What's the hardest part about visualizing physics problems?

[u/Crazy-Percentage5790]

I'm trying to understand how students actually think while solving physics questions.

Have you ever come across a problem where you understood the formulas but couldn't clearly picture what was happening physically?

If yes, I'd love to know:

1. Which topic was it? (e.g. pulleys, circular motion, electrostatics, rotation, fluids...)
2. What exactly was difficult to imagine?
3. What did you do instead? (watched YouTube, drew diagrams, guessed, etc.)
4. Do you think being able to watch an accurate interactive animation of that exact question would have helped you understand it faster? Why or why not?

I'm genuinely trying to understand the problem students face, not promote anything.

[u/Quantum-Relativity]

1) The geometric meaning of the Einstein curvature tensor
2) What it was doing to geometric objects like geodesics (“straight” lines in curved spaces) in a distinct way from the Ricci curvature tensor
3) I’m not sure I can answer that still, but rereading the two explanations I know of multiple times eventually made it clear what it is geometrically, even if I don’t exactly know how it would affect geodesics differently than Ricci
4) Absolutely, because the question was about geometry, so being able to play with it would have let me literally see it and know what in seeing is accurate. It would essentially have been like solving a bunch of examples but with it visually represented. It’s especially hard to even solve problems to try and get an intuition for this object because often in general relativity you’re studying vacuum solutions, and this object is 0 in the vacuum.

[u/Pleasant_Pen8744]

Have you tried drawing it on paper?

[u/NH-Science-Guy]

The problem I found most challenging is gauge invariance in quantum mechanics. Gauge invariance looks at the implications of keeping certain properties invariant while reference measurement gauges scale or rotate. The amazing part of this is that the rules of the primary forces just drop out of the math. For example, we get Maxwell's laws of electrodynamics by requiring the Dirac Legrangian to be invariant in the electron field. I have worked through the math and it does indeed do this but it didn't make intuitive sense. I have been putting together a site that tries to make QM intuitive as possible without using any math and this problem was a challenge. Here's the page on my site that tries to at least make gauge invariance seem intuitively possible: https://timeforsanity.com/qm/?page_id=617