Transformation Definition and 1000 Threads

Homework Statement: This seemed at first glance very easy. But there appeared some confusion. A is moving to the right with velocity v with respect to B. The proper time for A is ##t_a=t_b\sqrt{1-v^2/c^2}##. And B is moving to the right with velocity u with respect to C. Proper time for B...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra ... I need some help in fully understanding Lemma 8.4 ... Lemma 8.4 reads as follows: In the...

[BEGINNGING NOTICE] Before I begin showing my attempted solution, I would just like to quickly mention that this is a "repost" of the same question I had around a week ago. While I would usually use the "reply" function on the same thread, I believe that thread is getting pretty messy (sometimes...

Summary: The problem is to generalize the Lorentz transformation to two dimensions. Relevant Equations Lorentz Transformation along the positive x-axis: $$ \begin{pmatrix} \bar{x^0} \\ \bar{x^1} \\ \bar{x^2} \\ \bar{x^3} \\ \end{pmatrix} = \begin{pmatrix} \gamma & -\gamma \beta & 0 & 0 \\...

with distance between planets as 4x10^8m measured by you on the ship My attempt: t' = γ(t - ux/c^2) γ = 5/3 u = 0.8c t = 0.9s x = 4x10^8m answer is: -0.278 Therefore not possible My question is what if we traveled rightwards, from p2 to p1, would the answer change? Should my above information...

Unfortunately, I am not entirely confident of the above equations being able to do the trick and ultimately solve for the question. However, my guess is that using the equation written above for "boost", I could perhaps use ##v## and insert it into the ##x##-direction part of the matrix...

I'm stuck from the beginning. I though I understood the difference between ## \delta## and ##d##, but apparently I was wrong, because I don't know how to exploit it here... Any hint would be greatly appreciated Thank Ric

I have been getting back to studying physics after a long break and decided to go through the problems in Rindler. But there is something I don't quite understand in this problem. To first answer the second part, Exercise II(12), I wrote $$\frac{du_2}{dt} = \frac{du_2}{du_2^\prime}...

Summary: Homework Statement: Fourier Transform momentum space to normAl space Homework Equations: F(k)=e^-b|k| show that g(x)=(b/pi)×(1/(x^2+b^2)Hello,I need to that given function Fouirier transform and function of graphic. Thank you😃 Homework Statement: Fourier Transform momentum space to...

The strategy here would probably be to find the matrix of ##F##. How would one go about doing that? Since ##V## is finite dimensional, it must have a basis...

I want to know why an else solution can not get the right answer. And want to know the way to correct this solution.Supposed that a frame S'' is moving in the lab frame at ##\beta_x## in the x-direction, ##\beta_y## in the y-direction, now I want to find out the Lorentz transformation between...

In Landau Book 2 (Classical Field Theory & Relativity), he mentions that the transformation rules of the christoffel symbols can be gotten by "comparing the laws of transformation of the two sides of the equation governing the covariant derivative" I would believe that by the equations...

Can someone explain why I can't simply use a current divider once I've found the equivalent resistance and source current for the entire circuit? This would look like i0 = 0.044*(113.53/210). Req = 113.53. If it helps, the correct answers appear to be: i0 = 8.28 mA, i1 = 23.6 mA, i2 = 35.8 mA...

How can the function ##F(\mathbf{u})(t)=\mathbf{u}^{(n)}(t)+a_1\mathbf{u}^{(n-1)}(t)+...+a_n\mathbf{u}(t)##, where ##\mathbf{u}\in U=C^n(\mathbf{R})## (i.e. the space of all ##n## times continuously differentiable functions on ##\mathbf{R}##) be a linear transformation (from ##U##) to...

A particle is moving in the lab frame ##S'## at ##\beta'_z##. I want to transform coordinates and momenta of the particle to a frame ##S## moving at ##\beta_0##. At time ##t = t' = 0##: $$z = \frac{z'} { \gamma_0 (1 - \beta'_z \beta_0) },\, \gamma\beta_z = \gamma_0 ( \gamma'\beta'_z -...

I'm currently watching lecture videos on QFT by David Tong. He is going over lorentz invariance and classical field theory. In his lecture notes he has, $$(\partial_\mu\phi)(x) \rightarrow (\Lambda^{-1})^\nu_\mu(\partial_\nu \phi)(y)$$, where ##y = \Lambda^{-1}x##. He mentions he uses active...

After reading this NY Times article on the possibility of cloning pets becoming a viable business in China, I was wondering if it might also become an area where germline modification might be more extensively tested and worked out. Why this might happen in China: large size of domestic pet...

Backstory - I have not been in school for 5ish years, and am returning to take some grad classes in the field of Solid Mechanics. I am freaking out a bit about the math (am rusty). I have not started class yet, but figured I would get my books and start working through problems. This problem...

I read the Lorentz transformation can be obtained by solving the requirement of invariance of the wave equation. If one considers linear transformations this the same as the spacetime interval squared to be invariant. What are the other nonlinear transformations keeping the wave equation...

Hello Physics Forum, I am not sure what to to in this task, because the wavefunction is only given as A_0. Maybe someone can explain it to me. Thanks in Advance, B4ckflip

Hello, A discrete random variable X takes values $x_1,...,x_n$ each with probability $\frac1n$. Let Y=g(X) where g is an arbitrary real-valued function. I want to express the probability function of Y(pY(y)=P{Y=y}) in terms of g and the $x_i$ How can I answer this question? If any member...

Problem Statement: Consider three frames Σ (x, y, z, t), Σ' (x', y', z', t'), and Σ'' (x'', y'', z'', t'') whose x, y, and z axes are parallel at each point in time stay. Σ' moves relative to Σ with velocity v1 along the x-axis. The system Σ'' moves relative to Σ' with the velocity v2 along the...

Consider a one to one transformation of a ##3##-##D## volume from variable ##(x,y,z)## to ##(t,u,v)##: ##\iiint_V dx\ dy\ dz=\int_{v_1}^{v_2}\int_{u_1}^{u_2}\int_{t_1}^{t_2} \dfrac{\partial(x,y,z)}{\partial(t,u,v)} dt\ du\ dv## ##(1)## Now for a particular three dimensional volume, is it...

Hi, I'm worried I've got a grave misunderstanding. Also, throughout this post, a prime mark (') will indicate the transformed versions of my tensor, coordinates, etc. I'm going to define a tensor. $$T^\mu_\nu \partial_\mu \otimes dx^\nu$$ Now I'd like to investigate how the tensor transforms...

Hi, guys. Just found a missing thing in my brain: if atomic oxygen will meet free electron somewhere why doesn't it become fluorine or even argone?

Homework Statement Find the linear transformation [/B] T: R3 --> R2 such that: 𝑇(1,0,−1) = (2,3) 𝑇(2,1,3) = (−1,0) Find: 𝑇(8,3,7) Does any help please?

That's what I found. But the answer is arctan(sinθ*sqrt(1-v^2/c^2)/(cosθ+v/c))

Hi guys, I'm reading a book 'the theoretical minimum: special relativity and classical field theory'. In chapter 1.3, author explains the general Lorentz transformation. He said "Suppose you have two frames in relative motion along some oblique direction, not along any of the coordinate axes...

nmh{2000} 17.1 Let $T: \Bbb{R}^2 \to \Bbb{R}^2$ be defined by $$T \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 2x+y\\x-4y \end{bmatrix}$$ Determine if $T$ is a linear transformation. So if...

The transformation matrix for a beam splitter relates the four E-fields involved as follows: $$ \left(\begin{array}{c} E_{1}\\ E_{2} \end{array}\right)=\left(\begin{array}{cc} T & R\\ R & T \end{array}\right)\left(\begin{array}{c} E_{3}\\ E_{4} \end{array}\right) \tag{1}$$ Here, the amplitude...

Hello. I would like to draw (sample) several random vectors x from a n-dimensional multivariate normal distribution. For this purpose I want to use C++ and the GNU Scientific Library function gsl_ran_multivariate_gaussian ...

I will start with an example. Consider components of metric tensor g' in a coordinate system $$ g'= \begin{pmatrix} xy & 1 \\ 1 & xy \\ \end{pmatrix} $$ We can find a transformation rule which brings g' to euclidean metric g=\begin{pmatrix} 1 & 0 \\ 0 & 1\\ \end{pmatrix}, namely...

In deriving the Lorentz transformation, is it required to assume that the transformation to get from coordinate system ##\bf {x}## to ##\bf {x’}## should be the same as that to get from ##\bf {x’}## to ##\bf {x}## (with the simple correction of flipping the velocity)? If no, could someone...

I am looking at page 2 of this document.https://ocw.mit.edu/courses/chemistry/5-04-principles-of-inorganic-chemistry-ii-fall-2008/lecture-notes/Lecture_3.pdf How is the transformation matrix, ν, obtained? I am familiar with diagonalization of a matrix, M, where D = S-1MS and the columns of S...

Homework Statement Let ##\psi(x)=u(p)e^{-ipx}##, where $$ u((m,0)) = \sqrt{m}\begin{pmatrix} \xi\\\xi \end{pmatrix}\quad\text{where}\quad \xi = \sum_{s\in \{+,-\}}c_s\xi^s\quad \text{and}\quad \xi^+\equiv\begin{pmatrix} 1\\ 0 \end{pmatrix}\quad \xi^-\equiv\begin{pmatrix} 0\\ 1 \end{pmatrix}, $$...

Homework Statement The assignment is to transform the following differential equation: ##x^2\frac {\partial^2 z} {\partial x^2}-2xy\frac {\partial^2 z} {\partial x\partial y}+y^2\frac {\partial^2 z} {\partial y^2}=0## by changing the variables: ##u=xy~~~~~~y=\frac 1 v##Homework Equations...

Suppose that $T: \Bbb{R}^3 \rightarrow \Bbb{R}^3$ is a linear transformation and $$T \begin{bmatrix} 1 \\1 \\0 \\ \end{bmatrix} = \begin{bmatrix} 1 \\2 \\1 \\ \end{bmatrix}, \quad T \begin{bmatrix} 1 \\0 \\1 \\ \end{bmatrix} = \begin{bmatrix} 1 \\0 \\2 \\ \end{bmatrix}, \quad T...

On page 59 of Peskin & Schroeder, there's a section on the lorentz transformation of field operators which I've attached. I'm confused about the part towards the end where he does a change of variable on the integration measure; it seems like he's only rewriting the lorentz-invariant integration...

Symmetry transformations are changes in our point of view that preserve the possible outcomes of experiment: $$\Psi \rightarrow U(\Lambda) \Psi$$ In the Heisenberg picture, observables in a fixed reference frame evolve according to: $$P(t) = U^\dagger (t)PU(t)$$ while in the Schrodinger...

Homework Statement I'd like to diagonalise the following Hamiltonian for quasiparticle excitations in a Bose Einstein Condensate $$H= K_0 + \hat{K}_1 + \hat{K}_2 $$ where $$K_0 = \int d^3 r \left[ \phi_0 ^* (\hat{h}_0- \mu) \phi_0 + \frac{g}{2} |\phi_0| ^4 \right]$$ $$\hat{K}_1= \int d^3 r...

In a spherical polar coordinate system if the components of a vector given be (r,θ,φ)=1,2,3 respectively. Then the component of the vector along the x-direction of a cartesian coordinate system is $$rsinθcosφ$$. But from the transformation of contravariant vector...

What do we mean when we are talking about something that transforms under a representation of a group? Take for example a spinor. What is meant by: this two component spinor transforms under the left handed representation of the Lorentz group? When we talk about something that transforms...

We have all seen Lorentz transformations being written like this ##\Lambda ^\mu\;_\nu##, but why are they never written as ##\Lambda _\nu\;^\mu##?

Given a scalar function, we consider the following transformation: $$\delta f(x) = f'(x') - f(x) $$ Given a coordinate transformation $$x' = g(x)$$ But since ##f(x)## is a scalar isn't it true that ##f'(x') = f(x) ## Then the variation is always zero? What am I missing?

We make an infinitesimal Lorentz transformation of the Lagrangian and require it to be invariant. We then arrive at the following expression. $$\epsilon^{\mu\nu}j_{\mu\nu} = P_{\mu}\epsilon^{\mu\nu}X_{\nu}$$ which can be written as $$\epsilon^{\mu\nu}j_{\mu\nu} =...

Homework Statement Find the Thevenin equivalent at terminals a-b V1 = 70V V2 (dependent) = 4Vo R1 = 10Kohm R2 = 20Kohm Homework Equations ##V=RI## ##1/req = 1/r1 + 1/r2 + ... +1/rn## The Attempt at a Solution Found the current i = 1mA by KVL using Vo = 10ki then did source...

How to prove any orthogonal transformation can be represented by the product of many mirror transformations, please?What's the intuitive meaning of this proposition? Thank you.

If space only had one dimension would Einstein's speed of light postulate still lead to Lorentz transformation for motion along that one dimension? Relativity of simultaneity can obviously be demonstrated in one dimension (lightning bolts hitting opposite ends of stationary and moving train)...

Hi all, I am currently working on a creating a mathematical model of a longboard and am in need of advice. The pictures describe the sitaution. Side view Top view Back view The pictures depict a simplified longboard - the brown line is the deck and the black lines represent the...