Lorentz transformation Definition and 371 Threads

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Homework Statement Hey all, my algebra isn't as great as it used to be and I am having trouble with some of the algebra dealing with Lorentz transformation. Basically, I just need someone to do a quick step by step of how to go from x' to x (see the following). I started with the top...

Hi, From what I've learned so far, Lorentz transformation meets certain criteria, such as the constancy of EM wave propagation speed in vacuum, &/ casuality, among others. My question is, why would it/would it not be applicable to phenomena that have nothing to do with EM interaction? In...

Homework Statement Frame S and S' are moving with respect to each other in the x-axis with some velocity. An event happens in S' at x'_1 = 1.0 c*year at t'_1 = 1.0 year. Another event happens at t'_2 = 2.0 c*year at t'_2 = 0.5 year. The two events are simultaneous at some point in S. The...

Homework Statement Observer O sees a fire-engine leave its station 6363 m due north from Cape Canaveral, where the super-shuttle Lorentz had been launched 10^-5 s earlier. A space-cruiser flying north-east sees these two events also 10^-5 s apart, but with the shuttle launch occurring after...

Homework Statement Derive the Lorentz transformation by assuming that the transformation is linear, and does not change the perpendicular coordinates. Write the transformation as x' = A1 (x - vt), y' = y, z' = z, t' = A2 t + A3 x, Determine A1, A2, A3 by requiring that a flash of light...

Homework Statement A is at the base station and given in K co-ordinates B is on a spacecraft and given in K' co-ordinates. The velocity of the spacecraft is v=0.8c Question 1 After t = 2y (y = years) A sends a message by radio to B demanding a picture. Which time t' does B have when...

A 'cause' occurs at point 1 (x1, t1) and its 'effect' occurs at point 2 (x2, t2) as measured by observer O. Use Lorentz transformation to find t'2 - t'1 as measured by O' and show that t'2 - t'1 >= 0. that is Observer O' can never see the effect before the cause. I know that is possible to...

When you start in the rest frame of the electron, the Spinor w(p = 0) = (1 0 0 0 ) represents a positive energy state with spin up in the Z direction u = (0, 0 0 1),, that is the spinor is an eigenspinor of the operator S . u, where S is a 4 dimensional operator (S0, S) after a Lorentz...

Hello! need some help with length contraction. So according to lorentz transformation we got I don't know how to put symbols so ill use Y as gamma since they look alike :) dx' = Y dx - u Y dt So proper length refers to the frame where dt = 0 since u are measuring the ends at the...

hey, I heard about improper Lorentz transformations, but I did not really understand what they are. I just know that their determinant is -1, but what does this physically mean? Can somebody explain this to me?

Homework Statement 1The rockets of the Goths and the Huns are each 1000 m long in their rest frames. The rockets pass each other, virtually touching, at a relative speed of 0.8c. The Huns have a laser cannon at the rear of the rocket that shoots a deadly laser beam at right angles to the...

Hello This is a part of a simple paper about special relativity [PLAIN]http://img15.imageshack.us/img15/8789/91001769.jpg I don't understand the assumption in the red box .. why are they all squared ? thank you

The Lorentz transformation are given by (see the attachment) x'=(x-vt)/√(1-v^2/c^2 ) t'=(t-vx/c^2)/√(1-v^2/c^2 ) Let us transform the event (10^100 m,1sec) in the x-frame to the x'-frame that is moving in the usual geometry with the speed v=10^(-10) c. Could you see that that t'≈-10^81...

Hello I have been having trouble understanding equation 14.25 in Bjorken and Drell "Relativistic Quantum Fields" and how exactly it gets to it. Also I would like to explicitly find/derive what the operator gauge function is. Can anyone help please?

In the process of proving that the d'Alembert operator https://www.physicsforums.com/attachments/31306 is invariant under Lorentz transformations, it was required to commute two terms in the following expression for the transformed operator, which was obtained by switching the index on the...

I'm trying to teach myself special relativity. I use the book 'Introduction to Special Relativity' by Wolfgang Rindler. I have a question about length contraction. We consider 2 particles traveling along the x-axis of a reference frame S with a constant distance between them. We can always go...

Homework Statement 2 particles are created in a high-energy accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory is 0.650c, and the speed of each particle relative to the other is 0.950c. What is the speed of the second particle, as measured...

Is the d'alembertian of lorentz transformation matrix 0? and why? would it be 0 because it lorentz invariant? thanks

Ok so I am attempting to get a "feel" of the Lorentz equations. For a observer O' moving with velocity v respect to a observer O along the x direction the transformed variables are x and t. x' = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}(x - vt) t' = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}(t -...

\alpha=\left(\begin{array}{cccc} \gamma& 0&0& -\beta\gamma\\ 0&1& 0 & 0\\ 0 & 0 & 1 & 0\\ -\beta\gamma & 0 & 0 & \gamma \end{array} \right)x'^{\mu}=\alpha^{\mu}_{\nu} x^{\nu} \alpha is Lorrentz transformation matrix. Can I see something more about it? . It's symmetric. That is important...

x'=a_{11}x+a_{12}y+a_{13}z+a_{14}t y'=a_{21}x+a_{22}y+a_{23}z+a_{24}t z'=a_{31}x+a_{32}y+a_{33}z+a_{34}t t'=a_{41}x+a_{42}y+a_{43}z+a_{44}t \vec{u}=u\vec{e}_x Coefficients a_{nm}=a_{nm}(u) Why I suppose that coefficients are function only of velocity u? Inverse relations...

1. Homework Statement : Consider a two dimensional Minkowski space (1 spatial, 1 time dimension). What is the condition on a transformation matrix \Lambda, such that the inner product is preserved? Solve this condition in terms of the rapidity. 2. Homework Equations : Rapidity Relations...

i am reading Lillian R. Lieber's book on the einstein theory of relativity and i am a bit confused on page 65. she wants to take the equations: x=x'cosθ - y'sinθ y=x'sinθ + y'cosθ and compare them to: x'=β(x-vt) t'=β(t-vx/c2) she takes c as one so: x'=β(x-vt) t'=β(t-vx) she...

In Einstein's book Relativity he provides a derivation of the LT. link here http://www.bartleby.com/173/a1.html" In step 3 he brings in constants λ and μ and now I am lost. In the equation (x'-ct') = λ(x-ct) - isn't this the same as "zero = anything X zero"? How did λ and μ get...

In special relativity, velocity dependent forces transform. Let us then consider frictional forces, such as drag, which are velocity dependent in the first order. Do two observers moving relative to a third body measure different frictional effects?

Homework Statement Muons, which have a half-life of 2 x 10-6 s, are formed in the Earth's atmosphere at an altitude of 10 km. If they travel normal to the Earth's surface, and one half of them reach it before they decay, what is their velocity? Homework Equations Lorentz...

If an observer O' see a body that moves with constant velocity Ux along the axis x' in a positive direction. What is the velocity VxO of body observed by O? That is all the information I have. Can you help? :blushing:

Using the Lorentz transformation, at what speed relative to speed of light c must you travel so that your length along the direction of motion is seen to decrease by a factor of 2? For this speed, hwo much would your mass be increased? Please show steps, I'm confused with this question!

From this link http://en.wikipedia.org/wiki/Introduction_to_special_relativity" In the section entitled "Invariance of Length: The Euclidean Picture" the article discusses how rotations within an n-dimensional space keep length invariant. However, if you rotate and object into a higher, n+1...

I'm studying for my modern physics final and this problem is giving me trouble; Q: In a frame S, two events have spatial separation deltaX= 600m, delta y and delta z = 0, and a temporal separation deltaT= 1micro second. A second frame S' is moving along the same axis with nonzero speed v...

Let L_w be a Lorentz transformation between to systems that coincide at t=0(paralell axes assumed) and with relative velocity w along x_1. If L_u is the Lorentz transformation when the relative velocity u is in any direcction then we have that L_u=R_2 L_w R_1 where R_2 and R_1 are sapce...

Homework Statement 3. At what speed (measured in units so c = 1) must the train be moving in order for the points(X,T) = (1,1) and (X,T) = (5,2) to be simultaneous in the (X',T') coordinate system? Homework Equations Disclaimer: I'm not actually in a physics class, I'm in an elementary...

I have a question which i believe is pretty standard, spaceship traveling towards space staion at 0.80c it fires a missile at 0.40c what is the speed of the missle observed by the space station I'll tell you where I am at; I have set 2 inertial frames. A being that of the space station and...

Is there a difference between the Lorentz velocity transformation and the relativistic velocity addition? They give the same result...

1.) problem statement Relativistic protons that have a certain speed "v" are selected by measuring the time it takes the proton to travel between two detectors separated by a distance "L". Each detector produces an electronic pulse of very short duration (LaTeX Code: \\Delta t << L/v) when a...

Homework Statement two photons travel along the x-axis of S , WITH A CONSTANT DISTANCE L betweenthem. Prove that in S's the distance between these photons is L(c+v)^1/2/(c-v)^1/2. Homework Equations x'=gamma*(x-vt), x=gamma*(x'+vt), t=gamma*(t'+vx'/c^2), t=gamma*(t'-vx'/c^2) The...

Hello, I am new to the forums and I hope this fundamental topic has not been previously treated, as these forums don't seem to have a search function. I am studying general relativity using S. Carroll's book (Geometry and Spacetime) and I am having a fundamental problem with basis vectors under...

We know that many books have deduced Lorentz transformations through rigorous maths and they add little to our visions about what's going on. But in the pdf I have attached, I have tried to deduce this transformation with logical arguments. It is really simple and no tensors have been included...

Though I believe I have understood some basic ideas, theories and mathematic formulas of SR, I still have a pretty fundamental question: Many textbooks start SR with a light clock consisting of two mirrors and a light blip bouncing in between, claiming that when the light clock moves, the...

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...