Lorentz transformation Definition and 382 Threads

A Lorentz boost along the x-axis conserves area in the x-t plane. Can anyone think of an argument to prove this fact that's simpler than the one below? I don't want to assume the form of the Lorentz transformation, because I want to use the conservation of area as part of a derivation of the...

What is the vector form formula (not the martrice form) for lorentz transformation from system S' to S for a particle with 4-vectors (\vec{r'},ct') and (\vec{p'},E'/c) where S moves with an arbitary speed \vec{v} in relation to S'? thanks

With one clock stationary at the common origin for 10 time units and the other rocket clock traveling out and back at v=.6c. When both clocks are compared at the origin the elapsed time on the traveling clock will show less time by a factor of (.8) from the Lorentz Transformation. The...

An interesting question maybe, but only in so far as the equations: y' = y and z' = z are concerned. In http://www.bartleby.com/173/11.html" Einstein demonstates that if x= ct then x' = ct' in which he is absolutely correct, but if one were to try and do the same for y' and z' the result...

Homework Statement Using the Lorentz transformation, prove that s2 = s'2 Homework Equations s2 = x2 - (c2t2) x' = gamma * (x-Beta*ct) t' = gamma * (t - Beta*x/c) The Attempt at a Solution s2 = x2 - (c2t2) Therefore s'2= x'2 - (c2t'2) and x' = gamma * (x-Beta*ct) So x'2 =...

I know the Lorentz transformation in rectangular coordinates ct' = \gamma (ct - \beta x) x' = \gamma (x - \beta ct) y' = y z' = z I want to do this same transformation, but from cylindrical coordinates (r,\theta,z) to (r',\theta',z'). Any ideas?

Okay, I'm sure I must have overlooked something very trivial, so please help me with this: Two parallel infinite line currents of equal magnitude attract each other. The current can be thought of as consisting of positive and negative particles with equal linear densities, but each moving with...

How do we find d(gamma)/dt?:redface:

Hi Suppose \Lambda is a Lorentz transformation with the associated Hilbert space unitary operator denoted by U(\Lambda). We have U(\Lambda)|p\rangle = |\Lambda p\rangle and |p\rangle = \sqrt{2E_{p}}a_{p}^{\dagger}|0\rangle Equivalently, U(\Lambda)|p\rangle =...

Hello, If I understand well, since a Lorentz transformation applied on a particle induces a Wigner rotation which depends on the momentum, the spin reduced density matrix that is naively done by tracing out the momentum has no (Lorentz) transformation law. Only the overall system can be...

Homework Statement L1 and L2 are two lorentz trasformation. show that L3=L1 L2 is a lorentz trasformation too. Homework Equations The Attempt at a Solution

I have questions about the infinitesimal Lorentz transformation. but specifically about index manipulations. \Lambda^{\mu}_{}_{\nu}=\delta^{\mu}_{\nu}+\delta\omega^{\mu}_{}_{\nu} where \delta\omega^{\mu}_{}_{\nu} << 1 as found in many textbooks, we substitute this into...

My question deals not with the Lorentz Tranformation itself, but the matrix representation of it: I see readily how the space-time 4-vector: x^{\mu}=\left( c \ast t, x, y, z\right) transforms approptiately so that x^{\acute{\mu}}=\Lambda_{v}^{\acute{\mu}} \ast x^{\mu}=\left( \gamma \ast...

My https://www.physicsforums.com/showthread.php?t=297616" was a pretext to discuss the well-known fact that it is nearly possible to derive the full Lorentz transformation without taking into account the constancy of the speed of light. I went back to my physics hobby and read that in a few...

from the "direct" Lorentz transformation to the "inverse" one. Consider please that we know the "direct" transformation say for the time coordinates of the same event. It is considered that we can obtain the "inverse" transfrmation by simply interchanging the corresponding unprimed physical...

1. Start with the expression x'^2 + y'^2 _ z'^2 -c^2t'^2 and show, with the aid of the Lorentz transofmration, that this quantity is equal to x^2 + y^2 + z^2 -c^2t^2. This result establishes the invariance of s^2 defined by s^2 = x^2 + y^2 + z^2 -c^2t^2 2. s^2 = x^2 + y^2 + z^2 -c^2t^2...

Homework Statement Two events occur at the same place in an inertial reference fram S, but are separated in time by 3 seconds. In a different frame S', they are separated in time by 4 seconds. (a) What is the distance between the two events as measured in S'? (b) What is the speed of S...

Homework Statement An electron with rest mass m0 = 9.11E10-31 kg and charge e= 1.6E10-19 C was accelerated with an acceleration voltage U=30 kV a) What is its velocity , momentum and energy in a classical picture ? b)What is its velocity , momentum and energy in a relativistic picture ...

Hello there, a simple special relativity question, how can the Time Dilation and Length Contraction Formulas be derived from the Lorentz Transformation Equations?

The Lorentz Transformation tA = [tB+vxB/c^2]/sqrt(1-v^2/c^2) can be simplified to tA = tB (1-v)/sqrt(1-v^2), if we adopt these conventions: 1) Refer to v as a fraction of c. Thus every time we write v/c in the original formula, we write v, in the understanding that these v units...

Homework Statement Working on an exercise from Srednicki's QFT and something is not clear. Show that [\varphi(x), M^{uv}] = \mathcal{L}^{uv} \varphi(x) where \mathcal{L}^{uv} = \frac{\hbar}{i} (x^u \partial^v - x^v \partial^u ) Homework Equations (1) U(\Lambda)^{-1} \varphi(x)...

I am doing some study about the lorentz transformation between non-inertial frames. I wonder if the tranformation is the same as in SR. I need to do the transformation of EM fields in a constantly rotational frame. Can anybody help me with this one. Is there anybook I can refer to? Many thanks.

Can anybody please help me with the solutions for the following 2 probs- 1. Prove that Lorentz Transformation is rotation in 4D Minkowski's space. 2. If particle velocity is along x,y plane, calculate the angle transformation relation. Thanks in advance!

When it is about the "Lorentz transformations" I have in mind: There is indeed a state of real rest, defined by the ether. Hearing about "Einstein transformations" I would think: The notions of "really resting" and "really moving" are meaningless. Only relative motion of two or more uniformly...

Problem Write down the transformation from a frame S to a frame S' moving at +0.5 c in the x direction and then to another frame S'' moving at +0.5 c in the x direction relative to S'. What is the complete transformation from S to S''? What relative speed between frames S and S'' does your...

Can anybody tell me if there is anything analogous to Lorentz transformation in General Relativity (ie, in curved space)? If there is then what are the corresponding group generators and what is the corresponding algebra? I just wondered this question while reading about Lorentz group and I am...

In appendix 1 of Einstein's "Relativity, The Special and General Theory", a book intended for the general public, he gives a derivation of the Lorentz transformation. The math involved is pretty straightforward, but I wonder if anybody can clarify his reasoning for his equation 3 (below)...

Space ship Alpha travels at t = 0 and v = 4/5 c to the star Sirius which is 8.6 light years away. One year later spaceship Delta starts at v = 9/10 c to the same star. Question 1: When does Delta overtake Alpha, as measured from Alpha's, Delta's and Earth's perspective? Question 2: At which...

Let's say, there are two observers A and B moving with respect to each other with relative velocity v. Now, when we say, the speed of light is same for every observer, does it mean that the speed of light measured by A and B in their own frames, as well as the other's frame will be same? That...

An observer at the mid point between two frames A and B that are moving toward her, measures each of their speeds to be 0.75c. According to SR, the Lorentz transformation will determine the speed of A and B measured by the other to be less than 1.5c. (in fact less than c) Being aware of the...

I need to show that: 1. if E is \perp to B in one Lorentz frame, it is \perp in all Lorentz frames 2. |E|>|cB| in L. frame, |E|>|cB| in all L. frame 3. Angle b/t E and B is acute/obtuse in L. frame, it is acute/obtuse in all L. frame 4. E is \perp to B but |E|\neq|cB|, then there is a frame...

Homework Statement A spaceship has a speed of .8c relative to Earth. In its own reference fram, the length of this spaceship is 300m. a.) consider a light emiited from the tail of this spaceship. In the reference frame of the spaceship, how long does this pulse take to reach the nose> b.) In...

I have been studying the lorentz-transformation derivation but I can't quite get a proper answer as to why you can start with the assumption that: x' = ax + bt t' = cx + dt The assumption is that "the transformations must be linear". So my first question is, what does that mean, that a, b, c...

Which Lorentz transformation takes the lab system to the CM system? Lab system: p_a = (E^{lab}_a, \vec{p}_a) and p_b = (m_b, \vec{0}) CM system: p_a = (E^{CM}_a, \vec{p}) and p_b = (E^{CM}_b, -\vec{p}) For a binary reaction a+b->c+d, the textbooks I have say quite a lot about the...

Is Lorentz transformation one kind of coordinate transformation? If so, the conservation of inner product, which is the primary property of Lorentz Transformation, is trivial, isn't it? The vector transforms in some way, the metric transforms in the inverse way, so the inner product defintely...

Let S' = a stationary two-dimensional space-time coordinate system, and let the x'-axis of S' lie along the x-axis of another stationary two-dimensional space-time coordinate system S. Let S' move along the x-axis of S with a constant velocity v = 29,800m/s in the direction of increasing x...

On this page, and in many, many other resources both in textbooks and online, derivations of time dilation and length contraction are given which lead to; \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} t^{'}=\gamma t x^{'}=\frac{1}{\gamma}x Now a great many derivations of the Lorentz...

well, i have been going over this problem for about 4 hours and everytime i get closer and closer to some answer but I am never convinced i am right. THE PROBLEM: let lambda be the wavelength of light propagating in the x-y plane at an angle theta with respect to the x-axis in the (x,y,z,t)...

Hi Guys, I've attached 2 pages from the book of landau "The Classical Theory of fields", I have a question about the lorentz transformations in pages 10,11 after reaching the step: tanh(psy)= V/c How did he split the latter into sinh(psy) and cosh(psy) and added the "gamma" constant...

Is the lorentz transformation an active transformation or a passive one?

How to get inverse Lorentz tranformation from "direct" Lorentz transformation Hello, I am having trouble on deriving the inverse Lorentz transformation from the direct Lorentz transformation. I looked at some threads here and I found in here...

Hi, I don't fully understand the derivation of the Lorentz Transform. For example, in the transformation: t' = \gamma t - \gamma\frac{vx}{c^2} Where do you get the x-term from? I understand the derivation of gamma, and I see that when x = 0 (when the two frames coincide in origin)...

can anybody give me just equation of the transformation in a linear form ? without any complications just the equation of Lt. 10x

i am confused what a lorentz transformation really is or is it just a transformation described by the boost transformation.

I find in some textbooks the following generalization of the Galileo transformations x=k(x'+vt') x'=k(x-vt) with the same k because if we transform from I to I' or from I' to I then the distortion factor of lengths or time intervals should be the same. Are there objections?

When we state that: Knowing the direct Lorentz transformation we obtain the inverse one by changing the corresponding primed physical quantities with unpriomed ones and changing the sign of the relative velocity, we are based on what? Thanks

Homework Statement Suppose that an event occurs in inertial frame S with cooridinates x=75 m y=18 m ,z=4.0 m and t=2.0*10^-5 seconds . The inertial frame S' moves in the +x direction with v=c*.85 . The origins of S and S' coincided at t=t'=0. a)what are the coordinates of the event in S'...

I have been reading DF Lawden's nice book on tensor calculus and relativity. I keep going back to first chapter (p 9-11) as I did not 100% get his derivation of the "special" Lorentz transformation. He writes about a rotational transformation in one plane and then writes about a translational...

Homework Statement Two space ships are approaching each other a)if the speed of each is .9 *c relative to Earth , what is the speed of one relative to the other b)if the speed each relative to Earth is 30000m/s, what is the speed of one relative to the other Homework Equations The...

So I'm looking at some Lorentz transformation equations and it says x'=\gamma(x-vt) t'=\gamma(t-vx/c^{2}) y'=y z'=z I'm assuming the values for y', y, z' and z only hold true when the inertial frames of S and S' are moving at a relative velocity in the x-direction. With this being said, what...