Basics of Quantum Mechanics for Non-scientists
By: Vinicius Monteiro
Tags: Quantum Mechanics, Science, Quantum Physics, Quantum Computer, Physics

Classical / “Newtonian” Physics vs Quantum Physics

Classical Physics

You probably have a recollection of classical or also called “Newtonian” physics. It was discovered and outlined by Isaac Newton in his paper published in 1687. It basically tells us that an object, say a tennis ball, has a position, a velocity, and the position changes over time. It mathematically proves that if no force acts on the object, it will continue to move in a straight line, with such forces being, for example, gravity, wind or the other person catching the ball.

Figure 1: Classical representation [1]

In classical physics, the state of an object is the combination of its position and velocity. And if you know what forces are acting on it, you can determine the trajectory and predict where it goes next.

Quantum Physics

When you start studying the smallest particles, such as electrons and protons — things are a little bit more abstract.

You can predict the position, velocity, and other properties like spin (Spin: I’ll discuss in more detail), but it’s not with 100% accuracy, it’s not unquestionably the actual measurement. The state of an electron is rather a set of probabilities.

Imagine an electron orbiting an atom. It creates a sort of a cloud where some parts are denser. Some are thinner. Where it’s denser, it has a higher probability of an electron being there.

The ‘cloud’ oscillates like a wave, and that’s why it is said that an electron has a wave function. It’s not that the electron is a proper wave. There is no amplitude like a sound wave, but rather the amplitude is calculated. The wave here is more used as a metaphor.

Figure 2: Electron cloud. By author, inspired by [1]

Based on the density of each point of the ‘cloud’, it is assigned a number. This number is the amplitude of the “wave”. The probability of the electron being in a specific position is the square root of the amplitude. Before the location is observed, it is said that the electron is in a superposition of all possible outcomes.

The wave function of an electron is equivalent to the state in classical physics: position and velocity. And like there is an equation in “Newtonian” mechanics to calculate the motion of an object, there is also an equation to calculate the motion of a wave function — The Schrödinger’s equation: High energy parts evolve rapidly, low energy parts evolve slowly. [1]

Figure 3: Quantum representation [1]

Is it a particle? Is it a wave? No, it’s (super) an electron! — The double-slit experiment

As I explained, an electron oscillates like a wave. It has a wave function. You can’t exactly predict where it’s going to be, as you do with macroscopic objects. All you know is the probability of its location.

However, when you decide to observe the electron, the “wave” disappears/collapses, and it looks more as a particle — you see like a dot, a point in space. So it has this dual behaviour — when not observed, it’s a ‘wave’ when observed, it’s a particle — The double-slit experiment illustrates exactly that. It was performed in the 1970s, although it had already been discussed long before. It compares four different scenarios:

Classical particles going through single-slit vs double-slit Waves, like water waves, going through single-slit vs double-slit Electrons going through single-slit vs double-slit Electron going through double-slit, but with an ‘observer’ placed in the middle of the path to detect and prove that an electron went through the double-slit. Just in case.

1. Classical particles going through single or double slits have practically the same behaviour. In the screen on the other side, you will see marks close to the slits. Maybe some variations as the objects bump to each other or on the sides of the slit.

2. Waves behave just like waves. When it’s one slit, the marks will be centred around right behind the slit. As it’s a wave, the marks on the screen are bright spots equivalent to where the wave has higher amplitudes.

When there are two slits, on the other side of the screen it forms an interference pattern — Waves can oscillate up and down, when two waves oscillate in opposite directions they cancel each other out, when in the same direction it intensifies the amplitude. The result in the screen is greater amplitudes / brighter spots in the centre close to the slits and alternating dark/bright fading to both sides.

3. Electrons behave just like scenario 2 / waves, the interference pattern is noted when double-slits are used. However, first: Electrons are not really a wave; it doesn’t have an amplitude like waves do. The amplitude is calculated based on the denser points of the electron cloud. Second: The electron leaves up a mark in the screen just like a classical particle. The marks / bright spots are not shown based on the height of the amplitude, as it was done with water waves.

4. If scenario 3 wasn’t fun enough — when the detector/observer is placed in the middle, the electrons behave just like classical particles, the wave collapses. There is NO interference pattern at all on the other side, on the screen.