Lorentz transformations Definition and 175 Threads

Homework Statement Spaceship A of length 30m travels at 0.6c past spaceship B. Clocks in frame S' of spaceship A and S of spaceship B are synchronised within their respective frames of reference and are set to zero, so that t' = t = 0 at the instant the front of spaceship A passes the rear of...

Hey guys, In what circumstance or scenario would you use Lorentz transformations as a opposed to time dilation or length contraction? The reason that I ask this is because in all of the problems that I have worked with, the observer is always stationary relative to the event. For example, if...

You are probably familiar with the following two Lorentz transformations: x' = (x - vt) / sqrt(1 - v2/c2) and t' = [t - (vx/c2)] / sqrt(1 - v2/c2) Well I am having some issues interpreting what each variable refers to. You see, here is how I've been thinking of it: If you have one stationary...

Hi Everyone. There is an equation which I have known for a long time but quite never used really. Now I have doubts I really understand it. Consider the unitary operator implementing a Lorentz transformation. Many books show the following equation for vector fields: U(\Lambda)^{-1}A^\mu...

... in order that one's clocks will lose: (a) 1 second per day as observed from S? (b) 1 minute per day as observed from S? I was referencing this:( http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html#c2 ) hyperphysics page but I still can't seem to understand what I need to do to...

In the system of units where c=1, the Lorentz transformations are as follows: ## x'=\gamma (x-vt) \\ t'=\gamma (t-vx) ## In the limit ## v \ll 1 ##, we have ## \gamma \approx 1+\frac 1 2 v^2 ##, so we have, in this limit: ## x' \approx (1+\frac 1 2 v^2)(x-vt)=x-vt+\frac 1 2 v^2 x-\frac 1 2...

I'm going through Ray D'Iverno's "Introducing Einstein's Relativity", and there is a step he makes in deriving the Lorentz transformations that doesn't seem necessary to me. So I'm not sure what I'm missing. He derives them from Einsteins postulates of relativity. From the postulate that the...

Homework Statement Derive the transformations ##x \rightarrow \frac{x+vt}{\sqrt{1-v^{2}}}## and ##t \rightarrow \frac{t+vx}{\sqrt{1-v^{2}}}## in perturbation theory. Start with the Galilean transformation ##x \rightarrow x+vt##. Add a transformation ##t \rightarrow t + \delta t## and solve for...

Why is relative speed taken to be symmetrical i.e. speed of one frame of reference from a second frame is equal to that of the second frame of frame refrence from the first frame

I'm doing a class on special relativity and when doing some problems, I'm never sure whether I should be using the Lorentz transformations (Eg. x' = γ(x-vt) or t'=γ(t- (v/c^2)x)) or the Time dilation and Length contraction equations to find t or x! Can anyone explain if there's any way of...

Homework Statement Hello I need some advice on how to figure out Part F of the following problem. I was able to find the correct answer but in a very illogical way. I was wondering if I could get some help understanding the lorentz transformations necessary. Here is the full problem, I have...

Hope this derivation helps someone!

Any advice on my derivation layout?

Direct experimental evidence of time slowing down for moving clocks is well-known. With the advent of atomic clocks, round trip journeys taken by these clocks on slow moving(compared to light speed) jets show time differences with clocks that have not taken the journey. But is there...

Disclaimer: This isn't a homework assignment, so maybe it shouldn't be in the homework forums. If you feel it should be located elsewhere, feel free to move it, but the template doesn't really apply to this question so... * * *...

PROBLEM SOLVED - the worked example I was referring too was wrong :/ ---------------------------- Hello, I've been stuck on a question in one of my SR problem sets for some time now, and managed to find a worked solution to a similar problem online. I've attached an image of the problem (the...

I am attempting to read my first book in QFT, and got stuck. A Lorentz transformation that preserves the Minkowski metric \eta_{\mu \nu} is given by x^{\mu} \rightarrow {x'}^{\mu} = {\Lambda}^\mu_\nu x^\nu . This means \eta_{\mu \nu} x^\mu x^\nu = \eta_{\mu \nu}x'^\mu x'^\nu for all x...

Homework Statement A rocket ship carrying passengers blasts off to go from New York to Los Angeles, a distance of about 5000 km. (a) How fast must the rocket ship go to have its own length shortened by 1%? (b) Ignore effects of general relativity and determine how much time the rocket...

Homework Statement Two events occur in an inertial system K as follows: Event 1: x1 = a, t1 = 2a/c, y1 = 0, z1 = 0 Event 2: x2 = 2a, t2 = 3a/(2c), y2 = 0, z2 = 0 Is there a frame K' in which the two events described occur at the same place? Explain. Homework Equations Lorentz...

[Mentor's note: This question was originally posted and responded to in a non-homework forum, therefore it does not have the usual homework template.] Hey, don't know how to solve this: In an inertial frame S, consider a light ray on the XY plane forming a 60 degree angle with the x-axis...

Depending on where I go to get a good understanding of the Lorentz transformations, I run into two formulas for time (t): T=T_0 * \frac{1}{ \sqrt{ 1-\frac{v^2}{c^2} } } and t=\left( t' + \frac{vx'}{c^2} \right) * \frac{1}{ \sqrt{ 1-\frac{v^2}{c^2} } } What is the...

Hi all, What is the difference between Lorentz transformations and yt?. That is, the Lorentz transformations for moving between two reference frames are not the same as the relativistic ones. For example considering a frame F that is stationary and an inertial frame F' with velocity v. Time...

Homework Statement Prove that under an infinitesimal Lorentz transformation: x^\mu \to x^\mu+\omega^\mu_\nu x^\nu so: \phi\to\phi-\omega^\mu_\nu x^\nu\partial_\mu\phi the Lagrangian varies as: \delta \mathcal{L}=-\partial_\mu(\omega^\mu_\nu x^\nu \mathcal{L}) The Attempt at a...

Hello all, I have an exam on Monday and am having trouble with this problem, any help would be greatly appreciated! Q: A straight stick of length L' is at rest in the moving S' frame. The stick appears to have length L in the S frame. The S' frame is moving at a velocity √(2/3) c...

I'm currently going through my courses notes for relativity. We looked at Einsteins two postulates and then said that time must therefore dilate due to constant speed of light. That I understand, however I'm still confused about the Lorentz's transformations. My notes start with a basic form of...

I understand how contravariant 4-vectors transform under a Lorentz transformation, that is: ##x'^μ= \Lambda^\mu~_\nu x^\nu## [1] and how covariant 4-vectors transform: ##x'_\mu=(\lambda^{-1})^\nu~_\mu x_\nu##. [2] Now, I have come across the following relations...

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...

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...

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...

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...

Homework Statement First part of the problem: Newton’s second law is given by F=dp/dt. If the force is always perpendicular to the velocity, show that F=gamma*m*a, where a is the acceleration. Second part of the problem: Use the result of the previous problem to show that the radius of a...

Homework Statement Two particles in a high-energy accelerator experiment are approaching each other head-on, each with a speed of 0.9500c as measured in the laboratory. What is the magnitude of the velocity of one particle relative to the other? Homework Equations...

In a book ("The special theory of relativity by David Bohm") that I'm reading, it says that if (x,y,z,t) are coordinates in frame A, and (x',y',z',t') are coordinates in frame B moving with v in realtion to A, if we have (for a spherical wavefront) c^2t^2 - x^2 - y^2 - z^2 = 0 and we...

Starting with: x'=\gamma(x-vt) & x=\gamma(x'+vt') I know that I can derive t'=\gamma(t-vx/c^2)... however I can't seem to make it fall out mathematically. The suggested method is to cancel x'. Can anyone help me out on the steps? Much appreciated! :)

Are Lorentz transformations only work between inertial frames? if so, is there a simple counter-example e.g. for them not to work?

Homework Statement Suzanne observes 2 light pulses to be emitted from the same location, but separated in time by 3μs. Mark sees the emission of the same two pulses separated in time by by 9μs. a) How fast is Mark moving relative to Suzanne? b) According to Mark, what is the separation in...

Homework Statement The pion has an average lifetime of 26.0ns when at rest. For it to travel 10.0m, how fast must it move? Homework Equations Lorentz velocity transformation? The Attempt at a Solution I'm very lost... am I supposed to use u'x = (ux-v)/(1-vux/c2)? I thought I was following...

I thought Lorentz Transformations left Δt2-Δx2 invariant but, for example a frame moving at .5C for Δt =1 has Δx = .5 so Δt2-Δx2 = .75 If this is transformed by : to a rest frame Δt =0.65 has Δx = 0 and Δt2-Δx2≠ 0.75 not sure where I have gone wrong here, any help would be...

Preface to my question: I can assure you this is not a homework question of any kind. I simply have a pedagogical fascination with physics outside of my own studies in school. Also, I did a quick search through the forum and could not find a question similar enough to what I want to know, so i...

I am a newcomer to relativity, currently studying the subject on my own, via Modern Physics by Bernstein et al. I have a question based on pgs 57-58 of the text. Suppose that two reference frames S and S' are similarly oriented, and S' is moving with constant velocity v in the positive...

I often read sentences like, "if space is homogeneous, then the Lorentz transformation must be a linear transformation." What exactly does it mean to say that space is homogeneous, and how does it imply that the Lorentz transformations are linear?

Homework Statement Are the Lorentz transformations empirical laws? If so, are they empirically testable? Homework Equations The Attempt at a Solution I'm guessing they are. But how do you test the LT?

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...

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...

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...

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...

Homework Statement Prove that the spacetime interval -(ct)^{2} + x^{2} + y^{2} + z^{2} is invariant. [/itex] Homework Equations Lorentz transformations \Deltax' = \gamma(\Deltax-u\Deltat) \Deltay' = \Deltay \Deltaz' = \Deltaz \Deltat' = \gamma(\Deltat-u\Deltax/c^{2}) The...

I'm slowly trying to understand sp relativity. I admit I got lost in the last thread I posted :blushing:. But thanks to all who replied! I have a question about the Lorentz transformations formulas. This is more of a mathematical question about how the formulas are derived. If you have...