Lorentz Definition and 1000 Threads

Hello! I am reading "A First Course in General Relativity" by Schutz and in chapter 8 (second edition) he introduces Nearly Lorentz coordinate system. He says that we can always find some coordinates such that the metric is: $$g_{\alpha\beta}=\eta_{\alpha\beta}+h_{\alpha\beta}$$ with...

Spontaneous symmetry breakingI’m not sure if I understand spontaneous symmetry breaking.In the context of the Mexican hat (and marble) example, wouldn’t the actual path of the marble down the Mexican hat from the top be determined by several small factors that one would normally not consider...

Homework Statement attached: Homework Equations where ##J_{yz} ## is The Attempt at a Solution [/B] In a previous question have exponentiated the generator ##J_{yz}## to show it is the generator of rotation around the ##x## axis via trig expansions so ##\Phi(t,x,y,z) \to \Phi(t,x,y cos...

According to David Morin (link: https://books.google.com/books?id=Ni6CD7K2X4MC&pg=PA636), the time-derivative of the Lorentz factor is (##c=1##): ##\dot{\gamma} = \gamma^3 v \dot{v}##, and the four-acceleration: ##\mathbf{A} = (\gamma^4 v \dot{v}, \gamma^4 v \dot{v} \mathbf{v} + \gamma^2...

I have just started learning the Special Theory of Relativity. While deriving, I am facing some problems. I obviously have made some kind of mistake while using the equations... What is wrong if I don't use the time transformation equation in Event #2?

Homework Statement There are 2 particles(1,2) separated ∆x=L moving with the same velocity u_x in frame of reference S , there's an other reference S' moving at v . I have to calculate ∆x'. GAMMA(LORENTZ'S FACTOR) Homework EquationsThe Attempt at a Solution I have done x1=0 when t=0 So for...

Homework Statement I have a mother particle at rest, which decays to a daughter particle. The daughter has mass m, momentum p and energy E and is at an angle θ1. Now I have to assume that the daughter is emitted at an angle θ2, and the mother is moving along the x-axis with velocity βc. I need...

I'm curious to know what Lorentz symmetry is, and how it works. The wiki description is a bit too difficult for me to understand. And how does it differ from a computer's cubic symmetry? I understand that in cubic symmetry, the laws of physics or physical things look different depending on what...

I need to write a code to calculate the trajectory of the particle under lorentz force.Since the position depended equations are hard to solve I ll use a code, how can I appraoch this problem. I should use veloctiy-verlet algorithm or any suggestions ? You should consider that lorentz force is a...

Homework Statement Solve the Lorentz Force Equation (Find ##\vec{r}(t)##) under constant ##\vec {B}## and ##\vec {E}##. İnitial Velocity: ##\vec{v_i}=<0,0,0>## İnitial position: ##\vec{r_i}=<0,0,0>## (##\vec {B}## and ##\vec {E}## are given values) Homework Equations Lorentz Force: ##\vec...

Are these two subjects closely related? It seems a tensor can be invariant when viewed from any **co ordinate system and The Lorentz Transformation seems to allow 2 moving co ordinate frames to agree on a space time intervals. Is there some deep connection going on? **=moving frames of...

Homework Statement I'm stuck on part (d) but I've included the previous subquestions in case they're useful. The length of an asteroid is exactly 300 m = 1 µls (micro light-second) when at rest. Draw a carefully labelled space-time diagram to illustrate the following: (a) Depict the rest...

Consider a rod oriented along and moving along the x direction at a speed v in frame A. In it's turn, frame A is moving at speed u in the y direction relative to frame B. By my understanding of special relativity, the x component of the rod's velocity in frame B will be v/γu, and the y...

Lorentz transformation of electromagnetic field gives the relation ##E'=\gamma(E+v\times B)##. Lorentz force per unit charge is given as ##F=E+v\times B## without ##\gamma##. Don't we need coefficient ##\gamma## for F?

We can find the force by finding the E-field on the charge first, then applying Lorentz force formula. However, it isn't obvious to me at all how to find the E-field. If the charge were on top of the hemisphere I would be using spherical coordinates, but here I don't know which coordinate system...

As I understand it Horava Lifschitz theory breaks lorentz invariance at high energies. Does this mean we should see photons from gamma ray bursts leave a signal of varying speeds of light for different frequencies?

Hello! Can someone recommend me some good reading about the Lorentz group and its representations? I want something to go pretty much in all the details (not necessary proofs for all the statements, but most of the properties of the group to be presented). Thank you!

Is the Lorentz transformation matrix Λμν a tensor of order two and does it transform like a tensor ?

I have a picture below please have a look at it. The guy is using two conducting rods placed parallel to each other and placed below it are magnets. When battey is connected to rods and a conductor is placed over them it starts to move.That works according to flemmings left hand rule. I was...

Hello! I am reading some notes on Lorentz group and at a point it is said that the irreducible representations (IR) of the proper orthochronous Lorentz group are labeled by 2 numbers (as it has rank 2). They describe the 4-vector representation ##D^{(\frac{1}{2},\frac{1}{2})}## and initially I...

Hi All, My daughter did a science experiment on homopolar motors. The only variable was the number of magnets on each motor. We found out through the experiment that the more magnets we attached to the motor, the longer it spun before the battery died. I'm assuming it has to do with the...

Homework Statement I've never encountered Jacobians before, and having read up on them a bit I find the wording of the last part of this question confusing: A set of coordinates ##x'_{\mu}## in frame B is obtained from the set ##x_{\mu}## in frame A, by boosting B w.r.t A with speed beta along...

Homework Statement Derick is fleeing from the cops on a car on a relativistic train. At xr= 0.0m and tr =0.000s the cops at rest see Derick leaving the back of the train and head towards the front of the train on his relativistic car. The cops see him arrive at the front at xr = 1.875*10^5m...

I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen. The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 21. Between equations (1.5.53) and (1.5.54), the authors make the following statement: ##S^\dagger ( \Lambda ) = \gamma ^0...

I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen; the link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 11, equation 1.3.20. The authors have defined an operator ##L_{\mu\nu} = i( x_\mu \partial \nu - x_\nu \partial \mu)##...

The question: Show that the Lorentz condition ∂µAµ =0 is expressed as d∗ A =0. Where A is the four-potential and * is the Hodge star, d is the exterior differentiation. In four-dimensional space, we know that the Hodge star of one-forms are the followings. 3. My attempt Since the four...

I am looking at the generators of the Lorentz group. The literature commonly refers to the generators as Mij, Ji and Ki and defines: Ji = (1/2)∈ijkMjk I am confused about the factor of (1/2) in this equation as I thought that Mij is essentially the same as Ji This also shows up in Λ=...

I'm not sure if this belongs in special/general relativity or in this subforum. I'm currently trying to refresh and strengthen my E&M, and I remembered that one thing that bugged me when I first learned about magnetism was the velocity in the Lorentz force, $$\vec{F} = q\vec{v} \times...

We've just been introduced to Langrangians, and my lecturer has told us that the Lagrangian density ##\mathcal{L} = \frac{1}{2} (\partial ^{\mu}) (\partial_{\mu}) -\frac{1}{2} m^2\phi^2## is obviously Lorentz invariant. Why? Yes it's a scalar, but I can't see why it obviously has to be a Lorentz...

The Galilean transformations are simple. x'=x-vt y'=y z'=z t'=t. Then why is there so much jargon and complication involved in proving that Galilean transformations satisfy the four group properties (Closure, Associative, Identity, Inverse)? Why talk of 10 generators? Why talk of rotation as...

Homework Statement An electric dipole instantaneously at rest at the origin in the frame K' has potentials \Phi'=\mathbf{p}\cdot\mathbf{r}'/r'^3 and \mathbf{A}'=0 (and thus only an electric field). The frame K' moves with uniform velocity \mathbf{v}=\vec{\beta }c in the frame K. Show that in...

Hello all, I've been pondering a problem with a current carrying wire in a magnetic field. The Lorentz force is easy, ILB, with a velocity 90 degrees to the B field. So let the force accelerate the wire. Assume only one segment of the wire that has current in one direction, say up, is in the...

I am having a hard time trying to understand this transformation from lorentz:https://imgur.com/a/WYWMO (You should ignore the spanish part and just focus on the math). I can’t understand well why they turn into what you can see in the second picture, when taking really small values of x...

Hi everyone! Sorry for my bad English! Please, suppose you have a subject A that opens his arms like a "T", in each hand he holds a laser and shoots the light at the same time. There are 2 targets at the same distance and, to A, the light hits both targets simultaneously. I Know that in some...

Hello! I am reading Schutz A first course in GR and he introduces the Nearly Lorentz coordinate systems as ones having a metric such that ##g_{\alpha\beta} = \eta_{\alpha\beta} + h_{\alpha\beta}##, with h a small deviation from the normal Minkowski metric. Then he introduces the Background...

I don't fully understand the argument below used to derive the Lorentz transformation equation ##y'=y##. Suppose we have a rod of unit length placed stationary in frame S. According to an observer in frame S' (which is moving at a velocity v relative to frame S), this rod is moving and its...

Imagine that I have a straight, statically-charged, cylinder-shaped tube with arbitrary (ideally infinite) extent. The charge is distributed evenly over the tube such that the field inside the tube is zero. For convenience, let's line up the tube centered along the x-axis such that the...

We are always taught in books that a Lorentz transformation is possible as long as the Lorentz matrices ##\Lambda## in ##\vec{x}{\ }' = \Lambda \vec{x}## are not function of ##\vec{x}##. The reason for this is obvious, since in this way the relation ##t^2 - x^2 - y^2 - z^2 = t'^2 - x'^2 - y'^2...

I've heard that Planck length is the smallest length ever! but if something that his length is equal to Planck length and moving by speed dv which is infinitesimal change in speed or higher than that , then according to special relativity his length must be equal to L'=L \sqrt1-v^2/c^2 which...

The generators ##N^{\pm}{}_\mu = \frac{1}{2}(J_\mu \pm iK_\mu)## obey the algebra of ##SU(2)##. On the RHS we see the Lorentz generators of rotations and boosts, respectively. I considered the case where ##N^{\pm}{}_\mu = (1/2) \sigma_\mu##, i.e. the (1/2, 1/2) representation of the Lorentz...

Let's consider that I have an emitter that can emit both negative and positive electric charges. Here let's consider only scenarios with two particles (one negative and one positive) that start initially at the tip of some electrode, where one or both the charges will separate from at the same...

I've commonly heard it said that Lorentz invariance is equivalent to saying that special relativity is obeyed, although I also recall discussions arguing that this is not precisely and technically correct, although the two concepts heavily overlap. I also understand that Lorentz invariance has...

According to this pdf http://www.springer.com/cda/content/document/cda_downloaddocument/9783319011066-c2.pdf?SGWID=0-0-45-1429331-p175291974 Newton's second law is not invariant under Lorentz transformations. To find out the part that says so, use CTRL+F and type "Newton"; it's the first result...

Hello! I need to show that Lorentz Group is non compact, but has 4 connected components. The way I was thinking to do it is to write the relation between the elements of the 4x4 matrices and based on that, associated it with a known topological space, based on the determinant and the value of...

Let's assume that a light source is moving parralel to x-axis and is in point x,y,z in lab frame. Suppose it emits a light ray. In the rest frame that coincides with the lab frame, the light source is in point x',y and z. However, because of relativistic aberration the two light rays will make...

What is more cool... to be a member of the Poincare Group or Lorentz Group? What name would you choose for a school science team and why?

Hi. I'd like to ask about the calculation of Noether current. On page16 of David Tong's lecture note(http://www.damtp.cam.ac.uk/user/tong/qft.html), there is a topic about Noether current and Lorentz transformation. I want to derive ##\delta \mathcal{L}##, but during my calculation, I...

We know that Lorentz Force is a centripetal force so: $$qVBsenx=m\frac{v^2}{r}$$ and the value of V is constant (but not the direction) But if we write: $$qvBsenx=m\frac{dV}{dt}$$ we obtain that v is exponential. What is wrong ?

Hello! I understand that the vector formed of the scalar and vector potential in classical EM behaves like a 4-vector (##A^\nu=\Lambda^\nu_\mu A^\mu##). Does this means that the if we make a vector with the 3 components of B field and 3 of E field, so a 6 components vector V, will it transform...

Sometimes as I am reading about the history of physics I run across this phrase. Ponderomotive force. I have tried looking it up several times but can never find an answer that explains what is meant by this phrase. Can someone tell me in laymens terms what is a Ponderomotive Force? Sometimes...