Quantum mechanics is one of the most spectacular discoveries of modern science which occurred between 1900 and roughly 1930. A single generation of physicists took on a grand challenge to understand the microscopic realm which, around that time, was just becoming accessible to the experimental studies. What they found is by any measure shocking, unexpected, a completely a new way of thinking about how the microscopic realm works. And this new description, quantum description, as it turns out has tremendous implications not just for tiny things, but also for our understanding of the wider picture of reality. In fact the main message, if you will that I will be driving home throughout these remarks, is that we are still struggling a hundred years later to really figure out what quantum mechanics is telling us about the nature of reality.
Development of quantum mechanics truly was a collective project. Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, these were some of the great minds that pushed this subject forward. Remarkably, to understand quantum physics or at least the core idea of the subject, it turns out that there is one single experimental setup that really captures the heart of the subject. In fact the great physicist, Richard Feynman, he as fond of saying that in one single experiment, the double slit experiment, you can see the heart of quantum mechanics lay bare.
So what I like to do is to turn to that experiment. And it is interesting to know, if any of you have looked into the history of quantum mechanics, there is a single paper in which this experiment is firstly described in 1927. The authors of that paper Davisson and Germer, they were forth coming in how this experiment came to be because it arose by virtue of an accident in a laboratory. What they were doing was that they were examining small chunks of nickel by firing electrons at the nickel crystals, very standard kinds of experiment back in those days. And it turned up that they made the electron beam too strong at one moment and it shattered the glass tube that was creating the vacuum within which this experiment was taking place. They cleaned up the pieces of glass, the tarnished nickel crystal on its surface that was oxidized. In that process of cleaning the nickel crystal, they unwillingly changed the experiment. The resulting new experiment that they unwillingly came to is the one we will discuss. But it is remarkable that they told that story. At least from the modern perspective, we as scientist these days more or less, if we have an error, do something wrong, we don’t go tell anybody about it. We just write up the final result as if that was we were trying to do all along. So it is wonderful to see in the history of these ideas, how these vital experiments emerge from that little mishap in the laboratory. All right so what is the experiment itself? I won’t so the actual version with the nickel crystal, it’s little hard to understand in that framework. I will show you the equivalent experiment that captures the exact same ideas.
Experiment with Bullets
And the experiment begins like this. We have the barrier with two openings. It’s called the double slit. We begin by firing large objects, for example bullets at this barrier. As you would expect those bullets that go through right slit will land in a band on the right aligned with it. Figure 1, depicts those bullets that go through the left opening land in a band aligned with it on the left, very simple straight forward experiment.
Experiment with Electrons
Now we are going to make one adjustment to this experiment. We are going to take those bullets and dial down their size, making them smaller, smaller and smaller, until they are as tiny as little particles, electrons. We would do exactly the same experiment. You would think, based upon what happened in above experiment, that if you fire these little electrons more or less we should get the same result. Those electrons that go through the right slit land on the right band. And those electrons that go through the left slit land on the left band. That is what you would think would happen. But the thing is, if you do this experiment, this is not what happens. Instead you find not just two bands aligned with two openings, instead you get whole series of bands, light-dark, light-dark. And the fact that you don’t get two bands, but you get more than two bands separated in this peculiar pattern is the heart of revolution in our understating of the world as shown in the figure 2. Kind a crazy, right?
Experiment with Water Waves
Five bands instead of two. How could that make such a difference? But it does. Because it challenges to explain how possible that data could emerge in this experiment. And the key in making progress comes from another area from science that every physicist learns from the time they are 3 or 4 years old which is an area of physics called waves. A particular feature of interest is something called wave interference. It is something that most of you have experienced, even if you didn’t name it correctly. If you are by a pond, and you have two pebbles, and you throw one pebble into the pond, you know what will happen. Pebble hits the water and it sends out these concentric ripples that spread outward. If you throw the other pebble in, you know what will happen, exact same thing. Concentric ripples will be sent outwards. But if you are careful observer and you throw these both pebbles, and if you look at what happens when the waves crisscross, you’ll find something interesting. There are locations where the peaks of the waves combine to make the water a little bit higher. There are other locations where the troughs of each wave cross to make the depth of the water little lower. But there are other locations where the peak of one wave crosses the trough of another, canceling out. At those locations where water isn’t moving at all, the waves have interfered and canceled each other out. Exactly the same would happen if I send water towards a barrier with two slits. Those parts of the water that go through right opening yield a concentric wave, also those parts of water that go through left do the same. As they crisscross, exactly the same thing happened in the pond, will happen. It will produce locations where the water is highly agitated, not agitated, highly agitated and so forth. In the back screen, we can put a nice bright band, where the water is highly agitated, and a dark band where it is not agitated.
In both of the above experiments, the data is the same-bright, dark, bright, dark, bright, and dark. And yet, what’s happening in both the experiment seems very different. In the second I’ve got water waves going towards the barrier and in the first I’ve got little particles going through the barrier. What therefore is, the conclusion, that somehow, in some profound way, little particles, little electrons, are related to waves. There has to be a wave like character to these particles, in order to explain that strange data. Somehow little particles that seem to exist in one little location are related to a wave, something that seems radically different, and something that is spread out through space.
Now if you think about this for a moment, you might say, well may be that’s not as puzzling as you are making it out. Because, let’s think about a water waves for a second. What is water made of? It is water molecules, H20 molecules. So even when you are talking about water waves, there are particles involved. There are just many particles that are moving in a choreographed manner. So may be what is happening in the case of electron is that the electrons are like molecules of the water and many electrons moving in a choreographed manner yield some kind of wave. That’s why I am getting this interference pattern in the screen. May be that’s what going on. And to test that idea we can change the experiment little bit. Instead of having many of these electrons, let’s fire these electrons one by one. Because one by one, there seems to be there doesn’t seem to be any collective behavior going on at all. So if you are to get same data, then the individual particles themselves have to have the wave like character. And remarkably, if you do this experiment firing those electrons one by one, each one hits the back screen as a little dot. At first there is just a random collection of dots, but if you wait long enough over time one by one by one, you get exactly the same wave like interference pattern. So, individual particles, themselves, somehow have wave like quality to them. Particles behaving like waves.
Probabilistic Interpretation
This was a puzzling idea, which leads to the basic question of; ok the data is suggesting that the particles are behaving like waves, but the waves of what? What are those waves? Erwin Schrödinger gave a very natural suggestion. Look, may be the wave is kind of a smeared out electron, a kind of electron mush, if you will. But for it to be the case, when you measured where an electron is you might find one-third of an electron here, a quarter of a here, you are just capturing a little bit of the mush, you only capture a little bit of electron. But every time you measure an electron, you always find out a whole electron, not a piece. So that idea of smeared out electron mush just didn’t work. People were puzzled, until Max Born came along. He introduced an essential new idea that is still with us today. It is kind of a crazy idea or remarkable idea. But one that works.
He said the wave is a kind of wave that we have never previously encountered in physics, in science. He said the wave associated with the particle like an electron is a wave of probability. He said the wave is actually describing the likelihood of that the particle, the electron, being at one location or the other. So if I a picture of a wave associated with the single electron, the idea is that the places where the wave is big are locations where the electron is likely to be found. Locations where wave is small, it’s unlikely to find electron there and places where the wave is zero, you will not find the electron at all. Wonderfully, this is not just an idea. Erwin Schrödinger came up with an equation that allows us to determine how this wave will evolve over time. And with that mathematical understanding of that probability wave we can make predictions. The idea is, if you have a probability wave for a given experimental setup, if you run that experiment over and over and over again, you should find the electron at one location over another, in a ratio that is proportional to wave heights. Imagine a simple curve is the probability wave describing where an electron is. If x represents one measurement of the electron position you found it in that location. The idea is that if these ideas are correct, if you continue to run identical version of this experiment over and over again, each time measuring the location, and putting a little x where you find it, then the number of x’s at any given location should ultimately fill out the shape of the wave. And in deed if you do that, run this experiment over and over again, measuring the position of the particle, and in each run of the experiment, keep on going, and over time, the measurements that you find will fill out the predicted ratios. Where the wave is big, you find the electron many times there. Where the wave is small, you will find it fewer times. And where the wave goes to zero, you never find the electron at that location.
Now, if you go back to the double slit experiment, think of the electron as a wave. Like a water wave, it can crisscross on its way to the back screen. Location where the wave cancels each other out, the dark regions, are the locations where you will find very few particles. Bright regions are locations where you will find electrons many times. So this is the core of new idea that we describe the world in terms of waves of probability as opposed to the older Newtonian picture.
