What is Lorentz: Definition and 1000 Discussions

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...

Can someone provide me with some original experiments conducted which verified the Lorentz magnetic force : F = q(v X B). Google does not give me any links except to explanations of the Lorentz force law.

Hi everyone! I have a problem with one thing. Let's consider the Lorentz group and the vicinity of the unit matrix. For each ##\hat{L}## from such vicinity one can prove that there exists only one matrix ##\hat{\epsilon}## such that ##\hat{L}=exp[\hat{\epsilon}]##. If we take ##\epsilon^{μν}##...

User Jack Fraser says that both ##X## and ##\Lambda## on his post are tensors. Is this right? Post: https://www.quora.com/While-deriving-the-Lorentz-transformation-how-do-you-know-that-the-transformation-will-be-linear

Homework Statement Prove that $$\begin{align*}\mathfrak{T}_L(x) &= \frac{1}{2}\psi_L^\dagger (x)\sigma^\mu i\partial_\mu\psi_L(x) - \frac{1}{2}i\partial_\mu \psi_L^\dagger (x) \sigma^\mu\psi_L(x) \\ \mathfrak{T}_R(x) &= \frac{1}{2}\psi_R^\dagger (x)\bar{\sigma}^\mu i\partial_\mu\psi_R(x) -...

The term "Lorentz transformations" only refers to transformations between inertial frames. However, if we differentiate velocity with respect to time, we obtain acceleration. The Lorentz factor says: t(0 reference frame observer at rest) / t(moving) = 1 / Sqrt[1–(v/c)^2] t0 / tm =...

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

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} =...

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)...

From a previous, now closed thread (Perok): "Technically, the Lorentz Transformation is not about observers but about reference frames." Sorry, I still don't get this. In frame A with observer A at the origin, x is the distance of the event X he sees measured on his rod, i.e. as...

From a previous thread, Nugatory: "If the answers already supplied are not enough for the original poster to work out for themself why x=vt+x'/γ, and not x=vt+γx′, is the correct expression, we can have another thread devoted to only that question." Here it is. Either Wiki is wrong or I am. In...

Obviously in the title I mention the user that recently got banned, but the reason I do is because s/he was having some trouble accepting that a B field transforms into a mixture of E and B fields per the Lorentz transformation (and other assorted quackery), so it got me thinking about why this...

The Lorentz transformations are mathematically simple. I had always imagined they could be easily derived. I however just found out from another PF thread that this is not so. Their originators Lorentz and Poincaré simply stated them without derivation. And the "proofs" I have seen to date have...

Hey there, I've suddenly found myself trying to learn about the Lorentz group and its representations, or really the representations of its double-cover. I have now got to the stage where the 'complexified' Lie algebra is being explored, linear combinations of the generators of the rotations...

Last night I was pleasantly surprised to discover that, given a particle trajectory x^2 - c^2t^2 = a^2 when viewed through a Lorentz transformation x' = \gamma (x-vt) t' = \gamma (t - vx/c^2) produces exactly the same shape x'^2 - c^2t'^2 = a^2 . I suppose this is equivalent to the...

Homework Statement I have an assignment to prove that specific intensity over frequency cubed is Lorentz invariant. One of the main tasks there is to prove the invariance of phase space d^3q \ d^3p and I am trying to prove it with symplectic geometry. I am following Jorge V. Jose and Eugene J...

I have an assignment to show that specific intensity over frequency cubed \frac{I}{\nu^3}, is Lorentz invariant and one of the main topics there is to show that the phase space is Lorentz invariant. I did it by following J. Goodman paper, but my professor wants me to show this in another way...

Homework Statement According to observer ##O##, a blue flash occurs at ##x_b =10.4m## when ##t_b =0.124 μs##, and a red flash occurs at ##x_r =23.6m## when ##t_r =0.138 μs##. According to observer ##O'##, who is in motion relative to ##O## at velocity ##u##, the two flashes appear to be...

I have a really naive question that I didn't manage to explain to myself. If I consider SUSY theory without R-parity conservation there exist an operator that mediates proton decay. This operator is $$u^c d^c \tilde d^c $$ where ##\tilde d## is the scalar superpartner of down quark. Now...

Does Hardy's paradox show that all realist interpretations cannot be made lorentz invariant? Or is it just realist hidden variable theories?

Homework Statement A proton moves with a speed ##v = 3 \cdot 10^5 \frac{m}{s}## in the parallel direction to ##i+k##. A magnetic field of ##1T##, in the ##i+j+k## acts over it. Which electric field must we apply in this region so that the Lorentz force over the proton is null? Homework...

Is it possible to derive the Lorentz transformation from time dilation and length contraction? If so, how should I start? I know how to derive it while considering 4 scenarios finding values of A, B,D,E in x'=Ax+Bt t'=Dx+Et and the transformation is: x'=(x-vt)/sqrt(1-v^2/c^2)...

Please tell me if Lorentz Transformation would be altered in any way if the invariance of c is explained, instead of postulated.

Homework Statement In this problem, we'll construct the ##(\frac{1}{2},\frac{1}{2})## representation which acts on "bi-spinors" ##V_{\alpha\dot{\alpha}}## with ##\alpha=1,2## and ##\dot{\alpha}=1,2##. It is convential, and convenient, to define these bi-spinors so that the first index...

The Lorentz factor shows how fast one frame will judge speeds in another frame to be taking into account the relative motion between the two frames. The speed of light is a factor in the Lorentz factor but I have heard that this is not because the speed of light is fundamental to it. So...

I put the level for this thread as I, but anything from B to A is acceptable here. I'm hoping this isn't too imprecise, but what are the easiest or simplest (or fastest) ways to derive the Lorentz transformation equations you know? I am not after blatant corner cutting here, by the way. Just...

This one may seem a bit long but essentially the problem reduces to some matrix calculations. You may skip the background if you're familiar with Lorentz representations. 1. Homework Statement A Lorentz transformation can be represented by the matrix...

Hello all. I am having some small trouble with applying the lorentz transformations to calculate lorentz contraction. Here's what I did: Let O be the rest system and O' be the system moving with velocity v w.r.t O along x axis. Consider a rod lying in the O' system with ends x1' and x2'...

How can we derive Lorentz Transformation ? I used one approach using the length contraction and time dilation and simultaneity but my prof wasnt much happy about it. Is there any other way to derive it ?

Hello people, I have been thinking about a concept that I was taught whilst learning GR, If I understand correctly it is that Lorentz symmetry becomes local when we consider GR. This makes sense to me as then the metric is generally speaking not Minkowski, only for a...

Homework Statement How can we derive Lorentz Transformation using the length contraction and time dilation equations of relativity ? Homework Equations ##γ = 1/ (\sqrt{1-u^2/c^2})## ##t = t_0γ## ##L = L_0/γ## The Attempt at a Solution [/B] In position Lorentz Transformation calculations...

Modal interpretations are a class of realist non local hidden variable theories. However, they cannot be made fundamentally lorentz invariant. However, neither can bohmian mechanics but BH is still emprically lorentz invariant. So are modal interpretation empirically lorentz invariant as well?

Hi there, I just saw some lectures where they claim that the Klein Gordon equation is the lowest order equation which is Lorentz invariant for a scalar field. But I could easily come up with a Lorentz invariant equation that is first order, e.g. $$ (M^\mu\partial_\mu + m^2)\phi=0 $$ where M is...

Hi. I came across the following statement , which seems wrong to me. Λμρ = ( ΛT )ρμ I have it on good authority (a previous post on this forum) that (ΛT)μν = Λνμ so I am hoping that the first equation is wrong ? It looks like the inverse not the transpose ? The equation Λμρ η μνΛνσ = ηρσ is...

Homework Statement Given the matrix $$ \Omega = \begin{pmatrix} 0 & -\psi & 0 & 0 \\ -\psi & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix}$$ show that ## e^{\Omega}## is a Lorentz transformation along the x-axis with ## \beta = tanh(\psi)## Homework Equations During the lesson we...

Hi, I've seen several explanations for sr on youtube. But they all start off explaining from a different perspective. I was wondering how the fundamental postulates of sr lead to the invariance of proper time between frames, and also what "order" everything is derived in. For example, does the...

How do I calculate the Lorentz factor with v=0. Or do I not calculate it since it can be said that the observer is in the same frame of reference?

Good afternoon, Not sure if this should be in the homework section or not but in any case... I'm having difficulty understanding the outputs from the Lorentz transform. Example problem. The Earth and sun are 8.3 light-minutes apart. Ignore their relative motion for this problem and assume...

Magnetic Lorentz force is the force experienced by any charged particle moving in a magnetic field.i want to clarify some doubts regarding this topic of Magnetic Lorentz force.some of them are: 1. Is it the Lorentz force that is actually responsible for the phenomenon of electromagnetic...

Hello! This is my first post on this forum, so make sure to tell me if I am doing something wrong :) I was trying to derive the Lorentz factor today, and I used the following page as a guide. The top answer by Jimmy360 is what I followed...

Hi all, just had a question about tensor/matrix notation with the inverse Lorentz transform. The topic was covered well here, but I’m still having trouble relating this with an equation in Schutz Intro to GR... So I can use the following to get an equation for the inverse...

As v approaches c, the Lorentz factor approaches infinity. The math and physics is well understood and observed. Is it true that, just mathematically, as v exceeds c the Lorentz factor approaches 0i for imaginary time constriction?

Hello, I do not fully understand nature of Lorentz contraction. Is it bona fide effect or not? https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment The article says: “This allows a more elegant and intuitive explanation of the Michelson-Morley null result. In a comoving frame...

I've been trying to understand representations of the Lorentz group. So as far as I understand, when an object is in an (m,n) representation, then it has two indices (let's say the object is ##\phi^{ij}##), where one index ##i## transforms as ##\exp(i(\theta_k-i\beta_k)A_k)## and the other index...

Hello! I am reading "A First Course in General Relativity" by Schutz and in chapter 8 (second edition) he introduces Nearly Lorentz coordinate system. He says that we can always find some coordinates such that the metric is: $$g_{\alpha\beta}=\eta_{\alpha\beta}+h_{\alpha\beta}$$ with...

Spontaneous symmetry breakingI’m not sure if I understand spontaneous symmetry breaking.In the context of the Mexican hat (and marble) example, wouldn’t the actual path of the marble down the Mexican hat from the top be determined by several small factors that one would normally not consider...

Homework Statement attached: Homework Equations where ##J_{yz} ## is The Attempt at a Solution [/B] In a previous question have exponentiated the generator ##J_{yz}## to show it is the generator of rotation around the ##x## axis via trig expansions so ##\Phi(t,x,y,z) \to \Phi(t,x,y cos...

According to David Morin (link: https://books.google.com/books?id=Ni6CD7K2X4MC&pg=PA636), the time-derivative of the Lorentz factor is (##c=1##): ##\dot{\gamma} = \gamma^3 v \dot{v}##, and the four-acceleration: ##\mathbf{A} = (\gamma^4 v \dot{v}, \gamma^4 v \dot{v} \mathbf{v} + \gamma^2...

I have just started learning the Special Theory of Relativity. While deriving, I am facing some problems. I obviously have made some kind of mistake while using the equations... What is wrong if I don't use the time transformation equation in Event #2?

Homework Statement There are 2 particles(1,2) separated ∆x=L moving with the same velocity u_x in frame of reference S , there's an other reference S' moving at v . I have to calculate ∆x'. GAMMA(LORENTZ'S FACTOR) Homework EquationsThe Attempt at a Solution I have done x1=0 when t=0 So for...