Lorentz transformation Definition and 382 Threads

Homework Statement The following is Exercise 2.1 from from Ray d'Inverno's 'Introducing Einstein's Relativity.' (a) Write down the Galilean transformation from observer ##S## to observer ##S'##, where ##S'## has velocity ##v_1## relative to ##S##. (b) Find the transformation from ##S'## to...

Hi, is there any general formula to find out the final velocity w, happened by a boost in x direction forst and then to y direction? I could find the boost matrices for both and I know it's not purely another boost, rather a boost and a rotation, but I am really confused which formula to use...

Hello people, I have a question regarding the x' component in the Lorentz/Galilean transformation. So from what i understand is that there are 2 coordinate systems used in the transformations. One is used as a reference point and one is used for moving away from this point. The moving away in...

Hello i have to find the Lorentz transformation for arbitrary velocity (v) relative to (O) the information's i have: 1-i have to use all 3 components of velocity ##(V_x, V_y, V_z )## 2- ##x'=\frac{x-vt}{\sqrt{1-\frac{v^2}{c^2}}}## ##y'=y## ##z'=z## 3-...

We know that when a rigid frame, say a rocket undergoes constant proper acceleration, its worldline is hyperbolic. The equation is given by: x^2 - c^2t^2 = \left( \frac{c^2}{a_0} \right)^2 Suppose P is such a worldline and worldine can also be written as: I understand how these are...

As known, any Lorentz transformation matrix ##\Lambda## must obey the relation ##\Lambda^μ{}_v####\Lambda^ρ{}_σ##gμρ=gvσ . The same holds also for the inverse metric tensor gvσ which has the same components as the metric tensor itself (don't really understand why every tex formula starts from a...

Homework Statement If two particles have velocities u and v in frame S, find their relative speed in frame S'. Homework EquationsThe Attempt at a Solution Isn't it strange that the relative speed doesn't depend on the velocity of the frame, ##\vec s##? Since the two particles have velocities...

Homework Statement Use the Lorentz Transformation equations to derive the formula relating the time period of a moving clock to that of a stationary clock Homework Equations X'=y(X-vt) Y'=Y Z'=Z t'=y(t-vx/c^2) The Attempt at a Solution t'=1/sqrt(1-(v/c)^2) . (t-vx/c^2)

Hi all,I am trying to understand relativity and Lorentz Transformation more clearly but I have some problems. Assume that we have frame F' which is moving at velocity v with respect to F. Now assume we have an object, O, moving at velocity, w, with respect to F. Frame F has its own time, t, and...

I'm trying to derive (14.25) in B&J QFT. This is ##U(\epsilon)A^\mu(x)U^{-1}(\epsilon) = A^\mu(x') - \epsilon^{\mu\nu}A_\nu(x') + \frac{\partial \lambda(x',\epsilon)}{\partial x'_\mu}##, where ##\lambda(x',\epsilon)## is an operator gauge function. This is all being done in the radiation...

I am having a personal discussion with somebody elsewhere (not on Physics Forums) and we are stuck at the moment because of a disagreement that I narrowed down to the question whether, in the context of SR, two observers in different reference frames can choose the origin of their coordinate...

My local PBS station broadcasts a physics series on a sub-channel. They call it The Mechanical Universe locally. PBS recently broadcast The Lorentz Transformation . It appears that one may view these on line, as the Lorentz Transformation began to load after I allowed it to pop-up. There are...

Homework Statement [/B] I'm trying to derive (14.25) in B&J QFT. This is ##U(\epsilon)A^\mu(x)U^{-1}(\epsilon) = A^\mu(x') - \epsilon^{\mu\nu}A_\nu(x') + \frac{\partial \lambda(x',\epsilon)}{\partial x'_\mu}##, where ##\lambda(x',\epsilon)## is an operator gauge function. This is all being...

Apriori -- before taking any of the postulates of special relativity into account -- we might say that the lorentz transformations between two frames K and K', where K' is moving w. speed v along the x-axis of K, is given by $$\vec{x}' = F(\vec x, t)$$ and $$t' = G(\vec x, t).$$ Now, i want...

Not sure if Velocity Addition belongs in introductory Physics but it seems relatively introductory to me. I'm having trouble with all aspects of grasping how to attempt these problems logically. Obviously the math behind them is super simple; I just more or less don't know what to plug in where...

Hello, I was reading and trying to follow up with Pierre Ramond's "Field theory: A modern primer" and got stuck in his step to step jumping. Kindly, see attachment and note that Eq (1.2.6) = g_{ρσ}=g_{μ\upsilon}\Lambda^{μ}_{ρ}\Lambda^{\upsilon}_{σ}. My question is what do I need from tensor...

Homework Statement It is not an official question but a request for pointers. I am trying to derive the Lorentz time equation to understand the intuition behind it. My math skills are not very good so it might be an obvious question for you. Please see below for my attempt. The variables are...

Homework Statement I am learning special relativity and we came across the invariant quantity s = x2 - (ct)2. Our professor wants us to prove it. I admit that this is a proof and belongs in the mathematics section but I didn't see an Algebra section and this is most easily identified by those...

Hi all, I'm trying to derive that t=δ(t'+vx'/c^2) Using x'=δ(x-vt) then substituting for x=δ(x'+vt') I should be able to isolate t and solve the problem but I am getting to the following point after simplification and can't figure out where to go next...? x'= δ[δ(x'+vt')-vt] (isolate...

Definition/Summary A Lorentz transformation is the relation between the coordinates of two inertial observers who use the same event as their origin of coordinates. A Lorentz boost is a Lorentz transformation with no rotation (so that both observers use the same coordinate-name for the...

Hello everyone. I am attempting to teach myself about special relativity, and have learned a derivation for the Lorentz transformation. Before I go any farther I want to clear up the parts I don't understand right now and check that I am correct about the parts I do understand. Here I will...

Is there anywhere I can see the explicit derivation for a massless real scalar and for the EM field? thank you.

Hi! I'm having problems with this homework my professor gave us this morning: Prove that Maxwell's equations is invariant under Lorentz Transformation. I'm just currently in third year, and we haven't been taught tensors yet. The extent of what I know mathematically is only until gradient...

To=(time of moving object.) T=(Time of standing object.) ^=power of number. sqrt=square of number.(x^1/2)Law of einstein say: T= To / ( sqrt( 1 - u^2/c^2 ) ) Lorentz law say: T= (To + u*Xo/c^2) / ( sqrt( 1 - u^2/c^2 ) )Why there is difference?? Is for other things?? I thought is for the same...

So i am working on a question, which is beyond my knowledge of Lorentz transformations and some help is greatly appreciated. I have a 4 velocity, u=γ(v vector,c) and its transformation properties are the standard lorentz boost. I don't quite understand how I am supposed to do this given that...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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 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 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...

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...

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...

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.

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...

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...

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...

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...

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...