QUANTUM MECHANICS PART II

Bridging uncertainty with information, delving into entanglement, & exploring interference.

This is the second part of my series.

Here are the goals of this series of posts:
1. Outline the major events that formed this branch of physics
2. Describe in, simple words, the fundamental main ideas of Quantum Mechanics (today’s focus)
3. Understand the essence of quantum computing
4. Understand aspects of current research into quantum technologies

Here’s an overview of my series of posts on Quantum Mechanics. I’ll publish these once a week beginning on the 12th of August.

What makes Quantum Mechanics so powerful is that it explores the interactions which occur at the smallest levels in the universe. We discussed the idea in the last part that we can never truly know the exact position and velocity of a particle at an instant of time; this is called Heisenberg’s Uncertainty Principal.

Let’s explore this idea further. Imagine if you have a box and you want to repeat 1000 experiments trying to find a particle’s velocity given its position. If you do this experiment, you end up with 1000 different velocities for the same position. No matter if you try to making this experiment better, you’ll find that the particle’s velocity has an intrinsic randomness — and you can’t get rid of this randomness no matter the number of trials.

On a broader scale, seeking information about this particle has hampered your own ability to be more certain about this particle. No matter how many identical trials you conduct, you’ll end up having information disappear from your measurements and randomness will pervade. This is summed up simply: Quantum information, unlike classical information, isn’t able to be perfectly copied exactly (the no-cloning principle).

Enter a thought experiment: you are James Bond and it’s target firing training. Except, headquarters ran out of paint balls, so, James, you will have to use bowling balls. Therefore, you grab your best impression of the Big Lebowski and proceed to bowl.

If you aimed only for the left door, you’d expect (from a bird’s eye view) the following image where the green circles are the bowling balls:

If you aimed only to the right door, here’s what you’d expect too as seen from the bird’s eye view. No surprises right?

But what happens if you do this experiment in real life?

In a famous experiment, an electron gun fires an electron against a wall with two slits, similar to the bowling balls. As a result, the electron, in accordance to being a particle (akin to being a bowling ball), should go through only one of the two slits. But, low and behold the electron will goes through each slit and act as a wave. As they go through the slits, they stop acting as a particle and act as a wave and, in doing so, the electrons interfere with their own waves. This produces an interference pattern on the wall as the result of an electron colliding with itself. This experiment is a reminder that some specific entities can behave as a particle and a wave.

The idea of a superposition allows to understand what happened. In Quantum Mechanics, we didn’t know which slit the electron went through, however, we can say that the one electron went through both slits at the same time as it was behaving like a wave.

You may ask HOW can two things exist at one specific point, (and dare I say) a state? When we measure something, a particle will collapse to one of its states from a superposition. If you looked at slits as the electrons went through, you’d expect them to collapse to one state and you might very well expect no interference pattern. This is called the measurement rule. Observing something can very well change the results, as this experiment reminds us.

Thus, things of the very smallest size and level are mischievous. They do things that they we have never experienced at the “macro” level of everyday life. Isn’t that neat?

You, James Bond, are a flip flop fanatic. And you want to send your pairs of your flip flops around the world — but you loathe free loaders and so you only send a single flip flop to your friend, Ron in New York City, and to your other friend, Jeremy in Los Angeles. Being flippant, you don’t know which side of the pair of flip-flops you sent where (*pun intended). So, as soon as Jeremy opens his package and finds the left flip flop, then Ron must have the right flip flop. And vice versa.

This demonstrates that a pair of things are perfectly correlated despite the distance between them (i.e. if Ron has left flip flop, Jeremy must have right flip flop). And particles behave in the same way.

Which aspect of a particle explains their correlation?

Particles have a spin; describing spin allows us to understand how a particle looks from different directions. Particles can have a spin of 0, which means they look like a dot from all directions. Particles can have a spin of 1 or 2 even (having 2 spin means that rotating a particle 1/2 revolution retains how it looks; 1 spin means you would have to rotate it 1 revolution to retain it’s orientation). But, there are spin 1/2 as well; these require 2 complete revolutions to retain their image.

Particles of spin 1/2 make up all the matter in our universe. Particles of spin 0, 1, and 2 make up the forces that hold this matter together (including electromagnetic forces, which we touched upon earlier).

In this beautiful world we live in, all particles take dancing lessons. All particles exist in pairs and all particles have a dance buddy called an anti-particle. In this dance, one of the two particles spins in one direction, but the partner anti particle spins (or dances!) in the opposite direction. As a result, the angular momentum of this dancing pair of particles cancels each other out and is 0.

Two particles are said to be entangled when a one part of a system affects another part of a system. A particle can be linked to another particle despite being miles away from each other and this quantum entanglement is only present until measurement.

Alright! That’s it for now — we’ll focus on Quantum States, Born’s Rule, and probabilities in the next post, scaffolding what we know so far!

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