What is Lorentz: Definition and 1000 Discussions

I started to study Simple Derivation of the Lorentz Transformation In this derivation, I gather that there are two rays of light being tracked--one going to the right of the origin and one going to the left of the origin. The right-going light is described by x=ct and x'=ct'. The...

Homework Statement During class today, I was told that: x' = γ(x-vt) y' = y z' = z t' = γ[t-(v/c2)x], where γ=(1-v2/c2)-1/2 (This is just the standard Lorentz transformation.) Then I was told that we could find dx/dt, the inertial velocity, by finding dx' and dt' and dividing...

γHomework Statement Stan is at rest on the Earth while Mary is moving away from the Earth at a constant speed of 0.600c. Stan and Mary start their timers when Mary passes Stan (in other words, t = t' = x = x' = 0 at that instant). (a) When Mary has traveled a distance of 0.900 *108m...

Plot the real & imaginary parts of dielectric function.

It recently came to my attention that there exists two "kinds" of Lorentz invariants: the covariant and the noncovariant ones. The covariant ones would be Lorentz scalars e.g. fully contracted Lorentz tensors. If one applies the Lorentz transformation to a covariant Lorentz scalar, one would...

I've seen a few short proofs that if that some transformation \Lambda preserves the spacetime interval, then \Lambda^\top g \Lambda = g where g is the spacetime metric. They have all relied on an argument using some simple algebra to show that (\Lambda^\top g \Lambda) x \cdot x = g x...

Consider Minkowski spacetime with signature (-+++) and coordinates (ct,x,y,z) with respect to the standard orthogonal basis. I'm looking for the smallest set of matrices that can generate any Lorentz transformation with respect to this basis. I came up with 8 matrices (see below). Am I missing...

The question I have is to do with the Relativity of Simultaneity of the type described by Einsten; whereby two light emitters are placed pulsing once every millisecond on board a spaceship traveling at the speed of light. One of these lights faces forward and the other faces aft. If time dilates...

Homework Statement Consider a light signal propagating in some arbitrary direction, with vx \neq 0 vy \neq 0 vz \neq 0 and vx2 + vy2 + vz2 = c2 Use the Lorentz transformation equations for the components of velocity to show that v'x2 + v'y2 + v'z2 = c2 Homework...

Homework Statement An electron is traveling at 5.0 × 106 m s−1 directly into the page at the point P shown in Figure 3. P is 4.0 cm from O. Again, D = 10 cm and the current i in each wire has magnitude of 1.0 A with the directions that you found in part (c). Find the magnitude and direction of...

The words Poincare and Lorentz sound pretty elegant. I think they are French words like Loreal Or Laurent. I know Poincare has to do with spacetime translation and Lorentz with rotations symmetry. But how come one commonly heard about Lorentz symmetry in Special Relativity and General...

Hi, I have a particle moving in a static electromagnetic field in which E and B have the following components: E=(Ex, 0, 0) B=(-Bx, 0, 0) and both depend on z, namely Ex(z) and Bx(z). The particle is moving along z with constant velocity v=(0, 0, vz). If I want to express Lorentz force...

There is a train(think of having only two boggie for a claer visualization ) in which two rod which are attached to the front and rear end of the train(say, the length between these rod is the length of the train). These are lowered by a single lever to touch the ground. These rods are at...

Hi all, modern physics student here. If the Lorentz contraction occurs at relativistic speeds, how does it gain mass yet get shorter? The best I can think of is that it has to depend in which reference frame one is in at the time. Does anyone know any useful links where I can read about this?

Alright, so excuse my ignorance, but I have no idea why the choice he uses for boosts is "convenient" Just to make sure everyone is on the same metric etc etc. Weinberg uses (-,+,+,+) with gamma defined traditionally and God-given units He requires that transformations..(oh my,,,how...

Btw I am obtaining all these equations from chapter 5 of Griffiths text. Lorentz force law is: Fmag = ∫I(dI x B) Does this give the force on a current carrying wire due to an external magnetic field? (i.e. has nothing to do with own wires magnetic field) I think the answer is yes since the...

Hi all, this is not a HW problem but one I made up myself, (so you won't find it in any txtbooks or solutions etc.). It also is much more advanced than for someone on the physics HW site, as I can see, so I thought it best to put here. I'm having trouble working out simultaneity and Lorentz...

when a charge particle is moving in electric and magnetic field, a force exert on this particle is Lorentz force. when this force apply to this particle, it accelerate and we know accelerated charge particle radiate. when a particle radiate an electromagnetic wave ( photon ) lose it's...

Hi! I'm trying to find the generators of the Lorentz group. Jackson lists them all, for example, the generator of a boost along x is: K=\left( \begin{array}{c} 0\;1\;0\;0 \\ 1\;0\;0\;0 \\ 0\;0\;0\;0 \\ 0\;0\;0\;0 \end{array} \right) Now, what I don't understand is: this matrix is a...

Homework Statement A charge q is released from rest at the origin, in the presence of a uniform electric field and a uniform magnetic field \underline{E} = E_0 \hat{z} and \underline{B} = B_0 \hat{x} in frame S. In another frame S', moving with velocity along the y-axis with respect...

In this video: Special Relativity: Length contraction in more detail http://www.youtube.com/watch?v=s3ZqBt8KWVQ&feature=mfu_in_order&list=UL for the derivation of Lorentz contraction equation at 2.48 the guy says, "I won't bore you with the details". I'd appreciate is someone would...

I'm reading a physics book and in the section on relativity they are using the Einstein summation convention, with 4vectors and matrices. They say that the transformations take the form: x^{\prime\mu}=x^{\nu}\Lambda^{\mu}_{\nu}+C^{\mu} where it is required that \Lambda^{\mu}_{\nu} satisfy the...

From Peskin and Schroeder: The finite-dimentional representations of the rotation group correspond precisely to the allowed values for the angular momentum: integers or half integers. From the Lorentz commutation relations: \left[J^{\mu \nu},J^{\rho \sigma}\right]=i \left(g^{\nu \rho}J^{\mu...

hi i was wondering whether the lorentz force is just caused by the fact, that moving charges produce a magnetic field, just like every current does, and this magnetic field interacts with the magnetic field in the environment, that causes the force or whether the lorentz force has nothing to...

I got the general form of a Lorentz transformation in a GR book, {\textbf{x'}} = {\textbf{x}} + (γ-1)\frac{{\textbf{x}•\textbf{v}}}{v^2}\textbf{v}-γ\textbf{v}t t' = γ(t-\frac{{\textbf{x}•\textbf{v}}}{c^2}) from frame S to frame S' moving with relative velocity \textbf{v}. How to...

Let's say that we have a particle flying through space, at a collision course with a planet. As seen from an observer on this planet, the particle has an enormous energy, and its wavelength is just slightly bigger than the Planck length. As the particle falls down the gravitational well of the...

Ok. I understand that the set of Lorentz boosts and space rotations is equivalent to the set of Lorentz transformations. I understand that they form a group, but what I cannot seem to grasp is this. What the explicit form of such 4x4 matrices? One needs to know this in order to show that the...

Paraphrasing Peskin and Schroeder: By repeated use of \left\{ \gamma^{\mu} , \gamma^{\nu} \right\}= 2 g^{\mu\nu} \times \textbf{1}_{n \times n} (Clifford/Dirac algebra), verify that the n-dimensional representation of the Lorentz algebra, S^{\mu...

Homework Statement Essentially, a particle is moving downward from the top of a tower at 0.98c, and the tower is moving up at 0.98c. I am to find the apparent height of the tower from the perspective of the particle Homework Equations Δx=γ(Δx′+vΔt′) Δt=γ(Δt′+vΔx′/c2)...

I am reading Quantum Field Theory by Michio Kaku, and I have come across some equations that I can't quite make sense of. I am hoping somebody can help me out. Please see attached. Thanks.

'One example of the Lorentz force is that, if two parallel wires are carrying current in the same direction, the wires will be pulled toward each other. The Z-pinch uses this same effect; the entire plasma can be thought of as many current-carrying wires, all carrying current in the same...

Hi all, I came up with the following problem myself and am trying to solve myself. I haven't seen it in any txtbook, grad or undergrad. Suppose you have the ground frame (Earth). Earth sees ship1 start at t=0, v=vo1, at x=xo1. Earth sees ship2 start at t=0, v=vo2, at x=xo2 All...

What is the relevance of Local Lorentz Invariance Violations if they would be detected in any future experiments? Does it mean there is absolute space and time in the microscopic sector below where current experiments can't probe or other absolute parameters since there would be preferred frame...

Hello So i saw this video on youtube explaining some basics of general relativity and they used example with 2 rockets moving paralelly with laser pointed from rocket A to mirror on rocket B. Heres my picture of it :D Where we are stationary observer watching those two rockets A and B...

Why is it that charge is Lorentz invariant (it's a scalar, independent of the frame of reference) whereas mass is not? Does this mean that the gravitational force a body exerts depends on the frame of reference, whereas the electric force doesn't?

is \overline{\Psi} γ5 \partial2 \Psi Lorentz Invariant? How does this term transform under Lorentz transformations? Here \Psi is a Dirac field. Thanks

Hello I have been thinking at EPR experiment during some time. It is very suggestive for me that the entanglement effects travel faster than ligth between the positions of 'Alice' and 'Bob'. I understand this is not contradictory with special relativity, due there is a not real exchange of...

So, first off, I'm thinking Lorentz invariant quantities are the same in any inertial frames S and S' regardless of their relative velocity. I'm thinking I need to show that \frac{d^3k}{(2\pi)^32E(\vec{k})} = \frac{d^3k'}{(2\pi)^32E'(\vec{k'})} where the primed & unprimed quantities denote...

1. What is the limitation of the Galilean transformation? 2. What are difference between Lorentz transformation and Galilean transformation?

Hi I read in text for calculation dielectric constant in Lorentz model, we only regard electric field that coupled with each oscillator. So the magnetic field of input wave has no effect in calculation of dielectric constant in this model?

The derivation of the Lorentz transformations is based on the homogeneity[of space and time] and the isotropy of space. Could one derive the same transformations wrt space which is not homogeneous or[not] isotropic? You may consider a few chunks of dielectric strewn here and there. I am...

Homework Statement Space ships A and B, each having a proper length of 100m, pass each other moving in opposite directions. According to the clocks on ship A, the front end of B takes 1.5 x 10^(-6) s to pass the entire length of A. a) what is the relative velocity of the two ships? b)...

For fun, I'm writing a simple special relativity simulator with a much smaller speed of light so that relativistic effects are clear even at low speeds. I already have time dilation and speed of light delay working. However, right now, the speed of light does NOT always appear to be the same for...

http://pirsa.org/11100056/ Can Lorentz Symmetry be Emergent? Speaker(s): Ted Jacobson Abstract: I will begin by discussing some of the strongest observational evidence for Lorentz symmetry, and the essential role that Lorentz symmetry appears to play in the consistency of black hole...

Homework Statement This problem asks you to work out the dielectric function of a gas of particles with number density n, charge q, and mass m, with a steady magnetic field applied in the z direction. Assume an electric field in the x direction, E_x(t)=E_xe^{-i \omega t} is applied. Write...

Homework Statement A raindrop carrying a charge of 25x10-12 coulombs falls at a velocity of 5 m/s between the poles of a permanent magnet. It passes through a 50 mm long region in which the magnetic field density of 0.9 T is directed horizontally. 1) determine the lorentz force of the...

Homework Statement For flat spacetime the coefficients of the Lorentz transformation are defined as \alpha^{\nu}_{\mu} = \frac{\partial x^{' \nu}}{\partial x^{\mu}} Whereas the Lorentz transformation is \begin{pmatrix} x_1' \\ x_2' \\ x_3' \\ x_4' \end{pmatrix} = \begin{pmatrix}...

Studying in the Heisenberg picture, we have \frac{\text{d}x_i}{\text{d}t}=-\frac{\text{i}}{\hbar}[x_i,H]=\frac{1}{m}\left(p_i-\frac{q}{c}A_i\right) where the last bracket is known as the kinematic momentum \pi . Now, to find \frac{\text{d}^2{\bf{x}}}{\text{d}t^2} I do the following...

Just underneath the diagram of the 3 S-systems at the top of this webpage; http://www.relativitycalculator.com/addition_relativistic_velocities.shtml It gives equations for Lorentz transformation between S and S' Does x' mean the distance between the origin of frame S' and the event as...

Homework Statement A projectile is fired from a canon at a velocity of 0.4c at an elevation angle of 30° to the X-axis. An observor is moving at a velocity of 0.1c relative to the canon along the X direction. (a) At what angle does the observor measure the projectile to be...