Spacetime Diagrams - Help With Drawing

In summary, when drawing spacetime diagrams for these two scenarios, it is important to remember that the length of an object is relative to the observer's frame of reference and to label the axes and important points on the diagram.
  • #1
Lissajoux
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Homework Statement



I need to draw carefully labelled spacetime diagrams (one per section) to illustrate the following:

a) The length of a 'rod' which is exactly [itex]1.0[/itex] light seconds long when at rest along the x′-axis in one frame, and which is moving along the x-axis at [itex]0.866c[/itex] in the diagram rest frame.

b) The addition of velocities as viewed from a spaceship, for the case of a missile launched at [itex]+0.80c[/itex] relative to the spaceship, itself traveling at [itex]+0.60c[/itex] relative to the Earth. Take the launch time to be at [itex]t=0[/itex] as the spaceship passes the Earth.

Homework Equations



Within the question statement and solutions, as relevant.

The Attempt at a Solution



I can't figure out how to draw the scenario in (a). No idea. Have managed to do some simpler ones and the one in the second part of this post, but I just can't get my head around how to draw this one.

I've had a go at (b), this is what I have for the spacetime diagram (see the included image) but I'm not sure if the scales and labels are correct, I just made the 3,4,5 values as that was convenient numbers that seem to work from some quick calculations, I think I can just do that.:

http://yfrog.com/5nspacetimediag1j

Any help, particularly with (a) as I think (b) is pretty much correct hopefully, would be much appreciated. :smile:
 
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  • #2




For part (a), the key concept to remember is that the length of an object is relative to the observer's frame of reference. In this case, we have two frames of reference: the rest frame (x') and the moving frame (x). We can represent these frames on a spacetime diagram using the x and x' axes.

To illustrate the length of the rod, we can draw a vertical line on the x' axis to represent the rod's position when at rest. Then, on the x axis, we can draw a diagonal line to represent the rod's position when moving at 0.866c. The length of the rod can be measured by the distance between these two lines on the x axis.

For part (b), your spacetime diagram looks correct. The scales and labels can be adjusted based on the specific values given in the question. Keep in mind that the scale on the x axis may not be the same as the scale on the t axis. Also, remember to label the axes and any important points on the diagram.

I hope this helps. Keep up the good work!
 

1. What is a spacetime diagram?

A spacetime diagram is a graphical representation of the relationship between time and space in Einstein's theory of relativity. It shows how an event can be viewed from different reference frames and how time and space can be distorted by gravity.

2. How do I draw a spacetime diagram?

To draw a spacetime diagram, you will need to choose a scale for the space and time axes. Then, plot the position of an object at different points in time. You can also add the world lines of other objects to show their paths in spacetime.

3. What is the purpose of a spacetime diagram?

A spacetime diagram is used to visualize and understand the complex relationship between time and space in Einstein's theory of relativity. It can also be used to analyze and interpret the behavior of objects in different reference frames and in the presence of gravity.

4. How do I interpret a spacetime diagram?

In a spacetime diagram, the horizontal axis represents space, and the vertical axis represents time. The slope of an object's world line represents its velocity, and the curvature of the world line represents its acceleration. The closer the world lines of two objects are, the more closely they are moving together in space and time.

5. Can a spacetime diagram be used to study black holes?

Yes, a spacetime diagram can be used to study black holes. It can show how the strong gravitational pull of a black hole can distort the fabric of spacetime, causing objects to follow extreme paths and even get pulled into the black hole's event horizon.

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