Originally Posted by wsabol
I feel like I could nit pick definitions(semantics) with you all day, but I won't, this isn't a physics forum, haha. Interesting problem OP. I imagine for two (very massive) sticks alternating are close to the speed light, we'd have a situation close to what happens when two black holes orbit each other are close proximity. The two gravity wells tangle up and do all kinds of crazy stuff, worm holes too if I remember correctly.
Anon: Great idea on the calcs. The way I see it, the stick accelerates coming up and coming down during the stroke. In other words, its 0 m/s at the top of the stroke (10 cm above head), 3e8 m/s as it heads the head. Its not just traveling 3e8 m/s the whole time :) Taking that into consideration, my calcs show that your stick will hit the head at the speed of light if you play 16th notes at 67,500,000,000,000,000,000 bpm.
Wouldn't the sticks, in relation to one another, fall more under the Principal of Mass-Energy Equivalence (E=mc^2) as opposed to relativity of time? Relativity of time clearly states there must be two observers for time dilation to occur, and at least one of them must be in motion.
Are you calculating the bpm as the distance they travel or their resulting speed at that many strokes?