Interactive Minkowski diagrams tool

[Ibix]

Selecting a scenario doesn't choose a velocity to boost, at least for me.

I didn't expect it to. You should, however, be able to click on a time-like line (one steeper than 45 degrees) and then click on the "Boost to selected line rest frame" button to boost to the frame where that line is vertical. If not, let me know.

I think you should include an example of how to read the diagrams for some of the secarios, and how the diagram explains or not the paradox.

It did occur to me - maybe next week. The short version is that you are looking at a displacement-time graph, with time vertical and displacement horizontal. Something stationary gives a vertical line; something traveling at c gives a 45 degree sloped line. In Newtonian physics, you could transform into the rest frame of a moving object by shearing the graph until the line of interest was vertical. In Einsteinian physics, the transform is a little more complex - and these diagrams are a great way to start building up intuition for what the Lorentz transforms are doing.

 

[Ibix]

At the rist of complicating the diagram too much, you might also like to consider drawing lines from the events through the origin -- the events along different curves are already lined up for this. For the green area, this would then be a grid for Rindler coordinates -- see the first diagram in the Wikipedia Rindler coordinates article.

The whole diagram would then be the Minkowski geometry equivalent of a rotating wheel with spokes in Euclidean geometry.

No time right now (could do with time-dilating my office), but I think it's worth a look. I think I might do that as another button, since it might get a bit busy, as you say.

 

[Cap'n Refsmmat]

I actually worked on a relativity simulator like this a couple years ago: http://www.refsmmat.com/jsphys/relativity/relativity.html

Different idea, though. Instead of letting the user construct a Minkowski diagram, it has a set of built-in scenarios (common teaching examples). It can display the Minkowski diagram or a 2D view of the scene. We also added in Doppler shifting for fun -- if you switch on "Apparent positions" in the Settings menu, you'll see the locations of objects as they would be seen from the cross mark at the center of the screen.

I used it a couple of times in a modern physics course to show examples, but now I've moved out of physics and don't have a good use for it. It's open source, so feel free to play with it.

 

[Ibix]

At the rist of complicating the diagram too much, you might also like to consider drawing lines from the events through the origin -- the events along different curves are already lined up for this. For the green area, this would then be a grid for Rindler coordinates -- see the first diagram in the Wikipedia Rindler coordinates article.

The whole diagram would then be the Minkowski geometry equivalent of a rotating wheel with spokes in Euclidean geometry.

Done! There are two buttons, one for hyperbolae only and one for hyperbolae with spokes. It's quite hypnotic to watch them boosting.

 

[edguy99]

Very nice, I have put it in my bookmarks. Thanks for posting.