Lorentz Definition and 1000 Threads

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...

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...

Homework Statement An electron and a positron are observed from the lab to move in opposite directions with a speed of 0.5c and 0.7c, respectively. Find the speed of the positron when observed in the electron's rest frame. Homework Equations in attached PDF The Attempt at a...

Here's a scenario: A rod shaped object 1m in diameter and 300m in length is moving through space at a velocity of .999994444429013c (picked that velocity arbitrarily for the 300:1 length contraction). The Lorentz factor is 300 for this problem. So the equation to figure length contraction is...

Are Lorentz transformations only work between inertial frames? if so, is there a simple counter-example e.g. for them not to work?

Hello, I was just going through some writings on the web reg.Lorentz transformation. Even considering the derivative factor,d, is anyway Lorentz transformation is some way, linked with Pythagoras' theorem? Correct me if I am wrong? -- Shounak

1. The question states: "Two lights are placed along the x-axis at positions x1 = 3.00 m and x2 = 5.00 m. The lights flash at times t1 = 1.00 ns and t2 = 9.00 ns. An observer in a rest frame moving to the right sees the lights flash in the same location. Assume that the origins of the two rest...

Homework Statement A particle moves such that its relativistic factor γ equals one million. Find β (=v/c). Give answer in the form β = 0.999..., with correct number of nines before first non-nine digit. Do not use a calculator Homework Equations (1-β^2)^(-1/2) = 10^6 The Attempt at...

So this is my first course in upper level physics, and I'm still trying to figure out special relativity. The problem: Two events occur at the same place in a certain inertial frame and are separated by a time interval of 4sec. What is the spatial separation between these two events in an...

Homework Statement Particle mu was created in the atmosphere and traveled 2km relative to Earth with a speed of 0.8c. Particle e was created in the same time and traveled parallel to mu with the speed of 0.6c. How much distance mu traveled relative to e? Homework Equations Lorentz...

Can anyone recommend some litterature on representations of the Lorentz group. I'm reading about the dirac equation and there the spinor representation is used, but I would very much like to get a deeper understanding on what is going on.

Homework Statement Suzanne observes 2 light pulses to be emitted from the same location, but separated in time by 3μs. Mark sees the emission of the same two pulses separated in time by by 9μs. a) How fast is Mark moving relative to Suzanne? b) According to Mark, what is the separation in...

Homework Statement The pion has an average lifetime of 26.0ns when at rest. For it to travel 10.0m, how fast must it move? Homework Equations Lorentz velocity transformation? The Attempt at a Solution I'm very lost... am I supposed to use u'x = (ux-v)/(1-vux/c2)? I thought I was following...

I thought Lorentz Transformations left Δt2-Δx2 invariant but, for example a frame moving at .5C for Δt =1 has Δx = .5 so Δt2-Δx2 = .75 If this is transformed by : to a rest frame Δt =0.65 has Δx = 0 and Δt2-Δx2≠ 0.75 not sure where I have gone wrong here, any help would be...

I am slightly confused with the invariance of four-volume element. The orthodox way to show it is to prove that Jacobian is one, that I did, however in many textbooks I find a reasoning that because we have Lorentz contraction on one hand and time dilation on the other hand, the product is...

Can anybody help me with the proof that E_p \delta ({\bf p}- {\bf q}) is a Lorentz invariant object? I did a boost along z axes and used the formula \delta (f(x)) = \frac{\delta(x-x_0)}{|f'(x_0)|} and the factor in front of the delta function indeed is invariant but within the function I...

Someone asked me how Faraday's Law of Induction and Ampere's Force Law, both which form part of Maxwell's Equations, are related. Ampere's Force Law is derived from the Lorentz Force Law. They are entirely compatible with Faraday's Law of Induction. Here's how...The Lorentz Force Law states...