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

In summary, the conversation discusses a scenario where a light source emits pulses of light at a constant interval in a frame O, while an observer in frame O' moving at a velocity v receives these pulses. Using a world line diagram, it is shown that the pulses are received with a temporal separation of (c\tau)/(c-v) and a spatial separation of (c\tauv)/(c-v) at the origin of O'. The solution involves finding the intersection of the two lines representing the light pulses and the observer's world line.
  • #1
Andy93
3
0

Homework Statement


A light source at the origin of the O frame emits short pulses of light in interval of [itex]\tau[/itex] 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[itex]\tau[/itex])/(c-v) and spatial separation of (c[itex]\tau[/itex]v)/(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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  • #2
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.
 
  • #3
I didn't realize it would be so simple, thanks a lot for the help. It worked out perfectly.
 

1. What is the concept of world lines in relativity?

World lines refer to the path of an object or particle in the four-dimensional spacetime continuum. They show the trajectory of an object's movement through both space and time, taking into account the effects of gravity and the curvature of spacetime.

2. How does relativity explain the concept of world lines?

In the theory of relativity, the concept of world lines arises from the idea that space and time are intertwined, and that the laws of physics are the same for all observers in any frame of reference. The curvature of spacetime caused by massive objects, as described by Einstein's theory of general relativity, explains the observed bending of an object's world line.

3. Can world lines be visualized?

Yes, world lines can be visualized using a space-time diagram, with time on the vertical axis and space on the horizontal axis. The world line of an object is represented by a curve on this diagram, showing the object's position in both space and time.

4. How does the concept of world lines relate to the theory of special relativity?

In the theory of special relativity, the concept of world lines is used to describe the relative motion of objects moving at different velocities. The shape of an object's world line is affected by its speed and direction of motion, as well as the observer's frame of reference.

5. Why are world lines important in understanding relativity?

World lines play a crucial role in understanding the effects of relativity, such as time dilation and length contraction. They also help to explain the behavior of objects in the presence of massive bodies, as well as the bending of light and other phenomena that are observed in the universe.

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