Physique Quantique/
Quantum Physics

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Wave-Particle Duality

Now that you have completed Quantum Physics 101 (Missed it? Go back to Quantum Physics 101 to help you understand.), you are ready to move on to the next step. Don't worry, you'll understand the next pages regardless of the order in which you read them, just as long as you start with Quantum Physics 101. Have fun!

Table of Contents:



Einstein's Phtotoelectric Plates


The Double-Slit Experiment 

Wave-Particle Duality

Which One Are They Really?

Wave-Particle duality is a very important concept in quantum physics, because without it, it is impossible to explain all of what particles do and why. But before we go into what it is, we first need to understand waves and particles. If you're already familiar with these concepts, fell free to skip to "Which Ones Are They Really?". 


      We usually think of subatomic particles as, well, particles. And since no one has ever seen a particle, our imagination has to take over and tell us how they would look. Since we tend to associate things we don't know with things we do know, most people think of particles as small marbles or as teeny tiny little planets, because we often hear about electrons orbiting around the nucleus like the planets around the sun. This isn't really what particles look like (physicists have never "seen" a particle because they're too small even for the most powerful of microscopes, but we know that they aren't perfect spheres), but for the sake of convenience, keep thinking about the "marbles" for now. We've know about particles since the Ancient Greeks (in fact, they're the ones who introduced the marble idea!), but since then, our concept of what a particle is has changed a lot. (For more information on the history of particles, see just about any book in my sources.),83,361x292/

   Particles are like little points in space. They have no volume. This is very important to understand. Say we think of a marble. Because it is a perfect sphere, its width, hight and depth are equal. For example, lets take a 2cm X 2cm X 2cm marble and put it in a coordinate grid. The bottom of the marble would be at 0 on the "y" axis, 1 ont the "x" axis and 1 on the "z" axis (assuming that 1 is equal to 1 cm on all three axes). On the image (left), this situation is shown but only the "X" and "Y" axes are represented. This is because it is difficult to represent three dimentions in a drawing, which only has two. In real life, each spot on or in the marble would have an (x, y, z) coordinate. Thus, the bottom of the marble would be at (1, 0, 1) rather than (1, 0), but that isn't too important for now. If I also put a particle in the grid, it has only one (x, y, z) coordinate. The entire particle is at this one spot. This may be a little hard to concieve of, (if so, you're normal!) but just hang on a little, you'll get used to it. In our everyday lives, everything has volume, so we have trouble imagining something without volume. Even the tinyest dot on a piece of paper has volume, but particles don't. If I shrink my marble down as little as I can, it can never be like a particle because it will always have many different unique (x, y, z) coordinates, no matter how close together they may be whereas a particle has only one single (x, y, z) coordinate. But some of you may be wondering how come particles have mass if they don't have volume .. and how come they all have different masses. Well, the answer is that physicists aren't sure yet. They think that it is due to an interaction with the Higgs Field (yes, this is related to the famous Higgs Boson, take a look at the notice in News to learn more), but this isn't important for now. What you really need to understand is how come particles are able to have mass anyway. We usually associate mass and volume in our everyday life. When we say something is massive, we don't really mean it has a great mass - we mean it has a great volume. Mass is independent from volume. Think of it as how much "stuff" is in any given object. Say we take two marbles with the same volume, maybe 8 cubic centimeters. One is made of gold (which makes a pretty expensive marble!) and one is made of wood. The one made of gold has more mass, but the same volume. It has more "stuff" - protons, electrons, neutrons and friends- in it than the wood. Now say we shrink both marbles down to a single point (I know, I said that this was impossible, but lets just imagine it for now). They will conserve their mass, but not their volume. In fact, if you counted the particles making up the matbles before and after their shrinking, that number wouldn't change. What used to be the gold marble is still more massive (meaning, it has more mass) than what used to be the wooden one, but now, neither has volume. And we're back to our particles that have mass - and can have different masses. See, that wasn't too hard, was it? 

Einstein's Photoelectric Plates


     Okay, so now we know what particles are, but how do we know they exist? We can't see them, we can't feel them ... so how do we know they're really there and that they're not just a figment of some physicist's imagination? For the answer to this question, we must turn to Albert Einstein and one of his inventions: the photoelectric plate. This weird contraption is used to transform light into electric current. What happens is that the light (made up of photons), hits a metal plate and excites the electrons which start to move and create an electrical current. Up until here, no proof that particles (like photons) are ... particles. Here's where we can prove it. The energy is transferred to the metal in little "chunks", not in a continuous flow. If the particles were actually waves, the energy would be delivered continuously. But since they're particles, the energy is delivered in little bits every time a single photon hits the metal plate. Physicists determined that this proved that photons are in fact particles (or at least in some ways and sometimes, but we'll get to that). 


       Waves are a huge part of our lives, even though we don't always know it. Sound and light are waves, the circles you see when you drop a rock in the water are waves ... they're everywhere! There are two types of waves: electromagnetic and mechanical. We're only interested in the former here, so that is the type we'll look at. There are also two ways waves can propagate taking on either a transverse or longitudinal form. Again, only the former is important for what we're going to look at. 

The image (left) is a representation of a transverse wave. The trough is the lowest point of each wavelength while the crest is the highest point of it. A wavelength is the distance between two crests or two troughs. Electromagnetic waves don't need matter to move around, but mechanical waves do. That is why light, an electromagnetic wave (if you're thinking "WAIT! Wasn't light a particle earlier?", you're right. We'll get to that later, so just think of it as both for now.), can travel through space, through emptiness, and a radio wave, a mechanical wave, can't. The air around us is what lets us hear sound waves. In empty space, they wouldn’t go any further than the end of what is emitting them.     

   When two waves meet, they create an interference pattern. If two troughs meet, they create and even deeper trough because they get "added" to each other and if two crests meet, they create an ever higher crest for the same reason. On the other hand, when a trough and crest meet, they cancel each other out. If they are equal (meaning the crest is as high as the though is deep), they leave nothing and are completely annihilated, but if the trough is deeper than the crest is high, a smaller wave will remain. The troughs and crests will simply not be as high or low as they were before. This is very important to understand, because it is a key element in proving that particles are also waves. So now that we know what waves are, lets see how we know that they exist. 

The Double-Slit Experiment

      Thomas Young, an English physicist, conducted what we now call the Double-Slit experiment. In essence, he shot a beam of photons towards a wall with one hole it  behind which a wall with two holes in it stood. A light sensor was behind the second wall. Had the photons behaved like light, you would have expected that there would be light only behind the two holes of the second wall. But here, there was light everywhere on the sensor, at varying degrees of intensity which looked like the result of an interference pattern. This showed scientists that photons also waves, because they create an iterferance pattern. Therefore, Young's double-slit experiment proved that particles (photons and, as it was later demonstrated, electrons) are really waves. 

Which one are they really?



   Einstein says that they are particles, Young says that they are waves. So ... which one are they really? The truth is that, as John Gribbin says in his book In Search of Schrödinger's Cat: "in reality, [they] are neither waves nor particles" (p. 192). (Original citation in french: "quoique en réalité, [elles] ne soient ni une onde ni une particule" p. 192). "Particles" posess both the properties of a wave and those of a particle. Many hypotheses have been suggested, like that of a particle being pushed around by a corresponding wave, but what we now think is the "real" answer came with the Copenhagen Interpretation. Another less prominent but still very present idea is the superposition of states. We will briefly explore both these ideas. 

   The Copenhagen Interpretation is basically an attempt by the most eminent physicists of the 1920's to find a "logical" explanation to what quantum physics had become. They came up with "a sort of" an explanation for this Wave-Particle Duality that they had been struggling to make sense of. The Copenhagen Interpretation states that the wave-like properties that a particle has are actually a description of the probability that the particle is at any given place on the wave at any given moment. I won't go into too much detail about this now, because this idea refers to Heisenberg's Uncertainty Principle. What you need to understand is that this interpretation wants us to believe that the particle is everywhere on the wave at once. This is difficult to comprehend, because we must accept that the particle, at any given moment, can be at many places. Many different places. All at once. This doesn't happen in our day to day lives. Take a moment to wrap you head around this. (We've all had one of those days when we wish we could be at many different places at once, but that's another story.) So when we say that a photon, when it is studied in the double-slit experiment, creates an interference pattern with itself, what we really mean is that because it is at many places at once, it "bumps" into itself in all the other places it is. Imagine it like this. Say that you can be at two places at one. There aren't two of you, just one, but that one can be two places at once. So you, lets say you "A", wakes up early and goes for a run while you "B" also stay home and sleeps. When you-A come home and you B wake up, you'll meet. Now say that on your run, you A saw that there was an accident on your way to work. Nothing you B could have heard about on the radio or know about before seeing it, but just enough so that you B will be late for work. You A obviously tell yourself that there is an accident so you B take another route to work and get there on time. This is like and interference pattern. The photon changes its own path by interfering with itself. So, by being at two places at once, you have changed the outcome - just like the photon***. You helped yourself be on time to work, the photon created an interference pattern. Thus, according to the Copenhagen Interpretation, a "particle" is neither a particle nor a wave. It's a particle that is in many places at once and so makes up a wave. 

   *** Well ... the photon doesn't tell itself to move, it physically bumps into itself, but you get the general idea. 

 The superposition of states is another idea that tries to explain wave-particle duality. It leads us to believe that a "particle" is both a wave and a particle at the same time until it is measured. When it is measured, the particle "chooses" whether it is a wave or a particle. Being measured, in superposition vocabulary, is anything that can "see it": it can be a machine acting on it, another particle interacting with it, an experiment conducted on it ... So lets explain this idea a little bit more. Say we take a photon. This photon is a particle and a wave. All at once. Why? Because we don't know which one it is and according to superposition theory, the particle doesn't know until we do. Weird ... right? Mr. Erwin Schrödinger thought so too, so he came up with an analogy to expose the "craziness" of the idea. Unfortunately for him (but fortunately for us), rather than seeing the "absurd" side of Mr. Schrödinger's story, the scientific community embraced what he had to say, and the experiment he proposed has now become one of the most iconic examples of the superposition of states - and maybe even of quantum physics - that ever was. Ever heard of Schrödinger's cat? The story goes as such: take a cat - any cat, it doesn't really matter. Put the cat in a box. With the cat, fill the box with a clock linked to a rock that might or might not fall and break a vial of volatile poison after a certain time. Close the box. Now, we said that the rock might fall and break the vial after a certain time - might. The might comes from the fact that the probability that the rock will fall is linked to how much time has passed since it was put in. In this way, after one minute, the probability that the vial has been broken (and that the cat is dead) is maybe 5%. After 5 minutes, the probability might be 25%. Now, say we take the box after 10 minutes. The probability that the cat is dead (the vial is broken) is 50% and the probability that the cat is alive (and that the vial isn't broken) is also 50%. This means that the cat has an equal chance of being dead or alive. Until we open the box, we have no way to know or predict weather the cat is dead of alive. Remember this: we have no way to even guess at the cat's state: we just don't know. Schrödinger said that since we don't know, until we open the box, the cat is BOTH dead AND alive and the vial is BOTH broken AND unbroken. The vial will essentially "choose" weather it is broken or not when something measures its state. Being measured could be someone looking into the box, introducing a machine into the box, listening to try to determine if the cat is breathing or not***, etc. Until this time, the cat remains both dead AND alive at the same time, however absurd that may seem. The cat is only dead OR alive once it is measured. Now lets apply this idea to wave-particle duality. The superposition theory states that the particles are just like the cat. Until something measures them, they are both a wave and a particle at the same time. When they are measured, they "decide". This would explain why particles sometimes behave like particles and sometimes behave like waves. 

*** Some people say that the cat can be considered a measurement because it knows if it is dead of alive, but for the moment, we'll disregard this and assume that the cat doesn't know weather it is dead of alive. 

   You might find this idea strange and difficult to accept. If so, you're NORMAL. Welcome to the weird and wonderful world of quantum physics. And if you don't like thinking about a particle choosing whether it is a particle or a wave, you're not alone. Many physicists agree with you! This is one of the reasons why many scientists prefer the Copenhagen Interpretation to the Superposition of States. However, both theories have their merits, benefits and downfalls. 

   Some of you might be wondering: the double slit experiment was only preformed with photons and electrons, but wave-particle duality seems to be accepted as a generalized phenomenon. How do we know that it applies to anything other than photons and electrons? Over the years, there has been experimental and mathematical proof in many different situations, none of which are very important to your understanding of wave-particle duality. As long as you understand that wave-particle duality is a generalized concept throughout all of the subatomic world, you should be fine. 

   So the question still remains: are particles waves or particles? Well, that depends which theory you like best. What is important to remember is that sometimes, subatomic particles behave like particles and sometimes they behave like waves.