Lorentz Definition and 1000 Threads

This is purely a historical question that came up in another thread. I always thought LET was the theory put forward by Lorentz that said the Lorentz-Fitzgerald formula contracts objects moving through the aether. Clocks slowed down due to a shortening of their components. Light was an...

Hi, I was looking at this derivation https://en.wikipedia.org/wiki/Derivations_of_the_Lorentz_transformations#From_group_postulates and I was wondering 1- where does the group structure come from? The principle of relativity? or viceversa? or what? 2- why only linear transformations? I remember...

Suppose the E-field is ##-E_y\hat y##, and B-field is ##B\hat z##. Mass is ##m##. z | |_____x / y ##m(\ddot x \hat x + \ddot y \hat y) = q(-E_y \hat y + (v_x \hat x + v_y \hat y) \times B \hat z)## By grouping terms with ##\hat x## and ##\hat y## together, ##m\ddot x = -qv_yB##...

Here the 3 set of equations we know, the Maxwell Equations, Lorentz Force, and Coulumb Force, actually I doubt a lot what set of equations represent all the electromagnetic aspects, I try research over the internet and I found a lot of contradictions in the answers, someone says we can get the...

So as the summary suggests, I am studying Electromagnetism, magnetic properties of matter and Magnetization vector in particular. As a first example and to introduce the Magnetization vector (M), my textbook shows a ferromagnetic substance in a uniform magnetic field (B). Then, every atom of...

Hello fellow physicists, I need to prove that when ##\omega << \omega_0##, Lorentz equation for refractive indexes: ##n^2(\omega) = 1 + \frac {\omega^2_p} {\omega^2_0 - \omega^2}## turns into Cauchy's empirical law: ##n(\lambda)=A+\frac B {\lambda^2}## I also need to express A and B as a...

Hello fellow users, I've been given the Lorentz model to calculate the refraction index of a dielectric, the formula in its simplest way states that: ##n^2(\omega) = 1 + \frac {\omega^2_p} {\omega^2_0 - \omega^2}## Where ##\omega_p## is the plasma frequency and ##\omega_0## is the resonance...

So for the formula, u'=u/(δ(1-(uv)/c^2) u=2.06E8 and v=0. I am only looking at the y components here. Since v=0 it really becomes u'=u/δ or u'= u*sqrt(1-(u^2)/c^2)). Anyways when I plug this in I am getting 1.49E8 when the answer should be 0.951E8. Am I not using the correct formula here?

Hello, why time is the fourth dimention and not another quantity or variable? General relativity has as a special case the special relativity, so Lorentz transformations are contained in general relativity but are they in a more general form than that of special relativity generally? If they...

Hi all - related to a question I asked some time ago: If one introduces a momentum cutoff, the result in the most basic case is Lorentz violation. That is, some form of preferred frame must be introduced. I'm wondering what this does to the vacuum state? That is, how does one keep the vacuum...

[Mentors' note: This thead was forked from another thread - hence the reference to "these replies" in the first post] I am wondering why all these replies only discuss Lorentz transformations in 1+1 spacetime dimensions. That is the easy bit. The problems in understanding arise in 2+1...

The Lorentz tranformations are: ##x' = \gamma (x-vt) ## ##t' = \gamma(t - \frac{vx}{c^2})## Consider an event (x,t) happening in S frame. Let S' frame be moving w.r.t. S frame along x direction with speed v whose origins coincide at t=0. We find that the new coordinates of this event are...

Hello, i can't understand how does the author found this expression relating ##x_{c}## and v. I already tried by a lot of geometrical ways, knowing that the tangent of the angle between the dotted line and the x-axis should be v, but the results are illogical. Could you help me? I am start to...

Good evening, I'm trying to solve this exercise that apparently seems trivial, but I wouldn't want to make mistakes, just trivial. Proceeding with the first point I wonder if my approach can be correct in describing this situation. From the assumptions, the two fields are in this...

The three events; t = 0s, x=0 t=1.3s, x=1.3 light seconds t=2.6s, 1.3 light seconds

I have been reading the book of Chris Quigg, Gauge theories, Chapter 3, sec 3.3 in which he explains how local rotations transform wave function and variations in Schrodinger equation forces us to introduce the electromagnetic interaction between the particles. I need a bit deep concept of the...

Hello everyone, I am new here, so please let me know if I am doing something wrong regarding the formatting or the way I am asking for help. I did not really know how to start off, so first I tried to just write out all the ##\mu \nu \rho \sigma## combinations for which ##\epsilon \neq 0## and...

Hi guys, I'm being introduced to magnetism, and the direction of the Lorentz force is quite confusing since it's involving a vector product. Which method would you recommend me in order to easily deduce the direction?

I'm trying to understand how the Lorentz force can explain why magnets attract and repel. The explanations that I have found have mostly involved the magnets moving in a way that decreases the forces between them ( ) but I have not been able to find any intuitive explanation involving the...

On the Yale University Prof Shankar Youtube vid 'Lorentz Transformation' Prof Shankar writes up on the board that x = ct and then x prime = c t prime. It is the basis of all that follows. But i don't understand. at x = 0, t = 0 and x prime = 0 and t prime = 0. He's got that written up...

Let me define ##L_{x;v}## as the operator that produce a Lorentz boost in the ##x##-direction with a speed of ##v##. This operator acts on the components of the 4-position as follows $$L_{x;v}(x) =\gamma_{v}(x-vt),$$ $$L_{x;v}(y) =y,$$ $$L_{x;v}(z) =z,$$ $$L_{x;v}(t)...

In the Hamiltonian formalism, the space-time transformation are realized via canonical transformation, and the transformations are generated by Poisson brackets of certain functions of phase-space variables. In Newtonian mechanics, Galilean boosts are generated by the sometimes called dynamic...

Hi, I've read a number of posts here on PF about Einstein's clock synchronization convention. In the context of SR we know the transformation law between inertial frame's coordinates is actually the Lorentz one. The invariant speed for Lorentz transformation is c (actually it coincides with...

Ateempt of solution: There are two key coordinates in this scenario, the leftmost tip of the rod, which in ##S'## is ##C_{0} = (t', 0, ut',0)## and the opposite tip ##C_{1} = (t', L,ut',0)## An angle ##\phi## could be found through a relationship such as ##tan(\phi) = \frac{ \Delta x}{ \Delta...

Image below. Is the Lorentz transform just switching between a stationary frame and a moving frame? I forgot to write Alice's frame but I assume that is obvious.

When deriving the Maxwell Stress tensor, the Lorentz formula is converted from point particle: F=qE+qv x B Into current and charge density: F=ρ E + j x B However an argument can be made that we can't "fieldify" both q and E at one step, and thus, a "coercion" of the field to a value is...

The Lorentz transformations of electric and magnetic fields (as given, for example in Wikipedia) are $$ \begin{align*} \bar{\boldsymbol{E}}_{\parallel} & =\boldsymbol{E}_{\parallel}\\ \bar{\boldsymbol{E}}_{\perp} &...

I made a derivation of a general transform of the lorentz factor but i still looking in books that the lorentz factor is 1/sqrt(1-v^^2/c^^2) and my derivation is perfectly correct, my result is 1/(sqrt(1-v^^2*sin(a)/c^^2)+v*cos(a)), if we put here 90 degrees we get the classical lorentz factor...

Hello again. I am sorry I got another problem when learning QFT regarding the Lorentz transformation of derivatives. In David Tong's notes, he says I am not sure how to transform the partial derivatives. Explicitly, should ##\frac {\partial} {\partial x ^{\mu}}## transform to ##\frac...

We take an arbitrary spacetime point ##(x,t)## in any observer's reference frame ##A##. Let ##(x(v),t(v))## be the co-ordinates of this same event as seen from a frame ##B## moving at a velocity ##v## wrt ##A##. As ##v## varies, the set of points ##(x(v),t(v))## constitute some curve ##C##. So...

I read in one book about the deduction of Lorentz transform. It writes: ' $$ \begin{aligned} t^\prime & = \xi t + \zeta x (1) \\ x^\prime & = \gamma x + \delta t (2) \\ y^\prime & = y (3) \\ z^\prime & = z (4) \end{aligned} $$ from (2), it gives: $$ \begin{aligned} {dx \over dt} = -{ \delta...

Brief intro: I'm awful at maths and really interested in physics. My friend asked me to solve a question but I can't seem to wrap my head around it... The question: If I'm listening to a song that lasts 5 minutes and 30 seconds and my twin brother travels to the moon and back while the song...

This approach is seeming intuitive to me as I can visualize what's going on at each step and there's not much complex math. But I'm not sure if I'm on the right track or if I'm making some mistakes. Here it is: ##A## has set up a space-time co-ordinate system with some arbitrary event along his...

I have to derive the Lorentz time transformation given the equation for gamma and the equation for the Lorentz space transformation. I started by using relevant equations from the Space derivation done in class (also the one that Ramamurti Shankar does). Here is a picture of what I have tried...

If you take a bar magnet and place a wire with current a short distance from the end, Lorentz's law can be used to accurately predict the location and magnitude of the resulting forces. The same is true if you use a large volume uniform magnetic field to create an induced field in a bar ferrite...

Hey everyone, I have generated a nice little velocity vs time graph that I would love if somebody could help me put to use. I have marked data points on the x-axis for the Y-value for every second on the function. Just to be clear: X-axis = time in seconds & Y-axis = velocity in meters/second...

a) I think I got this one (I have to thank samalkhaiat and PeroK for helping me with the training in LTs :) ) $$\eta_{\mu\nu}\Big(\delta^{\mu}_{\rho} + \epsilon^{\mu}_{ \ \ \rho} +\frac{1}{2!} \epsilon^{\mu}_{ \ \ \lambda}\epsilon^{\lambda}_{ \ \ \rho}+ \ ...\Big)\Big(\delta^{\nu}_{\sigma} +...

This is note about O(3,3) space-time. The related article is: https://doi.org/10.3390/sym12050817 Here's some background: In O(3,1) space-time (Minkowski), the six generators of rotations and boosts can form an SU(2) x SU(2) Lie algebra. This algebra is then used generically by all the...

I was looking at this video , and I was wondering if a (Riemannian)manifold violates the "lorentz invariance" would it become a discrete manifold?

I am totally new to the theory of Special Relativity, but find it very facinating. As a young man I saw a few documentaries on how Einstein saw a clock's movement reaching noon, and how he, traveling in a tram heard the gong only later. He then thought about what if he traveled at the speed of...

The following exercise was proposed by samalkhaiat here. The given Lorentz identities were proven here. We first note that ##d^4 k = d^3 \vec k dk_0##, the ##k_0## integration is over ##-\infty < k_0 < \infty## and ##\epsilon (k_0)## is the sign function, which is defined as $$\epsilon...

This exercise was proposed by samalkhaiat here Given the defining property of Lorentz transformation \eta_{\mu\nu}\Lambda^{\mu}{}_{\rho}\Lambda^{\nu}{}_{\sigma} = \eta_{\rho \sigma}, prove the following identities (i) \ (\Lambda k) \cdot (\Lambda x) = k \cdot x (ii) \ p \cdot...

This thread is motivated by samalkhaiat's comment here I know that the Lorentz Group is formed by all matrices that satisfy $$\eta = \Lambda^{T} \eta \Lambda \tag{1.1}$$ Which is equivalent to $$\eta_{\mu\nu}\Lambda^{\mu}{}_{\rho}\Lambda^{\nu}{}_{\sigma} = \eta_{\rho \sigma} \tag{1.2}$$ If...

If the mu of the ferrite is high, as suggested, the B field on that section of wire is zero, and therefore there is no force on the wire. Instead there is a comparable force on the ferrite itself. But suppose you allow the ferrite to have different values of mu. If mu=1 the force is just...

Dear reader, there is a physics problem where I couldn't understand what the solutions. It is about the lorentz transformation of a bilinear spinor matrix element thing. So the blue colored equation signs are the parts which I couldn't figure out how. There must be some steps in between which...

I'm trying my hand at deriving Lorentz transformations using 3 postulates - it's a linear transformation, the frames are equivalent, so they see the same speed of each other's origins and that the speed of light is the same. Let's say frame ##S## is moving at velocity ##v## in the...

I think this should be t'= Lorentz factor* (1+v/c)t, but that doesn't make sense to me.

The Wikipedia article on Lorentz transformations is a bit confusing by its using speed and velocity almost interchangeably: of course γ (Gamma) stays the same, but (letting c=1) t'=γ(t-vx) , then if this is v⋅x, and x stays the same, then there would be a difference if something were going away...

Are Lorentz transforms actual "rotations" in the commonly understood sense, or a non-intuitive formal mathematical operation?