Lorentz transformations Definition and 175 Threads

Many equations are affected by Lorentz transformations. Time, mass, volume of a moving object, momentum, force etc. I want to know if the following equations are affected by Lorentz transformations: 1. Distance=velocity*time (r=vt) 2. E=hv 3. j*=ot 4. F=G*m1*m2/r^2 Also, is the Newton's...

Hi, I've been breaking my head on the matrix form of the lorentz transformation between one set of coordinates in one inertial frame (t,x^1,x^2,x^3) and what those coordinates will be in another inertial frame (t',x'^2,x'^2,x'^3). Now I understand that if have a set of coordinates in one...

what does it mean by "any \Lambda^{\alpha}_{\beta} that can be converted to the idendity \delta^{\alpha}_{\beta} by a continuous variation of parameters must be a proper lorentz transformation"?

Hi guys, I'm currently struggling to show something my lecturer told us in class. We have that \Psi\left(x\right) \rightarrow S\left(L\right)\Psi\left(L^{-1}x\right) under a Lorentz transform defined L = exp\left(\frac{1}{2}\Omega_{ij}M^{ij}\right) with S\left(L\right) =...

c^2 occurs frequently in special relativity: in the Lorentz transformations, in forumlas for the interval, relativistic energy, and others too. Is there an intuitive reason for the high occurence of c^2?

Two observers A and B are in relative motion with a constant velocity[for example, along the x-x' direction].If A knows the the position of B accurately , the motion of B gets enormously uncertain[and vice verse] in his calculations/considerations.How is he going to derive the Lorentz...

Let us consider the B-E and F-D statics: {<}{n}_{i}}{>}{=}{\frac{1}{{exp}{(}{{\epsilon}_{i}{-}{\mu}{)}{/}{kT}}{\mp}{1}} Now we observe the formula from a boosted frame.The left side is a scalar and should not change in response to the Lorentz transformations.What about the right hand side?The...

Homework Statement Event A occurs at xA = 500m. Event B occurs 5 microseconds later at xB = 1500m. With what speed must an observer move in the positive x direction so that the events occur at the same point in space in the observer's frame?Homework Equations Lorentz transformation...

Homework Statement A3. Show that the Lorentz transformations on a spacetime 4-vector can be written as x'μ = (Lμν)*(χν) . Find the matrix L. Prove that (in matrix notation) Lτ gL = g where g is the Minkowski spacetime metric.Homework Equations Any help suggesting at least equations will be...

Hello. When one is converting between coordinate systems, the Jacobian arises as a necessary consequence of the conversion. Does this occur with transformations between relativistic systems, and, if so, is this manifested through the prevalence of gamma in the transforms? Any guidance would...

I'd like to start by mentioning that I have very little in the way of experience on the subject, so forgive me if my confusion is somewhat trivial.. My problem lies with understanding what the fundamental variables in the Lorentz Transformations actually represent. For example, it is to my...

I've just read the statement "The Lorentz transformations have a representation on the fields" Can anyone explain the meaning of the word representation? I can't seem to get a satisfactory explanation anywhere and the notes don't go into much more detail on it.

a)So I'm reading over my notes and they say that under the Lorentz transformation L, \phi \rightarrow \phi' where \phi'(x)=\phi(x') where x'^\mu = (L^{-1})^\mu{}_\nu x^\nu I don't really understand why this is true. Why is it not just \phi'(x)= L \phi(x) Clearly this fails because the LHS is...

I asked my prof why the Lorentz transformations had to be linear (which my textbook assumed when deriving them), and he mentioned some stuff about homogeneity and ended with "it's advanced, just believe". Can anyone offer a simple explanation?

Homework Statement In the old West, a marshal riding on a train traveling 35.0 m/s sees a duel between two men standing on the Earth 55.0 m apart parallel to the train. The marshal's instruments indicate that in his reference frame the two men fire simultaneously. (a) Which of the two men, the...

In a lecture on special relativity online, the form x'=x\cosh{\omega}-ct\sinh{\omega} t'=-x\sinh{\omega}+ct\cosh{\omega} is used for the lorentz transformations, where the velocity is v=\frac{c\sinh{\omega}}{\cosh{\omega}}. However, I'm wondering, couldn't you also do...

The group of four dimensional space time symmetries may be generalised to conformal transformations x \rightarrow x' defined by the requirement dx'^2 = \Omega(x)^2 dx^2 where dx^2 = g_{\mu \nu} dx^\mu dx^\nu (recall that Lorentz invariance requires \Omega=1). For an infinitesimal...

Define B( \theta, \vec{n} ) \in SL( 2 , \mathbb{C} ) by B( \theta , \vec{n}) = \cosh { \frac{1}{2} \theta} + \vec{\sigma} \cdot \vec{n} \sinh{ \frac{1}{2} \theta} where \vec{n}^2 =1 Show that this corresponds to a Lorentz boost with velocity \vec{v}=\tanh{ \theta} \vec{n}. Show that ( 1 +...

hey, does anyone there know how the angular momentum (L=r x p) is transformed under Lorentz transformations?

Homework Statement A light signal is sent from the origin of a system K at t = 0 to the point x = 1 m, y = 8 m, z = 13 m. a) At what time t is the signal received? b) Find ( x', y', z', t' ) for the receipt of the signal in a frame K' that is moving along the x-axis of K at a speed of 0.6c...

Homework Statement Consider a two-dimensional function φ = φ(x,t) that satisfies the relativistic wave equation given by: https://adgiiq.blu.livefilestore.com/y1pe5tdBVr0r62krIiWV_PQ42r1jrzQpWKz24xRgNe138phEqCNyZJKFXhBXqqL4YCvYeAsgVQtJJwovzjL0mKiNXyd6p1zHvkx/equation.jpg?psid=1...

Anyone help. I know I must be doing this wrong somehow Lightning hits both a tree and a pole. The spacetime coordinates for each is (x=0, t=10us) for the tree and (x=30000m, t=10us) for the pole relative to the ground. Therefore they occur simultaneously relative to the ground. A rocket comes...

1. Problem Horizontal rod of length x traveling along the positive y-direction at velocity u. Determine the orientation of the rod in frame S', which is moving at velocity v in positive x-direction. 2. Homework Equations Lorentz Transformation for length contraction, x' =...

There's something about the lorentz transformations which is somewhat confusing to me, and that is how to treat the "x" coordinate. Supposing I have some spaceship which is moving from Earth to some other planet located at a distance "D" (from earth) with a velocity v. Now, the spacetime...

Homework Statement The system S' moves in relation to the system S with velocity \upsilon along the -x- axis. At the time when the beginnings of the coordinate system are in the same point, clocks in both system shows t=t'=0. Which coordinates will have a reference point during the motion in...

I've spent a large portion of my day trying to figure this out and I figured my best answer is likely to come from here. Forgive me if I'm wildly wrong about anything, I'm somewhat basic with physics, largely due to the fact that I'm 15 and my maths is limited to a GCSE level. My dilemma is...

I am wondering about the order of operations concerning the Lorentz transformation of fields and the superposition of fields. I was given a problem: Two positively charged electrons start at the origin and then travel along the x-axis at a constant speed v in opposite directions. Calculate...

Iv just been reading a physics textbook and i feel iv completely missed something. It may help to draw a diagram and to read the thread slowly. Sorry if it is a little thick. My understanding of Special Relativity is that it allows two seemingly conflicting principles to co-exist, these being...

Lorentz transformations ("synchronising" reference frames?) Homework Statement A particle moves from (x,y,z,t) = (0 m,0 m,0 m,0 s) to (1 m,1 m,0 m,10 ns). i. What is the speed of the particle in this reference frame? ii. What is the speed of the particle in a reference frame moving...

Good evening, As an effort for trying to understand Lorentz transformations, I'm trying to use them to derive the "length contraction" result. Consider two reference frames, O (non-primed) and O' (primed), moving with respect to each other with a velocity v. Consider them to be under...

Hi, this is a question from a practice paper I have. I can't think how to do this. As far as I'm aware this has to be assumed to derive the Lorents transforms, so it must be by definition true, making the question pointless. Does anyone have any thoughts or suggestions on this? Regards, Pete

It seems that the common approach to obtain the equations for the Lorentz transformations is to guess at its form and then, by considering four separate situations, determining the values for the constants. From these equations, things like time dilation and length contraction can be worked out...

How can I convince myself of the following statement: If x2<0, there exists L orthochronous Lorentz tranformation such that: Lx = -x My concern is this: If for example, we take xµ=(1,0,0,0), then Lx in component form is: Λµβxβ=Λµ0x0 =(Λ00, Λ10, Λ20, Λ30). By definition, if it is an...

Homework Statement Two flashes of light strike at the same time, at the two orange circles on the diagram. The green train is traveling at a constant 150 kmh relative to the grey platform. The train is 1 km long. As measured by someone at point F on the grey platform, how much time passes...

Since the lorentz transformations do not change an object in the z and y directions, but it does in the x direction, is this why a ruler looks shorter in the space station example? (same everything on each station, one moving by your IFR) Also is it why the clock appears to be running slower...

I've tried several hours to understand Lorentz transformations(for space and for time)...it simply dosn't make any sense...I've posted here,on math section,because I need a better mathematical view over it... whitout this I can not understand much out of the restricted theory of relativity,thus...

Couple days ago, we get a lecture in relativity, I read quite a lot about it before so there was nothing new except one thing : our professor first started to conclude Lorentz transformation totally in a mathematical way by assuming gamma*(x-v*t) … (what I discovered that it is a known method...

I'm trying to work out how to use the Lorentz equations but so far I haven't been very successful. It would help if I had an example to let me know what I'm aiming for, so if someone would be kind enough to answer my questions about the fairly simple scenario below I would be very grateful...

Hello.The way the transformation of coordenates in Special Relativity are ussually derived presuposes linearity or try do demostrate such linearity using wrong arguments. For example some authors state that since linear and uniform motion remains linear and uniform after the transformation this...

What's the problem with using dimensional analysis to derive the Lorentz transformations?

Homework Statement Show that (D'Alembertian)^2 is invariant under Lorentz Transformation. Homework Equations The book (E/M Griffiths) describes the D'Alembertian as: \square^2=\nabla^2-\frac{1}{c^2}\frac{\partial^2}{\partial t^2} The Attempt at a Solution I don't really...

1. Using the Lorentz Transformations, show that the quantity px - Et is invariant, where p and E are the momentum and energy, respectively, of an object at position x at time t. 2. px - Et 3. I needed help on starting the problem. Where should I begin?

I'm reviewing for exams and don't understand when to use which Lorentz velocity equation to use. one goes v'=(v-u)/(1-vu/c^2) and the second v=(v'+u)/(1+v'u/c^2)

Prtesent the Lorentz transformations as dx=g(dx'+Vdt') dt=g(dx-Vdt) In my oppinion dx and dx' represent proper lengths measured in I and in I', dt and dt' representing coordinate time intervals. Do you aggree. Happy new year to all participamts on the Forum

hi all , i need some help concerning the expressions for lorentz transformation of the acceleration. i couldn't derive them?. thanks. :cry:

Homework Statement Events A and B are simultaneous in frame F and are 18 km apart on a line that defines the x-axis. A series of spaceships all pass at the same speed in the + x-direction, and they have synchronized their clocks so that together they make up a moving frame F'. They time...

Homework Statement A ship is moving at 0.45c with respect to earth, and a beacon is fired perpendicular to the ship at 0.65c with respect to the ship. Find the velocity of the beacon with respect to earth. Homework Equations The Attempt at a Solution My main problem here is...

Homework Statement A physics professor on Earth gives an exam to her students who are on a spaceship traveling at speed v relative to Earth. The moment the ship passes the professor she signals the start of the exam. If she wishes her students to have time To (spaceship time) to complete the...

Please have a critical look at the lines below: The simplest derivation of the Lorentz transformation simplified: J.M.Levy "A simple derivation of the Lorentz transformation and of the accompanying velocity and acceleration changes," Am.J.Phys 35,615 (2007) arXiv:physics/0603103 revisited.[1]...

Homework Statement I am trying to learn from Srednicki's QFT book. I am in chapter 2 stuck in problem 2 and 3. This is mainly because I don't know what the unitary operator does - what the details are. Starting from: U(\Lambda)^{-1}U(\Lambda')U(\Lambda)=U(\Lambda^{-1}\Lambda'\Lambda) How does...