Double-slit experiment with electrons

Caution: This post contains new and bizarre ideas which might hurt your brain!

In the last post about Schrodinger's cat, I mentioned the double-slit experiment with electrons. To physicists, "this beautiful experiment has in it the heart of Quantum Mechanics" - this means if you understand this experiment, you'll know the most important aspects as well as the weirdness of Quantum Mechanics. 

So let's start with the original double-slit experiment which was done with light. 

I. Young's double-slit experiment:

In the early 19th century, Thomas Young - an English polymath - performed an experiment in which light was passed through 2 narrow slits on a screen and incident on another screen some time later.

Image source: http://www.physicsoftheuniverse.com/topics_quantum_superposition.html

What was observed on the second screen are alternative fringes of darkness and brightness, as illustrated in the image above. The strange thing is a bright fringe was observed right at the region between the 2 slits, where all light should have been blocked and this region therefore should have appeared dark. The only appropriate explanation at that time is that light is wave. As it passes through the 2 slits, it is diffracted" (i.e: spread out). Each slit thus becomes an individual point source and light waves from the 2 slits "interfere" with each other to form a pattern of alternative dark and bright fringes on the second screen, which is called " the interference pattern". 

II. Double-slit experiment with electrons:

From the previous section, I hope it is clear to you that interference is characteristic of waves. Now let's go back to our main discussion in this post: the double-slit experiment with electrons. You can find its schematic set up and final observations in the end my #2 post: The tragedy of Schrodinger's cat.

Image source: https://community.emc.com/people/ble/blog/2012/01/12/entanglement-and-slit-experiments

The image above shows the positions of electrons as they incident on the second screen, with each white spot represents one electron. Do you find the similarity between this image with the one in section I of this post? Actually, they both show interference pattern! So, just like light, electrons are waves?! 

But hang on, we know from basic science knowledge that electrons are fundamental particles, so where did the waves come from? Perhaps we fired too many electrons at once and they somehow collided to form the interference pattern we saw? OK, so let's change it a bit so that only one electron is fired at a time. Can you guess what will be observed this time? The answer is in the video below.

As you can see, at first each electron seemed to land randomly on the screen. But as more and more electrons arrived, the interference pattern was gradually built up on the screen! This result means the wavy property is associated with each and every electrons in this experiment. It suggests that each electron somehow "split" so that it went through BOTH SLITS AT ONCE then interfere with itself and then recombined as a single particle on the second screen! Can we check this? Well, let's put a light source below the slits to 'see' if one electron really goes through both slits at once. As we do so, we detect each electron going through only one slit, but at the same time the interference pattern disappears! Electrons in this case behave exactly like particles. But if we remove the light source, electrons behave like waves again and the interference pattern reappears on the screen. These observations suggest electrons have wave - particle duality, which means it possesses properties of waves as well as particles, but follows the rule that if an object reveals wave-like properties in an experiment, it will not reveal particle-like properties in the same experiment and vice versa. This rule is called Niels Bohr's principle of complementary and is supported by the above example of the double-slit experiments with and without the presence of a light source under the slits.

So we know the wave-like property is associated with each and every electron in the double-slit experiment, but we haven't answer the question of what those waves are. One interpretation which was given by Max Born is that they are probability waves. The amplitude of these waves can be used to predict the region of space in which the electron is most likely to be found. Despite how bizarre the idea might seem, it has survived through all the experiments ever been set up so far and gives results in agreement with experimental results to the highest precision.

In extension, the wave-particle duality exits not only in particles but also in radiation. This fact has been confirmed by Compton experiment and Davisson - Germer experiment. It also exist in everyday objects, though its effect is too small for us to ever notice. For example, a human of mass 80 kg moving with speed 5 km/h will have an associated "matter wave" of wavelength (or, more accurately, de Broglie wavelength) of 4.6 x 10^-37 metres (this can be calculated from de Broglie's equation: lambda = h/p, where lambda is the de Broglie wavelength of "matter waves" associated with an object of momentum p, and h is Planck's constant whose value is 6.63 x 10^-34 kg.m^2/s). This wavelength is much smaller than the size of an atom - about a hundredth of a trillionth of a trillionth times smaller, to be precise - that's why we hardly notice the Quantum effects in everyday objects.   

So I think I can end my #3 post here. If you find some ideas hard to accept, don't worry, I was like you when I first encountered Quantum Mechanics. Actually, I have never met anyone who could grasp Quantum Mechanics from the first sight. It's too bizarre indeed that even Niels Bohr, one of its founders, had to say "Anyone who is not shocked by quantum theory has not understood it". So don't worry if you find yourself in the same situation. You'll get along with it in time.

--- Meo Fisica ---