Lorentz Definition and 1000 Threads

Assume that, in cartesian coordinate, we have a quark with momentum ##k=(k_0,0,k_0sin\theta,k_0\cos\theta)## and a fragmented hadron ##p=(p_0,0,0,p_0)##. Define, in light-cone coordinate, ##k^+ = k_0 + k_3 = k_0(1+cos\theta)##, and ##p^+ = p_0 + p_3 = 2p_0##. And the longitudinal momentum...

I am using a wikipedia page, Derivation of the Lorentz transformations and a lot of historical papers. To follow through I came up with my own transformations that do not contain the gamma factor: ##x^{'}=x-\beta ct## ##t^{'}=t-\beta \frac{x}{c}## When applying them to a waveform...

What is the formula to evaluate Lorentz force on a curved current carrying wire in a non-constant magnetic field (given by some known vector field). The standard form of Lorentz force (Fb=BxlI) when B and the wire's length 'l' are constants does not account for this case, nor does the...

Homework Statement Frame S' travels at speed V1 along the x-axis of frame S. Frame S'' travels at speed V2 along the x' axis of frame S'. Apply the Lorentz transformation twice to find the coordinates x'', y'', etc of any event in terms of x, y, z, t. Show that this is the same as the...

Franklin, "Lorentz contraction, Bell's spaceships, and ..." In the discussion of a new FAQ entry on the Bell spaceship paradox, the following paper came up: Jerrold Franklin, "Lorentz contraction, Bell's spaceships, and rigid body motion in special relativity," Eur. J. Phys. 31 (2010) 291...

Homework Statement At what speed v will the Galilean and Lorentz expressions for x differ by 0,10 percent? Homework Equations xL= (x'+vt')/√(1-(v/c)²) (Lorentz Transformation) xG=x'+vt' (Galilean Tranformation) The Attempt at a Solution I've tried: xG/xL = √(1-(v/c)²) =...

Hello! I'm currently reading some QFT and have passed the concept of Weyl spinors 2-4 times but this time it didn't make that much sense.. We can identify the Lorentz algebra as two su(2)'s. Hence from QM I'm convinced that the representation of the Lorentz algebra can be of dimension (2s_1 +...

I am currently studying special relativity on my own and I am looking into space time and space time diagrams. While reading through various sources I came across what seemed to be two methods to describe space time. X0, X1, X2, X3 (ct, x,y,z) -> Lorentz Metric X1, X2, X3, X4 (x,y,z,ict)...

Homework Statement Let A and B be 4-vectors. Show that the dot product of A and B is Lorentz invariant. The Attempt at a Solution Should I be trying to show that A.B=\gamma(A.B)? Thanks

I am starting to learn Special and General realitivity by reading through Bernard F. Schutz's book "A First Course in General Realitivity". However I can't seem to grasp the relationship between two reference frames as compared with a Space-Time diagram. I understand the geometry of the diagrams...

For two body decay, in CM frame, we know that the magnitude of the final particle momentum is a constant, which can be described by a delta function, ##\delta(|\vec{p^*}|-|\vec{p_0^*}|)##, ##|\vec{p_0^*}|## is a constant. When we go to lab frame (boost in z direction), what's the Lorentz...

Greetings All - Per F=BIL I can calculate quantity of Force on coil (or magnet), when I draw certain amount of current from the generator. So I need help in calculating the Force and then weight equivalent of it. Let's say I have Single coil [with 300 turns] generator [wire length = 92...

Homework Statement A particle's movement is described by \vec{r} in the inertial system IS. Find the velocity of the particle \vec{\dot{r'}} in the system IS', which is moving with arbitrary velocity v from IS. Both inertial systems are arbitrary.Homework Equations For the position vector the...

Greetings, I am trying to to show that the force in this form: \dot{P}=e(\vec{∇}\vec{A})\vec{\dot{x}}-e\vec{∇}\phi Is equal to the lorentz force. I have been trying the approach of some sort of vector identity but have not gotten anywhere. The equation and where I am trying to get...

Homework Statement Starting with the Lorentz transformation for the components of the velocity, derive the transformation for the components of acceleration.Homework Equations Lorentz Transformation for position and time : ##x'={\gamma}(x - vt)## ##t'={\gamma}(t - {\frac{vx}{c^2}})## Resulting...

For two-body decay ##A\rightarrow B+C##, if A is polarized, it is clear that we have: ##\frac{dN}{d\Omega}\propto 1+\alpha \cos\theta^*##, for final particle distribution. where, ##\theta^*## is the angle between the final particle's momentum ##p^*## and the polarization vector of ##A## in the...

Homework Statement Observer S' moves at a speed u compared to observer S in x-direction. Two events happen on the x-axis of S, with the coordinates x1 and x2 at times t1 and t2 measured in S. Let L = x2-x1 and T = t2-t1. a) If the events happen at the same time in S, does the same apply...

So I've been reading Einstein's theory of relativity, and at one point when discussing the Lorentz equations' proof that light remains constant, he just states it without mathematically doing it. Probably because it wasn't the super scientific version (?) but I wanted to see how he did it, so I...

Homework Statement Question as stated: In special relativity consider the following coordinate transformation between inertial frames: first make a velocity boost v_x in the x-direction, then make a velocity boost v_y in the y-direction. 1) Is this a Lorentz transformation? 2) Find the matrix...

BCS theory is able to derive the London equations and the Meißner-Ochsenfeld effect. Experimentally the Meißner-Ochsenfeld effect can be demonstrated via levitating superconducting rings. So we have the usual Lorentz force acting on the Cooper pairs carrying the current. However in order to...

How do we say that F=BIL SINΘ using the SI units?:confused: Newton(N)= Weber/m2 * ampere*meter. please explain as soon as possible.:approve:

As I understand it, the value of a 4-vector x in another reference frame (x') with the same orientation can be derived using the Lorentz boost matrix \bf{\lambda} by x'=\lambda x. More explicitly, $$\begin{bmatrix} x'_0\\ x'_1\\ x'_2\\ x'_3\\ \end{bmatrix} = \begin{bmatrix}...

The lorentz group SO(3,1) is isomorphic to SU(2)*SU(2). Then we can use two numbers (m,n) to indicate the representation corresponding to the two SU(2) groups. I understand (0,0) is lorentz scalar, (1/2,0) or (0,1/2) is weyl spinor. What about (1/2, 1/2)? I don't get why it corresponds to...

Homework Statement 1. Two events occur at the same place in a certain inertial frame and are separated by a time interval of 4 s. What is the spatial separation between these two events in an inertial frame in which the events are separated by a time interval of 6 s? Homework Equations...

Homework Statement Hi we have Lorentz operators J^{\mu\nu} = i(x^{\mu}\partial^{\nu} - x^{\nu}\partial^{\mu}) and these have [J^{\mu\nu}, J^{\rho\sigma}] = i(\eta^{\nu\rho}J^{\mu\sigma} + \eta^{\mu\sigma}J^{\nu\rho} - \eta^{\mu\rho}J^{\nu\sigma} - \eta^{\nu\sigma}J^{\mu\rho}) Now define...

I've managed to confuse myself and don't understand the difference between the formula for Lorentz time transformation (t'=γ(t-vx/c^2) and the time dilation equation t'=γ(t_proper) As I understand, proper time is difference between two events that happen in same place in a given reference...

Undergrad studying engineering here, and my physics class has been doing a unit about intro to special relativity. Essentially, all of our problems and studies concern themselves with velocities which are in the +x direction relative to a "home frame" (I think physicists call this standard...

The Lorentz group generators, in any representation, satisfy the commutation relation [S^{\mu \nu}, S^{\rho \sigma}] = i \left( g^{\nu \rho}S^{\mu \sigma} -g^{\mu \rho} S^{\nu \sigma} -g^{\nu \sigma}S^{\mu \rho} +g^{\mu \sigma} S^{\nu \rho} \right) and the Lorentz transformation is...

The question is given a straight rod parallel to the x-axis moving in the y direction at speed u, to find the angle between the rod and x'axis in R'. (the chosen method to solve being to write equations for the endpoints and transform them to R') I am looking at my book's solution and don't...

Homework Statement The question is quite basic; what is the Lorentz transformation of the follows 4-vectors from S to S' frame: A photon (P) in S frame with 4-momentum P = (E/c,p,0,0) and frequency f where hf = pc = E. h is the planks constant, p is the magnitude of 3-momentum...

Hello! I'm currently reading Peskin and Schroeder and am curious about a qoute on page 38, which concerns representations of the Lorentz group. ”It can be shown that the most general nonlinear transformation laws can be built from these linear transformations, so there is no advantage in...

Homework Statement > Figure 1: > > A spool is hung on a spring. A part of the coil hangs in front of a > homogeneous magnetic field. The coil is incorporated in an electrical > circuit. See Figure 1. > > the coil KLMN has a rectangle shape, has a height of 10.0 cm, a width > of 8.0 cm, and...

Homework Statement A spaceship is approaching a planet at a speed v. Suddenly, the spaceship explodes and releases a sphere of photons traveling outward as seen in the spaceship frame. The explosion occurs in the planet frame when the spaceship is a distance L away from the planet. In the...

I don't understand when I should use the Lorentz transformation versus time dilation or length contraction. I found this: http://www.phas.ubc.ca/~mav/p200/lttips.html but it's still unclear to me... "Length contraction applies when you are talking about a distance that is independent...

Hi, I'm having a major issue trying to work out where the resultant lorentz force might act when I have a wire coiled around a doughnut (toroid) shape. Am I right in saying that there will be a resultant lorentz force acting to crush the doughnut because there will be a slightly denser...

Hi all! First, this is neither a part of homework, university or anything like that , it is my own wondering. I have been searching a lot for how to calculate the Lorentz force acting on a single current carrying wire in Earth´s magnetic field which is 0.6 Gauss. for say a wire of voltage...

1. Consider a four vector x^{\mu}, that is timelike (i.e x^{2}>0. show that it is always possible to find a frame where the coordinates of x are of the form (x^{0'},0). Determine the lorentz transformation relating the initial frame to this particular frame 3. I figured that assuming that the...

I want to determine the orbits of the proper orthochronous Lorentz group SO^{+}(1,3) . If I start with a time-like four-momentum p = (m, 0, 0, 0) with positive time-component p^{0} = m > 0 , the orbit of SO^{+}(1,3) in p is given by: \mathcal{O}(p) \equiv \lbrace \Lambda p...

Homework Statement Show that [\hat{\phi}(x_1),\hat{\phi}^\dagger(x_2)] = 0 for (x_1 - x_2)^2 < 0 where \phi is a complex scalar field Homework Equations \hat{\phi}=\int\frac{d^3 \mathbf{k}}{(2\pi)^3 \sqrt{2\omega}}[\hat{a}(k)e^{-ik\cdot x} + b^\dagger(k)e^{ik\cdot x}]...

Appendix 1 - simple Lorentz transformation derivation found at - http://www.bartleby.com/173/a1.html Given in equation (3) (x'-ct') = Y(x-ct) [Y = const.] by rearrangement, it yields, (x'-ct')/(x-ct) = Y. But it is stated that both (x-ct) and (x'-ct') are zero, so...

Why doesn't a stationary charge experience a magnetic force? And why does a moving charge produce a magnetic field? From a previous thread on the topic I understand it is from the relativistic interpretation of its electrostatic field. So then why shouldn't it affect a stationary charge?

Hello, I have few question for deriving the Lorentz transformation (LT): While deriving the LT, we draw a graph as x,y,z in one frame of reference and x',y',z' in the other frame of reference as S and S' as two frames of reference. Now the factor ct comes in, which is the flash of...

The question I have for my physics homework is "What does the velocity of an object need to be if it's Lorentz factor is 2?" I know the equation for the Lorentz factor is γ = 1/sq(1-(v^2/c^2)) I just don't know how to get the velocity out of it. I'm a bit of a math and physics noob so that...

Suppose I am in a stationary frame of reference S and there is a lamp post at a distance X from my origin in the positive X direction. Say you move at a velocity V along that axis and the distance of the lamp post in your frame of reference S' is X'. Then by Lorentz transformation equation X'...

Homework Statement A point charge +q rests halfway between two steady streams of positive charge of equal charge per unit length λ, moving opposite directions and each at c/3 relative to the point charge. With equal electric forces on the point charge, it would remain at rest. Consider the...

Homework Statement Muons are created in the upper atmosphere (at a height of 3000 m) and plummet downward toward a detector at ##v=0.980c##. The mean lifetime of a muon is ##t = 2.20~\mu s##. Find the mean lifetime of a muon measured by an observer on the ground. Find the distance that...

Homework Statement The problem can be found in Jackson's book. An infinitesimal Lorentz transform and its inverse can be written under the form ##x^{'\alpha}=(\eta ^{\alpha \beta}+\epsilon ^{\alpha \beta})x_{\beta}## and ##x^\alpha = (\eta ^{\alpha \beta}+\epsilon ^{'\alpha \beta})...

Homework Statement Ok I have a moving person (primed) going 50 m/s in the positive x direction, and I have someone stationary (unprimed) observing them. At t = 0, the moving person is at x(0) = 100m Write an equation for the object’s position as a function of time x(t) seen by the...

1.Hey, I am rather stuck on this question which you can see in the attached PDF. Now I began by taylor expanding the Lorentz Gamma factor (γ), up to second order and inserting this into the equation wherever I saw the gamma function, then rearranging. But I can't seem to get a function for F...

I have two questions having to do with the Lorentz transformation for the time...some preamble first: The Lorentz transformation for time along the x-axis is t'=\frac{t-\frac{ux}{c^2}}{\sqrt{1-\frac{u^2}{c^2}}}, where u is the relative velocity of S'. Why is there a dependence on x...