Lorentz transformation Definition and 371 Threads

I read the Lorentz transformation can be obtained by solving the requirement of invariance of the wave equation. If one considers linear transformations this the same as the spacetime interval squared to be invariant. What are the other nonlinear transformations keeping the wave equation...

Problem Statement: Consider three frames Σ (x, y, z, t), Σ' (x', y', z', t'), and Σ'' (x'', y'', z'', t'') whose x, y, and z axes are parallel at each point in time stay. Σ' moves relative to Σ with velocity v1 along the x-axis. The system Σ'' moves relative to Σ' with the velocity v2 along the...

Hi guys, I'm reading a book 'the theoretical minimum: special relativity and classical field theory'. In chapter 1.3, author explains the general Lorentz transformation. He said "Suppose you have two frames in relative motion along some oblique direction, not along any of the coordinate axes...

In deriving the Lorentz transformation, is it required to assume that the transformation to get from coordinate system ##\bf {x}## to ##\bf {x’}## should be the same as that to get from ##\bf {x’}## to ##\bf {x}## (with the simple correction of flipping the velocity)? If no, could someone...

Since for the two events of Samir starting the stopwatch, and the stopwatch reaching 10.0s, Samir and his stopwatch are stationary from his own frame of reference, I said it was the proper time and that delta t0 = 10s. Then the speed of the moving frame of reference was 0.6c. I thought placing...

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...

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...

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...

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...

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.

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...

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 ?

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...

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...

Suppose I had cylindrically-symmetric rotating magnet surrounded by a plasma. I rotate it on its axis at a constant angular velocity, and so the electric field E produced is non-solenoidal and can be described as the negative gradient of some potential V(x,y,z). The electric field is induced...

Homework Statement For massless particles, we can take as reference the vector ##p^{\mu}_R=(1,0,0,1)## and note that any vector ##p## can be written as ##p^{\mu}=L(p)^{\mu}_{\nu}p^{\nu}_R##, where ##L(p)## is the Lorentz transform of the form $$L(p)=exp(i\phi J^{(21)})exp(i\theta...

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...

Homework Statement Special Relativity Question. Consider objects 1 and 2 moving in the lab frame; they both start at the origin, and #1 moves with a speed u and #2 moves with a speed v. They both move in straight lines, with an angle θ between their trajectories (again in the lab frame). What...

I read the Special Theory of Relativity in Jackson's textbook, Classical Electrodynamics 3rd edition. Consider the wave front reaches a point ##(x,y,z)## in the frame ##K## at a time t given by the equation, $$c^{2}t^{2}-(x^{2}+y^{2}+z^{2})=0 --- (1)$$ Similarly, in the frame ##K^{'}## the wave...

Lorentz transformation of electromagnetic field gives the relation ##E'=\gamma(E+v\times B)##. Lorentz force per unit charge is given as ##F=E+v\times B## without ##\gamma##. Don't we need coefficient ##\gamma## for F?

Is the Lorentz transformation matrix Λμν a tensor of order two and does it transform like a tensor ?

Homework Statement I've never encountered Jacobians before, and having read up on them a bit I find the wording of the last part of this question confusing: A set of coordinates ##x'_{\mu}## in frame B is obtained from the set ##x_{\mu}## in frame A, by boosting B w.r.t A with speed beta along...

Homework Statement Derick is fleeing from the cops on a car on a relativistic train. At xr= 0.0m and tr =0.000s the cops at rest see Derick leaving the back of the train and head towards the front of the train on his relativistic car. The cops see him arrive at the front at xr = 1.875*10^5m...

I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen. The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 21. Between equations (1.5.53) and (1.5.54), the authors make the following statement: ##S^\dagger ( \Lambda ) = \gamma ^0...

This is an IB problem from November 2017. Two rockets are separated by 6E8m (2 sec x c, or two light-seconds), w.r.t. Earth, and are approaching Earth from opposite directions. Rocket A approaches from left at 0.6c. Rocket B approaches form right at 0.4c. According to Earth, when do they...

Homework Statement An electric dipole instantaneously at rest at the origin in the frame K' has potentials \Phi'=\mathbf{p}\cdot\mathbf{r}'/r'^3 and \mathbf{A}'=0 (and thus only an electric field). The frame K' moves with uniform velocity \mathbf{v}=\vec{\beta }c in the frame K. Show that in...

Hi everyone! Sorry for my bad English! Please, suppose you have a subject A that opens his arms like a "T", in each hand he holds a laser and shoots the light at the same time. There are 2 targets at the same distance and, to A, the light hits both targets simultaneously. I Know that in some...

I don't fully understand the argument below used to derive the Lorentz transformation equation ##y'=y##. Suppose we have a rod of unit length placed stationary in frame S. According to an observer in frame S' (which is moving at a velocity v relative to frame S), this rod is moving and its...

We are always taught in books that a Lorentz transformation is possible as long as the Lorentz matrices ##\Lambda## in ##\vec{x}{\ }' = \Lambda \vec{x}## are not function of ##\vec{x}##. The reason for this is obvious, since in this way the relation ##t^2 - x^2 - y^2 - z^2 = t'^2 - x'^2 - y'^2...

The generators ##N^{\pm}{}_\mu = \frac{1}{2}(J_\mu \pm iK_\mu)## obey the algebra of ##SU(2)##. On the RHS we see the Lorentz generators of rotations and boosts, respectively. I considered the case where ##N^{\pm}{}_\mu = (1/2) \sigma_\mu##, i.e. the (1/2, 1/2) representation of the Lorentz...

According to this pdf http://www.springer.com/cda/content/document/cda_downloaddocument/9783319011066-c2.pdf?SGWID=0-0-45-1429331-p175291974 Newton's second law is not invariant under Lorentz transformations. To find out the part that says so, use CTRL+F and type "Newton"; it's the first result...

Let's assume that a light source is moving parralel to x-axis and is in point x,y,z in lab frame. Suppose it emits a light ray. In the rest frame that coincides with the lab frame, the light source is in point x',y and z. However, because of relativistic aberration the two light rays will make...

Hi. I'd like to ask about the calculation of Noether current. On page16 of David Tong's lecture note(http://www.damtp.cam.ac.uk/user/tong/qft.html), there is a topic about Noether current and Lorentz transformation. I want to derive ##\delta \mathcal{L}##, but during my calculation, I...

Is the Lorentz transformation given by the equations valid only if the origin of S and S' coincides at t=t'= 0 and the other axis (x,y,z) remains parallel to (x',y',z') respectively?

Homework Statement i)A police spaceship P is chasing another spaceship A. Both ships have velocities βP = βA = 3c/5 as measured along the x-axis in the Solar System reference frame O. The police ship is a distance L = 1 light-second (i.e. the distance traveled by light in one second) behind...

Since force is transformed via: F'x= Fx ; F'y= Fy/ ϒ; F'z=Fz/ ϒ (F' is the force related to the moving frame, F is the force on the rest frame and ϒ=1/√1-v2/c2 ).I expect that G (Gravitational constant) will be transformed between moving and rest frame in order to satisfy force transformation...

Hello! Can someone explain to me how does a scalar field changes under a Lorentz transformation? I found different notations in different places and I am a bit confused. Thank you!

Homework Statement Hi all, I'm given an electron with momentum 2.0*10-20kgm/s and was asked to convert the momentum into units of Mev/c then calculate the total energy of the electron, the lorentz factor and the speed of the electron, I did this successfully but then the question got confusing...

Hi I was looking at the Lorentz transformation and I see that it moves in the x-axis if vt is positive. How can I re-arrange the lorentz transformations in a way that will cause the moving frame of reference to get closer to me. I was trying with x'=gamma(x-vt) but I don't know what x is equal...

Hi folks, This is the Lorentz transformation in 1D, x axis: I want to get the second term of the time t equation, I mean vx/c2, in two dimensions, I mean for a point in the XY plane. I know this term arises because if we want to syncronize a point B with the origin what we do is sending a...

The Lorentz transformation matrix may be written in index form as Λμ ν. The transpose may be written (ΛT)μ ν=Λν μ. I want to apply this to convert the defining relation for a Lorentz transformation η=ΛTηΛ into index form. We have ηρσ=(ΛT)ρ μημνΛν σ The next step to obtain the correct...

Homework Statement Reference frame S' moves at speed v=0.94c in the +x direction with respect to reference frame S. The origins of S and S' overlap at t=t′=0. An object is stationary in S' at position x′ = 140 m . Part B What is the position of the object in S when the clock in S reads 1.3 μs...

Why does it use t' in that equation and not t? Isn't the equation relative to what an observer in the external frame of reference see? So if it is why not using the time he register? (The equation is uploades in the photo)

Homework Statement Suppose that A', B', and C' are at rest in frame S', which moves with respect to S at speed v in the +x direction. Let B' be located exactly midway between A' and C'. At t' = 0, a light flash occurs at B' and expands outward as a spherical wave. (A', B', and C' are all on...