Raw Transcript
Why does light exist? Physicists actually have a good answer to that one. I spent so much time complaining about all the things that physicists can't explain. I've almost forgotten to tell you how stunning it is that they did manage to explain some things. Light exists because electric charges exist. The connection between the two is the probably most underappreciated insight that's come out of physics in the past 100 years. It's called a gauge symmetry. And today I want to try and explain how that works with as little math as possible. Everyone needs a goal in life. To understand where light comes from, we first have to talk about electrons. Electrons are particles, but they're quantum particles. So they're also waves. This means that they have a wavelength and they have an amplitude that goes up and down. The thing is though, a wave doesn't just have a wavelength and an amplitude. It also has what's called a phase. The phase tells you which part of the wave belongs to what point in space. You could say, for example, in this case, the minimum belongs to the position x= 0. Or maybe the minimum belongs at x= 1. These two are the same waves with the same amplitude, but their phase is shifted. Mathematically a phase shift just means adding a constant in the argument of the s or cosine function. The important thing about these phases is now that they are relative. We can measure a difference between phases but we can't measure the absolute value. The absolute value is meaningless. You fix it by convention by saying okay the phase was zero at this location at this time and that might make your maths more convenient but it's not physically meaningful but think about it that absolute phases of quantum particles are just convention and therefore shouldn't matter is very similar to Einstein's insight that absolute velocities can't be measured and therefore shouldn't matter and that worked very well for Einstein didn't it gave Each symmetry is based on the same idea. Make sure that arbitrary conventions don't matter. The challenging part is though that relative phases can be measured. So the absolute phases have no physical meaning. They are convention and you can choose them however you like. But that choice shouldn't affect the relative phases because you can measure those. To be fair, that all sounds rather lame. Okay, I get to pick the absolute phase and I can measure relative phases. Okay. Okay. What's the big deal? The big deal is that once you have electrons, this tells you how the electrons must move. To see this, imagine the entire space is full of electrons and they can move around because physics will be rather boring if nothing could move. I can then compare the phases of electrons in two places. Say I have one here and one here. I bring them together and compare them and I read off the phase difference. If I shift the absolute phases the same way in both places and bring them together and compare, same result. So all is good. Nothing depends on my choice of the absolute phases. But we said that the phases can be whatever I want. They are convention. This means they can change from one place to the next. So I should be able to choose a different face here than there. And now if I move this over and compare them, that does depend on my arbitrary choice. This isn't good because you see this relative phase that's measurable. And now it depends on my arbitrary choice of phases in both places. This is bad. Physicists call this arbitrary choice a gauge. And that gauge, it shouldn't matter for the physics because you could pick a different one than I and we'd never agree on anything. It's like Germans have a different gauge for politeness than Americans. But back to the physics, now comes the big insight that made all of particle physics work. You need to know how to adjust the phase as you move the electron. So what you do is you add information at every location in between the two places that tells you how you need to shift the phase so that this arbitrary choice doesn't matter. The way you do this is that you assume this information in between it also depends on your arbitrary gauge. And if you take both together the electron plus this extra information and the arbitrariness drops out. If we have something that has a value at every location in space and time, physicists call that a field. So this information that you add, that's what's called the gauge field. Gauge phases field moving electrons. What? Bear with me. I have an example. Suppose you have an old-fashioned beam balance. If you have the same length of beams on both sides and the same weights, it's in balance. Now let's say that adding weights is like shifting the phases by an arbitrary amount. If you add the same weights on both sides, nothing changes. This is like saying the physics remains invariant under this arbitrary choice. If it's the same in both places, but if you add a bigger weight on one side than on the other, that ruins the balance. This is like setting a different phase in one place than the other. This is your gauge. But that would mean the physics depends on this arbitrary choice. Not good. So what you do is that whenever you add a weight, you also adjust the support of the balance arm. This is what the gauge field does. If you change both together, you always keep the balance with the gauge field. The gauge doesn't matter. This is basically how gauge symmetries work. You tie two changes together so that the net cancels out. And you do this because quantities which are physically measurable shouldn't depend on arbitrary conventions. With a little bit of maths, what you need to move the electron from one place to another is a derivative. Suppose you have some wave, say a sign with some argument that could depend on space and time. Now you add an arbitrary phase here. That's your gauge. If you take a derivative, this will make an extra term. This extra term is the reason why if you compare the electrons in two places your gauge matters. It should not. So mathematically what one does is to say whenever I have a derivative I must also add a new term and this term that's the gauge field. It changes exactly so that it cancels this derivative from the gauge. Okay. So this was it with the maths for today I swear. Now, let's talk about what this means. The first question you might have is, okay, but what does any of this have to do with light? You said there'd be something about light. Yes. So, the thing is that once you introduce this gauge field, it develops a will on its own. It's there to keep the electron phases properly lined up. But it can do things even if there's no electron inside anywhere. In particular, it's got ripples that can travel. And those are the photons, the quanta of the electromagnetic field. They are what light is made of. Again, this is very similar to Einstein's theories. Space curves around masses. But even if there are no masses, space can have ripples that travel. In Einstein's theories, these are the gravitational waves. For the electron, they are electromagnetic waves. So this is why we have light because we have electric charges. Another thing that you can learn from this is that you can't have an electron without an electric field. You knew this already, but I think it's a somewhat underappreciated point because it means that this electron in the standard model chart, it doesn't exist. We've never seen it. The electrons that we actually observe, they always have a cloud of photons around them. This idea is called gauge symmetry. goes back to Herman Vor in the late 19th century and it doesn't just explain light. The entire standard model of particle physics is based on this. Physics shouldn't depend on arbitrary conventions. Is it a coincidence that gauge symmetry is so very similar to the ideas underlying Einstein's theory of gravity? Maybe. But a lot of physicists think that it means both have the same origin, some common underlying theory of everything. However, while Einstein's general relativity is similar to particle physics in some regards, it's very different in other ways, but that's another story that shall be told another time. So, we have light because we have electric charges. You might then ask, well, why do we have electric charges? Physicists don't have a good explanation for this one. They've certainly tried uh they've tried with unified theories and theories of everything, but none of those have really worked so far. Personally, I think the reason we have electrons is because it's the simplest particle you can think of. It comes from the simplest symmetry there is in all of mathematics. It's just this one phase. Indeed, getting the electrons and the light with them is the easy part. The difficult part is explaining all the other properties of the standard model. But regardless of how you look at it, gauge symmetries are how nature works. And that's why light exists. When there's light, there's darkness. That's not just true for physics, but also in the daily news. If you want to make your news reading smarter and more efficient, I recommend you have a look at Ground News, who've been sponsoring this video. 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