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Lorentz Transformation

The Lorentz Transformation explains how the speed of light is observed to be independent of the reference frame and to understand the symmetries of the laws in electromagnetism. It is in accordance with special relativity, but is derived before special relativity was postulated.
The transformation describes how measurements of space and time by two observers are related. They reflect the fact that observers moving at different velocities may measure different distances, elapsed time and even different orderings of events. This supersedes the Galilean transformation of Newtonian physics because the Galilean transformation is only a good approximation for relativity smaller speeds than the speed of light.

The Lorentz transformation for frames in standard configurations can be shown in the following simple forms:

t^'=γ(t- vx/c^2 )
x^'= γ(x-vt)
y^'=y
z^'=z

Where v is the relative velocity between frames in the x-directions, c is the speed of light and γ is the Lorentz factor.

Energy, momentum and force in special relativity

The Oh-My-God particle was an ultra-high-energy cosmic ray (most likely an iron nucleus) detected on the evening of 15 October 1991 over Dugway Proving Ground, Utah, by the University of Utah's Fly's Eye Cosmic Ray Detector. Its observation was a shock to astrophysicists (hence the name), who estimated its energy to be approxima

Electron-Position Pair Kinetics

An electron-positron pair moves with velocity v=c(beta) in frame O. Annihilation of the pair produces two photons of energies E1 and E2 emerging at angles theta(1) and theta(2), with respect to the velocity (v). Find expressions for the energies E1 and E2 in terms of the electron mass, the speed (beta) and angle theta(1).

Identify and implement the role of fluency in reading and comprehension.

Identify and implement the role of fluency in reading and comprehension. Please see attachments. The primary purpose of reading is to gain meaning from connected text. Important for this purpose is that recognition of text becomes a fluent process. Fluency is considered to be composed of three components: accuracy, automatici

At speed, how long is the garage measured in the car's frame of reference?

Part 1 When parked, your car is 4.98 m long. Unfortunately, your garage is only 4.19 m long. How fast would your car have to be moving (in c) for an observer on the ground to find your car shorter than your garage? Do not enter unit. The answer is not .3983 Part 2 When you are driving at this speed, how long is your gar

Fields, Gauges and Potential

In a certain region of space, we have the potentials shown in the attachment. a) What is the electric field E in this region? b) What is the magnetic field B in this region? c) Given the gauge function in the attachment, find the new potentials V' and A'. d) What is (are) the source(s) that created these potentials? (Note:

Lorentz Transformation and Tilting of Objects

A meterstick is parallel to the x axis in S and is moving in the +y direction at constant speed vy. Show that the meterstick will appear tilted at an angle theta' with respect to the x'axis of S' moving in the +x direction at beta=0.65. Compute the angle theta' measured in S'.

Reference Frames - Proving that Two Events are not Simultaneous in a System

Consider two events in the S-system that occur at different points (x, y, z) and (x2, y2, z2) but at the same time t0. Show that these two events are not simultaneous in the S' system but are separated by a time interval -V*gamm*change in x/c^2 (see attachment for equation written out in symbols).

Electromagnetics - Lorentz Transformation

Show that B^2 - E^2 / c^2 is invariant under a Lorentz transformation.

Electromagnetic fields due to a surface current

See attached file.

Lorentz transformation problem.

A red light flashes at position xR = 3.00 m and time tR = 3.00 x 10-8 s and a blue light flashes at xB = 9.0 m and time tB = 4.80 x 10-8 s. (All values are measured in the S reference frame.) Reference frame S' moves constantly to the right. Both flashes are observed to occur at the same time in S'. a. Find the relative velo

Invariant mass of systems

1. Consider two particles of equal mass m. Determine the system mass for each of the following cases. (a) Both particles are moving in the x-direction with kinetic energies K=5m. (b) One particle moves in the y-direction with K=5m and the other moves in the +x-direction with K=5m. (c) Given that both systems contain tw

Four Momentum in Different Frames

A pion of mass m moves with a speed u in the positive y direction in frame S with parametrs BETAu = u/c and GAMMAu = (1 - BETAu^2)^-1/2. The pion decays into two gammay rays. An observer S' moves in the positive x direction with speed v = (BETA)(c) [this is a different BETA and GAMMA than before] and detects the two photons.

Use the Lorentz transformations to show that the spacetime interval is invariant, &#61508;s'2 =&#61508;s2 for relative motion along one direction.

1. Use the Lorentz transformations to show that the spacetime interval is invariant, &#61508;s'2 =&#61508;s2 for relative motion along one direction. See attached file for full problem description.

References Frames of Causally Disconnected Events

Show that if two events are causally disconnected, their time sequence will be reversed in some inertial reference frames.

Lorentz Transfers

Show that the spacetime interval (delta s) is invariant under the lorentz transfermations: i.e. show that (c (delta t))^2 - (delta x)^s = (c(delta t'))^2 - (delta x')^2 delta s = s1 - s2 delta t = t1 - t2 delta x = x1 - x2 c= speed of light in a vacuum ; 's indicate a different system

Relativistic Time and Length Dilation

Two space ships each 100m long when measured at rest travel toward each other at a speed of .85c relative to earth. a) How long is each ship as measured by someone on earth? b) How fast is each ship traveling as measured by someone on the other ship? c) How long is one ship when measured by an observer on the other?

Using Lorentz Transformations for Proofs

The equation for a spherical wave front of a light pulse that begins at the origin at t=0 is: x^2+y^2+z^2-(ct)^2=0. Using the lorentz transformation show that such a light pulse also has a spherical wave front in S' by showing that x^2+y^2+z^2-(ct)^2=0 in S'.

Determining Motion of Inertial Frame and Coordinates

An event occurs in inertial frame S with coordinates: x=75m, y=18m, z=4m, t=2.0xE-5sec. The inertial frame S' moves in the +x direction at v= .85c. The origins of S and S' coincide at t=t'=0. a) What are the coordinates of the event in S' (x', y', z', t')? b) Use the inverse transform on the results of a to obtain the or

Velocity transformation: What is the speed of ship A as observed from ship B? Of ship B as observed from ship A?

See attached file. Two spaceships approach the Earth from opposite directions. According to an observer on the Earth, ship A is moving at a speed of 0.753c and ship B at a speed of 0.851c. What is the speed of ship A as observed from ship B? Of ship B as observed from ship A? Answers: 0.978 and -0.978

Solve: Time Dilation

Hi. I'm confused about the following problem: Problem: The radar antenna on a navy ship rotates with an angular speed of 0.22 rad/s. What is the angular speed of the antenna as measured by an observer moving away from the antenna with a speed of 0.62c? I don't know how to find delta t and delta t0. Is 0.22 rad/s the proper

Lorentz Transformation

The frames S and S' are in the standard configuration with relative velocity 0.8c along Ox.... See Attachment

Lorentz Transformation

See the attachment.

The Lorentz Transformation

A clock in the moving coordinate system reads t'=0 when the stationary clock reads t=0. If the moving frame moves at a speed of 0.800c, what time will the moving clock read when the stationary observer reads 15.0 hr on her clock? Use Lorentz Transformation.