The Science of Everything Podcast - Episode 14: Principles of Quantum Mechanics

Episode Date: February 7, 2011

An introduction to the key principles of quantum mechanics, beginning with an examination of the quantum-mechanical description of the behaviour of electrons around atomic nuclei. This is followed by an overview of some of the other major principles of quantum theory, including the Heisenberg Uncertainty Principle, the Pauli Exclusion Principle, quantum tunnelling and entanglement. The episode concludes with a discussion of alternative interpretations of these quantum phenomena. Recommended pre-listening is Episode 8: The Atom.

You're listening to The Science of Everything podcast with your host, James Fodor. This is episode 14, principles of quantum mechanics. In this episode, we're going to look at, well, the basic principles of quantum theory, including the development of a quantum mechanical theory of the atom through Broi's explanation of quantization, the Schrodinger equation, and quantum orbitals. And then after that, we're going to have a look at some additional principles of quantum mechanics, including the Heisenberg Uncertainty Principle, the Pali Exclusion Principle, Quantum, Entanglement, and Decoherence. And then, if we have time, we might just take a quick look at different interpretations of what quantum theory actually means.

So this episode continues on from episode 8, which was the history of the atom. In that episode, I outlined some early investigations into explaining how atoms work, which was based mostly on classical theory. This episode will examine how scientific discoveries, after that, built upon earlier classical theories of the atom, developing what we now call the quantum mechanical theory of the atom. Before we start with that, however, I just want to define a basic term, that is, what does quantum mechanics mean? The term quantum basically just refers to the smallest, distinct elements of matter or energy that you can have. and the word mechanics of course just refers to motion.

So quantum mechanics is just basically the study of the motion and interactions of very, very small particles of energy and matter. And before proceeding further, I'd just like to note that it is recommended that you listen to episode 8 before listening to this one, because it will give you some of the background information that will help you get more out of this episode. Okay, so from the end of episode 8,

you recall that we presented Bohr's model of the atom whereby electrons orbited around the nucleus because of the electromagnetic attraction between electrons and protons in the nucleus. However, Bohr's model could not explain why these orbiting electrons did not emit electromagnetic radiation as they accelerated around the nucleus, and therefore, and if that happened, as would be predicted by Maxwell's equations, why atoms did not spontaneously become unstable and cease to exist. So the classical theories, particularly of electromagnetism, that upon which early models of the atom, including Bors model, were constructed, were simply not sufficient to fully explain the behaviour of what was going on. So a new approach was clearly needed, and this is where quantum mechanics comes in. So in 1923, a physicist by the name of DeBroy reasoned that if light could behave like particles and waves in different circumstances, as I explained in episode 8, light had been, observed to behave in waves in some circumstances and as particles in another

circumstances. If photons could behave this way, then why not electrons? Why couldn't they also behave as waves as well as particles? Prior to that time, electrons were just thought to be particles, but Debrose thought, well, why not waves? If photons can be particles and waves, maybe electrons can too. And so using this basic idea, he constructed what is called the standing wave model of electrons around about the nucleus, and this in turn formed the basis for subsequent quantum mechanical theories of the atom. So at the time he presented this idea of electrons of standing waves, this was very speculative and was greeted with much skepticism, but eventually it was, well, actually before too long,

this model was verified by experimental evidence observing electron diffraction and interference effects. And so this provided very strong evidence for the fact that electrons did be as standing waves. Now, if you don't know what standing waves are or what interference effects are, I'll explain those in due course. But first of all, I want to look at an experiment which provided substantial support for DeBroy's theory and also is probably one of the, probably the single most important experiment in quantum theory. This is called the double-slit experiment. So in this experiment, what happens is electrons are fired one at a time at some kind of flat sheet detector that will register the hits of electrons. So this detector sheet is like some

photographic film or something. It can detect individual electrons or photons. The experiment can also be done with photons, but we'll talk about electrons for the moment. This screen can detect the incidence of individual electrons, one electron at a time, hitting different parts in it, and it sort of flares up as silver or something when an electron hits there. So it's like a piece of photographic film. However, in between this sort of electron gun and this detector screen is another flat sheet with two vertical slits in it. That's why it's called the double slit experiment, because this sheet here has two slits in it, sort of next to each other, separated by a short distance. Now, why two slits? Well, that will become clear and due course.

So what's happened is the electrons are fired out from the emitter one at a time, and they're detected one at a time as discrete individual particles. So it's just like we were firing a machine gun at the detector. They're emitted one at a time. We know they're emitted one at a time from various other theories, and we know they're detected one at a time because we can see one being detected, one electron being detected by the screen at different points.

By the way, if we just imagine that we do that experiment without the two-slit thing in the way, what we get is kind of a normal distribution of electron hits, so more of them are around the center of where the gun, is aimed at and then some of them around the sides and a decreasing number moving away from that. So it's sort of probabilistic where the electron actually ends up because obviously there are various factors that influence its motion, but they're all centered around where the gun is aimed. Okay, so that's what happens when we don't have any slits, but enter the double slit once again.

What we find is that after enough particles have been, after enough electrons have been fired from the gun, an interference pattern is observed in the distribution of the particles on the, on the detector, just like we had passed a wave of water through the slits. So an interference pattern occurs when two waves interact with each other. So, you know, waves are composed of peaks and troughs, up bits and down bits. If you have two waves, they can overlap with each other so that maybe two troughs and two peaks overlapping, forming bigger peaks and bigger troughs, or vice versa, you can have peaks overlapping troughs and troughs overlapping peaks so that it kind of cancelled each other out.

that's what interference is, a wave interference. If you had some kind of wave generator and did this experiment with water, you would find that a wave would be produced at the exit point of each of the two slits, because each of the slit allows sort of part of the wave to come through it and produces its own sort of wave that propagates out away from it, kind of like if you threw two pebbles into a pond, each would produce its own wave. Same thing happens when the water wave passes through the two slits in this double-slit experiment. And so because there are two waves, they interfere with each other,

and what you get at the end detector point, if you have some way of detecting where the water waves are ending up, is an interference effect. And it's kind of hard to describe what that looks like, but it's very distinct. It looks completely different from if you just had no slits there and just had the single wave. The waves interfere with each other. So that's if you have water. But as I said, even when we're firing one electron at a time, we observe this. interference pattern in the distribution of the individual electron hits.

So remember the electrons are still being detected as single particles, but if we do enough of them, we observe that the distribution of these individual pixel particle hits looks the same as an interference pattern of a wave. So what's going on here? This doesn't make sense, because we're only firing one electron at a time. How can a single electron interfere with itself? And surely a single electron only passes through one of the two slits. it can't pass through both.

But it seems like it is passing through both, because we're getting the interference pattern that happens when a wave passes through both slits and then interferes with itself. And as I said, this doesn't just happen with electrons. It happens with photons and other subatomic particles as well. Not just subatomic particles. It's actually being done with larger molecules too, but the effect is most pronounced with things like photons and electrons.

So this experiment, and it's been done in a number of different ways, replicated many, many different times. This is a very robust effect. This experiment shows that photons and electrons behave as waves and particles. Particles, because they can be admitted as a single particle and detected as a single particle, a single discrete unit, but waves because they seem to interfere with themselves while they are moving between emitter and detector. So they behave as waves and particles at the same time and seem to interfere with themselves. The same particle is somehow passing through both slits and interfering with itself in the process before it's detected at the screen.

This principle is called wave particle duality, and that name's a bit of a misnomer, because it's not the fact that the electrons or photons are sometimes waves and sometimes particles at different times. It kind of looks like that. What is actually happening, though, is the true nature of photons and electrons is neither wave nor particle, but it's something quite different, and that at different, depending on how we look at the system or how the system behaves, that system can produce either way, wave-like or particle-like behavior. But I'll explain that a little bit more of that later in the podcast. But that's the principle of wave particle duality that comes out of the double-split experiment. That is one of the foundations of quantum mechanics trying to explain what the heck is going on in the double-slit experiment. So how does this double-split experiment relate to the quantum mechanical model of the atom and DeBroy's standing-electron standing waves that I described before?

Well, these two phenomenon are brought together by what is called the Schrodinger equation, which was proposed in 1925, only a couple of years after DeBroy came up with his idea of electrons of standing waves. The Schrodinger equation is, a mathematical equation, that describes the wave-like behavior of electrons, and photons and other things like that, but particularly electrons. Now, the equation is written in terms of the change over time of something called the wave function.

This is analogous to, for example, you could write an equation explaining how sound waves change in terms, terms of air pressure variations. The Schrodinger equation is written in terms of how the wave function the wave function changes over time. It's all a bit abstract, but I'll try and explain it so that you can get the general idea of what's going on. So what the heck is a wave function? I've said that the Schrodinger equation explains the changes of a wave function, what's a wave function? A wave function is just a mathematical tool. It's an abstraction. It's not anything directly observable in the real world. So it's a mathematical tool in quantum mechanics that describes the quantum state of a particle or a

system of particles at a given point in time. So typically we write the wave function as a function space, momentum, spin, and other stuff like that that affects the behavior of the particle. So basically, the wave function is a relationship of different variables. We chuck in all of these factors like momentum, spin, which is another property, position, other stuff like that, and there are various other properties that we need to put in as well. And we come up with this wave function, which is the mathematical abstraction, and then we apply the Schrodinger equation to that wave function to explain how the wave function changes over time.

Now, this might sound like a whole bunch of mathematical gobbled to gook. How does it help us to explain anything? Well, it turns out that the Schrodinger equation and the wave function are very effective, in fact amazingly effective at explaining the behavior of quantum systems, including the double-slit experiment and DeBroy's standing wave model of electrons. And it turns out that the wave function, remember I said that it's a mathematical abstraction. You can imagine the wave function as being

kind of like a wave. It has amplitude, it has an amplitude and wavelength and stuff like that. So it goes up and down, just like a sign curve. In the real world, that wave function itself doesn't mean anything. But if you take the square of that wave function, so you multiply it by itself, multiply the value of the wave function at any point by itself, you square it. What you actually get turns out to be the probability of detecting the particle, so the photon or the electron, at that particular point at a particular time. So the wave function means nothing, not directly, but the wave function squared is the probability of finding the particle at that point.

So that's very interesting. That turns out to be a very useful predictive tool in describing the change and behavior in quantum systems. So this fact of wave function being square of the wave function being equivalent to probability actually helps us to explain what's going on. So when the electrons, say, is moving along, moving through both flits at once, and then interfering with itself, it's not really the electron that's moving through there or the photon. It's actually the wave function that's moving through there.

And because of this wave function is basically a wave, it kind of makes sense that it can interfere with itself and produce wave effects. But then when it gets to the detector, it, through a mechanism of decoherence and wave function collapse, which I'll explain a bit later. But basically, the wave function turns into a single particle, which we observe as a, a discrete particle at a particular point on the detection screen, and where exactly that happens on the screen is described by the square of the wave function at that particular point in space, which is, as I said, the probability of finding it at that particular point.

And this is how the probabilistic nature of quantum mechanics turns out, because you don't ever know exactly where you're going to find the electron or the photon or anything else, but you can find the probability of it being at any particular place. That probability is described by the wave function, and the wave function changes over time as described by the Schrodinger equation. So when we say electrons are moving about, what's actually moving about is the wave function of that electron. The wave function is sort of jiggling around.

Changing over time is described by the Schrodinger equation, and that changing of the wave function translates into changing probabilities of finding the electron in different places. So hopefully that's not too confusing. It is kind of weird. But so remember, you've got the wave function, and then the Schrodinger equation, which describes the change in the wave function,

and the square of the wave function describes the probability of finding the particle at a particular point in space. So, and using that, the Schroenger equation wave function, all that, detailed models were able to be constructed of quantum systems, for example, the double-slit experiment, which very accurately predicted the behavior of these systems and explained experimental results to an amazing degree of accuracy. And so I now want to take this back to DeBroy's explanation of quantization

and fixing up the ball model of the atom. How does all this help us with electrons orbiting a nucleus? Before I explain that, I need to explain the concept of a standing wave. Standing waves occur when a travelling wave is confined within a cavity between two fixed boundaries. So you can imagine a wave being generated, waves being propagated out from the centre of a bathtub. These waves will move outwards, they'll hit the edges of the bathtub, and then they'll reflect back inwards. As that reflection, reflected wave is moving in, say, towards the centre of the bath where the disturbance is being generated, you've also got the initial

waves still moving out was from the centre. And so these reflected and incident waves will interfere with each other. You'll get troughs, troughs on troughs, making deeper troughs, or troughs on peaks, making smaller peaks or whatever, or some combination of both. And as this interference happens, you will, or you may, depending on the circumstance, get what is called a standing wave. But standing waves can only exist under particular conditions. But first of all, I need. need to explain exactly what a standing wave is. The standing wave is, well, it's literally just what it says, it's a standing wave, it's a wave, so it fluctuates, but it doesn't actually look like that it's moving anywhere. So you can think of it as if someone is, if someone is holding a

guitar string and they're plucking in and it's vibrating backwards and forwards, it's vibrating up and down, that actually, it doesn't look like any wave is moving across the guitar screen. It just looks like it's vibrating up and down. If a wave was moving across the guitar string, it would look like there was a little sort of upward peak on one side of the string and a trough on the other side, and that moved across the string from one side and then reflected back and moved to the other. That would be a travelling wave, but the standing wave is just the string vibrating backwards and forwards. Or maybe part of it will be the left side of the string will be in a peak, and the other side will be in a trough, and then they'll kind of reverse, but it won't look like they're moving, they'll just sort of fluctuate up and down one side to the other.

If it's hard to visualize that, just look up a video on Google or something. it's not too hard to understand it once you see it animated. But standing waves like that actually occur when two waves are interfering with each other. And once again, you can see that from an animation. It takes a little bit of time to get your head around how interfering waves can produce a standing wave, but they can. And you can see that from animations if you look at them. But as I said, this can only occur under certain conditions,

and those conditions are when the wavelength has a certain whole number ratio to the size of the cavity in which the standing wave is confined. So if the wavelength of the waves that are building up the standing wave or the standing wave itself, if that wavelength would say 2.7 times the length of the cavity or even 1, or even something like 0.1245, the size of the cavity, that's an irregular ratio. What would happen there is that the standing wave would sort of occur, but it would be chaotic. Sometimes peaks would cancel each other out with truble,

troughs, other times they would not, and there would be no regular patent to it, and so you wouldn't get a standing wave, it would just kind of be random jiggliness, and then maybe all motion would just kind of cancel each other out, and there wouldn't be anything there. So you can only get a standing wave when you have particular wavelengths of the waves that are interfering with each other to produce that standing wave. You can't just have whatever, and those are determined by the width of, or the size of the cavity. Now, you can have, it's not that you can only have one wavelength, you can have shorter and shorter wavelengths, so you think of it as if the, think of the, think of the distance of the cavity being, say, one meter across, you could have a wave of wavelength one meter,

because that would fit in properly. You could also have, you could fit two of those wavelengths inside, so the wavelength could be half a meter, and then you have two wavelengths within the space, or you could have four or eight or whatever, but you couldn't have seven and a half wavelengths, for example, that wouldn't work. Or certainly, actually, you can sometimes have half wavelengths, but you definitely can't have something like 7.325. That just wouldn't work. It would cancel itself out into chaos. But you can have whole number multiples of the wavelength, So certain wavelengths work, but only those wavelengths when producing a standing wave within a defined cavity space.

And that explains why only certain energy levels of electrons are allowable around the nucleus. It's because an electron is a standing wave that exists in three-dimensional space around the nucleus. So when waves are described, usually they're described in two dimensions, and that's a useful analogy to a... apply to the electron when you think about it, but actually the electron is a three-dimensional wave. An example of another three-dimensional wave is an explosion. It's a wave, but it moves in three-dimensions.

It's kind of hard to visualize, but an electron is also a three-dimensional wave. So it exists in a certain space within three dimensions around about the nucleus, and this is, we still refer to as a shell, so you can think about it as a certain distance, a certain minimum and maximum distance away from the nucleus, the electron exists as a standing wave within that space. And that explains, as I said, why it can only take on certain wavelengths. Because maybe it can take on a wavelength of 2 or 2 or 4 or 8, but it can't take on a wavelength of 3.65 because that wouldn't work. It wouldn't be stable. It would interfere with itself chaotically and there'd be no electron there. The electron can only exist when there is a certain regular

interference of waves producing a stable standing wave pattern. That stable standing wave pattern is the electron. If you can't get a stable standing wave pattern like that, there is no electron. And so you can only get the electrons existing at certain distances with certain wavelengths. And we know from earlier experiments that the wavelength of an electron is proportional to its energy. And so if you can only have certain wavelengths fitting or... around the, fitting around the nucleus, then also you can only have certain energies. And that's why the energies of electrons around about the nucleus are also quantized.

You can only have certain energy levels, not just any energy level you like. That's all explained by the fact that electrons are standing wave patterns confined in certain three-dimensional space around the nucleus. But remember, the electron itself is not exactly the standing wave. This standing wave is just the wave function. When we try and measure where the electron is, we'll detect it as a particle existing at a single location somewhere around the nucleus. But we can never predict beforehand exactly where that will be. All we can do is take the square of the wave function.

Remember, the wave function is this standing wave pattern. We take the square of that at any particular point. That will give us the probability of finding the electron at that particular point, say distance away from the nucleus at a given time. But even if it's a very unlikely point, it's still possible to find it. find it there. We never know it's probabilistic, but we can use the Schroenger equation and wave function to explain the probabilities of where electrons will be. And so this new standing wave model description of the atom explains the quantization of energy levels and discrete emissions of the discrete lines in the emission spectrum that had puzzled earlier classical

observers. It also does away with the problem of electrons spiraling into the nucleus, according to classical theory, because according to the new quantum mechanical theory, Maxwell's equations no longer apply to this unique situation. So this quantum mechanical model of the atom not only has significant empirical and observational experimental support, but it also explains a wide variety of puzzles in the previous classical explanations of the atom. And so although it sounds kind of weird with probabilities and standing electron waves and things like that, it is a very successful model, and it is an integral part of the

of modern physics. So now I want to move on to look at some arguably even more bizarre principles and aspects of quantum mechanics. First of all, I'm going to start with the Heisenberg Uncertainty Principle, which was first described by Werner Heisenberg in 1927. Now, the first bit of background information, not only are photons and electrons describable by wave functions, so there's sort of particles and waves at the same time, probabilistically appearing in different locations as described by the wave function. Every particle can be described like that, and in fact, every group of particles can be described in such a manner. So, for example, even something like a car would have a wavelength associated with it. However, it turns out that as the mass of a

particle or system increases, the wavelength of that system correspondingly decreases. So anything above more than a few atoms in size has a wavelength that is so insignificant that is effectively non-existent. So only very small... That's why only very small systems exhibit quantum effects, like interference and stuff like that. It's not because these laws don't technically apply to the macro order, it's just that they become... the effects become so small that you can just ignore them. It's just like the force of Pluto's gravity does act on the Earth,

but it's so small that you might as well... You can just ignore it. It doesn't really do anything. But it is there. All right, so, and that's relevant to the Heisenberg Uncertainty Principle. Now, the Heisenberg Uncertainty Principle states that certain pairs of physical properties such as position and momentum, that's the one that's most often described, so I'll stick with that for this podcast.

Position being the location of an object, and momentum being velocity multiplied by mass. So properties like this can only, can simultaneously not be known to any arbitrarily high precision. That is, the more precisely one property is measured, the less precisely the other can be measured. So this principle basically states

that the more accurately you know the position of an object, of a particle, let's say an electron or a photon, the less accurately you can know it to momentum and vice versa. Now, I want to emphasize that, in spite of some explanations or descriptions of this principle, you may have heard, it's not an issue of measurement. It's not like the position and the momentum of, say, the electron, both exist, but we just can't know them both at the same time because of the coarseness of our measuring apparatuses or whatever.

The fact is actually that the position and momentum do not, cannot be accurately defined to even exist to within a certain level of precision at the same time. So it's an issue of what exists and not what we can actually measure that gives rise to the uncertainty principle. Why does this principle happen? Like, what's with it? It sounds kind of bizarre. Why can't we just measure it as accurately as we would like to?

Why can't we say that the position and momentum don't exist to arbitrary precision? Well, the reason is that the position of a particle, or of the object, is given by the square of the wave function. We know that from earlier in the podcast. And so that's related to the, you can think of it as the height of the side wave that describes the wave function of the particle, let's say the electron. So the height of this wave of the wave function is related to the position. The higher the wave, the more likely it is to be in a particular position.

However, the momentum of the electron is given by the wavelength or frequency, which is directly related to wavelength, of that, a wave function, which is the distance between two troughs or two peaks along the wave function. So if we just had a single sine wave like this, the wavelength of that wave would be precisely defined, because we could just measure the distance between two peaks or two troughs, and that would be the wavelength, and we could get that to any arbitrary precision that we liked. However, the trouble with something, and therefore because we knew the wavelength, we would also know the momentum of the particle. The trouble with that, though, is that such a sine wave would

exist theoretically over an indefinite distance. There's no real limit to how long it is. And so because of that, you get a continual pattern of peaks and troughs. So it continually goes up and down, up and down, up and down. And because the probability of the particle being located at a particular position is given by the, essentially the height of that sine wave, that means the particle could exist at any point in space. I mean, it's more likely at some positions than other, but the sine wave is going to keep going, you know, 10 light years in that direction and 10 light years in the other direction. It's going to be the same. It's going to keep repeating. So really we have no idea where the particle is. It could be here or it could just as likely be on the other side of the universe and when you have no idea. So you can see that, and this has nothing to do with our measurement apparatus. This has everything, this only relates to the wave function itself. So this is an existence from. When you have an exactly precisely defined wave function, the position of the particle is not defined. really at all. It's more likely in some positions than other, but it's not defined anywhere across the universe. The only way we can define the position of the particle more accurately is to add

these sine waves of different frequencies together. So we take one with a slightly different frequency and add it to the one with a slightly different frequency, add several of these together, and what you get is an interference pattern which localizes the wave pack to a particular location or to a more restricted location. Basically, the more wavelengths you add together, the more localized the wave packet becomes. This sounds a bit abstract, and it's hard to visualize, so I recommend looking this up on Google Images or something.

You get pretty good diagrams that explain how this works. But basically, the more different frequencies you add together, the more confined the peaks that you actually observe in this new wave function, the new sine wave, the more confined that is. So as you add this together, most of the wave function now becomes flat. most of it is destructive interference, but there are a few smaller areas that are higher peaks. And so what we've done is we've confined the position of the particle more accurately.

We know that it's got a much higher probability of being in these little wave packets where you've got large peaks and no probability or very little probability of being in these big long stretches of regions of the sine wave or the wave function where the destructive interference has occurred. Peaks have lined up with troughs and we've got no probability, it's just a flat line. So the more of these different frequencies we add up, it turns out, the more confined the wave packets being. So the more accurately we can know the position of the particle. But however, we've just added multiple different wavelengths together. And so now we don't know very accurately what the frequency of the, or momentum of the particle is.

And once again, this has nothing to do with the apparatus of which we are measuring. That would add an additional degree of uncertainty to the problem. But this only relates to the properties of the wave function. You can only define the position by making the wavelength a bit fuzzy, and therefore making the momentum a bit fuzzy, and conversely, you can only define the momentum accurately by making the position a bit fuzzy. And so that's why you can't measure them both to an arbitrary degree of accuracy. There's a limit to how accurate you can get them. The more accurate you have one, the less accurate you can get the other.

And so it kind of acts like a seesaw in that respect. One goes up, the other goes down. This is the Heisenberg uncertainty principle, and as I said, it applies not just to electrons, but to photons and the energy levels of all sorts of different things. Now why is this important? The Heiserberg Uncertainty Principle is very important because it allows a whole bunch of things to happen that normally would classically, that is in terms of Newton's laws, be impossible.

So as one example of this, we can tell from the Heiserberg Uncertainty Principle that there are no actual fixed orbital positions of electrons about the nucleus, just sort of average energy levels consistent with the maximum value of the wave function. So because we can't define the momentum of the electron or the position of the electron

exactly, there is no exact orbital location or position of the orbital. It's kind of within this general range. We can't know exactly where the orbital is. But there's another very interesting application of the Heisenberg uncertainty referred to as quantum tunneling. Now quantum tunneling refers to, is a quantum mechanical phenomenon where a particle can tunnel through an energy barrier that classically would be impossible for it to pass through because it's kinetic energy too. So you can think of a ball rolling up a hill. If a ball is rolling fast enough, it can roll up a hill and then down the other side. As the ball is rolling up the hill, it's going to slow down, because it's taking energy to get up this hill. It's expending kinetic energy to gain gravitational

potential energy. The more kinetic energy it initially has the high the hill that's going to be able to go up before it rolls down the other side and gets that kinetic energy back again. So in a classical system, the height of the hill that it's able to surpass is dependent upon the kinetic energy of the system. Quantum tunneling, however, effectively allows that, say, the system, well, a particle, but in this case think of it as a rock, a quantum rock would just be able to go from halfway up one hill, pass straight through the hill, and end up on the other side going down the other side. It wouldn't have to go over the top. Now, this doesn't actually happen with real rocks, but it does happen with quantum particles,

and once again, it doesn't really happen with them going over literal hills, but it happens in terms of energy peaks and troughs. So, for example, quantum tunneling can be used to understand certain types of radioactive decay. Basically, in radioactive decay, certain particles have to move from the nucleus to outside the nucleus. They have to escape from the atomic nucleus and become free particles. In order to do that, they first have to move a little bit further away from the nucleus before they can get a long way away. The point is that the forces in the nucleus are such that when the, say, proton or

the particles move a little bit further away from the nucleus, their potential energy actually increases at first. And so they require a certain amount of energy to get that initial short distance away, but then if they move even further away, their potential energy decreases, and so they can move to a lower energy state. The point is that they need to overcome that initial increase in energy in order to get to the lower energy state in the end. But classically, a large number of these decays would be impossible

because the particles never have enough kinetic energy for that to happen. However, because of quantum tunneling, they don't actually need all that kinetic energy. They can just spontaneously move from close the nucleus to far away, and then continue moving into a lower energy. state, they can just effectively tunnel from one position to another without having to go intermediate between the two. And that is possible because of the uncertainty principle. The exact details of it are complicated, so I won't explain it all here, but the point is

the energy of the particle is not well defined at one position or the other. So you kind of can't rule out things that, you can't rule out a tunneling event from happening because you don't actually know that it doesn't have enough energy to move from A to B. So we have to, when we're making calculations in terms of probabilities of where the particle's going to be, we have to include the influence of all possibilities, even those with more or less energy than we think the system probably has, because they still have a certain probability of happening. And the fact that quantum tunneling happens experimentally,

and we can observe it, experimentally, is very strong evidence for the correctness of quantum mechanical theory itself. So a very strange phenomenon, but it does happen, and it's been well observed. Another principle that I want to talk about, and this is sort of separate to Heisenberg uncertainty in quantum tunneling, is the Pauley-Excernstein, conclusion principle, which is developed in 1927 by Wolfgang Paoli. This states that no two fermions can occupy the same set of quantum numbers at the same time. Okay, what the hell does that mean?

What's a fermion? Well, I don't want to go into the details of this now. This is for another podcast, but a fermion is just a certain type of subatomic particle, and electron is a fermion. In fact, that's by far the most famous. So just think of these as electrons for the moment. So no two electrons can occupy the same set of quantum numbers at the same time. What are quantum numbers. Quantum numbers are just properties of the electron, basically. It's things like it's not momentum, well, yeah, it is momentum, it includes momentum, but it's other things as well. It's like angular momentum, spin, various other things. Don't think of these as too literal. They're just numbers that we apply to the electron that describe certain aspects of its behavior. More details

of that will be in a future podcast. Anyway, the point is that no two electrons can have the same set of all quantum numbers at the same time. They can have some of them being the same, but not all of them. And some of the quantum numbers also relate to the position of the electrons. So you can have electrons in the same, with the same quantum numbers in different positions, but not at the same position, not too close to each other. Now, this is a very important principle because it explains why the electron shells around an electron have a limited capacity. They can't hold an infinite number of electrons. There's a certain maximum number they can have, and then the electrons have to fill up higher energy levels. And this is because of the powerly exclusion principle. You can't just pack

200 electrons on the lowest energy level of a hydrogen atom, because that energy level can only hold two electrons. If additional electrons are going to be part of that atom, they have to move into higher and higher energy levels. And because of different numbers of combinations of quantum numbers that are possible, the total capacity of these electron shells increases as they move further from the nucleus, but there's still a limited number. And so this, this panel exclusion principle explains why electrons inhabit different energy levels around atoms, and that in turn explains why different elements and different substances have different chemical properties. If the electrons of all elements and all compounds were all just concentrated in the lowest energy level,

just all stuck in the same energy level, we really wouldn't have very much chemistry because nothing would really happen. Chemistry is all about electrons moving, switching from one energy level to another in order to move to a lower energy state. If without the Pali Exclusion Principle, that wouldn't be necessary because they'd all go immediately to the lowest energy state, and so you wouldn't have any chemistry. So the Pali Exclusion Principle is essential really for life and anything interesting to exist. And the Palli Exclusion principle is an aspect of quantum mechanics. So understanding quantum mechanics is very important for understanding the world. The last thing I want to quickly talk about is quantum entanglement.

The basic idea of quantum entanglement is that a quantum system can contain more than one object. it can contain two or more objects, which are linked to each other in such a way that if one, you can't describe one without describing the other. So, for example, we might have, two electrons might be created out of a certain radioactive decay or something, one with a property called spin up, the other one with a property called spin down. Never mind what spin is, it's just one of these quantum numbers that I mentioned before. It just describes the behavior of electrons. But the point is that they, there are always, spin is conserved, so it has to be, when it's created,

it will be created in pairs. One will be up and one will be down. It's kind of like how charge is conserved. Maybe you'll produce a proton and an antiproton, one positive and one negatively charged at the same time. That's another example of this. You can't describe one of these particles without looking at the other one, because the total charge has to be zero, or the total spin has to cancel out to being zero. You have to have one up and one down. And so that's what entanglement means, that property of one particle is directly related to properties of the other particle.

However, the thing is, when that radioactive decay occurs, or when that particle is grated, beforehand, there's no way of you telling which particle will have spin up and which will have spin down, or which will be the positive charge and which will be the negative charge. You just know that each has a 50-50 chance of being one or the other, but you don't know which is which beforehand. There's no way of telling. It's unpredictable and completely stochastic. It's random. But however, suppose you measure one of those particles, you measure it and find it spin up, or it's positively charged, or whatever the property is. When you do that, you know instantly that the other particle,

has to have the opposites, has to be spined down, or has to be negatively charged, whatever. The thing is, that information did not exist before you made that measurement. It's not like the particle was spin up or spin down beforehand, and you just found out it was, and you just found out which state it was in when you made the measurement.

The state didn't really exist in any meaningful sense before you made that measurement, or at least so one of the most popular interpretation of quantum mechanics goes. It's a bit controversial, exactly, but there's no real basis for saying that it was spit up or spin down before, you made the measurement because there was no way of telling, and it was purely probabilistic. Remember, electrons can interfere with themselves, so it's not like it went through one slit

or the other. It kind of went through both slits. That's the same thing as just in this case. It's kind of spin up and spin down at the same time until that measurement is made. Anyway, why is it so interesting? The point is that information about whether a particle is spin up or spin down or positive or negatively charged is instantaneously related from one of the particles to the other. And it doesn't matter how far apart they are. They could be on opposite sides of the universe. They could have been traveling for 20 million years after they were created, and then all of a sudden one is measured, and instantly the other one snaps into its position as being spin-up or spin-down appropriately. It seems that information is transmitted faster than the

speed of light, which violates the special theory of relativity, and Einstein didn't like this, and he referred to it as spooky action at a distance. It seems that one particle is somehow acting upon the other instantaneously, which is very strange, and it's not something we observe in other fields of physics. Now, this is where quantum mechanics becomes very tricky and very controversial in trying to interpret what this all actually means. Is it the case that the particles existed in one was spin-up and one was spin-down for all the time before you measured it? That would kind of eliminate the problem of the spooky action at a distance, but it will also require some kind of hidden variable to be determining beforehand which of the two state.

the particles were in beforehand. And there's various other experiments in quantum mechanics. For example, the double-sit experiment seem to indicate that that doesn't happen. The particle is not in a well-defined state before it is measured and before that interaction occurs. But there is actually a complicated mathematical proof called the Bell's Impossibility theorem

which shows that hidden variables, so variables or properties of the electrons that we can't observe, determine their properties, cannot actually explain away the problem of the entanglement paradox. They cannot eliminate the need for non-locality for this instantaneous transmission of information. Don't worry about why that occurs. Just understand that it is the case.

And so it seems like even if we did have these deterministic hidden variables, we would have to have this spooky action at a distance. But the trouble is if we don't have these hidden variables, then there are various ways of modelling the system so that this entanglement problem goes away, we don't have this instantaneous transfer information. But if we do that, we have to get rid of hidden variables. That's what Bell's Impossibility theorem tells us.

And if we get rid of hidden variables, if we assume that there are none, that that means the system, the quantum systems are truly random, that there's nothing that determines whether the particle is here or there. It's just purely random. And so that means, if that is true, that means at its core nature is stochastic, it's random, it's probabilistic, it's non-deterministic.

and Einstein didn't like that either, but Bell's Impossibility theorem has proved that Einstein can't have it both ways. He can't have it so that there's no instantaneous transfer of information and so that nature is deterministic at the same time. Either we give up one or the other, or possibly both, but we can't have them both at the same time. So aside from the questions of locality and probability,

there's also a question in interpreting quantum mechanics of what does the wave function actually mean? Does it refer to anything real, or is it just kind of a mathematical abstraction? one prominent interpretation called the Copenhagen interpretation of quantum mechanics, which is kind of the mainstream at the moment, says the way function isn't real. It's just an abstraction. In fact, we shouldn't even talk about the location or position or anything about the electrons

before they're measured, before they're observed, and basically it says we should just stick to things we can observe directly and not worry too much about the deeper interpretations of these things. Another theory called the Many Worlds interpretation says that, in fact, every possibility in a quantum system is realized in some world, but obviously we only exist in one of those worlds. And what's happening is every time a quantum system can end up in, say, one state or another, the universe sort of splits into two, and both of these eventualities happen. You know, the particles both spin up and spin down, but in different universes. And these universes are

causally disconnected from each other, so you can't communicate between them. That's why we don't see them. This many world's interpretation kind of explains a lot, but it requires the you to imagine that there is an effectively infinite number of parallel universes, constantly splitting into more and more universes. And that doesn't, for some people, including myself, that seems a bit contrary to Occam's Razor, which advocates selecting the simplest solution. So I don't know if that's the best explanation, but it's one possible explanation. Maybe it's true. Maybe there is an infinite number of universes constantly splitting off from. each other. So that hopefully gives you an idea of how complicated this question of interpreting quantum

mechanics is. The theory itself is very well defined. We have very good equations which are extraordinarily accurate in predicting the behavior of systems. Quantum mechanics is responsible for the electronics revolution, computers, the internet, lasers, many other technologies that we have are based upon understandings of quantum principles. So the theory works, but we don't really know what it means. We don't really understand whether it's fundamentally random or deterministic. We don't understand how non-local, how transmission of information happen faster than the speed of light. We don't understand whether there are many worlds or not. We don't really understand what it means to measure a system. So, like, does the, in what state is the electron before you measure it?

And what constitutes a measurement? Does they have to be an actual observer there? Or is it just interacting with the environment that kind of collapses the wave function and forces it the electron to take a particular one state. Some people say that its consciousness causes the collapse of the wave function, that it's a conscious observer that causes the wave function to take on one state. And so if, presumably, if there were no conscious observers around, the wave functions would not collapse. That's a minority position, but it's another interpretation

that tries to make sense of this very confusing theory that we call quantum mechanics. So this podcast has been a bit longer than usual, but quantum mechanics is very complicated, and I've only given you the briefest sketch of the theory, here. Okay, so that's the end of this episode. Hopefully you enjoyed it. And if you did, please leave a positive review on iTunes. I would much appreciate that and or share the, share word of the podcast with a friend or family member or someone else. If you have any comments or suggestions or feedback of any sort, please write to me. My email address is FODs12 at gmail.com. That's FODDS12 at

gmail.com. Thanks for listening and I'll talk to you next time.