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 ---

The tragedy of Schrodinger's cat

Note: This is just a thought experiment. No cats were harmed.

Hi everybody. It has nearly been 2 months since my last post. A friend even messaged me to ask if my blog is still alive :)) Yes, it is. It was just hibernating. Sorry for disappearing for too long.

Many of you might have heard of Schrodinger's cat. Those who haven't - don't worry, because I'm going to tell you now. It is one of my most favourite stories and I hope you'll like it, too:

"Imagine you have a safe with some kind of poison (or radioactive substance if you prefer) in it. This poison sprays out completely randomly, which means you cannot predict when it will do so. Now put a cat in the safe and close the door tightly. After 30 minutes, do not look inside the safe, can you tell if the cat is dead or alive?"

This thought experiment was devised in 1935 by an Austrian physicist Erwin Schrodinger. Classically and intuitively, the cat must (and can only) take either of the 2 states: dead or alive. But according to Quantum Mechanics, as long as you don't look inside the safe, the cat's state is a "superposition" of both states. Roughly speaking, it is BOTH DEAD AND ALIVE!

When I first told a friend this story, he was a very clever man and he asked me: "Well, doesn't make sense. What if I shake the safe and listen to the cat's sound? By that I can definitely tell if the cat is dead or alive without looking into the safe, can't I?" Good question. So I should have clarified from the beginning that by "look" I mean "any actions that allowed you to interact with the cat, including looking, touching etc...". (You might argue: "Touching, OK, that counts. But I don't really interact with the cat just by looking at it, do I?". But yes, you do! If you remember your first lesson about light, you'll also remember that to "see" something, you must first illuminate it with a beam of light and let that beam to be reflected back to your eyes. There must be some kind of interaction which reflected the light back. So by "looking" at something, you really do interact with it.)

Back to the case of Schrodinger's cat. Does this result make any sense? Well, though it seems counter-intuitive, it raises no paradox. Let's think about it this way: If you're very careful not to interact with the cat, you'll never know what it really is doing inside the safe. There is no evidence you can give to invalidate the conclusion "The cat is suspended in a state of both dead and alive". Otherwise, your action will alter its state and force it to choose either of the 2 states: When you open the safe and look inside, you can say immediately: "Ah hah, it is alive / dead. so you're wrong!" But remember I said the above conclusion only held as long as you didn't "touch" the cat. Therefore your evidence is invalid because you broke the rule.

"It is just in theory" - you might say. But in fact similar results have been found in practice. They prove the existence of a "superposition of states".

Does the above image ring a bell? Those who did Quantum Mechanics will find it familiar. This is in fact the double slit experiment with electrons. In this experiment, an electron gun accelerates electrons towards a screen which has 2 holes on it. The electrons then incident on another screen, allowing us to see their positions. When only one slit is open, most electrons arrive at the position directly opposite the slit, as expected, and as you get further away from this position, you find less and less dots, indicating less and less electrons arriving. So one might guess if we open both silt, there will be nothing difference: very bright at central region but gets fainter as we move sideways. But what was actually found is electrons form "fringes" on the screen, as shown in the image above, where there are alternative regions of brightness and darkness. HOW COME? Well, this pattern can only be explained if the following statements are true:
1, One electron goes through BOTH slits AT ONCE.
2, Electrons are waves. The pattern observed on the screen results from the interference of an electron with itself.
Does the first statement look familiar? You've met it in the story about Schrodinger's cat! One electron is at both slits at the same time - just like the cat is both dead and alive!
These properties of electrons cannot be explained by classical physics. But to a quantum-mechanical physicist, they are of no surprise. I will not go any deeper into this matter - just an example so that you see the idea of "superposition of states" does apply to our everyday world - it's not just a fictitious idea.
Double slit experiment with electrons is one of the most fundamental and important experiments in Modern Physics. I will discuss this cool subject, together with some basic ideas in Quantum Mechanics, in another post.

So, I will end this post here. Any questions? Fire away! I'll answer you by comments.

See you in post #3 !


--- Meo Fisica ---

PS: I don't own the images in this post. I found them on the internet.