Usefulness of Diagrams for Relativity: 1-5

[kent davidge]

On a scale of 1 to 5, how useful do you think are diagrams for understanding / studying special relavity? What about general relativity?

 

[kent davidge]

I'm asking this because I always feel like the equations have the last word on every subject, so that I have always put diagrams on the side in my studies.

But if I find them to be useful, then I will go towards them more.

 

[Ibix]

The equations are the last word - the only word, really. That doesn't mean that diagrams can't be a useful way of displaying the information. For example, I use Minkowski diagrams all the time because I am good at visualising things like that, and I can see how events move around as I change frames.

If you find them useful, use them. If you don't, don't.

 

[vanhees71]

Well, I'm not so decided about the (didactical) usefulness of Minkowski diagrams. My own problem with them is that I'm of course trained mostly in Euclidean geometry. At high school there's not even any other geometry taught (it's a shame, but at least our grand parents also learned about spherical geometry in high school, but in Germany the level of education in the STEM subjects is monotonously decreasing over time). That's a problem when it comes to the Minkowski plane, which is what's really depicted in the Minkowski diagram. There the measures are hyperbolic and the (1,-1) signature of the Minkowski plane's pseudometric is the really important concept to learn. So when you want to (semi-)quantitatively read off things from the diagram you have to carefully construct the unit lengths on the temporal and spatial axes of different inertial reference frames. I like geogebra to do this, because there you can directly use the equations (e.g. just to draw the unit-distance time- and spacelike hyperbolae to indicate marks of unit Minkowski distances on the coordinate axes of any inertial frame). For me usually the formulae are much simpler to understand than to read off a Minkowski diagram, because it's hard to look at it in the proper "hyperbolic view".

 

[martinbn]

What diagrams do you have in mind? Penrose diagrams are extremely useful.

 

[Ibix]

Well, I'm not so decided about the (didactical) usefulness of Minkowski diagrams.

I don't teach apart from what you see here, but I did find that Minkowski diagrams were the thing that made SR "click" for me. I don't use them as a substitute for maths, but they're a great support tool. I can visualise the hyperbolae and have a rough idea what a Lorentz transform ought to do to a scenario before I do the maths. I've found similar utility in a Kruskal diagram.

It's definitely a personal thing, though. I have always thought in visual terms so I find visual displays extremely useful as an aid to the maths.

 

[vanhees71]

Yes, sure. I also use them regularly, and I think many students get a better understanding of the quite difficult kinematical concepts of relativity. I think one has to provide both, the algebraic and the geometric approach (including visualization in terms of Minkowski or even more complicated diagrams in GR) to provide the best approach of understanding for different learning approaches.

 

[pervect]

One of our regular posters here has a very nice published paper about using space-tiem diagrams in SR, entitled "Relativity on rotated graph paper".

Basically, if one is able to draw the space-time diagram of a light clock, there's a simple rule that a unit light clock has a unit area when drawn at a scale such that light beams travel at 45 degree angles.

The problem is that it seems difficult to get PF readers to draw space-time diagrams. And consequently, it seems to be difficult to get them to look at , interpret, and understand space-time diagrams that others have drawn.

The key point of the technique is being able to draw the space-time diagram of a light clock in the first place. Given this, it's not hard to scale the diagram so that light travels at 45 degree angles, and the light clock has a unit area. And that is all that's really needed to use this graphical technique.