# Physics of Rock Climbing: Part III

It’s been a while, but you know what time it is. It’s time for another dose of Physics of Climbing. If you’re not caught up, be sure to check out our quantum mechanics and classical mechanics articles. This week, we get to talk about my favorite area in physics: relativity. In particular, we’re covering climbing through the lens of special relativity (SR). Don’t worry, general relativity is next!

If you’ve ever heard of Einstein, you most likely heard of him because of his developments and discoveries in relativity. Thus, today’s hypothetical climber’s name is Albert.

Albert is one of the most “granola” climbers out there. He’s super into nature, and he struggles to see how he, a human, is any more important than the rock he climbs. As he climbs his warm-up, Maxwell the Effort, he wonders what the rock sees. Would it be exactly the same, just from a different angle?

Since this stuff is interesting, of course the answer to that question is no. But, if they don’t agree, which one of them is correct? Albert had a hard time believing his perspective was any more valuable than the rock’s. Confused, Albert tries to take a step back from the problem (conveniently during a back step move on the route). He constructs two inertial (constant speed) frames: one is his own, climbing Maxwell the Effort, and the other is the rock at the chains. From Albert’s perspective, it looks like the chains are moving down closer to him at a constant speed, but from the rock’s perspective, it looks like Albert is moving up closer to the chains. Albert insists there is no preferred or correct frame. Indeed, he realizes everything is just relative, and there’s really no such thing as absolute time.

This has some major consequences; the details are too technical to discuss here, but trust me, Albert knows what he’s talking about. As Albert is climbing, he actually experiences time slower than his stationary belayer or the rock. Although these effects are very small at low speeds, we can see them at higher speeds (e.g. on planes or satellites). Nevertheless, the time Albert says it took him to send his route will actually be shorter than what his belayer claims. You can think of Albert’s watch as ticking slower than his belayer’s. However, as Albert is climbing, he will also claim the route is shorter than his belayer thinks. You can think of Albert’s ruler as being longer than his belayer’s, which looks contracted to Albert. These realizations delighted Albert because he proved that not only were his and the rock’s perspectives equally valid, concepts of space and time are equivalent as well (they make no sense without each other).

I will leave you with a final consequence of SR that I ponder all of the time: setting the cosmic speed limit, light never ages. That is, if a photon from your screen started its stopwatch at, say, the beginning of time, it would still read 0:00.00 (no passage of time).

Please comment your thoughts and questions! Keep an eye out for our next installment…we might just get to hang out with Albert again.

## 14 Replies to “Physics of Rock Climbing: Part III”

1. Ha! Finally my inability to climb 5.12 is explained! As I reach desperately for a molecule-sized finger hold, my mass distorts space-time, pushing that hold just out of reach! I then fall – noting briefly that I’m either approaching the ground or it’s approaching me. But my inevitable crash landing is, as they say, all relative. 😉

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2. This is a fascinating aspect of climbing — and trail running — “As Albert is climbing, he actually experiences time slower than his stationary belayer or the rock.” Great post!

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3. I am not very good at Physics but I somehow managed to grasp a general understanding of the relativity between time and space. Gee, thanks, Albert, for being such a good example!

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