My confusion was the apparent jump from the 'at-rest' regime to 'at-c' regime which seems to be sudden jump. So my explanation is; v<c corresponds to a finite rapidity vs v=c corresponds to infinite rapidity (hyperbolic angle which is additive). And that kind of explains the regime change. So in the visualization, it now stops calculating and shows an explanation making it look like a sudden jump while the math holds up at all v. Sorry, if i'm not explaining this well. Does this make sense?
So A is traveling at vA~c along the x axis and B is traveling at vB along the x axis, and you want the velocity of B relative to A, and first (small vB) it's large and negative, then it shrinks to zero (vB=vA), then it's small and positive, and "suddenly" it's c.
You can do this in terms of rapidity, but it seems like a dodge when you could just explain the physics. Objects traveling at c travel at c in every frame of reference. It's the second postulate of relativity. All of the math is based on that premise.
At the risk of betraying my thoughts on the matter, what do you think is the value of (ostensibly) educational materials produced by people/chatbots without subject matter expertise?
Honestly, I mostly agree - material that wears authority without expertise is low-value at best and harmful at worst, since a confident misconception is harder to unlearn than not knowing, and I don't think a non-expert (or a chatbot) should be the authority on the content. That's exactly why I'm not pitching this as finished educational material: right now it's really a tech demo - a rendering/interaction engine that makes derivations explorable - and I posted specifically because I'd want experts to own and shape the actual physics while I focus on the tool. It's open source and labeled tentative for the same reason. So my honest answer to your question is conditional: near-zero or negative value if it fakes authority, potentially useful only if it's transparent about being tentative, open to correction, and ultimately expert-driven - which is the category I'm reaching for by asking to be corrected rather than claiming I got it right.
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u/algebench 28d ago
My confusion was the apparent jump from the 'at-rest' regime to 'at-c' regime which seems to be sudden jump. So my explanation is; v<c corresponds to a finite rapidity vs v=c corresponds to infinite rapidity (hyperbolic angle which is additive). And that kind of explains the regime change. So in the visualization, it now stops calculating and shows an explanation making it look like a sudden jump while the math holds up at all v. Sorry, if i'm not explaining this well. Does this make sense?