Lorentz Definition and 1000 Threads

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...

1. Homework Statement : Consider a two dimensional Minkowski space (1 spatial, 1 time dimension). What is the condition on a transformation matrix \Lambda, such that the inner product is preserved? Solve this condition in terms of the rapidity. 2. Homework Equations : Rapidity Relations...

Hallo. A question about the relationship between the formulas found using the Lorentz transform and the invariance of the space time interval. Two events A and B occur at the same time and different space locations in system S, where A and B are at rest and at distance x. The system S'...

If we get on a train and time the train’s travel over 1000 meters, we can calculate the train’s velocity; v = dx/dt But if our watch is running slow, we will measure incorrectly and think the train was going faster than it really was. v’ = dx/dt’ We know that when something moves very...

1. Problem Horizontal rod of length x traveling along the positive y-direction at velocity u. Determine the orientation of the rod in frame S', which is moving at velocity v in positive x-direction. 2. Homework Equations Lorentz Transformation for length contraction, x' =...

Can anybody help me that how to work out the direction of Lorentz Force? Should I work out from the formula? Thanks.

we all know the lorentz group is of four disconnected components about the component connected to the unit element, is it coverable with single-parameter subgroups? put it in another way are all the elements in this component of the form exp(A)? i am studying relativistic quantum...

The notation below, is consistent with Wess and Bagger's https://www.amazon.com/dp/0691025304/?tag=pfamazon01-20. Given a Majorana spinor field in 4D, written in 2-component notation as \Psi(x) = \begin{pmatrix} \psi(x) \\\\ \bar\psi(x) \end{pmatrix} , \quad (\psi_\alpha)^* =...

Homework Statement Hi everyone, in Peskin & Schroeder, P36, the derivative part of KG field is transformed as eqn (3.3). But why does the partial derivative itself not transform? Homework Equations \partial_{\mu} \phi (x) \rightarrow \partial_{\mu} ( \phi ( \Lambda^{-1} x) ) = (...

I am interested in how the Lorentz maths were derived from the Maxwell electrodynamic and field equations. But not in a struct mathemetical sense as the math is outside my range but on a simpler conceptual level. For eg. contraction seems to have relevance wrt electron electrostatic fields and...

I am reading the definition in wiki ( nothing better at the moment) http://en.wikipedia.org/wiki/Lorentz_space It seems too vague for me, namely what they call "rearrangement function" f^{*}: f^{*}: [0, \infty) \rightarrow [0, \infty]; \\ f^{*}(t) = \inf\{\alpha \in \mathbb{R}^{+}...

There's something about the lorentz transformations which is somewhat confusing to me, and that is how to treat the "x" coordinate. Supposing I have some spaceship which is moving from Earth to some other planet located at a distance "D" (from earth) with a velocity v. Now, the spacetime...

Homework Statement The system S' moves in relation to the system S with velocity \upsilon along the -x- axis. At the time when the beginnings of the coordinate system are in the same point, clocks in both system shows t=t'=0. Which coordinates will have a reference point during the motion in...

The action for a fermion in curved spacetime is S = -\int d^4 x \sqrt{- \det(\eta^{ab} e_{a\mu}e_{b\nu})} \left[ i\overline{\psi} e^\mu_a \gamma^a D_\mu \psi + i m \overline{\psi}\psi \right] where g_{\mu\nu} = \eta^{ab} e_{a\mu} e_{b\nu} and the derivative operator acting on fermions is...

i am reading Lillian R. Lieber's book on the einstein theory of relativity and i am a bit confused on page 65. she wants to take the equations: x=x'cosθ - y'sinθ y=x'sinθ + y'cosθ and compare them to: x'=β(x-vt) t'=β(t-vx/c2) she takes c as one so: x'=β(x-vt) t'=β(t-vx) she...

I've spent a large portion of my day trying to figure this out and I figured my best answer is likely to come from here. Forgive me if I'm wildly wrong about anything, I'm somewhat basic with physics, largely due to the fact that I'm 15 and my maths is limited to a GCSE level. My dilemma is...