Lorentz Definition and 1000 Threads

Suppose we can boost from a frame ##S## to another frame ##S'## by using a Lorentz transformation ##\Lambda##. Also, ##\phi(x^\mu;\omega,\mathbf k)## is a mode function of a scalar field in frame ##S##. Then, how do we express this mode function in frame ##S'##? Here is my attempt. First, the...

Hello everyone, I would be thankful ir someone explained where I am mistaken in this reasoning on Einstein’s mental experiment on Special Relativity. Taking the railway as K reference frame, a light beam is thrown in the x positive direction the moment the train passes in the same positive...

So, I linked an image to Problem 1.26 below. As far as that problem, to save you the trouble, the answers (at least from what I have) are: a) ##\gamma = 1.7 ## b) ## t = 3x10^{-8} ## c) ## Pions = 30,555 ## d) ## Pions = 29,628 ## Fairly confident those are correct, but now this question...

Somebody, please explain to me about the Lorentz force between two parallel current-carrying wires in terms of the momentum conservation as the electromagnetic fields has momentum density. Especially, (1), If a short rectangular magnetic pulse due to an electric pulse in one wire will still...

I know the Lorentz matrix for a boost along any of the Cartesian axes. But, since all the components of the magnetic field has changed in the frames, the boost is along an arbitrary direction, rather tahn a particular axis. How do I solve the problem in this case?

In my book it's said that a conductor in a homogeneous magnetic field moves because there is a stronger magnetic field on one side and a weaker magnetic field on the other. Now that seems wrong to me. I mean, if we were to look at the Lorentz force that the magnetic field exerts on the...

For this problem and solution, I'm confused by part (c) and (d). I don't understand how the Lorentz formula ##ct' = \gamma (ct - \frac{v}{c}x)## can be used to find the ##ct'## axis. This is because they found the ##ct = \frac{v}{c}x## which is in terms of ##x## not ##x'##. Does anybody...

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As far as I know, there are two causes of the rotational motion of the charged ring. T he first torque is from Lorentz force: $$T=Q\mathbf{R\times ( v} \times \mathbf{B}_{r}) =-\frac{QR^{2}}{2}\frac{dz}{dt}\frac{d\mathbf{B}_{z}}{dz}$$ (where ##\mathbf{B}_{r}...

Two simple equations, yet I can't find any sources that explains it very well. If you have any suggestions on where I could find this then please link them! $$ \Delta{t'}=\gamma(\Delta{t}-\frac{v}{c^2}\Delta{x}) $$ Does it matter if S' is moving away to the right, or to the left, of S? I...

A car travels at low speed on a road from start to finish, and counts the number of turns of the wheel, which gives it a road length of N.2πR, where R is the radius of the wheel. Then he does the race again at relativistic speed. He sees the road with a Lorentz contraction. However, he has to...

The Lorentz transformation ensures different inertial observers measure the same speed of light. Are there other transformations, or other ways to setup a "space-time" that also have this property of invariance? Is the Lorentz transformation the unique solution?

This is the defining generator of the Lorentz group which is then divided into subgroups for rotations and boosts And I then want to find the commutation relation [J_m, J_n] (and [J_m, K_n] ). I'm following this derivation, but am having a hard time to understand all the steps: especially...

I was reading a discussion where some physicists participated* where the topic of Lorentz invariance violations occurring in cosmology is mentioned. There, they mention that we can imagine a Lorentz-violating solution to the cosmological equations. What do they mean by that? Can anyone specify...

Background: is the equation of Lorentz force for the force acting on a moving charge in electric and magnetic field. For the magnetic field only it is : F=qv×B. Question: For magnetic field only why is the force not F=q(v×B) = F=qv×qB

Can someone please explain to me how can we obtain this integral in eq. 5.27 from eq. 5.26? I quite do not understand how is it possible to make this adjustment and why the (p_(f))^2 appeared there in the numerator and also why a solid angle appeared there suddenly.

In Schutz 8.3, while proving that a Lorentz gauge exists, it is stated that $$\bar h^{(new)}_{\mu\nu} = \bar h^{(old)}_{\mu\nu} - \xi_{\mu,\nu} - \xi_{\nu,\mu} + \eta_{\mu\nu}\xi^\alpha_{,\alpha}$$ where ##\bar h## is the trace reverse and ##\xi^\alpha## are the gauge functions. Then it follows...

Hi every one.How can i prove the below equation? And then that it's Lorentz invariant quantitude ? Thanks for your help

The twin paradox is connected to the special relativity but I wonder simply if one might construct the paradox (or something very similar) based on the Lorentz’ (and FitzGerald) work alone? Several ingredients in the paradox, time dilation and Lorentz contraction, are often mentioned with...

Newton's gravity depends on the euclidean distance between two masses. Two comoving frames will have different values of length between masses so the forces will be different in two frames. Is it enough to prove that the gravity rule has to be modified?

(##c = 1##) The general definition of the four-current density is ##j^{\mu} = (\rho, \vec j)##, where ##\rho## is the charge density and ##\vec j## is the three-current density. This vector may be timelike, lightlike, or spacelike, because both positive and negative charges may be involved with...

Sorry for the extra question. Just have a lot of questions lately and I know some people around here are annoyed with that.

I made a tool for calculating and visualizing how the electric and magnetic fields transform under a Lorentz boost. Thought I'd share it here, in case anyone finds it interesting. https://em-transforms.vercel.app/

I am searching online for resources regarding studies done on the effect of the Lorentz force due to short circuit faults in capacitors. Although a DC-link capacitor only sees the ripple, there would be high current during a fault. Since F=(qE + JxB), I am curious what the effects of the high...

In section 3.8, Feynman does a derivation of the Lorentz transformation for mass starting from $$\frac{d}{dt}E=F \cdot v \hspace{1cm}(1) $$ But is this a valid starting point if you are going to show mass changes with velocity? He says (1) comes from chapter 13 of his Lectures which he...

1. The 2nd line on the 3rd page of your notes, you have x=ct and x'=ct', thus ux=dx/dt and ux'= dx'/dt' =c according to Einstein's assumptiuon. 2. But near the end of the last page, you wrote dx'/dt' = (ux -v)/(1-vux/c2) . Compare with 1. This equation can be valid only for ux=c and...

The Lorentz transform for velocities is as follows: $$u=\frac{v+w}{1+\frac{vw}{c^{2}}}$$ But which assumption exactly underlies this so that you get exactly this formula and not any other formula with approximately the same properties?

There are several "bumblebee" models [1], [2] where Lorentz invariance is violated usually resulting from a local vector or tensor field acquiring a nonzero vacuum expectation value We do not know whether we are in the true vacuum state or in a "false"/metastable vacuum state that could decay...

In this paper [1] which considers the possibility that the Lorentz symmetry could be broken, at page 4-5 the author says: "We now introduce a Higgs sector into the Lagrangian density such that the gravitational vacuum symmetry, which we set equal to the Lagrangian symmetry at low temperatures...

I have a quick question about the Galilean transform. If I have Alice running and Bob stationary. The Galilean transform will tell me the position of Alice from Bob's stationary position. Also if I have Alice's position which is moving it will tell me Bob's stationary position. If I want Bob...

In the frame of Observer C standing by the side of the road, the speed of Car A with respect to Car B = v1 + v2. (Galilean Transformation). In the frame of Car A, the speed of Car B < v1 + v2 (Lorentz Transformation). Please tell me if this understanding is correct.

While deriving Lorentz transformation equations, my professor assumes the following: As ##\beta \rightarrow 1,## $$-c^2t^2 + x^2 = k$$ approaches 0. That is, ##-c^2t^2 + x^2 = 0.## But the equation of the hyperbola is preserved in all inertial frames of reference. Why would ##-c^2t^2 + x^2##...

This is still a confusing concept for me. The Lorentz transformation for proper time is expressed as tau = (1-v sq/c sq)^1/2 x coordinate time. Now we are told that tau is an invariant quantity with respect to all moving reference frames. So how can tau be invariant if its value depends on v...

##\bar{\mathcal{O}}## is moving with a velocity ##v## relative to ##\mathcal{O}## along ##x^{1}## The Lorentz transformations between a Frame ##\mathcal{O}## and ##\bar{\mathcal{O}}## is given by: $$\Delta x^{\bar{0}} = \gamma\left(\Delta x^0 - v\Delta x^1\right)$$ $$\Delta x^{\bar{1}} =...

I have another question linked to the equations of Lorentz: The Theory of the Special Relativity (SR) of Albert Einstein comes from the equation of Lorentz and we have the following equation on the time t’ in the moving frame: The “space time” (x’, y’, z’, t’) is moving at a speed v measured...

Edit: Ugh accidentally posted instead of previewing, this is a lot of latex to write to give my attempted solution, but I'll keep doing that. I am using the chain rule (or dividing the differential of ##\vec v'## by that of ##t'##). I get $$d \vec v' = \frac{d \vec v \cdot \vec u}{\gamma c^2...

I have a question linked to the equations of Lorentz: The Theory of the Special Relativity (SR) of Albert Einstein comes from the equation of Lorentz and we have the following equation on the time t’ in the moving frame: The space time (x’, y’, z’, t’) is moving at a speed v measured from the...

Two spaceships are heading towards each other on a collision course. The following facts are all as measured by an observer on Earth: spaceship 1 has speed 0.74c, spaceship 2 has speed 0.62c, spaceship 1 is 60 m in length. Event 1 is a measurement of the position of spaceship 1 and Event 2 is a...

A π+ meson is an elementary particle with a mean lifetime, defined in its rest frame, of τ = 2.60×10−8 s. The meson decays to a muon (µ+) and a neutrino (νµ) via the reaction π+ → µ+ + νµ. A π+ traveling in the laboratory decays so that the µ+ travels in the same direction as the original π+ and...

Summary:: Special relativity and Lorentz Transformations - I got this problem from a first-semester course at university. I have been struggling for a few days and decided to get some help. A rocket sets out from x = x' = 0 at t = t' = 0 and moves with speed u in the negative x'-direction, as...

I am reading pretty much everywhere that LET (Lorentz Ether Theory, or call it Neo-Lorentzian Relativity, or whatever theory that involves a preferred undetectable frame with some yet unknown properties that make all the moving objects with respect to this frame length contact and time dilate)...

For a complex null tetrad ##(\boldsymbol{m}, \overline{\boldsymbol{m}}, \boldsymbol{l}, \boldsymbol{k})##, how to arrive at formulae (3.14), (3.15) and (3.17)? The equation (3.16) is clear as is. (I checked already that they work i.e. that ##\boldsymbol{e}_a' \cdot \boldsymbol{e}_b' = 2m'_{(a}...

I believe this does not belong to the homework category. I hope I won't be mistaken. I am reading a book to self-study special relativity, the following is an example mentioned in the book. When clock C' and clock C1 meet at times t'=t1=0, both clocks read zero. The Observer in reference frame...

Is there the simplest, direct, and easy-to-understand method that only needs to apply the most basic algebra and logic to completely and strictly derive the Lorentz transformation? Thanks for your help.

If ##\partial_{\alpha} J^{\alpha}(x) = 0## then ##Q \equiv \displaystyle{\int} d^3 x J^t(x)## is time-invariant. To show that if ##J^{\alpha}(x)## is a four-vector then ##Q## is also Lorentz-invariant, he re-writes it as \begin{align*} Q = \int d^4 x J^{\alpha}(x) \partial_{\alpha} H(n_{\beta}...

In the special theory of relativity, it seems impossible to derive the lorentz transformation without assuming that the lorentz factor is independent of the sign of the relative velocity. For some reason, I can't get my head around why this assumption is so easily made, as if it's trivial. Can...

In ch. 13, pg.349 of Wald it's asked to prove that ##g_{AA'BB'} = \epsilon_{AB} \bar{\epsilon}_{A'B'}## is a Lorentz metric on ##V## (containing the real elements of the vector space ##Y## of type ##(1,0;1,0)## tensors). Given the basis ##t^{AA'} = \dfrac{1}{\sqrt{2}}(o^A \bar{o}^{A'} + \iota^A...

Example of emf due to Lorentz magnetic force is motional emf. When rod PQ moves to the left, there will be downwards magnetic force acting on the positive charge in the rod PQ so point Q is at higher potential compared to point P so there will be potential difference (emf) between P and Q The...

In Q.E.D., the electrical part of the Lorentz Force between unlike and like charged particles is realized through the absorption and emission of photons. How is the magnetic part of the Lorentz Force realized in Q.E.D. via photon activity? As always, thanks in advance.

Hi, It's not homework but I still thought I better post it here. Please have a look on the attachment. For hi-resolution copy, please use this link: https://imagizer.imageshack.com/img922/7840/CL6Ceq.jpg I think in equations labelled "12", 'e' is electric charge and Ex is the amplitude of...