What is the World Line Diagram for Light Pulses in Two Frames?

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SUMMARY

The discussion focuses on the world line diagram for light pulses emitted from a stationary source in the O frame and received by an observer in the moving O' frame. The key findings indicate that the temporal separation of the pulses, as measured in frame O, is (cτ)/(c-v), and the spatial separation is (cτv)/(c-v). The participants successfully derived the intersection points of the light pulses and the observer's world line, confirming the calculations align with the principles of special relativity.

PREREQUISITES
  • Understanding of special relativity concepts, particularly time dilation and Lorentz transformations.
  • Familiarity with world line diagrams and their representation in spacetime.
  • Basic algebra skills for solving equations involving time and space coordinates.
  • Knowledge of the speed of light (c) and its implications in relativistic physics.
NEXT STEPS
  • Study Lorentz transformations and their application in different inertial frames.
  • Learn how to construct and interpret world line diagrams for various scenarios in special relativity.
  • Explore the implications of time dilation and length contraction in moving frames.
  • Investigate the relationship between simultaneity and observer motion in special relativity.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the implications of special relativity, particularly in the context of light propagation and observer effects in different inertial frames.

Andy93
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Homework Statement


A light source at the origin of the O frame emits short pulses of light in interval of \tau as measured in O. An observer located at the origin of the O' frame which moves at velocity v with respect to O along the x-axis, receives these light pulses.
Use a world line diagram to show the receipt of two consecutive pulses as measured in O if the first is emitted when the frame origins coincide. Show that measured in O the pulses are received at the origin of O' with the temporal separation of (c\tau)/(c-v) and spatial separation of (c\tauv)/(c-v).


Homework Equations





The Attempt at a Solution


The pulses of light travel at velocity c
The receiver travels at velocity v
I have drawn the world line (t-x plot) and I'm pretty sure it's Δt and Δx i need to calculate but I'm not sure how to go about it.
http://img24.imageshack.us/img24/4083/z559.png
 
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Your diagram looks good. Now you're trying to find where the two lines intersect. This is just like what you did in algebra class, except this time the variables are x and t instead of x and y.

Start by figuring out the equations for the two lines.
 
I didn't realize it would be so simple, thanks a lot for the help. It worked out perfectly.
 

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