Lorentz Definition and 1000 Threads

Homework Statement We have an homogeneus electromagnetic field with E \bullet B=0 and E \neq cB Find the velocity of the reference frames in which ony E exists. Homework Equations \mathbf{E}' = \gamma \left( \mathbf{E} + \mathbf{v} \times \mathbf{B} \right ) - \left...

I am quite confusing about Lorentz factor and Bondi factor. In special relativity, the change in time of a relatively moving frame and a observer frame can be written as ∆t=∆t'/√1-v2/c2 But if we consider the world line of these 2 frames, the change in time of a relatively moving frame...

G'day, I'm just doing some physics homework and decided to attempt to prove something. This is not a homework problem, I'm just unsure how to evaluate the limit. Using the equation for transformation of velocity U=(U'+V)/(1+(VU'/c2)), I'm trying to show that if V=-c, as U' approaches c, U...

Greetings, I have been having trouble deriving the equation for the general Lorentz boost for velocity in an arbitrary direction. It seems to me that given the 1D Lorentz transformations... matrix for Lorentz transformation in x-direction, X: {{1/sqrt(1-v^2), -v/sqrt(1-v^2), 0, 0}...

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I also posted this in the homework help for introductory physics, but it wasn't getting any responses, so I guess it's slightly more advanced. Homework Statement Let L_b(a) denote the 4x4 matrix that gives a pure boost in the direction that makes an angle a with the x-axis in the xy plane...

Homework Statement Let L_b(a) denote the 4x4 matrix that gives a pure boost in the direction that makes an angle a with the x-axis in the xy plane. Explain why this can be found as L_b(a) = L_r(-a)*L_b(0)*L_r(a), where L_r(a) denotes the matrix that rotates the xy plane through the angle a and...

Some time ago, I came across a nice justification (by Einstein IIRC) for the formula x'^2 + y'^2 + z'^2 - c^2t'^2 = x^2 + y^2 + z^2 - c^2t^2. The argument went something like this: (1) x'^2 + y'^2 + z'^2 - c^2t'^2 = x^2 + y^2 + z^2 - c^2t^2 = 0 for light. (2) *reasoning I forget*, therefore...

what does it mean by "any \Lambda^{\alpha}_{\beta} that can be converted to the idendity \delta^{\alpha}_{\beta} by a continuous variation of parameters must be a proper lorentz transformation"?

because it seems the Lorentz transformations constitute special relativity itself

Hello all, I am having a slight conceptual problem in rationalizing what happens when a current-carrying material is exposed to an orthogonal magnetic field. The Lorentz force experienced by the moving charged particle is generally given by (dropping directional notations for clarity): F = q(E...

Hi guys, I'm currently struggling to show something my lecturer told us in class. We have that \Psi\left(x\right) \rightarrow S\left(L\right)\Psi\left(L^{-1}x\right) under a Lorentz transform defined L = exp\left(\frac{1}{2}\Omega_{ij}M^{ij}\right) with S\left(L\right) =...

Homework Statement Hey all, my algebra isn't as great as it used to be and I am having trouble with some of the algebra dealing with Lorentz transformation. Basically, I just need someone to do a quick step by step of how to go from x' to x (see the following). I started with the top...

Hi, From what I've learned so far, Lorentz transformation meets certain criteria, such as the constancy of EM wave propagation speed in vacuum, &/ casuality, among others. My question is, why would it/would it not be applicable to phenomena that have nothing to do with EM interaction? In...

If I am at rest and I observe a train moving past me at .9c and then the train fires a projectile at .5c relative to it how fast do I observe the projectile moving? With the speeds given, the lorentz factor is 2.294. I made the incorrect assumtion that I could just take the .5c and divide it...

In elementary electromagnetics, we learned the formula of Lorentz force. While I am always confused about the origin of this formula. Because when studying electrodynamics, I always thought Maxwell equations incorporate all information we need to know about electromagnetic interaction, but I...

Homework Statement see attached .pdf. all parts of problem statement are italicized. Homework Equations see attached .pdf The Attempt at a Solution see attached .pdf Actually: my question is pretty qualitative. You can look at everything I've done with this problem so far...

Hello, Is there a way to find the lorentz factor of a point particle in a curved spacetime in terms of metric elements(diagonal) More specifically I was trying to write energy of a point particle in a curved space. thanks

This is something I feel I should know by now, but I've always been very confused about. Specifically, how does one determine what each representation of the Lorentz group corresponds to? I mean, I know that the (1/2,0) and the (0,1/2) representations correspond to right and left handed spinors...

Why the reciprocal of the damping rate in this model equal to the phonon lifetime? Can somebody give me a detailed exaplanation. Thanks.

The "v" of the Lorentz Force If I have a rotating magnetic dipole that is rotating at an accelerated rate, then it is clear that the "v" of the "B" increases around the axis of that dipole's rotation. In addition, this should affect the "v" of the "q" affected by the "B", but the force induced...

Hi, I was wondering if the spin of a particle changed under Lorentz boosts. I think what it comes down to is if S^2 commutes with the generators of Lorentz boosts (the components of S only generate the rotations of the spinor I think). I think that should be true (an electron should always be a...

Homework Statement Consider the Lorentz transformations: ct' = gct - Bgx x' = gx - Bgct y'=y z'=z Show that the primed frame corresponds to a "rocket" frame moving at speed v in the x direction relative to the unprimed frame. (Sorry about my notation: g = gamma) Homework...

the title is pretty clear, so we have this F=q( E+V/c X B) the force for a point charge q in an electromagnetic field. and we have the formula to the hamiltonian of electromag force: H= (P+ q/c.A)/2m _ e\phi. the question is how can I get the F from the hamilton principle, using the...

What if someday we would have news that Lorentz Invariance Violation was detected? Is this possible at all? But our Special Relativity is based on Lorentz Invariance and the more general General Covariance in General Relativity. Does this mean that Lorentz Invariance violation is almost...

c^2 occurs frequently in special relativity: in the Lorentz transformations, in forumlas for the interval, relativistic energy, and others too. Is there an intuitive reason for the high occurence of c^2?

Homework Statement From Lorentz Transform, x^{\prime} = \gamma (x - vt) From textbooks and wikipedia, L_0 = x'_2 - x'_1 = \gamma (x_2 - x_1 ) Where x_1 and x_2 = L Thus, \L_0 = \gamma L Question is this: If i take the same method and us the Inverse Lorentz transform, i seem to...

In my EM course I've encountered what is called the "Lorentz contrast". If I derive the wave equation using the scalar and vector potential, I end up with a non-homogenous wave equation with the term: (left hand side), or more precisely, the divergence of said term. What does it mean...

Homework Statement Frame S and S' are moving with respect to each other in the x-axis with some velocity. An event happens in S' at x'_1 = 1.0 c*year at t'_1 = 1.0 year. Another event happens at t'_2 = 2.0 c*year at t'_2 = 0.5 year. The two events are simultaneous at some point in S. The...

Homework Statement Observer O sees a fire-engine leave its station 6363 m due north from Cape Canaveral, where the super-shuttle Lorentz had been launched 10^-5 s earlier. A space-cruiser flying north-east sees these two events also 10^-5 s apart, but with the shuttle launch occurring after...

Hi, Would someone know where I can find a derivation of the lorentz-invariant lagrangian density? This lagrangian often pops-up in books and papers and they take it for granted, but I was actually wondering if there's a "simple" derivation somewhere... Or does it take a whole theory and...

Sorry if I should be posting as homework, but it's not homework anymore and I'm just curious about the answer. My question is simple and doesn't require answering the actual homework question I had. If there is a force on a charge in one inertial frame of reference, will there also be a force...

A vector in special relativity is the quantity: V = V^\mu \hat{e_\mu} On a change of coordinates, the basis vectors co-vary with the coordinate derivatives: \hat{e_\mu'} = \frac{\partial x_\mu'}{\partial x_\mu} \hat{e_\mu} The vector elements are the opposite. They are said to be...

Is it possible that Lorentz invariance is just a lower limit of a larger manifold that has a priveleged frame? Even if Bell's experiments can't transmit signal faster than light. The spirit of relativity is still violated by say instantaneous correlation between 10 billion light years. As...

And if so, How? From the post 15 and 16 of the thread https://www.physicsforums.com/showthread.php?t=474719" But total charge and total current, Q and I, do form a 4-vector, don't they? There seem to be two ways to solve this, but I can't figure out which one is right. Properly...

Homework Statement A particle moves at speed u_{x}= +0.0c according to an observer in the frame S. a)Calculate the velocity of the particle, u_{x}'_{Gal} and u_{x}'_{SR} as measured by an observer in S'. Let \beta range from -0.95c to +0.95c in increments of 0.05. Put your results in a...

Homework Statement Derive the Lorentz transformation by assuming that the transformation is linear, and does not change the perpendicular coordinates. Write the transformation as x' = A1 (x - vt), y' = y, z' = z, t' = A2 t + A3 x, Determine A1, A2, A3 by requiring that a flash of light...

Two observers A and B are in relative motion with a constant velocity[for example, along the x-x' direction].If A knows the the position of B accurately , the motion of B gets enormously uncertain[and vice verse] in his calculations/considerations.How is he going to derive the Lorentz...

Let us consider the B-E and F-D statics: {<}{n}_{i}}{>}{=}{\frac{1}{{exp}{(}{{\epsilon}_{i}{-}{\mu}{)}{/}{kT}}{\mp}{1}} Now we observe the formula from a boosted frame.The left side is a scalar and should not change in response to the Lorentz transformations.What about the right hand side?The...

Homework Statement A is at the base station and given in K co-ordinates B is on a spacecraft and given in K' co-ordinates. The velocity of the spacecraft is v=0.8c Question 1 After t = 2y (y = years) A sends a message by radio to B demanding a picture. Which time t' does B have when...

A 'cause' occurs at point 1 (x1, t1) and its 'effect' occurs at point 2 (x2, t2) as measured by observer O. Use Lorentz transformation to find t'2 - t'1 as measured by O' and show that t'2 - t'1 >= 0. that is Observer O' can never see the effect before the cause. I know that is possible to...

Can anyone explain how Lorentz factor is defined (the one from theory of diffraction, not special relativity)? I read that intensity of diffracted beam is proportional to Lorentz factor, but I could not find its definition. On what parameters does the Lorentz factor depend? How does the...

Hello, I've been trying to puzzle this one out and even the mighty internet has not been particularly helpful, so here goes: Say you have a current carrying copper wire perpendicular to a magnetic field. Let's give some values for clarity: the length of the wire is 1m, the current is 3A...

Hey all, Simple question, so hopefully it gets answered quickly. I hate SR, but am marking an assignment on it. Here's the set-up Alice is standing still on a train traveling at 3/5c and Bob is on the platform at rest. A series of lights are set up along the track, yada yada. Bob sees...

Is there a way to derive Lorentz transforms by knowing just Galilean/Newtonian relativity (adding up velocities) and Pythagoras theorem? I do not understand the principle of homogeneity or any higher mathematics. I can derive t' = gamma * t by using common sense and Pythagoras theorem. I am...

Basically the question is about a penning ion trap. You need to use the equation for the Lorentz Force, which I have. It says the trap electrodes have a potential: V(x,y,z) = A(2z^2 - x^2 - y^2); There's a superimposed uniform B-Field B = B(z hat) It then asks you to write down an...

When you start in the rest frame of the electron, the Spinor w(p = 0) = (1 0 0 0 ) represents a positive energy state with spin up in the Z direction u = (0, 0 0 1),, that is the spinor is an eigenspinor of the operator S . u, where S is a 4 dimensional operator (S0, S) after a Lorentz...

Hello! Hopefully somebody could give me a push from behind on this one :) Homework Statement Show that the classical wave equation is lorentz invariant. The Attempt at a Solution I tried to exchange all derivatives by the chain rule: (c^2 \frac{d^2 }{dt^2} + \frac{d^2 }{dx^2} + \frac{d^2...

Hi, I'm reading a book on SR/Field theories that simply posits the space-time interval and from that defines a Lorentz transform as any transformation which leaves the interval invariant. My question is how do we posit the space-time interval in this manner using only the postulates of...

Hello! need some help with length contraction. So according to lorentz transformation we got I don't know how to put symbols so ill use Y as gamma since they look alike :) dx' = Y dx - u Y dt So proper length refers to the frame where dt = 0 since u are measuring the ends at the...