Lorentz Definition and 1000 Threads

Homework Statement Hi guys! I must show by brute force that ##\Delta s^2=-c^2\Delta t^2+\Delta x^2+\Delta y^2+\Delta z^2## is invariant under Lorentz transforms. Homework Equations Lorentz transforms: ##\Delta t' = \gamma \left ( \Delta t -\frac{\vec v \cdot \Delta \vec x}{c^2} \right...

Hi, I was looking at a basic derivation of the lorentz transformation on youtube. I was wondering at what point do you incorporate the fact that speed of light is same in every reference frame because the guy only uses some algebra on a few equations that come from basic geometry and classical...

Homework Statement I must show that the one dimensional wave equation ##\frac{1}{c^2} \frac{\partial u}{\partial t^2}-\frac{\partial ^2 u}{\partial x^2}=0## is invariant under the Lorentz transformation ##t'=\gamma \left ( t-\frac{xv}{c^2} \right )## , ##x'=\gamma (x-vt)##Homework Equations...

Difficulty regarding notation for Lorentz transformation Please can somebody explain to me the relation between Δ^{σ}_{μ} and Δ_{σ}^{μ} as symbols representing a Lorentz transformation? Thanks.

I have spent much effort trying to prove that det|\Lambda\mu\upsilon| = +1 or -1 (following a successful effort to prove (3.50g) on p87 of MTW) From the result of \LambdaT\eta\Lambda = \eta I've produced four equations like: \Lambda00\Lambda00 - \Lambda01\Lambda01 - \Lambda02\Lambda02 -...

Homework Statement From Zangwill, Chapter 2. Suppose that the instantaneous forces on a charge, q, when it is moving with velocities \vec{v}_1 or \vec{v}_2, are \vec{F}_1 and \vec{F}_2, respectively. Without choosing a coordinate system, show that \vec{B}(\vec{r}) can be determined by working...

\partialμ\phi\partialμ\phi and \partialμ\partialμ\phi with \phi(x) a scalar field

Homework Statement Two particles have velocities u, v in some reference frame. The Lorentz factor for their relative velocity w is given by \gamma(w)=\gamma(u) \gamma(v) (1-\textbf{u.v}) Prove this by using the following method: In the given frame, the worldline of the first particle is X...

Ok, this should be an easy one but it's driving me nuts. When we take the Lorentz transformations and apply them to x2-c2t2 we get the exact same expression in another frame. I can do this math easily by letting c=1 and have seen others do it by letting c=1 but I have never seen anyone actually...

[This is mostly about notation] I was working on a problem where I had to prove that div(B) remains invariant under lorentz transformations. That was not too hard, so I came up with div(B) = \partial_{\mu} B^{\mu} must equal div(B) = \partial'_{\mu} B'^{\mu} so I did a...

Can one explain the relativistic energy transformation formula: E = \gamma\ E', where the primed frame has a velocity v relative to the unprimed frame, in terms of relativistic time dilation and the quantum relation E=h\ f? I imagine a pair of observers, A and B, initially at rest, each...

SL(2,C) to Lorentz in Carmeli's "Theory of Spinors" On page 56 of "Theory of Spinors", Eq. (3.84a), Carmeli gives the formula for the Lorentz matrix in terms of Pauli matrices and an SL(2,C) matrix g: \Lambda^{\alpha\beta}=(1/2)Tr(\sigma^\alpha g \sigma^\beta g^*) His sigma matrices are the...

If a particle of mass m and charge q (where q can be negative or positive, and the velocity should be positive if q is positive and negative if q is negative) is passed through an electric field of potential Vd, what is the velocity v of the particle? Or possibly this should be a vector...

Why do we say that t'=t for Galilean transformation, when the low velocity limit of the Lorentz transformation is t'=t+vx/c2? If x is really big, then doesn't time cease to be absolute, no matter how small v/c is?

Hi all Here, I attached a figure presenting the Lorentz-Drude function. The resonance number is clear from the m in the equation. But I like to know if the number of poles in Lorentz model is the same as the number of resonance or not. I am confused. I would be very grateful if you can help me...

Let's say I'm pushing and accelerating an object using a long stick, like this: H--------------O --> H is my hand, O is the object. The force I use is F, the distance I push is s, the energy I use is Fs The force pushing the object <= F The distance that the object is pushed < s...

Hi there, In my course solid state physics, there is a part about the Lorentz oscillator. At a certain part, this is written: "X(t) = X_0sin(-ωt+α) This changes into: X(t) = X_0 exp(-iωt) by choosing X_0 as a complex number and putting the phase factor into the complex amplitude."...

Can someone help me in understanding where I am wrong when thinking about the derivation of the Lorentz field in a dielectric. I give the derivation in italics (although the familiar reader should not need to read it) and after that I present the paradox. The basic idea is to consider a...

This is probably a stupid mistake I am making, but I can't figure it out. My apologies in advance... I am familiar with the text-book derivation of the Lorentz transformation (I don't have any problem with it). It starts out stating: x2+y2+z2-c2t2 = x'2 + y'2+z'2-c2t'2 meaning that a...

Hi buddies Homework Statement Show that the Lorentz Force Law generalizes to F=q_e (\vec E+ \vec v \times \vec B)+ \frac {q_m}{\mu _0} (\vec B - \frac{\vec v}{c^2} \times \vec E)[/tex] when there are magnetic monopoles Homework Equations - The Attempt at a Solution Well, not much to say...

Hello! I'm trying to derive the general matrix form of a lorentz boost by using the generators of rotations and boosts: I already managed to get the matrices that represent boosts in the direction of one axis, but when trying to combine them to get a boost in an arbitrary direction I always...

Hi! I am new here, thought to join as I am trying to learn Relativity, in this case Special Relativity. I have solved a bunch of problems already but ... The Lorentz Transform formulation I am dealing with is a 4x4 matrix. I understand the invariance of the spacetime interval and have...

Hey guys. I'm having doubts about something in a GR text I read (Gravitation - T.Padmanabhan). In general, for Lorentzian 4-manifolds, we call a basis of smooth vector fields ##(e_{\mu})^{a}## (that is, a set of smooth vector fields that define a basis for the tangent space at each event of...

In a recent course on special relativity the lecturer derives the Lorentz transformation matrix for the four vector of position and time. Then, apparently without proof, the same matrix is used to transform the EM field tensor to the tensor for the new inertial frame. I am unclear whether it...

Hi, Homework Statement A system, with cylindrical symmetry and charge density ρ(r) = ρ0e-r2/a2, where a is a given constant, is given. The system moves at a constant velocity V in the z^ direction. V<<c. The charge density in the lab's reference frame is approx. equal to that in the rest...

Hello there, I'm having a real problem understanding when a certain 'something' (for example Eddington-Finkelstein coordinates) is Lorentz invariant or how you can 'calculate' it. Heck, I'm not even sure if a coordinate system must be lorentz invariant, or if the metric in the equations...

if we assume a charge particle enters in a uniform magnetic field with velocity V w.r.t inertial frame as shown fig. then according to the situation shown there will be force acting on particle due to magnetic field (neglecting B field induced due to charged particle itself). But now if we...

I would be very grateful if someone would kindly explain this generalization of the Lorentz force law to the special relativity domain. I am not entirely sure if what I have jotted down is exactly as the speaker intended to convey. But here is what I have got. Please bear with me...

Hi all, Here is the problem. I want to try to do some calculations with seeing how much time a relativistic ship has before it can dodge a dust grain. I am having some trouble applying the Lorentz Contraction Equations to get consistent results. Take two frames, the coordinates of the...

I was thinking when I take the Lorentz formula for a location γ.(x – v.t) as an observer in S and find the ratio compared with the location for an observer within the inertial system S’ it selves: 1/γ . Δx But I made a mistake and took 1/γ. x When I use the found ratio (for derivation...

I want to discuss this because I afraid that the answer is no. In SR we stuck with the transformations from Poincare Group because this transformations leave invariant the exact form of the Lorentz Metric tensor. Any other transformation will change the components of the Lorentz Metric Tensor...

what is physical meaning of Lorentz gauge condition in classical electrodynamics??

Homework Statement An electron in an electric field E = 3.0x107 ex NC-1 and a magnetic field B = 3.0 ez T has velocity v = 1.0x107 (2ex - ey) ms-1. Calculate electromagnetic force on the electron. Homework Equations F = q (E + v X B) where q = e- = -1.6x10-19 C The Attempt at a...

Can Lorentz Transformation be applied directly to a four velocity vector? I mean let v_{α} be a four velocity vector. Is there a form of Lorentz tfm matrix such that: v^{'}_{α} = \Lambda^{β}_{α}v_{β} ?

Homework Statement We were told that it is a simple algebraic substitution to derive the t' expression from the x and x' equations for a lorentz transformation. However, I keep reaching a dead end in the algebra. Homework Equations x=B(x'+vt') x'=B(x-vt) B=1/(Sqrt(1-(v/c)^2)) B^2 = c^2/(c^2...

Hello friend, I want to know how to derive lorentz transformation. Even though i have book that derived lorentz transform,i am not able to understand. I hope you give me an easy derivation of it!

Hello friend, Can you give me an example that shows simultaneous events in one reference frame not simultaneous in other reference frame with the help of lorentz Transformation?

Homework Statement Derive the relation: E' = \gamma (E + \beta p c)Homework Equations p' = \gamma p \\ E^{2} = p^{2} c^{2} + M^{2}c^{4}The Attempt at a Solution start off with stationary frame S E=mc^{2} then in moving frame S' E'^{2} = p'^{2} c^{2} + E^{2}: lorent transform momentum: E'^{2} =...

So, I'm trying (keyword trying) to learn a bit of special relativity on my own via the Stanford lectures on Youtube by Leonard Susskind, but I'm running into a problem. According to the lectures, for two different reference frames with co-ordinates marked (x, t) and (x', t'), the latter...

Hello! I'm currently reading Ryder - Quantum Field Theory and am a bit confused about his discussion on the correpsondence between Lorentz transformations and SL(2,C) transformations on 2-spinor. He writes that the Lie algebra of Lorentz transformations can be satisfied by setting \vec{K}...

Homework Statement Prove that the proper orthochronous Lorentz group is a linear group. That is SOo(3, 1) = {a \in SO(3, 1) | (ae4, e4) < 0 } where (x,y) = x^T\etay for \eta = [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 -1] (sorry couldn't work out how to properly display a matrix). Homework...

The cosmic microwave background is anisotropic: the temperature is distributed as a dipole with the temperature at the poles differing by ±0.00335 K from the mean. This defines a Lorentz frame: we can boost by several hundred km/s to make the dipole vanish, on average. This new frame could...

i have a quick question, that is according to the lorentz transformation, the moving frame will have the longer time than the frame in the rest. so is that means if I'm on a moving car for my whole life, my time will greater than those who are in the rest relative to the earth?

Is there a simple way of deriving Lorentz transformation? I don't find the typical derivations in textbook so convincing, which seems to use too many intuitive postulations...

Physics books rarely make the distinction between active or passive Lorentz transformations. The usual Lorentz transformations of the spacetime coordinates in two different inertial frames seem to me to be passive transformations, because by definition passive transformations are coordinates...

Homework Statement Two spaceships A and B are launched from a point X, in opposite directions. At time t=15 minutes, spaceship A crashes. The velocity of the spaceships relative to X is 1.3x10⁸m/s. How far did the collision happen from B, as observed by astronauts on the spaceship...

I would like to get a detailed description, how the world looks for a moving observer in Special Relativity compared to the way it looks for an observer at rest. Do you know any reference, where I can find such a description? Can you maybe even tell me, where to find two pictures of the sights...

I am very confused by the treatment of Peskin on representations of Lorentz group and spinors. I am confronted with this stuff for the first time by the way. For now I just want to start by asking: If, as usual Lorentz transformations rotate and boost frames of reference in Minkowski...

I had 1 year ago a little discussion with DaleSpam about the short Lorentz derivation (triangle) if a photon alone can be seen as a light beam. 1) The long Lorentz derivation seems me correct, so no discussion about that 2) For the short Lorentz derivation with the triangle (c.t , v.t and...