EBK AN INTRODUCTION TO MODERN ASTROPHYS
EBK AN INTRODUCTION TO MODERN ASTROPHYS
2nd Edition
ISBN: 9781108390248
Author: Carroll
Publisher: YUZU
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 4, Problem 4.1P
To determine

The derivation of Lorentz transformation Equations.

Expert Solution & Answer
Check Mark

Answer to Problem 4.1P

The derived equations are.

x=xut1u2c2y=yz=zt=tuxc21u2c2

Explanation of Solution

Assume an inertial frame with space and time coordinate as S=(z,y,z,t) and another inertial frame as S=(x,y,z,t).

The coordinates of second inertial frame can be expressed as

    x=a11(xut)y=yz=zt=a41x+a44t

Write the expression for spherical wave front.

    x2+y2+z2=(ct)2        (1)

Here, ct is the radius and coordinates are x, y and z.

Write the expression of wave front for second inertial frame.

    EBK AN INTRODUCTION TO MODERN ASTROPHYS, Chapter 4, Problem 4.1P x2+y2+z2=(ct)2        (2)

Conclusion:

Substitute a11(xut) for x, y for y, z for z and a41x+a44t for t in Equation (2).

    (a11(xut))2+y2+z2=(c(a41x+a44t))2x2(a112a412c2)2(a112u+2a41a44c2)xt+y2+z2=(a112u+a442c2)t2        (3)

Compare Equation (3) with (1).

a112a412c2=1a112u+2a41a44c2=0a112u+a442c2=c2

Solve the above equations.

x=xut1u2c2y=yz=zt=tuxc21u2c2

Thus, derived Equations are

x=xut1u2c2y=yz=zt=tuxc21u2c2

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Text book image
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
Text book image
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON
Length contraction: the real explanation; Author: Fermilab;https://www.youtube.com/watch?v=-Poz_95_0RA;License: Standard YouTube License, CC-BY