Daniel Pavlov

Transcription

Consider the innocent seeming idea that even if none of us where there to see it, the world would still exist. Most of us don't believe that when we closed our eyes, everything around us dematerializes, only to come back into existence instantaneously when we open them. Assumptions like this are very ingrained in our minds, and yet in Quantum theory, many of our basic assumptions are false or seriously up for debate. So what is Quantum mechanics? It's an attempt to explain a lot of strange phenomena that are often most noticeable when we look at particles smaller than atoms. BUT, make no mistake, quantum mechanics isn't just "the physics of small things"; It's a complete overhaul of Newton's mechanics; the explanation for why chemistry even happens, and in general just a huge rethink of how the world works. Our adventure into Quantum Mechanics starts off with the question "what is stuff?" How does it act? We're all pretty familiar with how things acts in our daily lives so this question seems a bit trivial, but people discovered there was another side to stuff that becomes more obvious when you look at very small objects. They started to say strange things like "stuff acts like particles, but also like waves". We'll see how Quantum Mechanics solves that confusion by telling us, stuff is even weirder than that. Firstly what is a wave, and what is a particles, and what are the tell tale signs that you're dealing with one or the other? Particles pretty familiar to us. One thing about them is they are localized to one area where as waves are very spread out and are in more than one place at once. There is another way that waves are very different from particles, and that is the way they interact with each other. Particles do this, where are as waves do crazy things like. This phenomenon is called a superposition or interference. Basically, when two waves meet they can either reinforce each other, or cancel each other out or a bit of both. You can use these two properties of waves to design a pretty clever experiment that tests if you are dealing with waves or particles. It's called the double slit experiment and seriously, you are going to want to remember this one because in my opinion it's the most important experiment in quantum mechanics, and we'll come back to it so many times. First we'll talk about the experiment when its done with small particles. You need a gun that will shoot particles here. Then you put up a board that will detect where the particles land. In between you set up another board, but one with two slits in it that particles can get through. What happens when you shoot the particles? Most won't get through, but those that do will mostly end up in two big clusters behind the holes. The situation with waves is very different. We'll have the same set up except now we'll create waves at this end and at that end the board will measure where the waves hit with the most intensity. First we'll cover one hole up and see what happens. The wave goes through the hole and then starts to make semicircular wave fronts. Therefore the wave hits most intensely right behind the open slit. So you might expect that when you have both holes open that the pattern will look like this: but it doesn't at all. When both slits are open, the wave splits up and then interferes with itself. Where two peaks or two troughs meet, they make a bigger peak or trough. Where a trough and a peak meet, they cancel each other. Imagine these are water waves and you're in the water. If you're in these waters you are getting bobbed up and down a lot. On the other hand, these waters are pretty calm. So at the wall, you can expect the waves to hit most intensely around these areas and least in these, so you'll get a pattern like this for intensity. Most things we are familiar with seem to act like particles, so people expected that, even when we're dealing with things so small we couldn't see them with our eyes, they would be particle like. Let's put that to the test using the double slit experiment on something extremely small, say an electron. We won't be able to see the electron as it goes through, but what we'll do is put in a special screen on this side, that lights up wherever an electron hits it. We are going to use an electron gun that only fires one electron through at a time. Here goes. Well, that looks like they are particles to me, because a wave would be spread out across the whole screen, not arriving in localized dots like this. But wait, look at the pattern forming on the screen. That's not what we would expect of particles at all. In fact I'll show you that this result seems impossible. Firstly let's see what happens when we cover up one slit. We get one splog of points behind the open slit. OK, but we just found out that electrons are like particles in that they are in one spot and not spread out, so each electron must go through just one slit. Hmm We already know electrons going through this one slit must make a pattern like this, and similarly for electrons going through the other slit, so we should expect this.. Which is not at all what we get at all! This result seems to be defy logic, and that is a big problem for physicists. You see, if the universe is inconsistent with itself, there would be no point of trying to make sense of it, it won't work, and physicists would be out of the job. Luckily for us, a few smart people came up with a cunning solution. This solution is called Quantum mechanics, and if it is troubling then please just remember- we were desperate. You see our previous reasoning implicitly assumed many things that we usually hold to be true, but if we can let a couple of these go, then we can come up with a solution. Our first assumption was that because the electron looked particle like when we observed it means it looks particle like while we are not observing it. This is the kind of assumption that is really important in science. We like to think that our experiments are simply unveiling the reality that was already there, not changing it completely. Quantum Mechanics lets that comforting idea go. Instead, while we are not looking, Quantum Mechanics doesn't say anything about the actual electron itself, instead it talks about something called the electron's wavefunction. The wavefunction is this wave that exists at all times even though the existence of the electron sometimes becomes questionable. It's a wave similar to a water wave. Therefore in this double slit situation, it interferes with itself, and so the intensity profile of the wave looks like this, just like with the water waves: Ok great, we're got this wave but what on earth has it got to do with our electron? This is where we need to let go of our second assumption. Basically, ever since Newton, physicists have believed that there isn't random chance in how the universe acts. If you think back to our experiments with regular particles, we said they didn't all land in the same spot. However, according to Newton's Laws, this is just because they must have been going in slightly different directions and speeds at the start. If you could get them all the same, they'd all fall on exactly the same spot. In Quantum Mechanics though, the opposite is true. Even if it were possible to get the electron gun to shoot exactly the same each time, the electrons won't all land in the same spot. There is an element of chance involved and there is absolutely no way to predict where a particular electron is going to go. That's like saying when I let an apple go, 2/3 of the time it will fall down, and 1/3 of the time it will fall up, for no reason, and there is no possible way you can predict which way the apple will fall next time you drop it. However, quantum mechanics doesn't say that where the electron turns up is completely random, then our pattern would look like this: Where as what we get is this for the double slit experiment and this for the single slit one: We can see the electrons seem more likely to turn up in some spots, how do we figure our where? Reenter, the wavefunction. Remember the intensity profiles for the wavefunction is in each case like this and this. As you can probably guess now, the electrons are most likely to turn up where the intensity of the wavefunction is big. If you want more details on how to calculate let me know in the comments and I might make a video about it. Ok, so let me recap. When we are not looking, the electron itself may or may not exist, but in its place is some sort of wave. Quantum mechanics says that while you're not experimenting on it, the electron doesn't have a position. Even its wavefunction is spread out. But when we attempt to measure the position of the electron, the universe realizes it needs to produce an electron, so it picks where the electron will turn up, semirandomly, based on the wavefunction. Ha, yeah I know. Well, I'll leave you with that for now, and next week I'll try to expose you to more of this quantum mechanics thing, but I'm sorry, it only really gets weirder. I hope you have a bunch of questions. Please ask them, and I'll answer them if I think I know the answer! See you next time!