Stadium/pea analogy + why this measurement is insane

1:14:10>> The the proton at the center of the hydrogen atom is measured in phento which is 10 theus15 m. >> Okay. >> The hydrogen atom itself is about an angstrom which is 10us 10. Okay. So there's a there's a 100,000 full difference between the size of a hydrogen atom and the size of a proton at the center of the hydrogen atom. And to visualize this unimaginable scale, I wanted to consider an analogy. Okay. >> Okay. >> If a single hydrogen atom is expanded to the size of a professional sports stadium, >> then the proton that's at its center is like the size of a P. >> Oh my god. >> At the 50 yard line. >> Oh my god. >> That's not That's not the worst part,

1:14:51though. Okay. In order to discern the size of the P, we are looking at an electron that is in the grand stance. >> Oh my god, >> this is so >> You see what I'm saying? Yeah, that's ridiculous. >> Because the electron is hanging out all the way out here. >> We're looking at the behavior of these electrons that are hanging out at the grand stands to figure out how big is the P on the 50 yard line. >> I just I have no I have nothing. I just don't even I don't even know what to say. insane that we can do these kinds of things. >> That's what I'm saying. That like that's Yeah. Cuz I'm trying to even think about how you would do that at macro scale. >> Yeah. Yeah. [laughter] Yeah. If I had a P. >> Yeah. Yeah. If I had a chaotic,

1:15:33>> what kind of telephoto? >> Oh, yeah. Right. Would I even >> lens would I need at the at the grandstand >> to be able to >> Yeah. >> Okay. So, the this is something that is so infantestimally small. Uh and meaning that the way in which we do all like the engineering we do to even be able to do this stuff has to be able to operate at these impossibly small >> Yes. >> scales. >> Yeah. And at impossibly small error, >> right? >> That's the main part. >> Right. Right. >> You're chasing down like 12 decimal places. >> Right. >> Okay. >> Right. That's a really important that's a really important point because it's not just like oh we got to know it's like >> to Yeah. to a level of specificity where

1:16:1312 dB is crazy, >> right? Which it's insane. It's like, no, it's not that. It's actually >> this. >> Yeah. Okay. >> Oh my god, my brain. >> Yeah. It's it's it's absolutely nuts. Okay. So, here here's how we're going to do it. >> Okay. We are going to calculate the transition frequency between different >> orbitals. Okay. >> Okay. When we do that, this is the equation of what an electron sees when it's on the outside. This is the binding energy of atomic hydrogen. So what is the energy of an electron that's bound to the proton in the center? What I love about this is this is the first line of their paper. The binding energy of atomic hydrogen can be expressed as

1:16:54>> and it's a giant equation. >> For those listening there's like I don't know 23 different characters and it's just it is >> and it depends on crucially it depends on two things okay it depends on something called the Ryberg constant which is like a fundamental energy scale. Okay. >> And it depends on the proton charge radius. Okay. >> Now, those are two different unknowns, >> right? And in order to figure out what those two unknowns are, you need two different observations. You can't just rely on one. So, you can't just rely on a single atomic >> energy spacing. You need to observe two different transition frequencies. I see. >> You need to observe two different colors. Yes. That are coming out of my atomic hydrogen.

1:17:34>> Okay. That makes sense. That makes sense. Now, the first one is the anchor measurement. That's already been done before. Okay, this is the ultra precise 1s to 2S transition. What they're doing in this paper is the 6p to 2s transition. The 6p orbital looks like that. It's dumbbells on top of it's like a Russian nesting doll of dumbbells. Okay, what they're looking for is an electron in this particular energy state going down to the 2s state. M okay what they want to do here is observe that transition frequency >> and this from the the 2s state was the the larger spherical state that we >> that we had talked about earlier this is even bigger than that this is like way out in the grandstands to let's say like

1:18:15on the on the sidelines >> right the electron is going from the grandstand all the way to like the the really nice seats >> and that transition is what they're trying to look for >> got it got it okay yep yep >> let's talk about why this is even an issue