What software can I use to make space-time diagrams?

[phoenix-anna]

TL;DR

For spacetime diagrams like those is Spacetime Physics, matplotlib and PowerPoint are likely not suitable.

In a few days, I will be hosting a Zoom-based meetup in which I will be explaining the Twin Paradox (time dilatation) and the Pole-in-a-Barn paradox (Lorentz contraction). To this end, I will need to make graphics of space-time diagrams like those in Wheeler's book Spacetime Physics. Can anyone suggest software that will be useful for this purpose? My experience with PowerPoint suggests that it is unsuitable and, since the axes are no longer perpendicular, most plotting software (such as Python's matplotlib) will likely also not be useful.

 

[vanhees71]

I find geogebra very useful for spacetime diagrams. You can program everything in terms of formulae, introduce interactive elements to change parameters, etc. For interactive use it's pretty comfortable. To make pdfs for your manuscripts is a bit cumbersome but also possible.

 

[Dale]

Summary:: For spacetime diagrams like those is Spacetime Physics, matplotlib and PowerPoint are likely not suitable.

Can anyone suggest software that will be useful for this purpose? My experience with PowerPoint suggests that it is unsuitable

I am not sure why you think that. My first spacetime diagrams were in PowerPoint. I use mostly Mathematica now.

For PowerPoint turn on snap to grid and use v = 0.6 c so that everything is nicely on the grid.

 

[robphy]

I'll give a list of some of what I have used.
But, of course, you need to decide what you want to draw,
and how you want to draw it and maybe share it,
and consider how easy it is for you to do it.

• I started drawing my diagrams in PowerPoint as @Dale did. (A few times I used InkScape.)
• I moved to Maple in order to draw diagrams programatically.
  as in https://arxiv.org/abs/physics/0505134 "Visualizing proper-time in Special Relativity"
• For papers, I used LaTeX, pstricks ( https://en.wikipedia.org/wiki/PSTricks )
  https://arxiv.org/abs/1111.7254 "Relativity on Rotated Graph Paper"
  (If I do something like this again, all within LaTeX, I might use
  https://en.wikipedia.org/wiki/PGF/TikZ or
  https://en.wikipedia.org/wiki/Asymptote_(vector_graphics_language) )
• Then I found GeoGebra (https://www.geogebra.org/ a free dynamical geometry system) as @vanhees71 did.
  
  Things can be done geometrically (find the intersection of this line and this conic)
  programmatically (draw a collection of these objects, animate this...)
  and interactively on the web [without having the user download additional software].
  
  I develop using the desktop version.
  Then I upload to the geogebra.org website so that it can be viewed on the web.
  [Maple, LaTeX, GeoGebra can produce vector graphics files
  that can be imported into PowerPoint as vector graphics.]
  
  https://www.geogebra.org/m/XFXzXGTq (Light-Clock, Michelson-Morley)
  https://www.geogebra.org/m/ETgBGFSX (accelerated observer; Bell Rocket/Spaceship)
  https://www.geogebra.org/m/HYD7hB9v#chapter/124221 ("Relativity on Rotated Graph Paper")
  https://www.geogebra.org/m/kvfsq664 (Rotated Graph Paper update)
  https://www.geogebra.org/m/Ny2s7H7N (coordinate systems)
  
  To look inside, click on the three vertical dots in the upper right corner.. Details.. download.
  Updates to Geogebra visualizations can use the same URL.
• I also find Desmos ( https://www.desmos.com/ ) to be useful.
  I've been doing more with Desmos... but it's tricky to do some things that are easier in GeoGebra.
  
  https://www.desmos.com/calculator/sk2zhnmjmm (spacetime diagrammer, v6)
  https://www.desmos.com/calculator/dha8izuxz1 (spacetime diagrammer, v5)
  
  https://www.desmos.com/calculator/r4eij6f9vw (v3)
  https://www.desmos.com/calculator/wm9jmrqnw2 (v3, time horizontal)
  
  NEW:
  https://www.desmos.com/calculator/tjngj63cat (accelerated observer)
  
  Updates to the Desmos visualizations result in new URLs.
• One can also try VPython/Glowscript.
  
  http://visualrelativity.com/LIGHTCONE/LightClock/
  http://visualrelativity.com/LIGHTCONE/LightClock/VisualizingProperTime-pair-LengthContraction.mp4
  http://visualrelativity.com/LIGHTCONE/LightClock/VisualizingProperTime-TwinParadox-v=8-A.mp4
  (The videos are frame-by-frame screen captures.)
  
  This needs to be updated from an ancient version of VPython to
  Glowscript [ https://www.glowscript.org/ ] or modern VPython.
  
  examples of Glowscript
  https://trinket.io/library/trinkets/6b2b9ad98b (doppler for sound)
  https://trinket.io/library/trinkets/3e25027ad1 (gauss law setup code)
  
  Updates to Glowscript visualizations can use the same URL.

 

[vanhees71]

I am not sure why you think that. My first spacetime diagrams were in PowerPoint. I use mostly Mathematica now.

For PowerPoint turn on snap to grid and use v = 0.6 c so that everything is nicely on the grid.

Sure, you can use any software that's capable making plots to make spacetime diagrams. Another way is of course gnuplot. My suggestion of geogebra was mainly based on the purpose to use it in some online-lecture (e.g., via zoom), where geogebra has the advantage that you can prepare it beforehand and interactively easily changing parameters with "sliders" etc.

 

[robphy]

since the axes are no longer perpendicular, most plotting software (such as Python's matplotlib) will likely also not be useful.

The strategy I used to deal with the Minkowski-perpendicular (but not necessarily Euclidean-perpendicular) axes is to think and compute vectorially.
First, determine the basis-vectors (and related structures, like my clock diamonds),
then express everything else as multiples or sequences of those basis-vectors.

Effecting a boost is achieved by boosting the basis-vectors.
While the diagram may appear deformed in the diagram frame,
the multiples of those basis vectors (i.e, the components in the original frames) won't change.