Lorentz Definition and 1000 Threads

Homework Statement I am trying to prove that Maxwell's laws are consistent with special relativity if one frame is moving in the x direction with another. Homework Equations In this case, I know that \frac{\partial}{\partial x'} = \gamma \frac{\partial}{\partial x} + \frac{\gamma v}{c^2}...

I have recently found that Mathematica has a "reader" which allows interactive calculations and plots to be shared. Here is a simple example, please let me know if there is interest in more such widgets.

Unfortunately, my knowledge on this is limited to wiki which I trust is relatively correct but I would like to clear up some ambiguity. (I don't mind technical but please back it up with a general explanation since I am completely new to this. The general explanations I value more.) Wiki...

If I construct a LT from an un-prime frame to a prime fame: S':=LT(S,v') and another to a double prime system: S":=LT(S,v"), then invert the first: S:=LT(S',-v') and substitute it into the second: S":=LT([LT(S',-v')],v"), I do NOT get the same transform as going directly between the double and...

Special Relativity states that a ruler flying by at near the speed of light will appear to be shortened as observed by a stationary observer in the lab frame. This is, of course, exactly what happens to macroscopic objects. The question is how far can we push this into microscopic realm...

Hello, My question is on coupling the photons to our Dirac field for electrons, we have the Dirac equation: (i\not{\partial -m })\psi=0 By Lorentz invariance we can change our space-time measure by: \partial ^\mu \rightarrow \partial ^\mu+ieA^\mu\equiv D^\mu Though I cannot see...

Hi, I'm currently reading the book "Quantum Field Theory for Mathematicians" by Ticciati and in section 2.3 he mentions that the Lorentz action on the free scalar field creation operators \alpha(k)^\dagger is given by U(\Lambda)\alpha(k)^\dagger U(\Lambda)^\dagger = \alpha(\Lambda...

Homework Statement First part of the problem: Newton’s second law is given by F=dp/dt. If the force is always perpendicular to the velocity, show that F=gamma*m*a, where a is the acceleration. Second part of the problem: Use the result of the previous problem to show that the radius of a...

I understand that for a fixed massflow the minimum amount of power required to generate a thrust is: P = Massflow * ∫v dv = massflow *0.5* [v2^2 - v1^2] However, is it possible to produce the same thrust with less power using the Lorentz force in an electromagnetic accelerator? If so, how can...

I am trying to understand how the Lorentz force affects bulk fluid motion when I have an applied electric field (y-axis), applied magnetic field (x-axis) and bulk fluid velocity (z-axis), all orthogonal to each other. I understand that if the fluid was at rest, an electrostatic force would...

I am trying to understand how the Lorentz force affects bulk fluid motion when I have an applied electric field (y-axis), applied magnetic field (x-axis) and bulk fluid velocity (z-axis), all orthogonal to each other. I understand that if the fluid was at rest, an electrostatic force would...

Homework Statement Two particles in a high-energy accelerator experiment are approaching each other head-on, each with a speed of 0.9500c as measured in the laboratory. What is the magnitude of the velocity of one particle relative to the other? Homework Equations...

I am trying to understand how the Lorentz force affects bulk fluid motion when I have an applied electric field (y-axis), applied magnetic field (x-axis) and bulk fluid velocity (z-axis), all orthogonal to each other. I understand that if the fluid was at rest, an electrostatic force would...

SU(2) a double cover for Lorentz group? I'm presently reading the new book, "Symmetry and the Standard Model", by Matthew Robinson. On page 120, he writes, "the Lorentz group (SO(1,3), pg 117) is actually made up of two copies of SU(2). We want to reiterate that this is only true in 1+3...

Is there anyone here who could help me understand the state of physicists understanding just prior to 1905 and Einstein's SR paper? I keep running into length contraction, considerations of simultaneity and its non-universal nature, Lorentz transformations, time dilation and other concepts that...

what is the formula of spin connection in GR ? can we show it in term of structure coefficients ?

Lorentz factor for moving inertial reference frames is λ = \frac{1}{\sqrt{1 - \frac{v2}{c2}}}, where v is the relative velocity between the frames. But in my textbook (I'm only just learning relativity), it says the Lorentz factor for a particle is λp = \frac{1}{\sqrt{1 -...

Hello, I've seen several derivations of it and I understand them, specially the one in two dimensions with the right angled triangle, but when I try it in 1 dimension, I always find that the condition that the speed of light is the same in all the inertial frames, isn't enough to specify what...

Homework Statement Consider an infinite line of charge with density λ per unit length lying along the z-axis. If the line of charge is stationary in frame S, use the Lorentz transform to find the current and charge densities in a frame S' which is moving with velocity v parallel to the...

I'm having some difficulty understanding the representation theory of the Lorentz group. While it's a fundamentally mathematical question, mathematicians and physicists use very different language for representation theory. I think a particle physicist will be more likely than a mathematician to...

(if I am not even wrong, please let me know :smile:) The generators of the (proper-orthochronous) Lorentz transformations are usually denoted by {J_{\mu \nu }} or by {M_{\mu \nu }}. They consist of angular momentum generators and boost generators. When discussing spinors, the notation changes...

Does a Lorentz boost change the "direction" of an electron's spin orientation? For example, if an electron is in a state "spin-up" along x, and this electron is subjected to a large boost along another direction, say z, will the electron's spin remain "spin-up" along x? What if the...

I have 2 coordinate systems which move along ##x,x'## axis. I have derived a Lorentz transformation for an ##x## component of momentum, which is one part of an 4-momentum vector ##p_\mu##. This is my derivation: \scriptsize \begin{split} p_x &= mv_x \gamma(v_x)\\ p_x &= \frac{m...

Homework Statement Particle track detectors are used to measure the speed of particles if the lifetime of the particle is known. Particle X has a lifetime of 256.2 ps. These particles are created in an experiment inside the detector by a given reaction. The particles leave 21.8 cm long tracks...

Am I correct in thinking that the quantum mechanical de broglie wavelength explains relativity's contraction of matter? because lambda = h/p, as the velocity of say a proton increases, the momentum also increases, and the wavelength should get smaller because lim p-->infinity of h/p = 0. At very...

My question is: what does "manifest" Lorentz covariance means for a field theory, as opposed to simply Lorentz invariance. Thanks for the replies!

In a book ("The special theory of relativity by David Bohm") that I'm reading, it says that if (x,y,z,t) are coordinates in frame A, and (x',y',z',t') are coordinates in frame B moving with v in realtion to A, if we have (for a spherical wavefront) c^2t^2 - x^2 - y^2 - z^2 = 0 and we...

I'm just getting started on relativity. I watched this a couple of day ago - But I didn't like the way Lorentz Transformation was derived (the assumption about the nature of the final transformations, to be more specific). I tried reading Einstein's original paper for a better derivation but...

When constructing the Lie algebra of the Lorentz Transformation, the references usually start with an infinitesimal proper-orthochronous transformation, and then find the infinitesimal generators. Let's call the set of these generators L. after finding L, the references usually compute the...

In several textbooks of QM I have read that Lorentz invariance is manifest in Heisnberg picture. How can we deduce that?

Homework Statement A Particle moves with uniform speed V'y = Δy'/Δt' along the y'-axis of the rocket frame. Transform Δy' and Δt' to laboratory displacements Δx, Δy, and Δt using the Lorentz transformation equations. Show that the x-component and the y-component of the velocity of this...

The Lorentz factor is used ubiquitously in relativity for transformation between frames and in describing various relationships. Wikipedia describes this as: ---------- The Lorentz factor is defined as: γ = 1/√(1-v2/c2) = 1/√(1-β2) = dt/dτ where: v is the relative velocity between...

So I know about the lorentz factor and how it describes time dialition, mass increasing etc.. but I was wondering how it was derived in the first place?

I am currently looking a bit into special relativity. Consider the matrix \Lambda=\left( \begin{array}{cc} \gamma & -\gamma \beta c \\ -\gamma \beta c & \gamma \end{array} \right) where \beta=\frac{v}{c},\quad \gamma=\frac{1}{\sqrt{1-\beta^2}} and c is the speed of light. Then, an observer...

Homework Statement Ok so a Kaon (m = 500MeV) is accelerated from rest along the z-axis to a final energy of 5GeV, I need to find two factors of a lorrentz transformation β and γ and write a four vector for this. Homework Equations β=p/E γ=E/m The Attempt at a Solution I have...

Concerning Rapidity, if tanh(Fi) = v/c, can it be concluded in general that the relative angle of two frames in combination with Lorentz Transformation is tan(theta) = tanh(Fi) = v/c, where theta is the relative angle?

How to arrive at Lorenz gauge condition? http://en.wikipedia.org/wiki/Lorenz_gauge_condition I know it's used to simplify the 2 partial differential equations of the potentials, but why can we put such a restriction on the potentials? Doesn't that restriction restrict the possible electrical...

Hey everyone, I'm trying to make sure I did this question right. Any ideas would be greatly appreciated. Thanks! Homework Statement The general force that bends the electron in the e/m experiment is known as the Lorentz force, F = q(E + v x B), where force F, electric field E, velocity v...

Homework Statement Given that the derivative θμ transforms as a covariant vector ,show that θμ transforms as a contravariant vector. Homework Equations Please look the attachement The Attempt at a Solution Does anyone know how i should go to prove it ?Is it just a trivial...

Homework Statement Show that the following is a Lorentz Transform: \Lambda _{j}^{i}=\delta _{j}^{i}+v^iv_j\frac{\gamma -1}{v^2} \Lambda _{j}^{0}=\gamma v_j , \Lambda _{0}^{0}=\gamma , \Lambda _{0}^{i}=\gamma v^i where v^2 =\vec{v}\cdot \vec{v}, and \delta _{j}^{i} is the Kronecker Delta...

Homework Statement ESTIMATE the Lorentz factor of a spaceship which travels to a nearby star 10pc from the solar system in 50 years spaceship time. Homework Equations Lorentz factor: γ = 1/√(1 - v^2/c^2 ) Time dilation: Δt' = γΔt The Attempt at a Solution Using the distance...

As per group property, one could make a product of gr members e.g. Lorentz boost (B) and rotation R, as they Commutativity is not valid, R.B or B.R, what should be considered and which order should be preferred? Generally it is known R.B1= B2.R .

Homework Statement An electron in electric & magnetic fields; E = 3.0x107 ex NC-1 B = 3.0 ez T has velocity v = 1.0x10^7 (2ex-ey) Calculate em force on the electron.Homework Equations I'm using the Lorentz force law here. F = q(E + v X B) I have an example solution using vectors to evaluate...

Homework Statement An electron in a magnetic field B=2.0T(ex-ez) has velocity v=(2.5x107 ms-1 (ex-ey) a) calculate magnetic force on electron at that instant b) what is the magnitude of this force Homework Equations I am using the Lorentz force law. F = q(vXB) & evaluating the directions by...

Homework Statement As the title suggests, I need help finding resources that clearly shows the step by step process of the derivation of the rest or invariant mass using the Lorentz transformation. Homework Equations Energy-momentum relation The Attempt at a Solution Not looking...

Starting with: x'=\gamma(x-vt) & x=\gamma(x'+vt') I know that I can derive t'=\gamma(t-vx/c^2)... however I can't seem to make it fall out mathematically. The suggested method is to cancel x'. Can anyone help me out on the steps? Much appreciated! :)

It is a well known fact that the Lorentz group of transfornations are linear. Now reading the wiki entry on the LG it spends a good deal explaining its identity component subgroup, the restricted LG group, and it turns out it is isomorphic to the linear fractional transformation group, which are...

I have been struggling to find an inverse to a Lorentz matrix \Lambda using formula: \Lambda^{-1}= \frac{1}{| \Lambda| }\textrm{adj}(\Lambda) from linear algebra. \Lambda = \begin{bmatrix} \gamma&0&0&-\beta \gamma \\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ -\beta \gamma & 0 & 0 & \gamma...

So my friend and I were going through problems and this came up... Consider 3 straight, infinitely long, equally spaced wires (with zero radius, separated each by a distance d), each carrying a current I in the same direction. blah blah blah... part c) asks us... If the middle...

Hi everyone, I was wondering, does the Lorentz force can be used to get the self force of a particle over it self? I'm in doubt because the fields that one uses to compute the force, in the lorentz force expression, are the external fields but one can compute the Liénard-Wiechert potetials...