Wrap-up banter and travel notes

1:22:00can't really do a derivative in the right sense right because the derivative a spatial derivative in some sense is the change between this quantity and this quantity divided by how how far apart they are. Well, if I change this guy and I don't change this guy, now my derivative is really not well defined. If I change them by the same amount, then that change cancels out and my derivative is fine. But if it's a local thing, then the derivative is no longer well defined. But what I can do is I can compensate for it. And um there was um there was a a famous physicist who actually said it's kind of like you know if every city had its own local currency >> and they just decided to change their

1:22:41currency denomination or whatever you would need some way some exchange rate >> to to make sure that I'm still paying for the right amount of stuff. >> Right? >> That's where a gauge field comes in. A gauge field is something you introduce to preserve the local symmetry where it's like okay I changed the phase here but not here. What do I have to do to to compensate for that to make sure that all of my mathematics is still fine then my I can still do a derivative. It's something that becomes like a covariant derivative where it depends on like where I'm taking the derivative. But all of these things introduce this thing called a gauge field which is a new entity. This can also be known as a

1:23:22connection. And the sole purpose of this field is to connect the different symmetry choices that I have in all of these different neighboring points. And it provides a rule on how to compare all of my different thingies. >> It's the like a currency exchange is like is like the easiest analys. >> Exactly. Yeah. And um it turns out that currency exchange is itself a field that is very very much real because that currency exchange has a certain value at each point, right? Depending on this city versus this city, this city versus this city, that that exchange rate has a different value at each point. So it becomes kind of like a field. That makes

1:24:02sense, >> right? Kind of like and so and so that field permeates spacetime. And the real miracle of gauge theory is that that field is when it's curved, when when it like changes, that exerts a force on the stuff that it's affecting >> and that force is it can manifest in real things. For example, in the electromagnetic field, that force is the electromagnetic force. That is the photon. the thing from the field that gauge field >> is like the the electromagnetic for vector that becomes a photon

1:24:44>> okay now this is >> this is getting crazy but that's what Yang Mills was doing dude >> okay >> that's what and Yang Mills was like this is crazy what if I take this to new heights and I start applying it to the the strong nuclear force and the weak nuclear force this is he he was actually at um he he had a shared office at Brook Haven at the time Brook Haven had this thing called the cosmotron and he shared an office with um Robert Mills >> and the two of them start talking about Mills's like fascination with symmetry right and the two of them start thinking okay how can I make this something that has to do with nuclear forces right can I can I make a quantum field theory for nuclear binding that explains all of the

1:25:25physics just based on symmetry it becomes it it's the start of something called Yang Mills theory >> right it was not at its when they devised it it was not at its final form. There were still problems. They were getting these things called like massless particles where like everything had no mass and they're like, "Nah, >> we have some photons." >> Yeah. Yeah. But not everything has no mass. And and and there were still a bunch of things that had to happen. Steven Weinberg came in later to to say, "Okay, we can actually combine that