marks two events on the light cone...

The left-handed Weyl operator is defined by the ##2\times 2## matrix $$p_{\mu}\bar{\sigma}_{\dot{\beta}\alpha}^{\mu} = \begin{pmatrix} p^0 +p^3 & p^1 - i p^2\\ p^1 + ip^2 & p^0 - p^3 \end{pmatrix},$$ where ##\bar{\sigma}^{\mu}=(1,-\vec{\sigma})## are sigma matrices.One can use the sigma...

On the attachment, I was told my joint pdf was right, but the support was NOT 0<y1y2<1 0<y2<1, so maybe it's right now? Obviously B and C are incorrect, too, since they don't integrate to 1. I'm probably making just a few simple mistakes. Thanks in advance!

I am not looking for a solution, just a "starting point"/guidance for calculating the expression: [M^{\mu \nu} , \phi_a] with M^{\mu \nu} being the angular-momentum operators and \phi_a being the field's component, which happens to transform under Lorentz Transformations: x'^\mu = x^\mu + \delta...

Homework Statement If ##D^*## is the parallelogram whose vertices are ##(0,0)##,##(-1,3)##, ##(1,2)##, and ##(0,5)## and D is the parallelogram whose vertices are ##(0,0)##, ##(3,2)##,##(1,-1)## and ##(4,1)##, find a transformation ##T## such that ##T(D^*)=D##. Homework EquationsThe Attempt at...

Hello! I want a formula (if there exists) to find the Laplace transformation of a nested function; a function within a function For example what is the LT of θ(f(t)), where θ is the step function? Is there already a formula for such things or should I follow the definition integrating etc..? I...

This question concerns a section from the book Modern Physics by James Rohlf. http://srv3.imgonline.com.ua/result_img/imgonline-com-ua-twotoone-Bs4zgy7pruqG.png He shows that the form of the Wave equation for light remains invariant under a Lorentz boost (4.42)...

I'm taking an introductory course in QFT. During quantization of the Dirac field, my textbook gives a lot of information on how annihilation and creation operators act on vacuum, but nothing about how they act on non-vacuum states. I need these to compute $$ \int \frac{d^3 p}{(2\pi)^3} \sum_s (...

Based on this lecture notes http://www.helsinki.fi/~hkurkisu/CosPer.pdf For a given coordinate system in the background spacetime, there are many possible coordinate systems in the perturbed spacetime, all close to each other, that we could use. As indicated in figure 2, the coordinate system...

Homework Statement Does a linear transformation ##g : \mathbb{R}^2 \rightarrow \mathbb{R}^2## so that ##g((2, -3)) = (5, -4)## and ##g((-\frac{1}{2}, \frac{3}{4})) = (0, 2)## exist? Homework EquationsThe Attempt at a Solution For a linear transformation to exist we need to know if those two...

By y I mean any perpendicular axis to the axis in which there is movement.

Hi, I have trouble understanding why the following relations hold true. Given the Minkowski metric \eta_{\alpha\beta}=diag(1,-1,-1,-1) and the line segment ds^2 = dx^2+dy^2+dz^2, then how can i see that this line segment is equal to ds^2 = \eta_{\alpha\beta}dx^\alpha dx^\beta . Further, we...

Homework Statement We're given some linear transformations, and asked what the null space, column space and row space of the matrix representations tell us Homework EquationsThe Attempt at a Solution I know what information the column space and null space contain, but what does the row space of...

Homework Statement For an event occurring at (x,t), consider the quantity I = x^2 - (ct)^2 Find a simple expression for this in the S' frame: I' = x'^2 - (ct')^2 How are I and I' related, and why is this noteworthy? The Attempt at a Solution So the question is under "Lorentz Transformation"...

So the question looks like this: Identify the time and/or amplitude transformations that must be applied to the signal x(t) in order to obtain each of the signal specified below. Choose the transformations such that time shifting precedes time scaling and amplitude scaling precedes amplitude...

Homework Statement [/B] A spaceship is approaching Earth from the far side of the sun. The Earth and sun are 8 light minutes apart and the ship is traveling at .8c. Two events are indisputable. 1) the ship is at the sun 2) the ship is at the earth. Assume that the Earth and sun are at rest...

Homework Statement (From Di Francesco et al, Conformal Field Theory, ex .2) Derive the scale factor Λ of a special conformal transformation. Homework Equations The special conformal transformation can be written as x'μ = (xμ-bμ x^2)/(1-2 b.x + b^2 x^2) and I need to show that the metric...

I'm getting quite stuck on this problem here. Galileo said that Xb = Xa - V*Ta. (This follows from dv = dx/t --> Xa - Xb = t*dv --> the above formula) Thus, it is concluded Xa = Xb + V*Ta, but why? In my thought experiment the objects are moving relative to each other, thus if A is moving away...

Homework Statement A rocket is traveling toward a galaxy with speed v. a) If NASA says that distance from Earth to the galaxy is d, what is the distance d' from Earth to the galaxy according to the astronauts? b) The astronauts experience a travel time to the galaxy t' and NASA records the...

With the change of variables-method for a many-to-one transformation function Y = t(X), what's the logic behind summing the different densities for the roots of x = t^-1(y)? Probabilities should be ok to add, but densities? Also, is there no way to extend this method for many-to-many...

Is there some geometry in which a coordinate transformation of a vector of magnitude zero transforms to a vector that does not have a zero magnitude? Since the formula for the magnitude of a vector is √(x12+x22+...xn2), I can see no way for it to have magnitude zero unless every component is...

Homework Statement Find the images of the following region in the z-plane onto the w-plane under the linear fractional transformations The first quadrant ##x > 0, y > 0## where ##T(z) = \frac { z -i } { z + i }## Homework EquationsThe Attempt at a Solution [/B] So for this, I looked at the...

Hey guys. So, as i was going through Griffith's Electrodynamics, and i came across this problem: In the solutions: How to they actually get to that expression for V = (V(bar)+vAx(bar) )Ɣ? I understand everything after that, but this just made me very confused. How do they get this from the...

Homework Statement [/B] Find the Legendre Transformation of f(x)=x^3 Homework Equations m(x) = f'(x) = 3x^2 x = {\sqrt{\frac{m(x)}{3}}} g = f(x)-xm The Attempt at a Solution I am reading a quick description of the Legendre Transformation in my required text and it has the example giving for...

Hi. First, excuse my English. In my lecture notes on classical electrodynamics, we are introduced to the Lorentz transformations: a system S' moves relative to a system S with positive veloticy v in the x-axis (meassured in S), spatial axis are parallel, origin of times t and t' coincide...

Homework Statement If the Helmholtz Free Energy remains constant, estimate the final pressure of 1.0mol of an ideal gas in the following transformation: (1.0atm, 300k) → (pfinal, 600k). Given Sgas = R. Homework Equations A = U - TS dA = -SdT - pdV The Attempt at a Solution If the Helmholtz...

In a standard problem of an electron released from the negative plate in an E field between 2 parallel plates in which the velocity must be determined why can the Lorentz transformation be used (involving v^2/c^2) when the electron is undergoing acceleration and there is nothing in the...

Let us see how the line element transforms under conformal transformations. Consider the Minkovski metric gij, a line element ds2=dxigijdxj, and a conformal transformation δk(x)=ak + λ xk + Λklxl + x2sk - 2xkx⋅s We have δ(dxk)=dδ(x)k=λ dxk + Λkldxl + 2 x⋅dx sk - 2dxkx⋅s - 2xkdx⋅s And so the...