Lorentz Definition and 1000 Threads

Reading Griffiths, he states that the Lorentz Transform is useful for describing where an 'event' occurs in a different inertial frame. What about describing the motion of a particle in this moving frame if I know its motion in my frame? Really, I'm looking at pickup ions in the solar wind. A...

Here is a problem: Imagine two equally charged capacitor plates parallel to the x-y axis, whose area is large enough compared to the distance between them that fringe effects can be ignored. The bottom plate (at z=0) is + charged, and the top is - charged. The vector field E is therefore...

Given the Lorentz matrix Λuv its transpose is Λvu but what is its transpose ? I have seen ΛuaΛub = δb a which implies an inverse. This seems to be some sort of swapping rows and columns but to get the inverse you also need to replace v with -v ? Also In the LT matrix is it the 1st slot...

Why is the Lorentz force calculated in Ansys so low? According to the formula F=B*I*l, it is supposed to be at least 1000 times higher. The model is really simple: a magnetically conductive plate in a static magnetic field inducts the magnetic field from the surrounding space, which makes its...

I can't understand the transformation can anyone explain it to me.and suggest a good book on it.

It's a long title. I ran out of space. It should be What are the microscopic, tensoral formulations of the Poynting theorem, Poynting vector and Lorentz force? (If these cannot be stated in a diffeomorphism invariant way, what theoretical good are they?) Oddly, I came up empty on an internet...

Let's say we have: \vec{E}=E_x\vec{i}_x+E_y\vec{i}_y+E_z\vec{i}_z and \vec{B}=B_x\vec{i}_x+B_y\vec{i}_y+B_z\vec{i}_z and the Lorentz Force 0=q(\vec{E}+\vec{v}X\vec{B}) which due to \vec{E}X\vec{B}=\vec{B}X(\vec{v}X\vec{B})=vB^2-B(\vec{v}\cdot \vec{B}) and transverse components only...

Hope this derivation helps someone!

Any advice on my derivation layout?

Hello, I'm reading Tong's lecture notes on QFT and I'm stuck on the following problem, found on p.11-12. A scalar field \phi , under a Lorentz transformation, x \to \Lambda x , transforms as \phi(x) \to \phi'(x) = \phi(\Lambda^{-1} x) and the derivative of the scalar field transforms...

i find here a representation of the Lorentz algebra. Starting from the matrix representation (with the ##\lambda## parameter) i see how one gets the matrix form of ##iJ_z## I am less comfortable with the ## -i y\partial_x + x \partial_y## notation Where does it come from? They say that it is a...

When one considers a Lorentz transformation between two frames ##S## and ##S'##, such that the coordinates in ##S## are given by ##x^{\mu}## and the coordinates in ##S'## are given by ##x'^{\mu}##, with the two related by x'^{\mu}=\Lambda^{\mu}_{\;\;\nu}x^{\nu} then a scalar field ##\phi (x)##...

Hello, a derivation of the lorentz transformation for an arbitrary direction of the relative velocity often makes use of writing the spatial position vector of an event as the sum of its component parallel and perpendicular to the velocity vector in one inertial frame and then transforming both...

I want to know how can i prove that Maxwell's equations for the propagation of electromagnetic wave are Lorentz invariant.

Hi everybody! Why we don't have to prove Lorentz invariance of the Vacuum state in QFT? This fact is quite obvious in QED and follows from Lorentz invariance of electric charges. But in general case? I don't know, but it seems to me this fact is not so obvious as it treated.

Hi, I have been studying lorentz force . The book says force experienced by a charge in magnetic field is But velocity is a relative concept . In one frame of reference(inertial frame) I might observe the charge moving with some velocity and in the 2nd frame(inertial too) I might observe the...

If two particles have velocities v1 and v2 in a rest frame, how do we prove that the relative lorentz factor is given by : γ(r)=γ(1)γ(2)(1−v1.v2) and why is this quantity lorentz invariant

When current flows through the armature winding of a dc motor, what exactly happens in there that produces the torque? Is there a force due to the interaction between two magnetic fields or Lorentz force acts on the conductor electrons? Basically, why does motoring effect take place? Is it due...

Hello, I am trying to build a motor. Just a prototype I guess and learning at the moment so just simple stuff but I can't make it work.. I have seen the examples of a homopolar motor and understand the direction of force due to Lorentz force. To be simple I don't want, and don't see the need...

It seems that combining two Lorentz boosts cause rotation: https://en.wikipedia.org/wiki/Lorentz_transformation#Composition_of_two_boosts Do you think this rotation is something that could be measured by gyroscope? Or is it like space rotates around the accelerating observer, and the observer...

Would magnetic charge be Lorentz invariant (the way electric charge is) if magnetic charge existed?

Dear PF Forum, First, I'd like to thanks this forum for helping this much and so far. I have a question about Lorentz Transformation. Lots of questions actually :smile: http://en.wikipedia.org/wiki/Lorentz_transformation#Boost_in_the_x-direction Instead of using t and x, I'd like to use ta and...

Dear PF Forum, After so many questions about Twins Paradox and Universe Frame of Reference, I'd like to know about Lorentz and Doppler. First. Here V is ##\sqrt{0.75}## ≈ 86.60%. If we put V in Lorentz Transformation formula as speed, we'll have Gamma = 2. Okay here's the question. Two probes A...

I was wondering about the following Λ=I+iT T are the generators and Λ a continuous LT transformation, thus it is real. Therefore T needs to be imaginary. And we can find two sets one being the generators for SO(3) J_i and the other for boosts K_i, which are both imaginary. Now I am wondering...

Homework Statement In laboratory's frame the angle between vectors E and H is given φ. Find the frame where these vectors will be parallel. Homework Equations The Attempt at a Solution I suppose I should require equal angle between each of the E' and H' and axes in the ''new'' frame. Means...

Homework Statement Light (plane wave) reflects from the mirror moving along X-axis with speed V. The wave is orthogonal to the mirror (φ=0°). Write the law for frequency change. Homework Equations I know Lorenz transformation for frequency. The Attempt at a Solution All I do not know is how to...

Hello, I have some mathematics background but little to no physics background. I am very interested in physics and am beginning to learn about relativity. Upon exploring the derivation of the Lorentz Transformation equation I noticed something that confused me a little. Again, I don't have much...

Hi All, Recently, in my earlier thread, I asked about the symmetry of Lorentz Factor (where +V == -V). I had several pointers about how to handle this (Thank you all those). However, it seemed unanimous that there was no explanation beyond the equation itself (math or physical). Also, I...

Do two inertial observers in relative motion agree on their relative velocity? Velocity is distance per unit time and they don’t agree on the distance or the elapsed time. If the apparent distance in the prime system is shorter and the elapsed time is longer, then it seems that the apparent...

Homework Statement [/B] So, I need to show Lorentz covariance of a Proca field E-L equation, conceptually I have no problems with this, I just have to make one final step that I cannot really justify. Homework Equations "Proca" (quotation marks because of the minus next to the mass part, I...

t' = γ(t - vx/c2) where t is the time in the stationary frame t' is the time in the moving frame v is the relative velocity between the two frames and x is the distance traveled in the time t in the stationary frame. ∴ x = vt substituting this into the Lorentz time equation gives us: t' = γt(1 -...

Hi All, I am trying to understand the directional independence of LT. In contrast, we all know that Doppler Effect is dependent on the direction of motion. I have tried to find any reasoning or explanation and could not find one so far. May be I did not use correct terms in my searches. If...

I'm thinking of an object or objects. How do I show that the objects form a representation of the Lorentz group in 1+1 D spacetime? Thanks for any help!

Sabine Hossenfelder said... Arun: This has never been proved. These deformations are problematic for other reasons, but they don't suffer from the density problem that I alluded to here, if that is what you mean, yes. LQG itself isn't actually based on a space-time network so the argument...

Homework Statement Given the lorentz system for ##\sigma=10, b = \frac{8}{3}, r = 28##, and ##x(t)## from the first lorentz system, show that we can solve for y(t) and z(t) for the modified lorentz system by finding ##\dot E##.[/B] Homework EquationsThe Attempt at a Solution I have found...

Homework Statement The following is Exercise 2.1 from from Ray d'Inverno's 'Introducing Einstein's Relativity.' (a) Write down the Galilean transformation from observer ##S## to observer ##S'##, where ##S'## has velocity ##v_1## relative to ##S##. (b) Find the transformation from ##S'## to...

Are all the hermitian and lorentz invariant lagrangians, invariant under the combination of CPT? If yes, how can it be proved?

Homework Statement Find the speed parameter β and Lorentz factor γ for an electron that has a kinetic energy of: a) 6.00 keV b) 2.00 MeV c) 4.00 GeV Homework Equations KE=(γ-1)*511 KeV SQRT(1/(1-β^2))=γ The Attempt at a Solution a) 6 KeV=(y-1)*511 y=1.0117 1.0117=SQRT(1/(1-β^2)) β=0.152 b)...

This thread is not about the lorentz invariance of the wave equation: \frac{1}{c^2}\frac{\partial^2\Phi}{\partial t^2}-\Delta \Phi = 0 It is about an interesting feature of a standing spherical wave: A\frac{\sin(kr)}{r}\cos(wt) It still solves the wave equation above, when it is boosted in...

s2 = t2 - x2 - y2 - z2 This equation is covariant (Lorentz covariance). The interval "s" is invariant (Lorentz invariance). Can you derive everything in special relativity from these facts? Or am I mistaken about that?

I just got to know about this concept, "Lorentz contraction". It says The size(measure) of objects decrease as we approach the speed of light(I think, I'm right!). If this is true, then the size of our sun should be slightly smaller, as the Earth races around the sun, at a speed of one-tenth of...

Hi, I am new here, but there is a question that really bugs me :-(. In Lorentz force why was the velocity defined as relative to the observer and not relative to thesystem generating the magnetic field. By defining it relativ eto the system relativity is not needed to explain how an observer...

Homework Statement A proton of mass "m" is accelerated up to a kinetic energy "K" and then collides with a stationary proton at rest. All that is left after the collision is a new particle of mass "M". (a) Write out the momentum and energy equations for the collision. (b) What is the maximum...

Lorentz Force: $$\vec{F}=q\vec{v_1}\times\vec{B}$$ v1 is the velocity of particle. And magnetic field is: $$\vec{B}=\frac{\mu_0}{4\pi}\vec{v_2}\times\frac{\hat{r}}{r^2}$$ If we combine them, we see that there are 2 velocities: v1 and v2... I just watched this video about relativity and...

If i have a current of both negative and positive charges(i know that there is also current from only negative and only positive charges,i'm not confused) along an infinite wire of square cross-section,and the we put a homogeneous magnetic field normal to the current,then a Lorentz force acts on...

The measured energy density of the vacuum has a disturbing discrepance with the one theorized by imposig Poincare invariance in QFT, usually referred to as the "vacuum catastrophe". On the other hand the Heisenberg indeterminacy principle leads to a nonzero vacuum expectation value for the...

Hi everyone! I have two questions that arose during the path integral quantization of theories involving fermions. First of all, when we prove the equivalence between the path integral formalism and the canonical quantization we make use of the eigenvalue defining equation...

Hey guys, So consider the following product of matrices: (p_{1}^{\mu}\cdot p_{1}^{\prime\nu} -(p_{1}\cdot p_{1}')\eta^{\mu\nu}+p_{1}^{\nu}p_{1}^{\prime\mu})(p_{2\mu}p_{2\nu}'-(p_{2}\cdot p_{2}')\eta_{\mu\nu}+p_{2\nu}p_{2\mu}') where eta is the Minkowski metric. I keep getting 2(p_{1}\cdot...

Hi Guys, I'm looking into the Lorentz model Since the acceleration/de-acceleration of electron can cause radiation hence create force, can anyone tell me how to modify the above equation to include the term of radiation force? Thanks. jack

Homework Statement In the inertial frame of observer A two events occur at the same position a time 10 ns apart. In the frame of the observer B moving with respect to RA, one event occurs 1m away from the other. What is the difference in time between the two events in B's frame. Solve by...