What is Lorentz: Definition and 1000 Discussions

Homework Statement i) Show that the wave equation: [( -1/c^2) d^2/dt^2 + d^2/dx^2 + d^2/dy^2 + d^2/dz^2 ]u(t,x,y,z) = 0 is invariant under a Lorentz boost along the x-direction, i.e. it takes the same form as a partial differential equation in the new coordinates. [Use the chain rule in two...

Hello I have been having trouble understanding equation 14.25 in Bjorken and Drell "Relativistic Quantum Fields" and how exactly it gets to it. Also I would like to explicitly find/derive what the operator gauge function is. Can anyone help please?

Homework Statement Event A occurs at xA = 500m. Event B occurs 5 microseconds later at xB = 1500m. With what speed must an observer move in the positive x direction so that the events occur at the same point in space in the observer's frame?Homework Equations Lorentz transformation...

Homework Statement A3. Show that the Lorentz transformations on a spacetime 4-vector can be written as x'μ = (Lμν)*(χν) . Find the matrix L. Prove that (in matrix notation) Lτ gL = g where g is the Minkowski spacetime metric.Homework Equations Any help suggesting at least equations will be...

Hello. When one is converting between coordinate systems, the Jacobian arises as a necessary consequence of the conversion. Does this occur with transformations between relativistic systems, and, if so, is this manifested through the prevalence of gamma in the transforms? Any guidance would...

Homework Statement Derive length contraction using Lorentz invariants. Homework Equations ds^2 = dx^2 +dy^2 + dz^2 - c^2 dt^2 The Attempt at a Solution Consider a rod parallel to the x-axis and moving with velocity v in the x-direction. We can measure the length of the rod of...

I'd like to start by mentioning that I have very little in the way of experience on the subject, so forgive me if my confusion is somewhat trivial.. My problem lies with understanding what the fundamental variables in the Lorentz Transformations actually represent. For example, it is to my...

In the process of proving that the d'Alembert operator https://www.physicsforums.com/attachments/31306 is invariant under Lorentz transformations, it was required to commute two terms in the following expression for the transformed operator, which was obtained by switching the index on the...

I don't understand why the lorentz factor is 1/[1-(v2/c2)]1/2 http://www.softcom.net/users/greebo/dila.jpg clearly you reach something different here.. i really don't get this, I'm sure it's something very simple

How is Lorentz invariance handled in GR? I know that there is no global Lorentz invariance in GR, instead it only holds locally, meaning that it is obeyed in the limit at infinity:when r goes to infinity by considering infinite distance or infinitely small point mathematical objects. But when...

Homework Statement Given that (φ/c,A) is a 4-vector, show that the electric field component Ex for a Lorentz boost along the x-axis transforms according to Ex' = Ex. Homework Equations E_x = -\frac{\partial \phi}{\partial x} - \frac{\partial A_x}{\partial t} A_x being the x component of the...

I'm trying to teach myself special relativity. I use the book 'Introduction to Special Relativity' by Wolfgang Rindler. I have a question about length contraction. We consider 2 particles traveling along the x-axis of a reference frame S with a constant distance between them. We can always go...

I have a question about the way lorentz transformations work with respect to a 'block' view of the universe. Take our universe as a 3d chart with 2 space dimensions and one time dimension (ignoring the other space dimension for simplicity). You chart it using some "god's eye view" reference...

Homework Statement 2 particles are created in a high-energy accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory is 0.650c, and the speed of each particle relative to the other is 0.950c. What is the speed of the second particle, as measured...

"Locally Lorentz" Mister Thorne Wheeler, "Gravitation" asks "What does it mean to say that the geometry of a sufficiently limited region of spacetime in the real physical world is Lorentzian?" The follow this up with two answers, neither of which appears to have much to do with the question...

Hi i have a problem with some work. a muon type neutrino interacts with a stationary electron, producing a muon and electron type neutrino. I have calculated the CM energy but now need to calculate gamma, the lorentz boost. γ=(Eν/2me)^1/2 How do i show this? the info i have is that...

Homework Statement So, I'm working through a relativity book and I'm having trouble deriving the Lorentz transformation for an arbitrary direction v=(v_{x},v_{y},v_{z}): \[\begin{pmatrix} {ct}'\\ {x}'\\ {y}'\\ {z}' \end{pmatrix}=\begin{pmatrix} \gamma & -\gamma \beta _{x} &...

Yesterday there was a thread here on a claimed violation of Lorentz invariance, but I can't locate it today. Was the thread moved? Can someone point me to its new location? (I don't remember the exact title of the thread, but the posts referred to a letter in the Sep 2010 issue of European...

I've just read the statement "The Lorentz transformations have a representation on the fields" Can anyone explain the meaning of the word representation? I can't seem to get a satisfactory explanation anywhere and the notes don't go into much more detail on it.

So the generators of the Lorentz Lie algebra relations obey [M^{\rho \sigma}, M^{\tau \mu}] = g^{\sigma \tau} M^{\rho \mu} - g^{\sigma \mu} M^{\rho \tau} + g^{\rho \mu} M^{\sigma \tau} - g^{\rho \tau} M^{\sigma \mu} where (M^{\rho \sigma})^\mu{}_\nu = g^{\rho \mu} \delta^\sigma{}_\nu -...

a)So I'm reading over my notes and they say that under the Lorentz transformation L, \phi \rightarrow \phi' where \phi'(x)=\phi(x') where x'^\mu = (L^{-1})^\mu{}_\nu x^\nu I don't really understand why this is true. Why is it not just \phi'(x)= L \phi(x) Clearly this fails because the LHS is...

Homework Statement Show that a Lorentz transformation preserves the sign of the energy of a solution to the Dirac equation. The Attempt at a Solution I'm not sure how to approach this. So I apply the Lorentz transform to the Dirac equation, and work through it to obtain the energy...

I asked my prof why the Lorentz transformations had to be linear (which my textbook assumed when deriving them), and he mentioned some stuff about homogeneity and ended with "it's advanced, just believe". Can anyone offer a simple explanation?

Homework Statement In the old West, a marshal riding on a train traveling 35.0 m/s sees a duel between two men standing on the Earth 55.0 m apart parallel to the train. The marshal's instruments indicate that in his reference frame the two men fire simultaneously. (a) Which of the two men, the...

In a lecture on special relativity online, the form x'=x\cosh{\omega}-ct\sinh{\omega} t'=-x\sinh{\omega}+ct\cosh{\omega} is used for the lorentz transformations, where the velocity is v=\frac{c\sinh{\omega}}{\cosh{\omega}}. However, I'm wondering, couldn't you also do...

Is the d'alembertian of lorentz transformation matrix 0? and why? would it be 0 because it lorentz invariant? thanks

Homework Statement The Field strength tensor Fuv encodes the electric and magnetic fields via: Ei=-cF0i, Bi=-1/2 eijkFjk, i=1,2,3 Show that E^2-c^2B^2 and cE.B are invariant under lorentze transformations, by writing them explicitly as invariant contractions using the tensors Fuv and euvab...

Homework Statement Given the Lagrangian density L=-{1 \over 2}[\partial_\alpha\phi_\beta(x)][\partial^\alpha\phi^\beta(x)]+{1\over 2}[\partial_\alpha\phi^\alpha(x)][\partial_\beta\phi^\beta(x)]+{\mu^2\over 2}\phi_\alpha(x)\phi^\alpha(x) for the real vector field \phi^\alpha(x) with field...

The group of four dimensional space time symmetries may be generalised to conformal transformations x \rightarrow x' defined by the requirement dx'^2 = \Omega(x)^2 dx^2 where dx^2 = g_{\mu \nu} dx^\mu dx^\nu (recall that Lorentz invariance requires \Omega=1). For an infinitesimal...

One way to derive Lorentz factor is imagining the experiment of the light clock. This experiment is about two observers. One observer is moving at a constant speed on the x-axis and the other observer standing at rest. The observer moving along the x-axis carries a light clock which shoots a...

Define B( \theta, \vec{n} ) \in SL( 2 , \mathbb{C} ) by B( \theta , \vec{n}) = \cosh { \frac{1}{2} \theta} + \vec{\sigma} \cdot \vec{n} \sinh{ \frac{1}{2} \theta} where \vec{n}^2 =1 Show that this corresponds to a Lorentz boost with velocity \vec{v}=\tanh{ \theta} \vec{n}. Show that ( 1 +...

Hi I am confused about these two related but different terms Lorentz invariance/covariance and General invariance/covariance As I understand it a Lorentz invariant is a scalar which is the same in all inertial reference frames i.e. it acts trivially under a Lorentz transformation an example...

Homework Statement an electron accelerated from rest through potential difference V1=0.868 kV enters the gap between two parallel plates having separation d = 21.9 mm and potential difference V2= 91.2 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's...

hey, does anyone there know how the angular momentum (L=r x p) is transformed under Lorentz transformations?

Ok so I am attempting to get a "feel" of the Lorentz equations. For a observer O' moving with velocity v respect to a observer O along the x direction the transformed variables are x and t. x' = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}(x - vt) t' = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}(t -...

I have recently learned the basics special relativity and it is amazing!, but I still have a few questions and I will be thankful if one can answer me. (I will rather open an extra thread for each question that bothers me, so each question can be handled independently.) So I would like to...

Lorentz force is explained or demonstrated using Fleming's Left Hand Rule or the Force equation using cross product. What I'm trying to ask here is, why is the direction fixed using the Left Hand Rule or the equation? Why is the direction here and not there? Equation and rules are the...

\alpha=\left(\begin{array}{cccc} \gamma& 0&0& -\beta\gamma\\ 0&1& 0 & 0\\ 0 & 0 & 1 & 0\\ -\beta\gamma & 0 & 0 & \gamma \end{array} \right)x'^{\mu}=\alpha^{\mu}_{\nu} x^{\nu} \alpha is Lorrentz transformation matrix. Can I see something more about it? . It's symmetric. That is important...

Homework Statement I have to find a relation for kinetic energy as a function of the lorentz factor, KE(gamma). It can only depend on the lorentz factor or on a constant. Homework Equations E_{tot} = \gamma m_{0} c^{2} E_{tot} = KE + m_{0}c^{2} = \sqrt{p^{2}c^{2} + m_{0}c^{4}} \gamma =...

Homework Statement A light signal is sent from the origin of a system K at t = 0 to the point x = 1 m, y = 8 m, z = 13 m. a) At what time t is the signal received? b) Find ( x', y', z', t' ) for the receipt of the signal in a frame K' that is moving along the x-axis of K at a speed of 0.6c...

I was given this as an extra-curricular activity... way over my understanding of physics, sophmore year undergraduate. But I can use a bit of help. I'm given data from a collision resulting in 2 muons. (this is exactly how the text is written to me, if any of these definitions are not...

Homework Statement Consider a two-dimensional function φ = φ(x,t) that satisfies the relativistic wave equation given by: https://adgiiq.blu.livefilestore.com/y1pe5tdBVr0r62krIiWV_PQ42r1jrzQpWKz24xRgNe138phEqCNyZJKFXhBXqqL4YCvYeAsgVQtJJwovzjL0mKiNXyd6p1zHvkx/equation.jpg?psid=1...

Homework Statement Show that the Lorentz force law follows from the following variational principle: S=\frac{m}{2}\int\eta_{\mu\nu}u^\mu u^\nu ds-q\int A_\mu u^\mu ds Homework Equations Definition of Field Strength Tensor Integration by Parts Chain Rule & Product Rule for Derivatives The...

For starters, there is the covariant vector (E/c, p). Dividing by the scalar invariant, h_bar/2∏, where k is the propagation vector, there is (ω/c, k). There must be a significant number of covariant objects in electromagnetism...

x'=a_{11}x+a_{12}y+a_{13}z+a_{14}t y'=a_{21}x+a_{22}y+a_{23}z+a_{24}t z'=a_{31}x+a_{32}y+a_{33}z+a_{34}t t'=a_{41}x+a_{42}y+a_{43}z+a_{44}t \vec{u}=u\vec{e}_x Coefficients a_{nm}=a_{nm}(u) Why I suppose that coefficients are function only of velocity u? Inverse relations...

I did more than one course of classical electromagnetism in college. Recently, however, after reading "How Relativity Connects Electric and Magnetic Fields" (http://galileo.phys.virginia.edu/classes/252/rel_el_mag.html) I was astounded to realize how little I knew about it! In college (if I...

Anyone help. I know I must be doing this wrong somehow Lightning hits both a tree and a pole. The spacetime coordinates for each is (x=0, t=10us) for the tree and (x=30000m, t=10us) for the pole relative to the ground. Therefore they occur simultaneously relative to the ground. A rocket comes...

Blandford & Thorne, Applications of Classical Physics: Taylor & Wheeler, Spacetime Physics: These definitions seem to be based on the notion of a "physical" or "practical" infinitesimal: a quantity too small to be detected. But how can we measure the accuracy of an imaginary detector...

Does anybody have a reference or can write out the general (so not just a boost in only one direction) Lorentz matrix in terms of rapidities?

Hi guys, Before responding to my post, please note that I am only familiar with the mathematics of nonrelativistic quantum mechanics, and don't know any quantum field theory. All I have is this vague idea that quantum field theory is the union of special relativity and quantum mechanics...