Space-Time Diagrams: Explaining & Setting Up

[w3390]

I have just started a class that deals with relativity. My professor uses space-time diagrams all the time but has never bothered to fully explain them. Every time I have questions about my homework problems, people tell me to work it out by drawing a space-time diagram. Could anyone explain to me how to set up one of these diagrams and what everything on the diagrams mean? Any help is much appreciated.

 

[tiny-tim]

Hi w3390!

Does this help? … http://en.wikipedia.org/wiki/Space_Time_Diagram"

 

[Dale]

A spacetime diagram is essentially just a plot of position vs. time. The main tricks about them are to remember that time is plotted on the vertical axis and time is scaled so that c=1 (meaning that the worldline of a pulse of light is drawn at 45 degrees.

 

[w3390]

Thanks for your help guys. However, my problem usually is when I am given some problem and told to draw this diagram. For example, if there were two spaceships(one at rest at the origin and one traveling some fraction of c) I get lost when trying to draw out the picture and draw the path the signals move when the two ships send signals to each other. This may just be one of those things you have to do for a while before you really understand it.

 

[Fredrik]

In that particular case, the motions of the two spaceships are represented by two straight lines. One of them coincides with the t axis, and the other has slope 1/v, where v is the velocity of the other ship (in units such that c=1) relative to the first. You also need to understand that the corresponding simultaneity lines (a line representing events that are all assigned the same time coordinate by some other observer) have slope v.

The world line of a light signal is always +1 or -1. (Edit: That should be "The slope of the world line...")

Perhaps you should find a slightly more difficult example and tell us where you think it starts getting difficult.

 

[w3390]

Actually, thanks a lot Fredrik. What you just said made complete sense and solves most of the problems I have been facing conceptually. But just to put into action what you have said, if the spaceship at the origin were to send the spaceship in motion a signal, the line would have to follow the sloped coordinate grid on its way to the moving spaceship?

 

[jtbell]

What sloped coordinate grid?

The light signal would be represented by a line angled upward at 45 degrees, starting from the emission event (position and time). The point where that line intersects the other spaceship's worldline gives you the position and time for the reception of the signal.

 

[w3390]

Okay, so whenever a signal is emitted that travels at the speed of light, the line is always drawn parallel to the 45 degree line?

 

[tiny-tim]

Okay, so whenever a signal is emitted that travels at the speed of light, the line is always drawn parallel to the 45 degree line?

Yup (±45º)!

So, for example, a signal sent to and fro between the spaceships (or anything else) will zig-zag at 45º to the axes.