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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

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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

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.

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

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'.

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